Блог Анкара

In This Chapter

^ Concentrating on the concentrations of mixtures ^ Using quality times quantity as the standard ^ Taking an interest in interest problems

Classic type of mathematical word problem is the mixture problem. But mixture problems go beyond just mixing up antifreeze with water or chocolate syrup with milk. Mixture problems involve all sorts of situations where you combine so much of one thing that has a certain amount of worth or density with so much of something else that has more worth or more density.

In this chapter, you find problems that multiply numbers of coins times their monetary value, pints of coolant with their concentrations and cartons of goodies with their product count. All these make for some interesting and, yes, even useful problems. So you can put your spoon away and find out what mixture problems are all about.

Standardizing Quality Times Quantity

The common theme in all mixture problems is that you take two or more different Amounts (quantities) of two different Concentrations (or qualities) and mix them together to get an amount (quantity) that’s the sum of the two ingredient quantities and a concentration (quality) that’s somewhere between the concentration of the two ingredients that you started with. Figure 14-1 illustrates this property or theme with containers.

Figure 14-1:

The quantities add up to the resulting amount.

Quantity A

Quantity B

Quantity A + B

Quality (percent, value) A

Quantity A X Quality A

Quality (percent, value) B

Quantity B X Quality B

Quality (percent, value) C

Quantity (A + B) X Quality C where A < C < B or B < C < A

The figure shows that when you add two quantities together, you get an amount or new quantity that’s the sum of the two quantities that are put together. The concentration or quality of the resulting mixture is a blend of the two starting substances — its concentration is somewhere between the two that are being combined.

Mixing It Up with Mixtures

Mixture problems involving actual substances occur when you take two or more different solutions or granular compounds or anything that will combine or Mix And create a new combination that’s no longer purely one or the other. When you pour chocolate syrup into milk, you add volume to the liquid in the glass, and the color of the milk mixture isn’t as dark as the chocolate or as white as the milk. The more chocolate, the darker the mixture. Yum!

Improving the concentration of antifreeze

The radiators of cars serve to cool down the engine with liquid that circulates around and pulls the heat away. The concentration of the fluid in the radiator can be changed to reflect the temperatures of the particular season. The concentration of antifreeze should be greater in the winter or cold months and less in the warmer months.

The Problem: A service station owner wants to mix up some 35 percent antifreeze. He wants to use up his current supply of 100 gallons of 20 percent antifreeze and add enough 40 percent antifreeze to bring the mixture up to 35 percent. How many gallons of 40 percent antifreeze should he add?

Vjj. VLA/V Keep in mind Quality x quantity For the two solutions being added together and the Quality And Quantity Of the resulting solution. Let X Represent the number of gallons of 40 percent antifreeze that needs to be added. The qualities are the percentages of the solutions, and the quantities are the gallons of the respective solutions.

Starting with [20 percent x 100 gallons] + [40 percent x X Gallons] = [35 percent x (100 + x) gallons], you see that the desired concentration, 35 percent, is between 20 percent and 40 percent. Also, the resulting quantity is the sum of the two quantities X And 100. Now rewrite the equation so it can be solved, replacing percentages with the decimal equivalents. Solving for X,

0.20 (100) + 0.40x = 0.35 (100 + X) 20 + 0.40x = 35 + 0.35x

0.05X= 15

15

0.05

300

It’ll take 300 gallons of the 40 percent antifreeze to bring the concentration up to what he wants. Hope he has a large enough container!

The Problem: The same service station owner from the previous problem still wants to make his 100 gallons of 20 percent antifreeze into 35 percent antifreeze. How many gallons of Pure Antifreeze will it take to raise the concentration?

^VLAiV You can use the same basic equation of Quality x quantity And multiply the unknown amount, X, By 100 percent. The equation takes the form of [20 percent x 100 gallons] + [100 percent x X Gallons] = [35 percent x (100 + x) gallons]. Writing this in a form to be solved,

0.20 (100) + 1.00x = 0.35 (100 + X) 20 + 1.00x = 35 + 0.35x 0^5x = 15 15

X = 7TFF . 23.077 0.65

It’ll take just a little more than 23 gallons of pure antifreeze to raise the concentration to 35 percent.

If you want to add pure antifreeze to what’s in your radiator right now, to increase the concentration, you have to take some of the mixture out of the radiator, first. The radiator holds only so much fluid. So, an even more interesting problem involves removing a certain amount of what’s in the radiator now and replacing it with pure antifreeze to achieve the level of concentration that you want.

The Problem: A man has a 16-quart radiator that now contains 16 quarts of 20 percent antifreeze. How much of the current mixture has to be removed and replaced with pure antifreeze to raise the level of concentration to 35 percent?

The basic structure for the mixture problem will have one more term in it. You’ll have a Quality x quantity Term that’s subtracted from the original amount. Let X Represent the number of quarts taken out and put back into the radiator. The end quantity will have to be the original 16 quarts.

[20 percent x 16 quarts] – [20 percent x X Quarts] + [100 percent x X Quarts] = [35 percent x 16 quarts]

Solving this equation,

0.20 (16) – 0.20x + 1.00x = 0.35 (16) 3.2 + 0.80x = 5.6 0.80x = 2.4

2.4

X = AOA = 3

Take out 3 quarts of the 20 percent solution and replace it with pure antifreeze.

Coffee, tea, or not

Two friends were at a restaurant and ordered coffee. The waiter came back with another cup. coffee to have with their dessert. One of the But the friend became very upset and returned it friends found a fly in his coffee and called for the again, saying that the second cup was the same waiter to take it away and bring a fresh cup of as the first cup. How did he know?

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Watering down the wine

Just as concentrations of solutions are increased by adding a pure substance, the concentrations can also be decreased by adding pure water. You perform this type of operation all the time, such as when mixing up orange juice from frozen concentrate or when fixing mixed drinks such as bourbon and water.

The Problem: How much water must be added to 8 ounces of 40 percent alcohol to produce a mixture that’s 7 percent alcohol?

Water is 0 percent alcohol, so use the Quality x quantity Setup to solve for X, The number of ounces of water needed.

[40 percent X 8 ounces] + [0 percent X X Ounces] = [7 percent X (8 + x) ounces]

Writing an equation and solving for X,

0.40 (8) + 0.00x = 0.07 (8 + X) 3.2 + 0 = 0.56 + 0.07x

2.64= 0.07X

2.64

0 07 = X x. 37.71

It’ll take about 38 ounces of water to get the alcohol down to the 7 percent level.

Mixing up insecticide

Farmers know how important it is to keep destructive insects out of their crop-producing fields. They apply enough insecticide to keep the bugs away, but they don’t want to overdo it and poison the field for the future. Mixing the insecticides and applying them where necessary is a complicated problem.

The Problem: To get rid of a nasty strain of root worm, an insecticide mixture should have a concentration that’s 9 percent insecticide. A farmer has two mixtures on hand — one with 5 percent insecticide and the other with 15 percent insecticide. What is the ratio of the 5 percent to 15 percent mixtures that should be combined to get a 9 percent mixture? If the farmer needs 40 gallons of mixture, how many gallons of each should she use?

^VLA/V First solve for the ratio of the different mixtures and then apply it to the quantity of 40 gallons. Use the Quality X Quantity Setup. Let X Represent the fraction of 5 percent solution and 1 – X Represent the fraction of 15 percent solution. Adding X + 1 – X You get 1, which is All Of the final mixture.

[5 percent x X ] + [15 percent x (1 - x)] = [9 percent x 1]

Solving for X In the related equation,

0.05 (X) + 0.15 (1 – X) = 0.09 (1) 0.05x + 0.15 – 0.15x = 0.09

0.15-0.10X=0.09 -0.10X=-0.06

_ A A/? C O

X = — = T0 = 5

The farmer needs to let 3, or 60 percent, of the insecticide be made up of 5

The 5 percent solution and 5, or 40 percent, of the mixture be 15 percent

Solution. In a 40-gallon situations, 60 percent is 0.60 x 40 = 24 gallons and the other 40 percent is 0.40 x 40 = 16 gallons.

Counting on the Money

Problems concerning money — no, I’m talking about Math Problems, not just any problem over money — involve the value of the currency or coin or vending unit along with the number of each of these monetary values. The theme of the Quality X Quantity Applies very well here, where the Quality Is the coin value, bill value, or commodity value in the problem.

Determining how many of each denomination

Coins and paper money come in many different denominations, allowing people to carry a lot of money with just a few bills or to make change for purchases using smaller bills and coins. What’s consistent for all money in all countries is that you determine the total amount that you have by multiplying the value of the coin or bill times the number of them that you’re carrying.

The Problem: Cassie has a total of $4.10 in dimes and quarters. If she has twenty coins in all, how many of them are quarters?

^VLA/V Multiply the value (quality) of a quarter, $0.25, times the number of quarters and the value of a dime, $0.10, times the number of dimes. The sum of the two results is set equal to $4.10. You know that the number of quarters and dimes equals 20. Also, you want to solve for quarters. So let Q Represent the number of quarters, leaving 20 – Q To represent the number of dimes. Setting up the equation and solving,

0.25 (q ) + 0.10 (20 — Q ) = 4.10 0.25q + 2 — 0.10q = 4.10 0.15q + 2 = 4.10

0.15Q = 2.10

2.10

Q = 015 = 14

Cassie has 14 quarters. You check your answer by determining the number of dimes, 20 – Q = 20 – 14 = 6. Multiply 14 x 0.25 = 3.50 and 6 x 0.10 = 0.60. The sum 3.50 + 0.60 = 4.10. So the solution checks.

The Problem: Grace has twice as many nickels as quarters and five less than three times as many dimes as quarters. If she has a total of $6, then how many of each coin does she have?

^VLA/rV Because both the nickels and dimes are compared to quarters, let Q Represent the number of quarters and write expressions for the number of nickels and dimes using the relationships. The number of nickels is written as 2q, and the number of dimes is 3Q - 5. Multiply each quantity of coin by its quality and add up the products, setting the sum equal to 6.

0.25 (q) + 0.05 (2q) + 0.10 (3q — 5) = 6.00 0.25q + 0.10q + 0.30q — 0.50 = 6.00 0.65q — 0.50 = 6.00

0.65Q = 6.50 Q 6.50

Grace has 10 quarters. If she has twice as many nickels as quarters, that makes it 20 nickels. And 5 less than 3 times 10 is 30 minus 5 or 25 dimes. Checking on the total, 0.25(10) + 0.05(20) + 0.10(25) = 2.50 + 1 + 2.50 = 6.

It isn’t always clear-cut which coin or piece of currency you want to use to have their amount represent the variable. You almost always have more than one choice for X. Your goal is to pick the money amount that makes writing the problem as easy as possible.

The Problem: A cash drawer contains singles, fives, tens, and twenties. There are two more tens than fives, eight less than twice as many twenties as tens, and ten more than twice as many singles than twenties. If the total amount of money in the cash drawer is $650, then how many of each bill is there?

Several different comparisons are going on here, each with the number of bills of a particular denomination being compared to the number of bills of another denomination. You need to pick a variable to represent how many you have of one type of bill and work from that amount.

One suggestion is to start by letting the number of fives be represented by F. Then the number of tens is represented by F + 2. Comparing twenties to tens, you write Eight less than twice as many twenties as tens By subtracting 8 from 2 times the number of tens, or 2(f + 2) – 8. Now take that number of twenties and write the number of singles (ten more than twice as many singles as twenties) As 2[2(f + 2) - 8] + 10.

You then write an equation taking the number of each type of bill times its monetary value, adding up all these products, and setting the sum equal to $650. But first, it’s a good idea to simplify the expressions for the numbers of

Each bill. The number of fives is F, Which is fine. The number of tens, F+ 2, is also as simple as it can get. But the number of twenties can be simplified. 2(f + 2) – 8 = 2f + 4 – 8 = 2f – 4. And the number of singles has a long way to go, because 2[2(f + 2) - 8] + 10 = 2[2f + 4 - 8] + 10 = 2[2f - 4] + 10 = 4f – 8 + 10 = 4f + 2. Now you’re set to go. Write the equation.

5 (F) + 10 (F + 2) + 20 (2f — 4) + 1 (4f + 2) = 650 5f + 10f + 20 + 40f — 80 + 4f + 2 = 650 59f — 58 = 650 59f= 708

F = l08 = 12

There are 12 five-dollar bills, two more tens than fives (or 14 ten-dollar bills), eight less than twice as many twenties as tens (or 20 twenties), and ten more than twice as many singles as twenties (or 50 singles). Checking this out for the total: 5(12) + 10(14) + 20(20) + 1(50) = 60 + 140 + 400 + 50 = 650.

Making a marketable mixture of candy

Some people prefer dark chocolate. Others go for the gooey chocolate-covered cherries. Many don’t care for coconut in their sweets. And most people are happy with any mixture of any kind. Different kinds of candies have different prices, depending on the ingredients. When you combine different candies in packages, the Quality Or price of each type is multiplied by the Quantity Or weight to determine the price of the mixture.

The Problem: Malted milk balls sell for $3 per pound, and chocolate-covered peanuts cost $4 per pound. How many pounds of each type of candy should be used to create a 5-pound box of candy that costs $3.60 per pound?

^VLA* Let M Represent the number of pounds of malted milk balls. Because the total amount of candy is to be 5 pounds, then 5 – M Can represent the number of pounds of chocolate-covered peanuts. Multiply $3 times M And add it to the product of $4 and 5 – M. Set that sum equal to $3.60 times 5. Each term has the price times the weight. Solve for M.

3 (m) + 4 (5 — m) = 3.60 (5) 3m + 20 — 4m = 18 20 —m =18 2 = M

If you use 2 pounds of malted milk balls, you’ll need 3 pounds of the peanuts to make 5 pounds. Checking, 3(2) + 4(3) = 6 + 12 = 18. If you divide the total price of $18 by 5 pounds, you get $3.60, the cost per pound.

The Problem: A box of candy is to contain chocolate covered cherries that cost $5 per pound, nougats that cost $3 per pound, assorted cremes that cost $2 per pound, and caramels that cost $6 per pound. There should be an equal amount (by weight) of the caramels and cherries. You want twice as many nougats as caramels and twice as many cremes as nougats. How much of each type of candy should be used if the box is to cost $4.25?

V£.?LA/V First, you have to stop drooling and think about the mathematics, not the candy. Because the caramels and cherries will have equal weight, it makes sense to assign a variable to represent the weights of those two candies. Let C Be the number of pounds of caramels and C Be the number of pounds of chocolate-covered cherries. For the nougat, you want twice as much as there are caramels, so that’s represented by 2C. And twice as much of the nougat is 2(2C) = 4C, For the weight of the cremes. Now multiply each weight of candy by the respective cost, add them together, and set the sum equal to 4.25.

5 (C) + 6 (C) + 3 (2c) + 2 (4c) = 4.25 5c + 6c + 6c + 8c = 4.25 25C = 4.25

4.25

25

0.17

So the mixture will contain 0.17 pound of chocolate covered cherries, 0.17 pound of caramels, 0.34 pound of nougat, and 0.68 pound of assorted cremes.

Running a concession stand

Picture this: It’s game night, and you’ve made a dash to the food vendor to get a quick snack. So did half the people in the stadium. Now you have time to stand in line and wait and ponder the problem of combining different foods and drinks available in the concession stand so that you can spend every penny of the money in your pocket — no more, no less.

The Problem: Stan had exactly $20.40 in his pocket and managed to spend it all at the concession stand. He bought three hot dogs, two servings of cheese fries, and one large drink for that amount of money. One hot dog costs $1.80 more than one serving of cheese fries. And a drink costs $1.20 less than a hot dog. How much did each item cost?

The number of items have to be multiplied by their respective prices, and the costs totaled. Set that total equal to $20.40 to solve for the individual prices. Let the cost of cheese fries be represented by C. Then a hot dog costs C + 1.80. A drink is $1.20 less than a hot dog, so it costs C + 1.80 – 1.20 = C + 0.60.

2 (C) + 3 (C + 1.80) + 1 (C + 0.60) = 20.40 2c + 3c + 5.40 + C + 0.60 = 20.40 6c + 6.00 = 20.40 6c = 14.40

C = 1440 = 2.40

6

So cheese fries cost $2.40, the hot dogs are $1.80 more than that (or $4.20), and the drink is $0.60 more than the fries (or $3).

The Problem: You’re buying supplies for the concession stand Friday night and need to purchase candy and pretzels and gum in bulk. Twix candy bars are 35<t each if you buy a case of 36. M&M’s bags are 36<t each if you buy a case of 48. Pretzels are 19<t a bag if you buy a case of 30. Cookies are 24<t a package if you buy a case of 33. And gum costs 18<t a pack if you buy a case of 40. You buy the same number of cases of cookies and gum. You buy twice as many cases of M&M’s as cookies. You buy two less than twice as many cases of pretzels as cookies. And you buy five fewer cases of Twix than M&M’s. If you spend $270.72 on all these supplies, then how many individual items do you have on hand to sell Friday night?

This problem just begs to be organized. A spreadsheet would be a big help here. But the next best thing is a table showing the item name, the number of items in a case, the cost per case, and a representation of the number of cases ordered. Because the number of cases of cookies and gum is the same, let the number of cases of these items be represented by G. The number of cases of M&M’s is 2g. The number of cases of pretzels is 2g – 2; and the number of cases of Twix is 2g – 5. Table 14-1 shows all the entries.

The equation consists of the sum of the products of the costs and the number of cases set equal to the total of $270.72.

7.92 _g) + 7.20_g) + 17.28 _2g) + 5.70_2g – 2) + 12.60_2g – 5) = 7.92g + 7.20g + 34.56g + 11.40g – 11.40 + 25.50g – 63 =

86.28G-74.40 = 86.28G=

G=

G=

You bought 4 cases of cookies and 4 cases of gum. You bought 8 cases of M&M’s, 6 cases of pretzels and 3 cases of Twix. Multiplying each number of cases by the number of items in that case, you have 4(33) + 4(40) + 8(48) + 6(30) + 3(36) = 964 items. Have fun!

270.72 270.72 270.72 345.12

345.12 86.28 4

Being Interested in Earning Interest

Earning interest on money invested is of utmost importance to the wise investor. Some funds pay a higher rate of interest but may be a bit risky. To offset the risk, the shrewd investor puts some money in a high-risk fund and the rest in a fund that doesn’t pay as well but one that can be trusted to give a return and not lose any of the investment.

Making your investment Work for you

The problems in this section assume the use of the Simple-interest formula, Compounded annually. In actuality, financial institutions use compound interest and computer programs to figure out these problems. But you get a good idea of how it works — and a pretty good estimate of the actual answer using the less complex simple-interest formula.

The simple-interest formula says that the interest earned, /,is equal to the amount invested (principal), P, Times the percentage rate, R, Written as a decimal, times the number of years (time), T. The formula is: I = Prt.

The Problem: Robert has $50,000 to invest. He wants to put some of this money in an account that earns 8 percent interest and the rest in a riskier account that promises to earn at the rate of 12 percent. He needs yearly earnings of a total of $4,500. How much of his $50,000 should he invest in each account?

^VLA* Write an equation in which the First interest Plus the Second interest Is equal to $4,500. The First interest And Second interest Are expressions that you write using the interest formula. This is another Quality Times Quantity Situation. Let X Represent the amount of money invested in the first account and 50,000 – X Be the amount of money in the second account. Assume that the time is one year. Then solve for X.

Robert needs to invest $37,500 at 8 percent and the rest, $50,000 – $37,500 = $12,500, at 12 percent.

The Problem: Stella has been watching several investment funds and has decided that she’ll deposit some of her $100,000 in each. She will put twice as much in the fund earning 5 percent as that earning 4 percent, $5,000 more in the fund earning 10 percent than in the fund earning 4 percent, and $5,000 less in the fund earning 6 percent as in the fund earning 4 percent. How much will she get in total interest earnings at the end of the year? How much did she invest in each fund?

.cVLA/v First, determine how much she’s investing in each fund by letting X Represent the amount in the 4 percent fund, let 2x represent the amount in the 5 percent fund, let X + 5,000 represent the amount in the 10 percent fund, and let X - 5,000 represent the amount in the 6 percent fund. Add up all the fund amounts and set them equal to 100,000 to solve for X.

X + 2x + x + 5000 + X – 500 = 100,000

5X = 100,000

100,000 20 000 X =-f-= 20,000

If X = 20,000, then the amounts in the 4 percent, 5 percent, 10 percent, and 6 percent funds are $20,000, $40,000, $25,000 and $15,000, respectively. Multiply each fund amount and percentage together to get the total interest.

$20,000(0.04) + $40,000(0.05) + $25,000(0.10) + $15,000(0.06) = $800 + $2,000 + $2,500 + $900 = $6,200. Stella should earn $6,200 in interest.

Determining how much is needed for the future

It’s all well and good if you have $100,000 or some such amount of money to invest. Wouldn’t we all just love that? Frequently, though, the question is more like, "How much do I need to invest in order to get that kind of interest?" Nonprofit organizations like to have Endowment funds (money put aside that’s never touched, with only the interest used to pay expenses). They want to know how much is needed in the endowment fund in order to have a particular income every year from the interest.

The Problem: The local Kiwanis Club needs $20,000 in interest annually in order to adequately fund its benevolence programs. It currently has $120,000 invested — one-third of it in a mutual fund earning 5 percent interest and the rest in a money-market fund earning 10 percent interest. This division of the funds is mandated by its endowment agreement. How much more money does the Kiwanis Club need, and how much does it have to have in each fund in order to earn that $20,000 annual interest?

First determine the total amount of money needed to generate the $20,000 interest each year when one-third goes into the 5 percent fund and two-thirds into the 10 percent fund. Then, after you find out how much is needed, you can see what the difference is between that and what the Kiwanis Club already has.

Think of the division of money as being divided into three parts — one part in the 5 percent fund and two-thirds in the 10 percent fund. Rather than use fractions, let the whole three-thirds be represented by 3X. Then let X Represent the amount of money invested at 5 percent and 2x represent the amount invested at 10 percent. Write the two interest terms, add them up, and set them equal to 20,000.

X (0.05) + 2x (0.10) = 20,000 0.05x + 0.20x = 20,000

0.25X= 20,000

20,000 80 000 X = AOR= 80,000 0.25

It needs to have $80,000 invested at 5 percent and twice that, $160,000 invested at 10 percent. So a total of $240,000 is needed in the two funds. Subtracting what it already has, $240,000 – $120,000 = $120,000. The Kiwanis Club is halfway to its goal. Looks like it’ll have to host a few more pancake breakfasts to get there!

Chapter 15

In This Chapter

^ Identifying obsessional problems

^ Managing upsetting intrusive thoughts

^ Facing fears and reducing rituals

^ Decreasing preoccupations with health and appearance

This chapter aims to introduce you to common obsessional problems and how to tackle them using CBT. Specifically, in this chapter we focus on obsessive-compulsive disorder (OCD), health anxiety, and body dysmorphic disorder (BDD). These problems can cause significant levels of distress and interference in daily living. However, if you have one or more of these disorders, you can use the CBT principles we outline in this chapter to reduce your obsessions and preoccupations. If you have a more severe form of these problems you should consider adding some professional help, but the core principles outlined here can still be of great help.

Many people have some degree of obsessional behaviour, such as checking or ordering, that don’t particularly interfere with their lives. This level of problem is usually regarded as Subclinical. However, problems like OCD are very disruptive and distressing when they reach more severe levels. A report from the World Health Organization (WHO) states that people with OCD can experience impact on their lives similar to those of people with AIDS.

Fortunately, obsessional problems are being diagnosed more accurately than ever before. Problems such as OCD are now among some of the most common psychiatric disorders. This increase is probably due to increased awareness and more accurate assessment measures. CBT is well-recognised as the psychological treatment of choice for obsessional problems, and has far superior relapse rates compared to medication.

Identifying and Understanding Obsessional Problems

Obsessional problems are among the most disabling of common emotional-behavioural problems. People with Obsessional problems Can spend many hours a day plagued by upsetting thoughts and feel driven to repeatedly carry out rituals or avoid situations. This section outlines three key obsessional problems, OCD, health anxiety, and BDD.

Some degree of obsessionality is entirely normal – for example, around half of all people have a particular thing that they check more than they think is necessary, such as whether the gas cooker has been switched off or the door’s been bolted. Obsessional problems have their roots in normal experiences, but the rituals and avoidance behaviours serve to make the frequency, severity, and duration of obsessions worse. The more you try to rid yourself of doubts, the more they tend to play on your mind.

We define the terms of obsessions in the list below:

An Obsession Is a persistent, unwanted thought, image, doubt, or urge that intrudes into your mind, triggering distress. Obsessions are said to have reached a ‘psychiatric problem’ level when they cause significant levels of distress, interfere with your life, and are present for more than an hour a day.

Preoccupation Means being absorbed with something troubling that’s on your mind. In this book we focus on preoccupations with appearance and health. Preoccupations are usually the result of you frequently focusing your attention on an idea (such as ‘I’m seriously ill’, or ‘I’m repulsive to look at’) or doubt that is distressing to you. Preoccupations are similar to obsessions in that they are regarded as problematic when they cause significant distress, interference in your life, and last for more than an hour per day.

Compulsions, Also called Rituals, Are the actions you may take in response to your obsessions or preoccupation, but do not particularly help you in your life. Compulsions can be observable behaviours (such as checking) or can be carried out in your mind (such as repeating a phrase in your head). Compulsions are usually attempts to either get rid of a thought, image, urge, or doubt; an attempt to reduce danger; or an attempt to reduce discomfort.

Avoidance behaviours Are things you do to avoid triggering your obsession or preoccupation. Your avoidance behaviour may be avoiding driving; avoiding visiting a hospital; or avoiding being seen in bright light.

Rituals and avoidance behaviours are the lifeblood of obsessional problems. Add to these catastrophic thinking (see Chapters 2 and 9), negative emotions (see Chapter 6), and attention bias (see Chapter 5), and you have the anatomy of obsessional problems.

Understanding obsessive-compulsive disorder (OCD)

According to the American Psychiatric Association, OCD is:

A problem in which the sufferer is plagued by either obsessions or compulsions, or usually both. Unwanted recurrent intrusive thoughts, impulses, or images that cause marked distress and are not simply excessive worries about real life problems. The sufferer makes attempts to ignore, suppress, neutralize the obsessions and recognises them as the products of their own mind.

Common obsessions in OCD include the following: Fear of contamination

Fear of accidentally causing harm to yourself or others

Preoccupation with order or symmetry

Religious obsessions, for example fear of offending God

Sexual obsessions, for example fear of being a paedophile

Fear of losing something important (such as a possession, paperwork, or ideas)

Fear of becoming violent or aggressive

Compulsions frequently associated with OCD include the following:

Checking (for example, if a light is switched off, or the front door is locked)

Cleaning or washing (such as yourself, others, or home) Counting

Repeating actions or special words, images, or numbers in one’s mind Ordering and making things ‘just so’

Hoarding (excessive keeping of possessions such as newspapers that have no real, value, interest, or function)

I *»" Making lists

I Replaying or repeating scenes, images, or actions in your mind

The prevalence of OCD is estimated to be around 2 per cent of the population, with some studies suggesting more. The severity and impact of OCD varies greatly, and in its most extreme form individuals can become totally housebound, even bedridden. Whilst the severity of symptoms can wax and wane, most people with OCD do function, do have relationships, and do hold down jobs or education, but will be under considerable extra strain. Clearly, very many people may recognise some degree of the excessive worries and rituals outlined above. The question is how much choice you feel you have to stop a ritual without distress, and how much interference OCD is causing in your life.

Recognising health anxiety

The American Psychiatric Association defines health anxiety as ‘preoccupation with fears of having, or the idea that one has, a serious disease, based on misinterpretation of bodily sensations’. These preoccupations can:

Persist despite medical evaluation and reassurance.

Cause significant distress or impairment in social, occupational, or other areas of functioning

Last at least six months

People with health anxiety misinterpret body sensations. Examples of common sensations and misinterpretations include the following:

Heart pounding: ‘I’m going to get heart disease.’ Lumps under the skin: ‘I have cancer.’ Tingling or numbness: ‘I have multiple sclerosis.’ Headache: ‘I must have a brain tumour.’ All of the above: ‘I’m dying.’

Compulsions commonly associated with health anxiety include the following:

Seeking reassurance from medical professionals about the nature of physical sensations

Seeking reassurance from others

Checking body parts by poking, prodding, and touching

I Checking for symptoms in medical textbooks or on the Internet I Examining oneself for signs of disease I Monitoring physical sensations

Common avoidance behaviours associated with health anxiety include the following:

Avoiding reading health-related stories in magazines or on TV Avoiding talking or thinking about death Avoiding touching body parts Avoiding having medical check-ups

Health anxiety is estimated to affect between 1-2 per cent of the population. It can result in people becoming tormented with fears that they have an illness that has not been properly diagnosed, or that they might become ill. Frequent trips to doctors are not uncommon when the person is gripped by anxiety and a fear that it would be irresponsible of them not to get themselves checked out. This can then result in even more worry that should they really be ill, they’ll be dismissed as a hypochondriac. We’ve seen many people who’ve ended up badly bruised from repeatedly prodding an area of their body, or have spent hours doing research in desperate attempts to check and see what may be wrong with them.

Understanding body dysmorphic disorder (BDD)

BDD is defined by the American Psychiatric Association as follows:

A preoccupation with an imagined defect in appearance. If a slight physical anomaly exists, the person’s concern is markedly excessive. The preoccupation causes clinically significant levels of distress and/or impairment in social, occupational or some other important area of functioning.

Don’t confuse BDD with an eating disorder, which is when a person restricts their weight, or binges and purges food. If you are very preoccupied with your overall size and shape and have difficulties with eating regular meals, consult with your doctor about whether you have an eating disorder. If this

Is the case, you may need help to tackle your eating behaviours as well as your preoccupation with how you look.

BDD preoccupations can focus on any area of the body and often affect multiple areas of the body. The face is the most common area of preoccupation, particularly the nose, facial skin, hair, eyes, teeth, lips, and chin. People with BBD believe that one or more of their features is too small or too big, or that their face doesn’t ‘fit together’, is out of proportion, isn’t symmetrical, or is just plain ugly.

Typical compulsions associated with BDD include the following:

Gazing or checking appearance in mirrors or other reflective surfaces Avoiding mirrors or other reflective surfaces

Seeking reassurance of attractiveness or how noticeable a ‘defect’ in appearance is, from other people

Checking features by frequent touching or measuring

Camouflaging features using clothing, padding, hairstyle, or make-up

Attempting to distract others from the supposed defective feature with jewellery or by accentuating other body parts

Frequently looking for and trying out new skincare, beauty, and haircare products

Researching or seeking cosmetic surgery Excessive exercise Steroid abuse

Some common avoidance behaviours in people with BDD include the following:

Avoiding social situations Avoiding ‘attractive’ people

Choosing lighting carefully in social situations or near mirrors Carefully positioning yourself around (or avoiding) mirrors Changing posture or covering flaws with hands or other items

Frequently starting in adolescence, BDD affects around 1 per cent of the population, and has a relatively high suicide rate compared to many other emotional problems, proving that BDD is much more than mere vanity. BBD affects men and women roughly equally. Individuals can often spend many hours a day preoccupied with their appearance, perhaps having to get up hours early in order to work on their appearance just to feel less unacceptable.

Identifying Unhelpful Behaviours

As we note in Chapter 7, the things humans do to reduce their distress in the short term often maintain problems in the long run – so the solution is the problem! In the case of obsessional disorders, behaviours such as avoidance, checking, washing, seeking reassurance, comparing, readjusting, and repeating (to name but a few) are the maintaining mechanisms.

Most clients we work with on their obsessional problem agree Intellectually That their behaviours perpetuate and aggravate their problems, but very often they say ‘Now I really see what you mean!’ after they experiment with them. Check out Chapter 4 for more information on designing and executing CBT experiments on your thinking.

The first step is to understand the concept of problem maintenance. The next step is to really experience how your behaviours affect your obsessions and preoccupation, by doing experiments.

In the broadest sense, you can try two kinds of experiment with your obsessional thinking:

Reduce (or stop) a particular ritual and see how this affects the frequency, intensity, and duration of your upsetting thoughts.

Increase A ritual or avoidance for a day and see what affect this has on the frequency, intensity, and duration of your upsetting thoughts.

Increasing a ritual or avoidance is often easier to do in the short term and often yields more results more rapidly.

Say you worry frequently about your house being burgled and you repeatedly check your doors and windows before leaving the house or going to bed. To find out whether your checking is part of the problem rather than the solution, record the frequency, duration, and intensity of your worry about burglary on a usual day of checking. Then spend another day trying as hard as you can to double your checking, and record the results. If you note a clear increase in your worry on the day of extra checking, the ritual behaviour’s clearly part of your problem.

Acquiring Anti-obsessional Attitudes

Research and clinical observation shows that a number of thinking styles are related to the development of obsessional problems. Fortunately, you can

Also use thinking to combat obsessional problems. The following sections offer alternative ways of thinking that can help you in your fight against your obsessional problem.

Tolerating doubt and uncertainty

In our and many other therapists’ experience, one of the main protestations that clients make about stopping rituals or avoidance behaviours is along the lines of ‘How can you guarantee me that what I’m afraid of won’t happen?’

The truth is, of course, that we can’t. But no one without obsessional problems gets those kinds of guarantees either, so clearly the problem Isn’t A lack of certainty. We can offer a different kind of guarantee, however: As long as you continue to demand a guarantee or certainty that your fears won’t come true, you’re likely to have your obsessional problem.

Instead, practice Consistently And Repeatedly Tolerating doubt and uncertainty without resorting to checking, washing, reassurance-seeking, or whatever you do compulsively. Your rituals only fuel your belief that you need certainty. Initially, staying with doubt may well feel uncomfortable, but if you stick with it your anxiety can reduce. Deliberately seek out triggers for your doubt and practice resisting the urge to carry out rituals, seek reassurance, or work things out in your mind.

Trusting your judgement

In an attempt to explain why individuals with obsessional problems check so much more than those without these problems, scientists explored the hypothesis that people with OCD have poorer memories. The rationale here was, perhaps, that people with OCD check or seek reassurance because they can’t remember properly. The scientists do make an important discovery: People with obsessional problems have no memory deficiency. What they do have, however, is poor confidence in their memories.

Poor confidence in one’s memory may be related to unrealistic demands for certainty (see the preceding section on how totolerate doubt and uncertainty), because no amount of checking removes that grain of doubt from your recall.

The best thing you can do to boost your confidence in your memory is to act as if you were more confident and cut back on rituals. Doing so consistently and repeatedly gradually helps you to build your confidence.

Treating your thoughts as nothing more than thoughts

One of the main thinking errors in obsessional problems is overestimating the importance of the intrusive doubts, thoughts, and images that occur naturally in your mind. Experts in OCD have shown that the following three key misinterpretations contribute to obsessional problems:

The probablity misinterpretation: The idea that having a thought about an event in your mind affects the probability of that event occurring. For example, ‘If I allow myself to picture myself hurting someone, then it’s more likely that I’ll do it.’

The moral misinterpretation: The idea that an unpleasant thought entering your mind reveals something unpleasant about yourself. For example, ‘Having thoughts of causing harm means I’m a bad and dangerous person.’

The responsibility misinterpretation: The idea that having a thought about an event means that you have responsibility for it happening or for preventing it from happening. For example, ‘Having an image of myself ill in a hospital bed means that I need to be more vigilant for signs of illness.’

Intrusive thoughts, images, doubts, and impulses are entirely normal. Your assumption that the thoughts that you’re having aren’t normal is the problem. The solution is to allow these thoughts to pass through your mind without engaging with them, trying to change them, trying to suppress them, or trying to hurry them along. As the song says, let it be! Refer to Chapter 5 for more suggestions on managing your mind without interfering with it.

Being flexible and not trying too hard

If you have an obsessional problem, you’re almost certainly trying too hard at something. You may be trying too hard to get your appearance or desk looking just so. Or, you may be trying to ensure that you or someone you feel responsible for is safe from harm or disease. Or perhaps you’re inclined to follow moral or religious instruction to the letter, rather than living within the spirit of these ideals.

Flexibility is one of the hallmarks of psychological health because it helps you adapt effectively to the real world. Consider carefully the real-life consequences of holding standards or ideals too rigidly. Do these ideals really help you live the kind of life you want? Are the costs on yourself and others worth the benefits? If not, try to define how you’d behave if you were free from your obsessional problem, or take a leaf from someone else’s book and try acting accordingly. Refer to Chapter 8 for more on doing a cost-benefit analysis.

Using external and practical criteria

A crucial difference between people with and without obsessional problems is regarding the criteria they use to decide when to stop a particular behaviour. People without obsessions tend to use external observations, or practical criteria, to evaluate situations and make decisions.

By contrast, people with obsessional problems tend to use Internal criteria -Such as something feeling ‘right’, ‘better’, or ‘comfortable’ – to make decisions. Here are two examples of internal criteria with their external alternatives:

A person with contamination OCD may wash her hands until she Feels That her hands are clean enough. Someone without this problem may tend to stop washing when she can See Her hands are clean or when she’s been through a quick and convenient routine.

A person with BDD may readjust her hair, trying to reduce her Feelings Of anxiety and to Feel satisfied inside With how she looks. Someone without excessive concerns about her appearance may stop styling her hair when it Looks the same as usual Or isn’t sticking up.

Strive to use ‘external’ criteria to decide when to stop an activity. Instead of stopping when you feel comfortable, force yourself to stop washing your hands or fixing your hair Before You feel comfortable. Making this change can help reinforce the fact that your criteria for stopping rituals are the problem and proves to you that your discomfort and anxiety can diminish spontaneously. Importantly, this technique can also show you that you Can Tolerate the discomfort of resisting your rituals.

Allowing your mind and body to do their own things

Complete control of your thoughts and body is:

Impossible: No one has it, not even highly trained doctors, athletes, monks, or psychologists!

Counterproductive: Attempting to completely control your thoughts results in more of the thoughts and sensations you were trying to get rid of. You may seem even more out of control as a result.

Undesirable: Being able to completely choose the thoughts that enter your mind effectively puts a stop to any originality and creative problem-solving. Being in control of your body would almost certainly result in your demise – after all, do you really know how to run a body?

Allowing your body and mind to go on autopilot is so much easier and more helpful than trying to control your thoughts and bodily sensations.

Normalising physical sensations and imperfections

Obsessional problems like OCD, BDD, and health anxiety can lead you to focus too much on your thoughts, physical sensations, and minor physical imperfections. These problems also lead you to attach undue importance and meaning to your sensations, physical imperfections, and upsetting thoughts.

Health anxiety is underpinned by you attaching too much importance to normal physical sensations.

OCD results from you attaching too much meaning to normal thoughts that intrude into your mind.

BDD is caused by you attaching too much meaning to your appearance.

Your problem is not the content of your thought, the flaws in your complexion, or the variation in your heart rate. Your problem is Your belief‘that these experiences are abnormal. To help yourself overcome your obsessional problems, take the view that your thoughts, flaws, and imperfections are Normal. Conducting surveys (which we talk about in Chapter 4) is an excellent way of gathering evidence that many of the things you focus on and worry about are normal human experiences.

Facing \lour Fears: Reducing (And Stopping) Rituals

In CBT, facing your fears and resisting the urge to carry out compulsions is called Exposure and response prevention. This term has two important components:

Exposure: Deliberately facing up to the places, people, situations, substances, objects, thoughts, doubts, impulses, and images that trigger off your feelings of anxiety and discomfort.

Response prevention: Reducing and stopping the rituals and any other safety precautions that you adopt.

In order to reduce or potentially stop your reliance on rituals, you must tackle your obsessions head-on. To accomplish this, you need to get better at tolerating doubt, allow thoughts and images to come and go from your mind, and be realistic about responsibility. And yes, you need to practice these skills!

You can make faster progress if you Deliberately Trigger off your upsetting thoughts and anxiety in a regular and consistent way. Refer to Chapter 9 for more detail on designing an exposure programme to help combat your anxieties.

Facing your fears when overcoming an obsessional problem is different from many other kinds of anxiety problems, because the object of your fear may be more Internal Than External. For example, facing the Mental image Of pushing someone on to a train track is just as important as actually standing on

Resist! Resist! Resist!

To overcome an obsessional problem, you need to develop a list of your main fears as well as your typical rituals and safety behaviours.

Keeping a daily record of the frequency of the rituals you wish to reduce helps you to keep track of your progress and motivates you to keep reducing. You can record the frequency on paper or buy a ‘tally counter’ (a ‘clicker’ that counts each time you press it) from a stationery shop.

When you’ve written your list, you need to systematically expose yourself to your main fears, while simultaneously reducing and dropping your rituals and safety behaviours.

Stopping your rituals alone is not sufficient to overcome your obsessions. You need to incorporate deliberate exposure to your fears in order to get the practice you need.

Belaying and modifying rituals

Delaying and modifying a ritual can be also be a useful lead up to dropping a ritual entirely:

I Delaying rituals. If you find stopping your rituals difficult, start off by delaying them for a few minutes. Gradually build up the time delay until you can resist a ritual long enough for your anxiety to reduce of its own accord.

Modifying rituals. If you can’t gear yourself up to stop your ritual entirely just yet, modify your ritual. Instead of going for the full-blown version of a ritual, allow yourself to perform only a shortened version. For example, if you normally vacuum every corner of a room, try making yourself stick to the areas that you can see, without moving any furniture or other objects.

Overcoming your obsessional problems is supposed to be an uncomfortable experience. If you’re working through the exercises in this chapter and not experiencing a temporary increase in your discomfort, then either you’re not exposing yourself sufficiently or you’re not resisting your rituals sufficiently.

If you plan to stop a particular ritual but end up doing it anyway, Re-expose Yourself rather than letting your obsessional problem win. For example, if you have a fear of contamination, touch the floor to re-expose yourself after washing your hands.

You may be very tempted to err on the safe side and allow yourself to carry out more rituals or safety measures than the average person. Retaining avoidance and rituals can leave you very prone to your obsessions returning. Keep working at your ritual reduction until your rituals are at least as low as those of the average person on the street. Think of rituals and avoidance as the roots of a weed you are trying to get rid of from your garden. If you don’t get weeds up by the roots, they are sure to grow back.

Being Realistic about Responsibility

One of the hallmarks of obsessional problems is a tendency to take too much responsibility. Individuals with OCD, for example, often take excessive responsibility for causing or preventing harm to themselves or others. A person with health anxiety may have an overdeveloped sense of responsibility for spotting possible health problems. Someone with BDD may have an excessive sense of responsibility for not causing offence or being humiliated because of her appearance. In all cases, this sense of responsibility can drive the person to carry out rituals and leave them feeling guilty if they don’t.

Dividing up your responsibility pie

A helpful technique for developing a more realistic perception of your personal responsibility is to create a Responsibility pie chart, As follows:

1. Identify an event you fear being responsible for (such as, the house being burgled, causing harm, falling ill, being rejected).

2. Write down the level of responsibility you would feel for the event if it occurred as a percentage.

You can have between 0 and 100 per cent of the responsibility for an event occurring.

3. List all the possible contributing factors to your feared event occurring, including yourself.

4. Create a responsibility pie chart.

Use a large empty circle to represent 100 per cent, or all the responsibility for an event occurring. You can draw a circle yourself, or use the circle provided in Figure 11-1.

Proportionally divide the pie into wedges, based on how much responsibility you assign to each of the factors you list in step 3. Be sure to put yourself in last.

Figure 11-1:

The starting point for your responsibility pie chart.

5. Re-rate your estimation of your responsibility for your feared event.

Use the 0 to 100 per cent scale described in step 2.

For example, Figure 11-2 shows the responsibility pie chart for Terry, a mother with OCD who obsesses about harm coming to her children from poisonous substances. Initially, Terry believes that she would be totally to blame if any harm befell her children. However, after working through the responsibility pie chart activity, Terry is able to gain a more realistic perspective on her level of personal responsibility.

You can also use the responsibility pie chart with negative events that Have actually happened And that you’re blaming yourself for, for example losing a job, a failed relationship, someone treating you badly, or a loved one getting ill.

Other people for keeping things clean and uncontaminated

The purpose of the responsibility pie is to help you see that you’re not 100 per cent responsible for an event happening. Many obsessional people give themselves more responsibility than is legitimate – or at least more than non-obsessional people do.

Taking Less responsibility Is something that you steadily need to train your mind to do. Actually, you’re retraining your mind to break your habit of Taking excessive-responsibility.

Retraining your attention

If you think you’re preoccupied with your appearance, health, or being responsible for harm coming to yourself or others Because you focus on it too much, Try to create a counterbalance by training your attention elsewhere. Chapter 6 gives you some more guidance.

Seeking professional help

Use the following checklist to determine whether an obsession or compulsion is normal or a problem for which you should seek professional assistance.

Your obsessional problems are impacting on your physical health. For example, you’re not taking prescribed medication, attending medical appointments, orfeeding and grooming yourself sufficiently.

Your obsessional problems are preventing you from leaving your home. Sometimes, people with severe OCD or BDD become housebound.

Your obsessional problems are having a serious impact on your social and occupational life. For example, you’re unable to continue working, you’ve lost a job, you’re avoiding contact with friends, or your partner has left you.

Your obsessional problems are preventing you from caring adequately for your children. This is a particularly painful point for many people with OCD. People with OCD

Typically take too much responsibility forthe welfare of their loved ones. However, if you contemplate the needs of your children and decide Impartially That your problems are stopping you from meeting those needs, get in touch with a professional.

You’ve given self-help an earnest try but are unable to overcome your problem.

Your family doctor may be familiar with obsessional disorders, but you maybe better off seeking out a specialist. Make an appointment with a psychiatrist for assessment. If your problem is so severe that you’re housebound, you may be able to get a home assessment via a community mental health outreach team. However, you may need to prepare yourself for going out of your safety zone and into a hospital or clinic.

Getting the best help for your obsessional problems is not always straightforward, but we do encourage you to not give up. If you meetthe criteria on the checklist above, please do seek help. Appendix A lists relevant organisations you can consider contacting for more information.

In This Chapter

^ Finding out what osteopathy is all about

^ Understanding how it works

^ Discovering what osteopathy can be good for

^ Knowing what to expect in a typical consultation

^ Knowing how to find a safe and effective osteopath

Ention the word osteopathy and most people think of bone cracking and bad backs. Yet osteopathy is so much more than this image. Some even argue that osteopathy is a complete system of healthcare for restoring and maintaining equilibrium in the body.

I’ve called this chapter Opening Up with Osteopathy not only because it opens the Treating Your Body part but also because osteopathy really does seem to ‘open’ the body by releasing tension, facilitating movement, and creating a sense of ‘space’ in place of restriction.

In this chapter, I tell you a bit about the amazing life story of the founder of this therapy and describe the techniques that are in the modern day osteopath’s repertoire. You’ll get an idea of what it’s like to have an osteopathic treatment and find out how even newborn babies are benefiting from it!

I also give you a checklist for the types of ailments osteopathy may be helpful for. You may be surprised by some of the things that are included in it.

Then I give you all the contact details that you need for tracking down fully qualified practitioners and tell you what those pesky letters after their names stand for.

Andrew Still, the founder of osteopathy, loved playing around with mechanical inventions all his life. He was born in a log cabin in Virginia in the US in 1828, the son of a preacher/physician, and the third of nine children. As a young boy he had to work hard helping his parents and was always looking for ways of improving the mechanical equipment that they used. He invented several labour-saving devices, including a more efficient churn for butter-making.

Still also applied his enthusiasm for mechanics to the physical body and became interested in finding ways of improving structural balance. He trained as a doctor by reading books and studying with his father and used his study of animal and human skeletons to begin to formulate his ideas about body mechanics.

Working as a doctor in the American Civil War, Still became disenchanted with the medical

Methods of the time – including blood-letting, crude surgery, and purging – which were not very effective in saving lives. This experience and the tragic loss of three of his children to meningitis, another to pneumonia, and his wife due to complications in childbirth, convinced him that a new form of medicine was needed.

Still went back to studying the body and came to believe that faulty body mechanics could affect organ function and the flow of blood and vital energy or ‘nerve force’. He went on to develop methods for improving body balance and invented various devices to assist in treatment. These included a special brace designed to stop patients falling off the treatment table during vigorous manipulations!

Finding Out about Osteopathy

Osteopathy Is a system of diagnosis and treatment that identifies and relieves structural and mechanical problems of the body. This therapy is concerned with the framework of the body, that is, the muscles, bone, tendons, ligaments, and cartilage – all the bony and sinewy bits – and the nervous system that co-ordinates their smooth functioning. This framework is sometimes referred to as the neuro-musculo-skeletal system – a bit of a mouthful but it manages to cover everything in one word! Osteopaths are interested in both the Structure And the actual Functioning Of the components of this system.

A (very) brief history of osteopathy

Osteopathy was created by Dr Andrew Taylor Still, a rural physician in the US in the 1890s. He was not impressed by some of the more barbaric medical practices popular at the time and wanted to find a more natural way of treating

The body. He thought up the name by combining two ancient Greek words, Osteon, Meaning ‘bone’, and Pathos, Meaning ‘suffering’ or ‘disease’. Still believed that if you could create good neuro-musculo-skeletal balance, then the body would function better and self-healing could occur.

Still faced strong opposition from the medical establishment for his enthusiasm for natural medicine but he was an energetic and determined man who stuck to his principles. One of my favourite quotes of his, that seems to sum up his stance, is, ‘I have no desire to be a cat, which walks so lightly that it never creates a disturbance’. He went on to establish the American School of Osteopathy in 1892 and trained thousands of osteopaths (including some of his own children and siblings) within his lifetime. He also admitted women and black people as students, which was highly unusual at the time, and was a vociferous opponent of the slave trade, which still existed. He continued to practise and teach osteopathy until his death in 1917 at the ripe old age of 89.

One of Still’s graduates, a Scot, Dr John Martin Littlejohn, brought osteopathy to the UK and founded the British School of Osteopathy in 1917. This school still exists as a major osteopathic training institution. Gradually, other schools have been established.

Modern day osteopathy is still based on Still’s work but has also developed to include new techniques and approaches. Psychological, social, and lifestyle factors are also considered important.

Osteopathy has been at the forefront of regulation in the field of complementary medicine and osteopathy practice is now governed by law in many countries. It is currently one of the most popular forms of complementary therapy in the West.

Grasping the idea behind osteopathy

^W-fft/- According to Dr Still’s osteopathic theory, all disease can be related to disor-^^/^N Ders involving the spine, muscles, joints, and nerves. He claimed that struc-’ ^ x ‘ tural imbalance affected nerve and blood supply to the body’s organs and

Termed these imbalances Osteopathic lesions. Still devised methods of manipulation, stretching, and massage of the soft tissues to release blockages and areas of tension, increase mobility, and improve the flow of blood and lymph. In this way he aimed to restore normal function of the nerves and organs and enable the body’s natural healing mechanisms to come to the fore.

Still maintained that osteopathy is a holistic system of medicine that takes into account not only the structural problem, or physical imbalance, itself but also underlying contributing factors in terms of lifestyle, diet, and emotional health.

Imbalances in the neuro-musculo-skeletal system (the structural support of the body and its communication systems) can be caused by physical injuries, poor posture, bad work habits, repetitive strain, badly designed seating, and so on. Stress, emotions, and psychological factors can also play a part as they lead to tension, which in turn affects muscles, nerves, and blood supply.

The osteopath takes all these factors into account and each person is treated individually. So, for example, if a person has neck pain the osteopath may consider various possible contributing factors, including damage from past injuries or accidents, occupational factors such as long hours using computers or frequent carrying of heavy loads, poor bed or pillow support at night, stress and worry leading to muscular

Tension, pelvic imbalance leading to irregular gait, or child-bearing and pregnancy.

For example, John, 59, went to an osteopath complaining of a persistent stiff neck. He was surprised when the osteopath linked this problem to pelvic misalignment and his regular jogging. The osteopath eased stiffness in his ankles from an old sports injury, gave him exercises to strengthen weakened muscles, and fitted John with Orthotics – Specially made insoles for his running shoes – to balance his gait. To John’s surprise, within just a few days of his treatment and wearing the orthotics his neck pain disappeared. He now wears the orthotics constantly in both his ordinary and running shoes, does the exercises regularly, and has occasional osteopathic check ups. The neck pain has not recurred.

Osteopaths therefore aim to identify underlying causes of imbalance and then to restore mobility, release restriction, ease tension, facilitate circulation, and enhance general well-being in order to affect improvements in body functions.

Osteopathy Today

The 1993 Osteopaths Act made osteopathy one of the first complementary therapies to be regulated and licensed in the UK. A register of osteopaths was set up in the UK in 1998 and the title ‘osteopath’ became protected by law in 2000. Since that time it is illegal for anyone to call themselves an osteopath unless they’ve completed a recognised training course and are registered with the General Osteopathic Council. Training is normally for a minimum of four years.

The General Osteopathic Council (GosC; Www. osteopathy. org. uk) is an independent body set up following the Osteopaths Act in order to establish and maintain professional standards, accredit training courses, and maintain

The register of osteopaths. The GosC also aims to make osteopathy a recognised medical specialty.

Seven approved osteopathic colleges exist in the UK and more than 5,000 practitioners. Some practitioners are medical doctors who have chosen to study osteopathy as a postgraduate course.

British trained osteopaths study for a minimum of four years and their training includes anatomy, physiology, differential diagnosis (accurate identification of disease from symptoms), clinical skills, and extensive clinical practice. Treatment is almost entirely based on manual therapy techniques, and students do not perform surgery or prescribe medicines. (However, they may be given these rights in the future since the British government has included osteopathy in their list of professions allied to medicine.)

In contrast, in the US, osteopaths undergo full medical training and are entitled to prescribe medicines and perform surgery. The US has had full licensing since 1972, and US osteopaths have been eligible for membership of the British Medical Association since 2005. However, these practitioners may have had quite limited training in manual manipulative therapy as compared to their British counterparts. For more information, consult the American Osteopathic Association at Www. do-online. osteotech. org/index. cfm.

Within member states of the European Union, apart from the UK, France, and Switzerland, no standardised training in osteopathy is available. In Australia and New Zealand, osteopathy is a growing profession.

Exploring Different Types of Osteopathy

Once osteopaths have completed their general training, they may go on to do further specialist training. Popular forms of specialisation are cranial osteopathy, paediatric osteopathy, and visceral osteopathy. Other osteopaths may also specialise in sports medicine.

Cranial osteopathy

Cranial osteopathy was developed from the work of an American osteopath, Graham Sutherland, in the 1930s. Contrary to the orthodox medical view that the bones of the skull or cranium become fixed in adult life, Sutherland believed that they retain a degree of flexibility. He believed that the sheath, which encloses the cerebrospinal fluid (CSF) and attaches to these cranial

Bones and the spine – known as the Dural membrane - can become less flexible due to birth trauma, injuries, and falls. He reasoned that this in turn would affect the flow of cerebrospinal fluid (CSF), circulation of blood and lymph in the body, and the drainage of sinus fluids in the head. Sutherland also believed this would affect normal bending and movement of the spine and cause joints to become restricted in their pattern of movement.

Sutherland claimed that the rhythmical pulsing of CSF, which should normally be around 6 to 18 times per minute, could be felt with the hands. Interestingly, this rhythm has been found to continue to pulse for a few minutes even after a person’s heart and breathing stop in the process of dying.

He developed a range of gentle techniques to determine the quality and movement of this cranial rhythm, to release tension and restrictions and to restore balance.

Some people feel that nothing is going on at all during such treatment and simply feel pleasantly relaxed. However, the cranial osteopath has a highly developed sense of touch and is trained to detect real differences in cranial rhythm – although this ability is difficult to verify scientifically.

Because of the lack of scientific evidence, the theory and practice of cranial osteopathy remains controversial, even amongst osteopaths. However, it is practised by a growing number of osteopaths, particularly, but not exclusively, by those specialising in paediatric osteopathy, the treatment of babies and young children. Cranial osteopathy is also ideal for the elderly, weak, or frail, or for anyone who prefers a very gentle approach.

Cranial osteopathy has been used for premature babies; infant problems such as colic, teething, and sleeping or behavioural problems; ear and sinus problems; headaches and back, digestive, and respiratory problems, to name but a few.

Some osteopaths use cranial osteopathy as just one of the techniques at their disposal, while others specialise almost exclusively in cranial work. To find an osteopath who has completed a recognised postgraduate course in cranial osteopathy, contact the Sutherland Society (Www. cranial. org. uk), which has more than 300 members both in the UK and overseas.

Paediatric osteopathy

Paediatric osteopaths use a range of gentle techniques, including cranial osteopathy, to treat newborns and young babies. This approach has been pioneered by British osteopath Stuart Korth, who founded the Osteopathic Centre for Children (OCC; Www. occ. uk. com) and created diploma training in paediatric osteopathy for qualified osteopaths.

My son first had cranial osteopathy from a very skilful osteopathic colleague and close friend of mine, Deidre Stubbs, the day after he was born. He had had a wonderfully easy, natural birth at home, without any sort of medication or difficulty, but Deirdre came over to see him and offered to check him over. I remember her gently laying her hands on either side of his head and telling me of some restrictions that she felt. To my amazement, simply from these sensations, she was able to correctly identify which way he’d come out of the birth canal (facing forwards, twisted slightly to my left-hand side, and with the umbilical cord around his neck!). She made some fine movements with her fingers to ease the restrictions that she felt and at the exact moment that she felt a release, my day-old son took a deep breath and then fell into a blissful sleep.

In the course of his early years my son was very fortunate to have further cranial osteopathy at

Times of need from the outstanding and renowned osteopaths, Professor Laurie Hartmann, a pioneer of minimal velocity (very gentle) manipulative techniques, and Stuart Korth, founder of the Osteopathic Centre for Children and developer of postgraduate training in pae-diatric osteopathy. Both recommend that treatment be given at major landmarks in children’s development, such as when they first start to crawl, sit, stand, and walk, and after any major traumas such as falls or accidents. Being very active, fast growing, and accident prone, my son needed treatment quite a few times.

I sometimes wonder if one of the effects of these treatments was to give my son such good body balance that, as a teenager, he is now a competent and enthusiastic skateboarder and an outstanding climber.

The OCC has clinics in London and Manchester and treats children from birth to 18 years, as well as women during pregnancy. The OCC has become particularly renowned for its work with premature babies and children with cerebral palsy. However, as is the case for all paediatric osteopaths, it also offers treatment for a wide range of children’s ailments, including ear infections, colic, teething, asthma, sleeplessness, growing pains, and epilepsy.

Various osteopathic colleges, such as the British School of Osteopathy (www. bso. ac. uk) and the European School of Osteopathy (Www. eso. ac. uk) also offer specialist children’s clinics. Contact the individual schools for further information.

Visceral osteopathy

Visceral osteopathy originally grew out of work done by two American osteopaths, H. V. Hoover and M. D. Young, in the 1940s, who attempted to synthesise the work of Dr Still, the founder of osteopathy, and John Upledger, the creator of cranio-sacral therapy.

The word Viscera Refers to the soft internal organs of the body – the lungs, heart, digestive organs, and reproductive organs. Jean-Pierre Barral, a graduate of the European School of Osteopathy in the UK, developed visceral osteopathy in the 1970s. He became interested in patterns of stress in the body tissues around these internal organs and how gentle osteopathic techniques could be used to release them.

Barral devised a system of soft manipulations of the internal organs and surrounding tissues to treat these abnormal stress patterns. He claims that this visceral osteopathic treatment can facilitate improved organ function, body system function, fluid circulation, mobility, and general wellness. He also developed a system of thermal diagnosis after discovering that areas of tension could be located by the increased heat that they give off.

In 1985, Barral established a training programme in visceral techniques at the Upledger Institute in the US, which has been taken by many osteopaths and other physical therapists.

Visceral osteopathy is considered to be particularly suitable for people after surgery, trauma, injury, or pregnancy but can also be used to rebalance the body after chronic illness such as repeated cystitis (bladder infection).

While cranial osteopathy is a postgraduate specialisation for registered osteopaths who have already had substantial training in anatomy and physiology and a minimum four years of study and clinical practice, another healing discipline also exists, cranio-sacral therapy, that may be learnt and practised by non-osteopaths with much shorter and limited training.

Cranio-sacral therapy was developed by another American osteopath, Dr John Upledger, in the late 1970s. He was a professor of biomechanics and clinical researcher at Michigan State University and became interested in the importance of the membranes that surround the central cord in the spine and the brain in the skull.

Building on the ideas of Dr Sutherland about the significance of the cranial rhythmic impulse

(CRI) and the ebb and flow of cerebrospinal fluid (CSF) in the spinal chord and the skull, Upledger came to believe that this could affect the function of every cell in the body.

He developed a system of using extremely light pressure on the cranium (skull), or sacrum (tail-bone), or elsewhere on the body to ease these membranes and establish smooth, unrestricted flow of the CSF.

This work is even more controversial than cranial osteopathy in that no real research evidence exists to support its use. However, many people report finding cranio-sacral therapy deeply relaxing and beneficial. For more about this therapy, check out Www. upledger. com.

However, little research evidence exists to support this practice and it remains controversial and not yet widely practised by osteopaths. No specific association has been established for visceral osteopaths. To find an osteopath who practises this approach, you have to simply ask around amongst osteopathic practitioners.

Understanding How It Works

The neuro-musculo-skeletal system provides the support structure for the body; the mechanics for movement in order to stand, sit, run, and carry out everyday activities; and the communications network for controlling this system. The neuro-musculo-skeletal system is made up of the following:

U Bones: The hard, solid bits that make up the human skeleton – more than 200 of them exist in the body

U Joints: The meeting point of two or more bones – usually to facilitate movement

U Muscles: Bundles of fibres that can contract in order to create movement of the bones

U Ligaments: The stringy bits that connect to your bones and keep your joints stable, stopping them from moving about all over the place

U Tendons: Strong, fibrous cords at the end of muscles that attach onto bones or other solid structures in the body

U Soft tissue: The collective name for all the tissues that connect, support, or surround the structures or organs of the body, including the ligaments, tendons, and muscles and also the tissues inbetween, fat, and nerves – basically all the soft and non-solid bits

U Nerves: Bundles of fibres that carry signals from one part of the body to another, such as the optic nerves that carry signals between the eyes and the brain

Damage to any of the above can cause pain and strain and have a knock-on effect on other body systems or internal organs.

Pain signals can build up, leading to increased inflammation and irritation and an accumulation of waste products produced by the body in response to the pain. These occurrences disrupt the normal flow of blood and fluids, which further exacerbate the pain and tension and may cause increased immobility. According to osteopathic theory, this disruption in normal fluid flow and body mechanics impairs the body’s ability to regulate and heal itself.

Osteopathy is designed to break this cycle of pain, tension, and inflammation by relaxing the muscles, calming the nerves, easing restriction, and reestablishing normal circulation and function.

Discovering Whom and What Osteopathy Is Good For

Almost anyone is suitable for osteopathy. Most osteopaths treat men, women and children, the elderly, pregnant women, persons active in sports, and so on.

Conditions that osteopathy can treat

A typical osteopath’s clientele may include manual workers, office workers, drivers, homemakers, musicians, dancers, athletes, and children. The most common complaints are bad backs, neck problems, and joint problems such as tennis elbow, frozen shoulder, and arthritis. Increasing numbers of doctors are incorporating osteopathy into their practices or referring to private osteopaths.

Acceptance of osteopathy is even filtering down to emergency medicine. I was involved in a road traffic accident recently and my passengers and I suffered severe whiplash. We were taken by ambulance to the A&E department of the local hospital and were surprised to be told by the examining doctor there to seek out an osteopath for treatment! We did this and it brought great relief.

However, osteopathy certainly isn’t limited to joint pains and strains. An osteopathic colleague of mine recently did a clinical audit (a record of all the different conditions that patients have brought to him over the last year). It contained the following: Back pain; neck pain; joint problems (such as frozen shoulder, tennis elbow, arthritis); sports injuries; headaches or migraine; asthma or other respiratory problems; menstrual problems; sleep problems; digestive problems; ear infections and tinnitus (ringing in the ears); circulation problems; sinus problems; cystitis and bladder problems; repetitive strain injury; neurological problems such as head trauma and epilepsy; pregnancy related problems such as back pain, heartburn, and water retention; infant disorders including colic and teething; and developmental delays and learning difficulties. Quite a list!

Increasingly, osteopaths are finding that people are referring themselves for all kinds of problems and reporting benefits.

First visits to osteopaths are often made at times of crisis, such as when a person suddenly experiences acute back pain. However, more people are now using osteopathy preventively and going for regular or occasional maintenance treatments to maintain good ongoing structural balance.

Evidence that it works

Research trials investigating osteopathy for different ailments have yielded mixed results. Many early studies suffered from design flaws but increasingly good studies are being produced that do confirm the benefits of osteopathy for a range of problems, including back pain and middle ear infections in young children.

A lot of publicity was given recently to a review paper by researchers from the Peninsula Medical School at Exeter University, which claimed no evidence existed that osteopathic manipulation can effectively relieve any conditions including back pain! This claim has been vigorously refuted by the General Osteopathic Council, which argued that the review was very limited, did not take account of the multi-faceted nature of back pain, and excluded all good research carried out since 2000. For example, an excellent trial carried out in 2004, funded by the Medical Research Council, provided pretty good evidence that spinal manipulation plus exercise helped reduce low back pain.

For more about osteopathy research, check out the information and links of the National Council of Osteopathic Research (NCOR) at Www. brighton. Ac. uk/ncor/about/index. htm.

When not to use osteopathy

With care and experience, gentle osteopathic techniques can be used for any condition but vigorous manipulations should not be used in case of the following:

U Osteoporosis (brittle bones)

U Severe rheumatoid arthritis (bone inflammation)

U Osteoarthritis (bone degeneration)

Neck adjustments must be performed with great care in people with a history of stroke or high blood pressure.

Particular care must also be taken with the elderly and young children or infants. Gentle cranial techniques (check out the section on cranial osteopathy for more on this) are ideal for such people.

What to Expect in a Typical Consultation

A consultation with an osteopath will generally start with some questions and answers.

Questioning

An osteopathic consultation usually starts with detailed medical history taking and questions about your general health. You may have been asked to fill in a questionnaire beforehand to save time. The osteopath will also ask you details about your symptoms, how bad they are, how long they’ve gone on for, what makes them better/worse, and so on. Since the osteopath is interested in a holistic approach, you may also be asked questions about your diet and lifestyle.

Understanding diagnostic methods

The questions will be followed by a physical examination. For this examination you’re usually asked to undress down to your underwear but sometimes certain garments can be retained; for example, if you have a neck problem you may only be asked to remove your upper outer garment(s). Some osteopaths provide a loose robe to be worn during examination and treatment.

Your osteopath diagnoses on the basis of:

U Observation and movement: The osteopath will observe your general posture, gait, and breathing pattern to learn about your structural balance. You may be asked to walk up and down as your gait is observed or to bend from side to side, or forwards and backwards, to assess the ease of movement of your spine. This observation may be followed by more detailed investigation of your range of movement for specific joints. For example, if you have a shoulder problem the osteopath may want to gauge how far you can raise or lower your arm.

U Reflex testing: The osteopath may test your reflexes – doing so can involve tapping at certain points on the body with a small rubber instrument, such as just below the knees. When the tap is made, your leg will

Involuntarily jerk as the nerve sends a message to the brain and this is then relayed to your muscle causing it to contract. (This jerk is the same mechanism as when you mistakenly place your hand on something hot and involuntarily draw it away.) The osteopath uses these techniques to check that all your reflexes are working properly.

U Palpation: The osteopath may also use hands and fingers to palpate the tissues surrounding your joints in order to assess the level of inflammation, muscle tension, and pain.

U X-rays or scans: Occasionally the osteopath may recommend that you have an x-ray or other medical test such as an MRI scan. If you’ve already had an x-ray taken of a joint or bone problem, take it with you to your consultation as all osteopaths are skilled in reading these.

Getting to grips with osteopathic techniques

Osteopaths have a range of specially designed techniques literally at their fingertips to help restore balance in the body, release muscular tension, ease pain and stiffness, increase mobility and range of movement, and improve circulation and general well-being.

Osteopaths have many techniques in common with other manual therapists, such as chiropractors, but tend to favour light manipulations, stretch and release techniques, and massage. In contrast, chiropractors often make more use of x-rays and more vigorous manipulations. Take a look at Chapter 15 to find out more about chiropractic therapy.

Here are some common techniques used by osteopaths:

U Manipulations: These are physical adjustments performed by the

Osteopath to joints, muscles, or their surrounding tissues. The aim is to release muscular tension or spasm and to ease restriction, thereby restoring better mobility and circulation.

A common type of manipulation is the ‘high velocity low amplitude thrust’. This technique involves positioning the body carefully and then applying a rapid thrust to a joint, or the bones of the spine, in order to release restriction and tension. Sometimes an audible Crack Or Pop Is heard as the tissues are released. If this technique is done well, you can have an immediate increase in the range of movement afterwards.

This type of manipulation isn’t suitable for those with weak or brittle bones.

More gentle forms of manipulation include positional release techniques, which are light adjustments used for areas of acute pain, inflammation, or injury, or on people who are weak or frail.

U Joint mobilisation/articulation: This involves the osteopath rhythmically moving a joint and applying gentle stretches to the surrounding tissue in order to release tension and ease restriction.

U Myofascial release: This technique employs slow stretching and easing out of muscles and surrounding tissues to release tension, increase range of movement, and facilitate healing.

U Muscle energy techniques: These are various techniques employing contraction and stretching of the muscles that are used, to release muscle tightness and restore range of movement.

U Direct pressure: The osteopath may apply direct pressure to certain trigger points in order to release tension and pain.

U Massage: Different types of massage may be used to ease muscle tension, stretch the tissues, and promote circulation.

These techniques are often accompanied by advice on posture, exercises, diet, and self-help techniques such as the use of heat treatments to enhance circulation or ice packs to ease swelling and inflammation.

The osteopath may also use other specialist techniques such as cranial osteopathy (very gentle techniques on the cranium (skull) and sacrum (tail-bone)), or visceral (work on releasing tension in the soft tissues around the internal organs) techniques. For more about these techniques, check out the ‘Exploring Different Types of Osteopathy’ section earlier in this chapter.

Knowing what to expect at the end of treatment

After your osteopathic treatment has ended, your appointment is likely to conclude with the following:

U The osteopath may demonstrate or advise on certain exercises for you to practise between sessions.

U You may be advised that initially your symptoms may worsen – sometimes the tissues react to the treatment – and to take things easy. This effect normally subsides in a day or two and then real improvement can be felt.

U The need for further treatments and the time between them will also be discussed.

U You’ll be advised to get up and get dressed slowly and to have a glass of water if you want. Ideally you need to rest, or at least avoid such activities as heavy lifting, manual labour, vigorous exercise, and long-distance driving immediately after treatment.

Anticipating treatment duration and frequency

Osteopathic treatments usually last half an hour but can be from 20 to 60 minutes. Treatments may be at weekly intervals initially and then become more spaced out once your condition improves. Sometimes just a single treatment may be all that is needed. More often a short series of two to six treatments may be necessary. For certain chronic conditions, regular maintenance treatments may be helpful.

Knowing Whether Your Osteopathic Treatment Is Working

The main reason you sought out osteopathy will probably have been because of pain, injury, and/or decreased mobility. So obviously if the treatment is working well you’ll expect these to have improved.

However you need to bear in mind a few things:

Don’t expect immediate results. It may be a couple of days before things settle down and you feel the full benefit of your treatment. Allow your body to rest and heal after treatment.

If you experience a really marked increase in pain, or deterioration in your symptoms, contact your osteopath for advice.

Discuss with your osteopath what improvements you can realistically expect over what sort of timescale. You may need a short course of treatments to obtain the full benefits.

As treatments go on, you should feel more improvement in your symptoms and be able to have longer intervals between treatments.

U For best results, it is important to attend regularly and to follow the exercise and lifestyle advice given to you by your osteopath.

U If you have no improvement after a course of treatment then osteopathy may not be effective for your condition and you may need to consider another form of therapy. Discuss this situation with your practitioner.

Common Questions about Osteopathic Treatment

Here are some questions that I’m often asked about osteopathy:

U Will it hurt? Not usually, no. You may feel a slight click or hear a pop during manipulations but these are just signs that the manipulation has been successful. Gentle manipulation, stretching and massage techniques, and cranial techniques are usually very comfortable and relaxing.

U Do I have to take my clothes off? Not everything, no. You’re usually asked to remove outer garments or wear a robe during treatment if you feel uncomfortable.

U Will I be lying down or sitting up? Some manipulations are performed when you’re lying down on the treatment couch while some are done when you’re in a sitting or standing position. Most treatment couches have a Nose hole To enable you to get comfortable and breathe easily while lying on your front.

U Will other equipment be used? A rolled towel or pillow may be placed strategically against your body to cushion it during certain manipulations. Some osteopaths are trained in trigger-point acupuncture and may use acupuncture needles in selected sites to release tension and pain. Some also use lasers, magnet healing, or massage devices for the relief of pain.

U How does the osteopath know what techniques to use? The osteopath’s long and rigorous training equips them well in deciding which is the most safe and effective treatment for your particular ailment.

U What happens if I’m scared of vigorous manipulations? Discuss your anxiety with your osteopath who can modify treatment to suit your needs.

Osteopathic treatment is most effective if you’re relaxed and comfortable. Have confidence in your practitioner and ask for a blanket or towel for additional warmth if you feel cold during treatment.

If for any reason you feel faint or nauseous, or if you experience new pain during treatment, always let your osteopath know.

Finding a Good Osteopath

To find a qualified osteopath in your area contact the General Osteopathic Council (GOsC) at: 176 Tower Bridge Road, London SE1 3LU (Tel: 020 7357 6655; e-mail: Info@osteopathy. org. uk; Www. osteopathy. org. uk). Anyone using the name ‘osteopath’ must now be registered with this professional body.

Look for the letters after the person’s name. All approved osteopathy colleges now offer courses to degree level. Therefore osteopaths who’ve completed courses since that date will have either BSc (Hons) Osteopathic Medicine, BSc (Hons) Osteopathy, B. Osteopathic Medicine or B. Osteopathy, after their name. British osteopaths trained before degree status became available on courses may use D. O. (Diploma in Osteopathy) after their name. Medical doctors who have done an accelerated course at the London College of Osteopathic Medicine (LCOM) have the letters MLCOM (Member of LCOM) after their name. American trained osteopaths have the letters DO (Doctor of Osteopathy) after their names.

Here are some other recommendations for finding an osteopath:

U Ask friends, family, and colleagues for personal recommendations. U Some sports and leisure clubs provide osteopathy.

U Consider visiting the teaching clinics at the major schools of osteopathy. All students practise under close supervision from experienced practitioners and fees are often low, too. Contact the schools direct for details at:

• British School of Osteopathy, Tel: 020 7407 0222; Www. bso. ac. uk

• College of Osteopaths, Tel: 020 8905 1937;

Www. collegeofosteopaths. ac. uk

• European School of Osteopathy, Tel: 01622 671 558; Www. eso. ac. uk

• London College of Osteopathic Medicine (medical practitioners only), Tel: 020 7262 5250

• London School of Osteopathy, Tel: 020 7265 9333; Www. lso. ac. uk

• Oxford Brookes University, Tel: 01865 484 848; Www. brookes. ac. uk

• Surrey Institute Of Osteopathic Medicine (SIOM), Tel: 020 8394 1731; Www. nescot. ac. uk

Questions to ask your osteopath

Consider asking your osteopath about the following issues:

U Qualifications. Normally practitioners are very happy to provide details of their training and qualifications. If you have any doubt as to their validity, check them.

U Insurance. To be a member of the Register of Osteopaths, your practitioner must be appropriately insured.

U Experience. Question your practitioner about their experience in treating your particular ailment and their usual degree of success!

U Logistics. Find out what fees you can expect and the likely frequency and duration of treatment that you may need.

Counting the cost of osteopathy

The majority of osteopaths work in private practice and their fees generally range from Ј25 to Ј55 per session. Practitioners in central locations or with extensive experience may charge more. Sessions are usually 20 to 30 minutes. Typically, two to six sessions may be required. Some osteopaths give discounts if a series of treatments are necessary.

Increasing numbers of osteopaths now work in GP practices and NHS clinics. Ask your doctor if you can be referred to an osteopath on the NHS. In such cases the treatment is usually free, although you may have a long wait.

Many private health insurances now cover osteopathy. You may need to be referred by your doctor in order to claim. Check this with your provider.

Some osteopaths offer concessions for retired persons or those on benefits. Ask your osteopath for details.

Ensuring satisfaction

If you’re dissatisfied with your treatment, first talk things over with your practitioner.

If you think that the practitioner has been negligent or unethical in any way, including incompetent treatment and inappropriate touching, contact the

General Osteopathic Council. This independent organisation has a well-established complaints procedure for dealing with any concerns from members of the public.

Helping Yourself with Osteopathy

Osteopaths advise many self-help exercises to aid posture and breathing. Here’s a great one that I find really helpful to ease a stiff neck when working at a computer.

1. Sit with your back straight and imagine a string pulling you up from the top of your head, straightening your spine and lengthening your neck.

2. Tuck your chin in slightly so that your neck is in a straight line.

3. Put your hands behind your back and interlock your fingers with the palms facing upwards.

4. Pull down with your hands stretching your arms downwards and at the same time push your shoulders back and allow the shoulder blades to move towards each other.

5. Holding your arms in position, again check that your back is straight and chin tucked slightly in. Imagine the string at the top of your head pulling you up a little farther.

6. Hold for the count of ten, breathing evenly, and then release.

This exercise gives an excellent stretch, improves posture, and releases tension in the neck and shoulders. If you’re typing a lot, I suggest repeating it every hour.

I am indebted to the excellent medical osteopath, Dr Jovan Djurovic for teaching me this exercise. I’ve found it invaluable and hope you’ll find it useful too!

In This Chapter

^ Boiling down the basics of vapor pressure

^ Seeing how pressure, volume, temperature, and moles work and play together ^ Diffusing and effusing at different rates

T first pass, gases may seem to be the most mysterious of the states of matter. Nebulous and wispy, gases easily slip through our grip. For all their diffuse fluidity, however, gases are actually the best understood of the states. The key thing to understand about gases is that they tend to behave in the same ways — physically, if not chemically. For example, gases expand to fill the entire volume of any container in which you put them. Also, gases are easily compressed into smaller volumes. Even more so than liquids, gases easily form homogenous mixtures. Because so much open space occurs between individual gas particles, these particles are pretty laid back about the idiosyncrasies of their neighbors.

Chapter 10 sets down the basic assumptions of the kinetic molecular theory of gases, a set of ideas that explains gas properties in terms of the motions of gas particles. In summary, kinetic molecular theory describes the properties of ideal gases, ones that conform to the following criteria:

Ideal gas particles have a volume that is insignificant compared to the volume the gas occupies as a whole. The relatively small volume of a 20-ounce soda bottle, for example, completely dwarfs the individual gas particles inside the bottle, making their sizes irrelevant to any ideal gas calculation.

Ideal gases consist of very large numbers of particles in constant random motion.

Ideal gas particles are neither attracted to one another nor repelled by one another.

Ideal gas particles exchange energy only by means of perfectly elastic collisions — collisions in which the total kinetic energy of the particles remains constant.

Like all ideals (the ideal job, the ideal mate, and so on), ideal gases are entirely fictional. All gas particles occupy some volume. All gas particles have some degree of inter-particle attraction or repulsion. No collision of gas particles is perfectly elastic. But lack of perfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon kinetic molecular theory of ideal gases. In this chapter, you’re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called "gas laws."

Getting the Vapors: Evaporation and Vapor Pressure

Q.

Because kinetic molecular theory explains the movement of particles between different phases, it comes as no surprise that we find gases in the presence of liquids. Within a liquid, individual particles have any of a range of kinetic energies. At any given moment, some fraction of particles on the surface of the liquid possesses enough kinetic energy to escape into the gas phase. Collections of these gas-phase "refugee" particles, hovering over the surface of a liquid, are called Vapor. The process by which particles escape the surface of a liquid into the vapor phase is called Evaporation. Of course, the escaped particles may fall back into captivity in a process called Condensation. Given enough time, the rate at which particles escape comes to equal the rate at which they are recaptured, and this state of affairs is called a Dynamic equilibrium.

Vapor pressure Is the pressure at which vapor is in dynamic equilibrium with liquid. As evaporation occurs, the pressure above the surface of a liquid increases because more particles are added to that volume. Eventually, the pressure over the surface of the liquid equals the vapor pressure of that liquid, at which point evaporation equals condensation. Why does increased pressure produce condensation? What is pressure, anyway? In short, Pressure Is a force applied over an area — like the area of the surface of a liquid, for example. At the molecular scale, pressure arises from the collisions of countless particles with that surface. At higher pressure, then, more gas particles are colliding more frequently with the surface of the liquid. These collisions make it more difficult for liquid-phase particles to escape and make it more likely that gas-phase particles will be recaptured. The final important piece of information to retain about vapor pressure is its relationship to boiling; specifically, when the vapor pressure of a liquid reaches the atmospheric pressure, a liquid will boil.

Vapor pressure depends on temperature because temperature affects the dynamic equilibrium. Adding heat to a sample increases the average kinetic energy of the particles within that sample. Temperature is simply a measure of the average kinetic energy of the particles in a sample. So at higher temperatures, particles possess greater kinetic energy and are more likely to escape into vapor phase. The higher the temperature, the higher the vapor pressure.

Pressure is also directly related to altitude. If you’ve ever tried to take a deep breath from a mountaintop, you know that the air is "thinner" at higher elevation, making it harder to get sufficient oxygen. This is because the relative atmospheric pressure is lower than at sea level, and fewer oxygen particles are in a given volume of air.

Legend has it that watched pots do not boil. Rigorous experimentation has proved this maxim to be false. Some kitchen theorists claim that placing a tight-fitting lid on a pot (to prevent unauthorized pot-watching) actually causes water to boil at a higher temperature than does water in a pot with no lid. Is this claim plausible? Why or why not?

A. The claim is plausible. Placing a tight-fitting lid on a pot of water traps water vapor inside. Because the lid traps vapor inside, the pressure in the space above the water increases beyond the atmospheric pressure in the kitchen. As heat is added to the water, the vapor pressure increases. Boiling occurs only when the vapor pressure of the water reaches

And/or exceeds the pressure over the surface of the liquid. So, water in the lidded pot must be heated more than water in an open pot before it will boil.

Of course, water in a lidded pot may nevertheless boil More quickly, Because the lid also traps heat that would otherwise escape.

1. In a little hut on top of Mount Fuji in Japan, Tomoko boils water for her breakfast. Meanwhile, atop Half Dome in Yosemite National Park, Jim boils water, too. If Tomoko’s water boils at 86°C and Jim’s water boils at 90°C, which of the two is at the higher altitude (and therefore the more hardcore hiker)?

Solve It

2. On the planet Blurgblar, pressure decreases linearly with altitude. A Blurgblarian yodeler prepares tea atop the 2,250m peak of Mount J-11. The yodeler notes that the water boils at 283K. Meanwhile, at sea level, a Blurgblarian chemist measures the boiling point of water to be 298K. An unfortunate Earthling physicist suddenly emerges from a time-space wormhole on the surface of Blurgblar. Gasping at the cyanide-laced atmosphere, the physicist observes that a nearby Blurgblarian Boy Scout is boiling water at 293K. At what altitude does the physicist find himself?

Solve It

Playing with Pressure and Volume: Boyle’s Law

Although the explanation of vapor pressure and evaporation endures for only a few paragraphs in the previous section, it mentions four important variables: pressure, volume, temperature, and the number of particles. Relationships between these four factors are the domain of the gas laws. We take a look at these in this section and the rest of the chapter.

The first of these relationships to have been formulated into a law is that between pressure and volume. Robert Boyle, an Irish gentleman regarded by some as the first chemist (or "chymist," as his friends might have said), is typically given credit for noticing that gas pressure and volume have an inverse relationship:

Volume = Constant X (1/Pressure)

This statement is true when the other two factors, temperature and number of particles, are fixed. Another way to express the same idea is to say that although pressure and volume may change, they do so in such a way that their product remains constant. So, as a gas undergoes change in pressure (P) And volume (V) Between two states, the following is true:

Pi X V1 = P2 X V2

The relationship makes good sense in light of kinetic molecular theory. At a given temperature and number of particles, more collisions will occur at smaller volumes. These increased collisions produce greater pressure. And vice versa. Boyle had some dubious ideas about alchemy, among other things, but he really struck gold with the pressure-volume relationship in gases.

Q. A sealed plastic bag is filled with 1L of air at standard temperature and pressure (STP). You accidentally sit on the bag. The maximum pressure the bag can withhold before popping is 500 kilopascals (kPa). What is the internal volume of the bag at the instant of popping?

A. 0.2L. The problem tells us that the bag has an initial volume, V1, of 1L, and an initial pressure, P1, of 101.3 kPa (the pressure at STP). (See Chapter 7 if you’ve

Momentarily forgotten the definition of STP.) The pressure inside the bag reaches 500 kPa before popping, so that value represents P2. So, the only missing variable is the final volume. Solve for the final volume, V2, by plugging in the known values:

V2 = (1L X 101.3 kPa)/500 kPa = 0.2L

Tinkering with Volume and Temperature: Charles’s Law and Absolute Zero

Lest the Irish have all the gassy fun, the French contributed a gas law of their own. History attributes this law to French chemist Jacques Charles. Charles discovered a direct, linear relationship between the volume and the temperature of a gas:

Volume = Constant X Temperature

This statement is true when the other two factors, pressure and number of particles, are fixed. Another way to express the same idea is to say that although temperature and volume may change, they do so in such a way that their ratio remains constant. So, as a gas undergoes change in temperature (T) And volume (V) Between two states, the following is true:

V1 / T1 = V2 / T2

Not to be outdone by the French, another Irish scientist took Charles’s observations and ran with them. William Thomson, eventually to be known as Lord Kelvin, took stock of all the data available in his mid-19th century heyday and noticed a few things:

First, plotting the volume of a gas versus its temperature always produced a straight line.

Second, extending these various lines caused them all to converge at a single point, corresponding to a single temperature at zero volume. This temperature — though not directly accessible in experiments — was about -273 degrees Celsius. Kelvin took the opportunity to enshrine himself in the annals of scientific history by declaring that temperature as Absolute zero, The lowest temperature possible.

This declaration had at least two immediate benefits. First, it happened to be correct. Second, it allowed Kelvin to create the Kelvin temperature scale, with absolute zero as the Official Zero. Using the Kelvin scale (where °C = K – 273), everything makes a whole lot more sense. For example, doubling the Kelvin temperature of a gas doubles the volume of that gas. When you work with Charles’s Law, converting Celsius temperatures to Kelvin is crucial.

Q. A red rubber dodge ball sits in a 20.0°C basement, filled with 3.50L of compressed air. Eager to begin practice for the impending dodge ball season, Vince reclaims the ball and takes it outside. After a few hours of practice, the well-sealed ball has a volume of 3.00L. What’s the temperature outside?

A. -22°C. The question provides an initial

Temperature, an initial volume, and a final volume. You’re asked to find the final temperature, T2. Apply Charles’s Law, plugging in the known values and solving

For the final temperature. But take care — Charles’s Law requires you to convert all temperatures to K (where K = °C + 273). After a few hours outdoors, it’s safe to assume that the temperature of the ball has reached equilibrium. Because the volume of the ball decreased, expect the outdoor temperature to be lower than the temperature in the basement:

T2 = (293K X 3.00L) / 3.50L = 251K

This temperature corresponds to -22°C. Vince may have some judgment issues.

5. Jacques Charles’s ghost attempts to inflate his sagging celestial hot air balloon with short bursts from a burner. The initial volume of the balloon is 300L (ghosts don’t require large balloons). Trying to impress the passing spirit of a recently departed Seductrice, Jacques lets fly a long burst from the burner. The long burn increases the temperature of the air within in the balloon from 40.0°C to 50.0°C. How much does the balloon inflate?

Solve It

6. Always helpful, Danny persuades his little sister Suzie that her Very Special Birthday Balloon will last much longer if she puts it in the freezer in the basement for a while. The temperature in the house is 20.0°C. The balloon has an initial volume of 0.250L. If the balloon has collapsed to 0.200L by the time Suzie catches on to Danny’s devious deed, what is the temperature inside the freezer?

Solve It

All Together Now: The Combined and Ideal Gas Laws

Boyle’s and Charles’s laws are convenient if you happen to find yourself in situations where only two factors change at a time. The universe is rarely so well-behaved. What if pressure, temperature, and volume all change at the same time? Is aspirin and a nap the only solution? No. Enter the Combined Gas Law:

P1 X V = P2 X V2

T

T

Of course, the real universe can fight back by changing another variable. In the real universe, for example, tires spring leaks. In such a situation, gas particles escape the confines of the tire. This escape decreases the number of particles, N, Within the tire. Cranky, tire-iron wielding motorists on the side of the road will attest that decreasing N Decreases volume. This relationship is sometimes expressed as Avogadro’s Law:

Volume = Constant X Number of particles

Combining Avogadro’s Law with the Combined Gas Law produces the wonderfully comprehensive relationship:

PXV PXV

T1 X N T2 X N2

The final word on ideal gas behavior summarizes all four variables (pressure, temperature, volume, and number of particles) in one easy-to-use equation called the Ideal Gas Law:

PV= NRT

Here, R Is the gas constant, the one quantity of the equation that can’t change. Of course, the exact identity of this constant depends on the units you’re using for pressure, temperature, and volume. A very common form of the gas constant as used by chemists is R = 0.08206L atm K-1 mol-1. Alternately, you may encounter R = 8.314L kPa K-1 mol-1.

Q. A 0.80L container holds 10 mol of helium. The temperature of the container is 10°C. What’s the internal pressure of the container?

A. 2.9 X 102 atm. Consider your known and unknown variables. You’re given volume, number of particles, and temperature. You’re asked to calculate pressure. The equation that fills the bill is the Ideal Gas Law, PV = NRT. Rearrange the equation to solve for P, So that P = (nRT) / V. Now, before you blithely plug your known values into the equation, be sure that all

Your units agree with those used in the gas constant you’ve chosen. Here, we use R = 0.08206L atm K-1 mol-1. So, we must convert the temperature (10°C) into Kelvin, K = 10 + 273 = 283 K. Next, plug in your known values and solve:

Pressure = (10 mol X 0.08206L atm K-1 mol-1 X 283K) / 0.80L = 2.9 X 102 atm

That’s nearly 300 times normal atmospheric pressure. Stay away from that container.

7. The 0.80L container from the example question breaks a seal. Because the container stored a poisonous gas, it was itself stored within a larger, vacuum-sealed container. After the poisonous gas expands to fill the newly available volume, the gas is at STP. What is the total volume of the secondary container?

8. A container with a volume of 15.0L contains oxygen. The gas is at a temperature of 29.0°C and a pressure of 1.00 X 104 kPa. How many moles of gas occupy that container?

Solve It

Solve It

9. The volume of a whoopee cushion is 0.450L at 27.0°C and 105 kPa. Danny has placed one such practical joke device on the chair of his unsuspecting Aunt Bertha. Unbeknownst to Danny, this particular whoopee cushion suffers from a construction defect that sometimes blocks normal out-gassing and ruins the flatulence effect. So, even when the cushion receives the full force of Aunt Bertha’s ample behind, the blockage prevents deflation. The cushion sustains the pressure exerted by Bertha, so that the internal pressure becomes 200 kPa. As she sits on the cushion, Bertha warms its contents a full 10.0°C. At last, and to Danny’s profound satisfaction, the cushion explodes. What volume of air does it expel?

Solve It

Mixing It Up with Dalton’s Law of Partial Pressures

Gases mix. They do so better than liquids and infinitely better than solids. So, what’s the relationship between the total pressure of a gaseous mixture and the pressure contributions of the individual gases? Here is a satisfyingly simple answer: Each individual gas within the mixture contributes a partial pressure, and adding the partial pressures yields the total pressure. This relationship is summarized by Dalton’s Law of Partial Pressures, For a mixture of individual gases:

Ptotal = P1 + P2 + P3 + . . . + Pn

This relationship makes sense if you think about pressure in terms of kinetic molecular theory. Adding a gaseous sample into a volume that already contains other gases increases the number of particles in that volume. Because pressure depends on the number of particles colliding with the container walls, increasing the number of particles increases the pressure proportionally.

Q. A chemist designs an experiment to

Study the chemistry of the atmosphere on the early earth, billions of years ago. She constructs an apparatus to combine pure samples of the primary volcanic gases that made up the early atmosphere: carbon dioxide, ammonia, and water vapor. If the partial pressures of these gases are 50 kPa, 80 kPa, and 120 kPa, respectively, what’s the pressure of the resulting mixture?

A. 250 kPa. However difficult early earth

Atmospheric chemistry may prove to be, this particular problem is a simple one. Dalton’s Law states that the total pressure is simply the sum of the partial pressures of the component gases:

PTotal = P(CO2) + P(NH3) + P(H2O) = 50 kPa + 80 kPa + 120 kPa = 250 kPa

10. A chemist adds solid zinc powder to a solution of hydrochloric acid to initiate the following reaction:

Zn(s) + 2 HCl(ag) — ZnCl2(aq) + H2(g)

The chemist inverts a test tube and immerses the open mouth into the reaction beaker to collect the hydrogen gas that bubbles up from the solution. The reaction proceeds to equilibrium. At the end of the experiment, the water levels within the tube and outside the tube are equal. The pressure in the lab is 101.3 kPa, and the temperature of all components is 298K. The vapor pressure of water at 298K is 3.17 kPa. What is the partial pressure of dihydrogen gas trapped in the tube?

Diffusing and Effusing with Graham’s Law

"Wake up and smell the coffee." This command is usually issued in a scornful tone, but most people who have awakened to the smell of coffee remember the event fondly. The morning gift of coffee aroma is made possible by a phenomenon called Diffusion. Diffusion is the movement of a substance from an area of higher concentration to an area of lower concentration. Diffusion occurs spontaneously, on its own. Diffusion leads to mixing, eventually producing a homogenous mixture in which the concentration of any gaseous component is equal throughout an entire volume. Of course, that state of complete diffusion is an equilibrium state; achieving equilibrium can take time.

.♦fcjWEfl Different gases diffuse at different rates, depending on their molar masses (see Chapter 7 for details on molar masses). The rates at which two gases diffuse can be compared using Graham’s Law. Graham’s Law also applies to Effusion, The process in which gas molecules flow through a small hole in a container. Whether gases diffuse or effuse, they do so at a rate inversely proportional to the square root of their molar mass. In other words, more massive gas molecules diffuse and effuse more slowly than less massive gas molecules. So, for gases A and B:

Rate A Jmolar mass B Rate B molar mass A

Q. How much faster does hydrogen gas effuse than neon gas?

A. 3.2 times faster. First, "hydrogen gas" refers to dihydrogen, H2. Next, consult your periodic table (or your memory, if you’re that good) to obtain the molar masses of dihydrogen gas (2.0g mol-1) and neon gas (20g mol-1). Finally plug

Those values into the appropriate places within Graham’s Law.

Rate H2 — ^/2~0 — 32 Rate Ne

So, dihydrogen effuses 3.2 times faster than neon.

11. Mystery Gas A effuses 4.0 times faster than oxygen. What is it the likely identity of the Mystery Gas?

Solve It

Answers to Questions on Gas Laws

You’ve answered the practice questions on gas behavior. Were your answers ideal? Check them here. No pressure.

D Tomoko is at the higher altitude. As altitude increases, atmospheric pressure decreases. As temperature increases, vapor pressure increases. Liquids boil when their vapor pressure exceeds the external (atmospheric) pressure. So, because Tomoko’s water boils at a lower temperature, she must be at a higher altitude, where atmospheric pressure is lower. Tomoko is the hardcore hiker.

MM 750m. Boiling point decreases linearly with external pressure. Because the atmospheric pressure on Blurgblar decreases linearly with altitude, boiling point and altitude also have a linear relationship on this odd planet. To calculate the altitude where the physicist emerged, you must determine the linear relationship between altitude and boiling point. The total elevation increase between sea level and the peak of Mount J-11 is 2,250m. The decrease in boiling point over that change in altitude is -15K (298K – 283K). So, the boiling point decreases by 1K for every 150m increase in altitude:

2,250m / 15K = 150 m/K

The dying physicist observed a boiling point 5K lower than the one observed at sea level. So, the physicist is 850m above sea level:

5K X 150 m/K = 750m

CM 0.4L. You’re given an initial pressure, an initial volume, and a final pressure. Boyle’s Law leaves you with one unknown: final volume. Solve for the final volume by plugging in the known values:

V2 = (1 atm X 0.5L) / 1.25 atm = 0.4L

MM 2.5 atm. Under the initial conditions, gas at 5 atm resides in a 1.5L volume. When the seal is

Removed, the entire 3L of the container becomes available to the gas, which expands to occupy the new volume. Predictably, its pressure decreases. To calculate the new pressure, P2, Plug in the known values and solve:

P2 = (5 atm X 1.5L) / 3L = 2.5 atm

MM 10L. You’re given the initial volume and initial temperature of the balloon, as well as the balloon’s final temperature. Apply Charles’s Law, plugging in the known values and solving for the final volume. Be careful — all temperatures must be expressed in units of K:

V2 = (300L X 323K) / 313K = 310L

The difference in volume due to heat-induced inflation is 310L – 300L = 10L.

MM -39°C. Charles’s Law is the method here. The unknown is the final temperature, T2. You’re given an initial temperature, as well as the initial and final volumes. After converting the temperatures to units of K, plug in the known values and solve for final temperature:

T2 = (293K X 0.200L) / 0.250L = 234K

This final temperature corresponds to -39°C. That’s one serious freezer.

MM 280L. The number of moles of gas (10 mol) remains constant. The other three factors (pressure, temperature, and volume) all change between initial and final states. So, you need to use the Combined Gas Law. The initial values (2.9 X 102 atm, 283K, 0.80L) all derive from the example problem. The final temperature and pressure are known (273K, 1 atm) because the question states that the gas ends up at STP. So, the only unknown is the final volume. Rearrange the

Combined Gas Law to solve for this value:

V2 — P1 X V X T — 2.9 X 10latmX°.80L X 273K — 2.2 x 102 atm 2 T1 x P2 283K x 1atm

Hh 59.7mol. This problem simply requires use of the Ideal Gas Law, arranged to solve for number of moles, N. Don’t forget to convert temperature to units of K and to use the appropriate version of the gas constant, R.

N = RXZ — 1.0 x 104 kpa x 15.0L — 59.7 mol

R x T 8.314JkPaxL x 302K mol x K

H 0.244L. You’re given an initial volume, initial temperature, and initial pressure. You’re also given a final pressure and a final temperature. The only unknown is final volume. Rearrange the Combined Gas Law to solve for final volume, V2.

V2 — P1 x V X T 2 T1x P2

105 kPa x 0.450L x 310K 300K x 200 kPa

— 0.244L

Despite the fact that the final temperature is higher than the initial temperature, the final volume is much smaller than the initial volume. In effect, 10 trifling degrees are no match for the pressure exerted by Bertha’s posterior.

Jj 98.1 kPa. The system has come to equilibrium, so the interior of the tube contains a gaseous mixture of dihydrogen and water vapor. Because the water levels inside and outside the tube are equal, you know that the total pressure inside the tube equals the ambient pressure of the lab, 101.3 kPa. The total pressure includes the partial pressure contributions from dihydrogen and from water vapor. Set up an equation using Dalton’s Law:

Ptotal = P(H2) + P(H2O)

Rearrange the equation to solve for P(H2) and substitute in the known values to solve:

P(H2) = 101.3 kPa – 3.17 kPa = 98.1 kPa

|f| Dihydrogen, H2. The question states that the ratio of the rates is 4.0. Recall that oxygen gas is dioxygen, O2, with a molar mass of 32g mol-1. Substitute these known values into Graham’s Law.

Rate A

Rate O

— 4.0 —

•v/32"

Vmolar mass A

Square both sides of this equation to bring values out from underneath the radicals.

16 =

32

Molar mass A

Next, rearrange to solve for the molar mass of Gas A:

Molar mass A = (32/16)g mol-1 = 2.0g mol-1

This molar mass is consistent with dihydrogen, H2.

In This Chapter

► The problem of high heels and other enemies of the feet

► Reflexology

► Foot massage routine

M mne Great universal truth exists outside the boundaries of any race, reli- Gion, or culture. A truth that has stood for centuries throughout human

History, it is so fundamental that most of us take it for granted. That truth is

This: Almost nothing beats a good foot rub.

Yes, I’m aware that some people are not big fans of foot rubs and in fact don’t want their feet touched at all. In this chapter, however, I flagrantly disregard these people, because the vast majority of us absolutely love foot massage. In fact, entire civilizations have been built up and sustained for the sole purpose of giving certain people enough power, money, and influence to be able to get other people"to rub their soles.

You may know a certain person in your own circle who is famous for giving "good foot." Some people seem to have a special knack for it, almost as if foot massage were a completely separate entity from body massage. Foot massage isn’t really separate from the whole-body massage we discuss in Chapter 11, but feet definitely deserve a chapter of their own. After all, feet have a massage technique all their own, called Reflexology, Which we cover in this chapter.

Hiyh Heels and Other Enemies of the Feet

If you’re a woman and you wear high heels, you have an especially big problem to deal with. I’ll never forget the first woman I saw on my massage table with high-heelitis. She was lying down, relaxed and comfortable, but her legs and feet were still bent into the position they would have been in if her shoes had still been on — feet extended, toes pointed down, calves flexed. Extended wearing of those torture devices we know as high heels can actually change the shape of your lower body. The effects reach all the way up into your hips, lower back, and spine.

If you’re a man and you wear high heels, you’ll have the same problems with your calves and lower back, plus the added problem of seldom finding anything at a clothing store that truly matches your choice of footwear. What a dastardly predicament!

The common problems certain shoes cause are some of the reasons that a large number of massage pros wear Birkenstock-type sandals. We want to give our feet and bodies a little break from the pounding they take on the cruel streets of life.

Part of the reason feet get so sore is the delicate nature of their structure. They sustain your entire weight during walking, standing, running, and so on. Thousands of pounds of cumulative pressure, day in and day out, press on 26 relatively small bones. Add to that the fact that you have approximately 72,000 nerve endings in each foot, making them some of the most sensitive parts of your body, and you can see why keeping your feet happy can be a tough job.

Reflexology

The feet deserve massage, just for being feet, but another reason exists for concentrating some extra time on your feet and perhaps even devoting an entire session to foot massage. I’m talking about Reflexology.You’ve probably heard this strange word somewhere before, right? Maybe on the Discovery Channel, or in a magazine with a picture of a New Age M. D. on the cover. But did you really know what the word meant? Quiz yourself by trying to complete the following sentence. Reflexology is:

A. The practice of stimulating certain points on one area of the body (usually the feet) that have an effect on corresponding reflex areas in other parts of the body.

B. The art of developing fast reflexes for use in such real-world situations as gunfights and race car driving.

C. The act of flexing something over again after you’ve flexed it once already.

D. None of the above.

The answer, as you may have suspected, is A, but just knowing that doesn’t do you much good, does it? Not unless you know a little of the background of reflexology and the philosophy behind this unique therapy, as well.

Zone Therapy

V.

The origins of modern reflexology are rooted in another treatment method called Zone therapy. In 1917, Dr. William H. Fitzgerald of Boston City Hospital published a book called Zone Therapy, or Relieving Pain at Home. In it, he stated that many types of health problems could be helped, or even cured, by applying pressure to various strategic points, mostly on the hands.

This whole idea did not catch on like wildfire, but one of Dr. Fitzgerald’s associates, a therapist in his office named Eunice Ingham, took the idea and tweaked it a bit, experimenting with many people, mostly on their feet, which she thought were more sensitive than the hands. Eventually, she wrote her own books, Stories the Feet Can Tell, And that follow-up favorite, Stories the Feet Have Told. Ingham’s work and her books heralded the birth of modern reflexology.

The work of Eunice Ingham is continued today at the International Institute of Reflexology, founded in 1973. You can call or write the institute to request books, charts, tools, and more.

But just what is Zone therapy Anyway? According to zone theory, your body can be divided (metaphorically, of course) into long slender pieces. Everything that’s going on in any one part of a particular zone can be felt in a distant part of that same zone. You can see, then, how something happening in your abdomen can be reflected, or felt, in your foot. By stimulating a certain point in the foot, you can treat the pancreas, for example.

All of this talk about reflexes and zones may leave you feeling a little "zoned out" yourself, but don’t let that worry you. The whole concept is pretty simple if you just remember that the bottoms of the two feet put together can be looked at like a miniature map of the entire body. So the head is up by the big toe, the spine goes down the middle, and so on. Figure 14-1 shows a reflexology chart.

Figure 14-1:

A reflexology chart.

Plexus Diaphragm Gallbladder

Transverse colon

Ascending colon

Ileocecal valve

-Brain——

Head & sinuses Pituitary gland

Thyroid, neck, parathyroid

Thymus Heart

Thyroid area

Liver Adrenal glands Stomach Pancreas Duodenum

Spinal area

Small intestine Bladder

Tailbone Sciatic nerve

Arm Shoulder

Spleen Kidney

Descending colon

Sigmoid colon

Some people swear by reflexology as a life-saving healing method. In fact, the woman I learned the technique from was diagnosed with a serious form of cancer and not given much chance of survival. None of the conventional treatments seemed to be helping, so as a last resort she turned to a Greek man in his nineties who specialized in reflexology. He also recommended coffee enemas. Within several months, this woman was cured and has been living a normal, productive life for over 20 years. (After the experience, however, she did develop a slight aversion to coffee shops.)

Frankly, nobody can tell you why reflexology works. But the truth is it often does. Reflexology is still a Theory, But one with practical applications, and it certainly won’t hurt you to give it a try. It may indeed help your overall health, but at the very least reflexology is guaranteed to feel darn good on your feet.

Foot Massage Routine

This section gives you a 20-minute foot massage routine based on the principles of reflexology. The routine is so easy to do that almost anyone can follow

The instructions and perform the entire routine from start to finish the very first time, even members of the United States legislature. So, of course, that means you should have no problem at all.

Positioning

First, get yourself and your partner in a comfortable position. The partner-reclining position shown in Figure 14-2 is the one favored by professional foot massagers around the world, but you can also position your partner on a bed or massage table so that her feet are just at the edge. She can even lie on the floor. Also, pay attention to the way you’re bending over to access your partner’s soles and toes. You don’t want to hurt yourself while trying to help someone else.

You can perform this routine through stockings or socks if you don’t want to remove them. So far, though, no method has been devised to perform reflexology through a pair of shoes.

Points to remember

If you want to remain friends with the person you’re giving the foot massage to, keep in mind a few things when you’re about to dig into her soles:

Start on the left foot. This compliments your partner’s natural digestion and circulatory patterns.

Don’t use oil, because it makes the foot too slippery. Corn starch works well to absorb excess moisture, so rub some on your partner’s feet before you begin.

I> Always talk to your partner and ask for feedback.

Don’t diagnose any problems or treat someone for serious disorders (leave that to physicians).

Don’t use any instruments or tools to push against the feet (such as pencil erasers for example, which have been known to get lodged between toes). Use only your fingers and thumbs.

^ Never push so hard that you cause pain or discomfort. If your partner is in pain, ease up your pressure a little bit.

V* Finish one foot completely, and then go on to the next.

You can make certain basic, time-tested moves on the feet. These moves have been passed down by practicing reflexologists from generation to generation, and now you can use them, too. This section provides you with detailed explanations of these moves and how to use them yourself.

Cradling

Cradle your partner’s foot (at either the ball of the foot or the ankle) in both palms, with your fingers pointing straight ahead. Then move your hands back and forth rapidly, just an inch or so (as shown in Figure 14-3). This move is especially good for warming up, and you can also use it in the middle of a foot massage to give your partner a little extra pleasure. Cradling feels so good it was called "dessert" by one of my colleagues who specialized in reflexology at a spa where I worked.

Thumb talking

The most basic move of all in foot reflexology is "thumb walking," which is a lot trickier than it looks. Start by placing the pad of your thumb firmly against your partner’s foot (as shown in Figure 14-4a). Then bend the thumb and creep it forward like an inchworm across the surface, pressing in while you do so (as shown in Figure 14-4b). Every time you bend your thumb, move your hand forward just slightly. You may want to practice this technique a little before subjecting your partner to a spastic or weak inchworm movement.

Figure 14-3:

This move is called "cradling," and it feels most delicious.

Figure 14-4:

Start with your thumb in the position on the left (a); then

Inch your thumb forward while

Bending it to wind up in the position on the

Right (b).

Index finger technique

Sometimes (for example, when you’re working on the sides and tops of your partner’s feet), using your thumbs is just plain awkward. That’s when you can use the length of your index finger to slide next to the ankles and between the long bones that run from the heels to the toes, for example, as shown in Figure 14-5a.

Figure 14-5:

Using your index finger (a), hooking in(b), wringing (c), and doing circles (d).

Hooking in

Using the tips of the thumbs or index fingers, bend slightly at the last knuckle and "hook in" at the point you’re targeting (see Figure 14-5b). This technique allows for some pinpoint pressure on the bony, intricate surfaces of the foot.

Wringing the foot

Because the arch of the foot corresponds to the spine in reflexology, this technique is like giving a chiropractic adjustment to the foot. Grasping your partner’s toes with one hand and her heel with the other, give a gentle twist in opposite directions as if wringing out the arch of the foot (as shown in Figure 14-5c).

Ankle circles

Holding your partner’s ankle in one hand, circle her foot around in both directions (clockwise and counterclockwise) for several seconds, stretching the muscles and tendons in the area, and warming up the ligaments (see Figure 14-5d).

Step-by-step

Begin by getting into the most comfortable position, as mentioned earlier, and then do this warm-up:

I)S Cradle the ball of the foot. V Cradle the ankle. Do ankle circles. Stretch the toes back and forth. I J> Squeeze the foot.

Now you’re ready to move into the 15-step foot massage routine that follows, which is based on the work of Claire Marie Miller in North Carolina.

Remember to start on the left foot, complete the entire routine, and then repeat the process on the right foot. Refer to Figure 14-1 if you need help.

1. Head: Your head is rilled with lots of important anatomical highlights, such as the brain. It’s worth spending a few extra minutes here as you begin your reflexology routine.

To affect the reflexes of the head, do some small, focused, thumb walking in three lines down the big toe and three lines across the bottom of the big toe.

2. Neck: The neck can be an area of nagging pain. Sometimes working the reflex areas for the neck can help bring relief.

Do thumb walking back and forth along the base of the big toe, right where it attaches to the foot. To specifically treat the region at the base of the back of your skull, "hook in" with your thumb on the lower, inside part of your big toe, between it and the second toe. This is often a key point for relieving headaches and neck tension.

3. Face: Yes, even the face has a reflex on the foot, which is perhaps why it seems so easy to put your foot in your mouth.

Do thumb walking across the top of the big toe, then "hook in" right at the base of the toenail.

4. Sinuses: The sinus cavities are hollow areas in your head, behind your face. Keeping them clear and healthy helps you breathe more easily.

The points for the sinuses can be found on the bottoms of all of the little toes. To stimulate them, do three lines of thumb walking down the bottom of each toe, and "hook in" right in the center of each toe for a couple seconds.

5. Ears/eyes: The ears and eyes have reflexes by the base of the middle toes. Stimulating those reflexes may help you keep your senses of sight and hearing keen and alert.

Using your knuckles or both thumbs, press in on the spots on the bottom of the foot between the second and third toes (for the eyes) and between the third and fourth toes (for the ear reflexes). You can press both areas at the same time. The spots are on the very edge of the bottom of the feet, almost on the webbing between the toes themselves.

6. Lungs/chest: The area around the balls of your foot reflects your air passages, bronchial tubes, lungs, and chest muscles. If you stop breathing, you may run into some serious problems, and so you will benefit by paying attention to the healthy functioning of your lungs.

Use the index finger technique for this reflex, sliding the length of your finger between the long metatarsal bones on top of the foot and pressing in against them. You can also switch your hand around and slide your finger between the same bones from the bottom.

7. Diaphragm: The diaphragm (discussed in more detail in Chapter 7) Is the muscle at the bottom of your lungs that is responsible for keeping you breathing. So, if you like breathing, try to keep this muscle happy.

Pushing the toes up toward your partner’s head with one hand, use the thumb of the other hand to walk back and forth along an imaginary line at the base of the ball of the foot, approximately two inches from the toes.

8. Spine: Many people experience back pain, and many of those same people seem to have pain in the arches of their feet as well. A coincidence? Not when you know that the arches of the feet correspond in reflexology with the spine.

Do thumb walking up and down the reflex for the spine, which is basically the arch of the foot. You may want to switch thumbs when you’re moving up the arch and back down, which will make this technique less awkward.

Then "wring" the spine out by twisting the arch of the foot. Hold the heel with one hand and the toes with the other, while twisting gently in opposite directions.

9. Inner organs: The center of the bottoms of the feet correspond to several of your internal organs, and this is the area where you can easily get confused. You may want to study the chart in Figure 14-1 quite closely as you go about stimulating the reflexes here. The internal organs are where you take the outside world in and transform it into your body. Important digestive and filtering processes take place here.

When you’re working on the left foot, do thumb walking in the center below the lung and diaphragm reflexes, where you’ll find the areas corresponding to the stomach, the pancreas, the spleen, and the heart. Then walk your thumb from left to right across the center of the foot and down the outside, which corresponds with the last half of the large intestine.

When working on the right foot, walk the thumb in the same area, but as you do, you’ll be stimulating the liver and gallbladder instead. Then walk your thumb up the outside edge of the heel and across the center of the foot to stimulate the first half of the large intestine.

Understanding the large intestine reflex is easier if you consider both feet together. Picture the large intestine going up the right side of the abdomen, across the upper abdomen, and down the left side (because this is what it actually does). Now you can imagine how you’re affecting this reflex by walking your thumb up the outside of the right foot, across the center of both feet, then down the outside of the left.

10. Small intestine: "A Man is only as happy as his digestive tract." This ancient saying, which I Just made up this minute, highlights the importance of healthily functioning intestines.

Using your thumbs to walk helter-skelter in all directions, crisscross back and forth over the bottom of the heel, which corresponds to the lengthy loops of the small intestine.

11. Hips/knees: Your hips and knees are your foundation, and stimulating these reflexes can help keep you in balance.

Walk your thumbs along the upper part of the foot toward the outer edge, midway between the toes and the heel, moving in all directions around the general area of the Cuboid bone, Which is the little protuberance that sticks out the farthest in the middle of your foot on the outside edge.

12. Sciatic: The largest nerve in your body, the sciatic can be the unfortunate victim of a proportionally large amount of pain.

Using the thumb and index finger, pinch all along the back of the base of the heel, then up a couple inches along the Achilles tendon toward the calf. Repeat several times.

13. Reproductive organs: Men and women, as you’ve undoubtedly noticed by now, have different reproductive organs. But, as it so happens, the associated reflexes are located on the same areas of the feet for both sexes.

Halfway down from the center of the ankle bones, toward the bottom of the heels, you’ll find the reflexes for the reproductive organs. The inner ankle points correspond to the uterus or prostate, and the outer ankle points correspond to the ovaries or testicles. Use your thumb or the tip of your index finger to "hook in" for a few seconds on these points. You can also walk your thumb up over the top of the ankle from one point to another, which stimulates the fallopian tubes.

What to do if you find a problem

While you’re exploring the various reflex areas on your partner’s foot, you may come across a very specific spot that is significantly more tender than the rest You’ll be able to tell you’ve hit a tender area, because your partner will suddenly jerk her foot out of your hand and shout, "Whoa, what’s That Spot?" When this happens, consulting your reflexology chart, discovering the corresponding reflex, and immediately proclaiming the presence of a life-threatening disease in that area of the body is not a good idea. Feel free to tell your partner which part of the body the tender area represents, but that’s all you should do. This is not a time to show off

Your newfound knowledge of foot anatomy and proclaim yourself a medical expert.

Rather than diagnosing her "illness," tell her that if the pain persists in that spot, she should consider consulting with her physician and get a general checkup. You actually may have stumbled upon a viable health concern here. Then again, your partner may have stepped on a tack the day before, in which case, the tender spot you’re hitting in the center of her left foot is simply a boo-boo, not the sign of a diseased spleen.

Stimulating the reproductive organ reflex points for pregnant women is said to help induce labor. Although I’ve never heard of a woman going into premature labor due to a massage to the foot, just to play it safe, stay away from this area completely if your partner may possibly be pregnant. Some people skip foot reflexology altogether on potentially pregnant people for this reason.

14. Bladder and kidneys: Save these reflexes for the end of the routine, because they’re organs of elimination, and stimulating them promotes a cleansing reaction.

Starting near the heel, use thumb walking up and back along the arch of the foot, almost up to the ball of the foot. This line is a little more onto the bottom of the foot than the spine reflex (explained in Step 8). Repeat twice.

15. Overall squeeze of the foot: Never finish a foot without saying goodbye to it first. You may want to reapply some of the warm-up moves from the beginning as a cool-down here. Reflexology can be rather intense, and leaving your partner with some nice, pleasurable sensations at the end is a good idea.

Finish with an overall squeeze of the foot, very quickly touching all the areas youVe worked on before, cradling a little bit, and generally being nice. Some people like to apply a soothing skin cream at this point. Cooling mint preparations feel especially good, and you can find plenty of mint cream options at popular bath stores.