these exercises are for your own benefit, do NOT send your answers to USAFI. The written assignment is the last section in each lesson. In order for you as a correspondence student to derive the maximum benefit from this course, we strongly recommend that you take advantage of USAFI's lesson service and complete all lessons with an average grade of 70 or better. You may either use separate sheets of paper or, preferably, the lesson sheets provided by USAFI to prepare the written assignments. Make your work neat and easy to follow. Often more than one step is required when solving a problem with a slide rule. When this occurs you will be expected to show the results obtained for each step. This will be illustrated by an example later in this study guide. After you have completed a written assignment for a lesson, be sure to put the following on each sheet: rank or rating, name, service number, address, course number, and lesson number. Then mail it to the United States Armed Forces Institute, Madison 3, Wisconsin, or to the oversea USAFI with which you are enrolled. An instructor will grade your work and return it to you with any comments he thinks helpful. In order to avoid confusion, all illustrations in this study guide have been labeled in alphabetical order-figure A, figure B, etc. The illustrations in your text are labeled in numerical orderFig. 1, Fig. 2, etc. Questions If you have difficulty with any part of the course, consult your Education Officer or write to the United States Armed Forces Institute, Madison 3, Wisconsin, or to the oversea USAFI With which you are enrolled. State your question clearly, making sure to indicate the course number and title, lesson number, and page in the text in which your difficulty occurs. Certificate To qualify for the USAFI Certificate of Completion for the course: You must complete successfully the end-of-course test. Approximately 2 to 3 weeks before you expect to take the endof-course test, you should request the test from the United States Armed Forces Institute, Madison 3, Wisconsin, or from the oversea USAFI With which you are enrolled. Obtain an application blank from your Education Officer or from USAFI if necessary; fill it out carefully and make sure it is properly certified by the USAFI Test Control Officer who will receive and administer the test. The test is to be taken after you have completed lesson 11. Lesson 1 The Scales of the Slide Rule There is a good deal of background information about the slide rule you will want to learn before performing any operations. In this lesson you will learn what the slide rule can do and what advantages it has over arithmetical calculations. You will also learn how to hold the slide rule for maximum efficiency. Next, you will become acquainted with the names of the various parts of the slide rule. Finally, you will practice locating numbers on the C, D, and CI scales. Text Assignment Preface, pages iii-v How To Use This Book, pages vi-vii Chapters I, II, and III, pages 1-24 (to "The A and B Scales") Study Notes Page iii. You will note that the use of the slide rule is in no way limited to the mathematician or the engineer. It can be used by any person who wishes to make calculations for any reason whatsoever. Unfortunately, many people look upon the slide rule as a complicated tool that can be mastered only by exceptionally talented individuals. You will probably be surprised how simple it is to operate a slide rule if you take the time to practice. Page iv. In addition to the Practice Problems in the text be sure to work the self-examinations for further practice. If your materials repeatedly stress practice, it is only because this is the path you must follow to acquire the proficiency necessary to perform sliderule operations with ease and confidence. Page 1. You cannot add or subtract with a slide rule. Whenever addition or subtraction is involved in the problem you are attempting to solve, this portion of your solution will need to be done by longhand. Page 2. Become thoroughly familiar with the names of the parts of the slide rule as shown in Fig. 1. These names will be used over and over throughout the course. Your text points out that there is a great saving in time and energy in performing calculations with the slide rule rather than by longhand. However, the answer obtained on the slide rule is not usually exact beyond 3 or 4 places. For example, the answer obtained when 348 and 69 are multiplied by longhand is 24,012. This same calculation on the slide rule gives 24,000. Similarly by longhand, 0.0112 multiplied by 0.166 gives 0.0018592. With a slide rule the calculation gives the somewhat less exact answer of 0.00186. Since most calculations in everyday life do not require accuracy beyond 3 or 4 places, this is not a serious disadvantage. Nevertheless, you should be aware of this limitation and not attempt to use a slide rule in your work if greater accuracy is required. Page 4. There is no harm in checking your slide-rule calculations by the longhand method when you attempt your first few calculations. This procedure will probably prove to you that the slide rule is an accurate instrument. If your answer on the slide rule differs from that obtained by the longhand method don't be too quick to assume the answer obtained on the slide rule is incorrect. More errors are made by the longhand method, than by the slide-rule method. After a short time, discard the habit of checking slide-rule calculations by the longhand method or there will be no advantage in using a slide rule. Page 8. The thumbs are used to move the runner along the stock as shown in Fig. 3. Check the runner on your slide rule. On one side of most slide rules you will find a spring between the runner and the stock. Keep this spring on the top of the slide rule away from the thumbs. In this way the pressure from the thumbs will not tend to tilt the runner. Page 12. Take a good look at your slide rule. If you are using one furnished by USAFI you will find 6 scales on the left side of its front face. Reading from top to bottom these are the A, B, CI, C, D, and K scales. Now if you will turn your slide rule over you will find 3 additional scales under the celluloid inset on the right-hand side. From top to bottom these are the S, L, and T scales. Note that the celluloid strip on the reverse side of the USAFI slide rule contains a hairline for locating numbers. Pages 13-14. The first scales you will study are the C and D scales. In the early part of this course you will use these scales for multiplication and division. Note that the C and D scales have identical markings. Become familiar with the terms "left index," "right index," "division," "section," and "space" which apply to the various markings on the slide rule. Since the scales on a slide rule are only concerned with the order of the digits in a number, the left index can be thought of as 10 just as well as 1. One section to the right of the left index another number 1 appears. This should be thought of as 1.1 or 11. The next section to the right would be 1.2 or 12, etc. Do not confuse the 2 which appears 2 sections to the right of the left index with the 2 which appears 1 division to the right of the left index. It is important that you understand the discussion of the decimal point. Remember that only the order in which the digits of a number appear determines its location on the C and D scales. This means you may remove or transfer a decimal point in a number without changing its location on these scales. To illustrate, note the location of the number 16.7 on the C scale in Fig. 6. The numbers 0.167, 1.67, 167, 1,670, etc., would be located at the very same place on the C scale. Page 15. In locating these numbers on the C and D scales, have the left index of the C scale directly over the left index of the D scale. Then use the hairline of the runner to locate the number. Any number whose first digit is 1 will be located in the division between 1 and 2. Similarly any number whose first digit is 2 will be located in the division between 2 and 3. Page 16. How do the locations of 108 and 1,008 differ? The 108 is located 8 spaces to the right of the left index while the 1,008 is located 8 tenths of a space to the right of the left index. Page 17. At times it becomes necessary to round off numbers before they can be located on the slide rule. The rule given here does not apply only to rounding off a 5-place number to 4 places. For example, 12,349 rounded off to 4 places is 12,350. If 12,349 is rounded off to 3 places, it becomes 12,300. You consider only the digit immediately to the right of the place to which you wish to round off. If it is 5 or more, add 1 to the digit to which you are rounding off and change the digits after it to zeros. If it is less than 5, do not change the digit to which you are rounding off-just change the digits after it to zeros. Pages 17-19. Do you see why all 3 digits in a number such as 294 can be located exactly on the C and D scales, whereas the third digit in a number such as 295 must be estimated? Is it necessary to round off the number 1,955 before locating it on these scales? Would you need to round off 2,955 before locating it? If you can answer these questions satisfactorily you have a good understanding of the material discussed so far. If you are unable to answer these questions, reread the pages in your text about locating numbers whose first digit is 2. Pages 20-23. Three-digit numbers whose first digit is 4 or more can be located exactly on the C and D scales only if their third digit is 0 or 5. Thus, 4.35, 0.715, 830, and 60.5 can be located exactly. On the other hand 4.37, 0.719, 832, and 60.6 must be estimated to the third digit. Pages 23-24. The CI scale is discussed here only briefly. It is the same as the C and D scales, except that it's read from right to left. Thus, you begin with your runner on the right index and then move it to the left as you locate your number. If you place your hairline on 4 of the C scale, on what number will the hairline fall on the CI scale? The answer is 25. If you place the hairline over 5 on the CI scale, on what number will it fall on the D scale? The answer is 2. These examples do not consider the proper placement of the decimal point which will be discussed later. Self-Examination Select the correct answer in each of the following exercises. Check your answers with those given in the Key immediately following this self-examination. Do NOT send your answers to USAFI. 1. Which of the following parts of the slide rule contains the D scale? a. Slide c. Stock b. Runner d. None of the above 2. The number 36.973 would be located on the C scale as a. 36.0 b. 36.9 c. 37.0 d. 37.1 e. None of the above 3. Which of the following numbers would have the same location on the C scale as 3.1416? a. 0.0003142 b. 314 c. 31,415,760 d. All of the above e. None of the above 4. Which digit of a number determines the division in which the number is located on the CI scale? a. 1st b. 2d d. 4th e. Can be any of the digits |