International projectionist (Nov-Dec 1933)

16 INTERNATIONAL PROJECTIONIST December 1933 to read the answer 9 directly under the 3 on the movable scale. In other words, the answers to a series of calculations using the same multiplicand can be obtained with one setting of the slide rule. Figure 4 shows the relation between the scales when multiplying 5 by 2. Of course, the commercial slide rule is so drawn up that the scales show divisions between the unit numbers, making it possible to multiply fractions of numbers as easily as whole numbers. It is apparent that for a multiplication of certain numbers it will be necessary to move the scale to the left instead of to the right. If, for example, it is desired to multiply 6 by 5, the right hand index is placed directly over the 6 and the answer, 30, read directly under the 5. (Figure 5.) In the foregoing calculation, we find that we don't read the answer 30 directly from the slide rule, inasmuch as the number 3 only appears under the 5 of the movable scale. The figures making up the two scales may be considered not only as united but, for purposes of calculation, as tens, in which the divisions between each figure (not shown on the drawing), would then be considered as units; as hundreds, in which case the units between each number would be considered as tens; even as thousands, in which case the divisions between numbers would be hundreds; or as decimal portions of one, as for instance, the numbers might be considered as tenths, in which case the divisions between would be hundredths; as hundredths, in which case the divisions between would be thousandths, and so on. This brings up a consideration of placement of the decimal point when making slide rule calculations. When multiplying two figures which are such that it is necessary to slide the movable scale to the left, the answer will contain as many figures to the left of the decimal point as the sum of the figures to the left of the decimal point in the two numbers being operated upon. For instance, when multiplying 84.7 by 4.6, the answer would contain three figures to the left of the decimal point (in other words, would lie between 100 and 999), obtained by adding the number of figures (two) before the decimal in the two numbers being operated upon. For instance, when multiplying 23.1 by 355.0, the answer would lie between 1,000 and 9,999, or, in other words, would have 5 b 789 3 Figure 4 multiplicand to the number before the decimal in the multiplier (one) . However, when it is necessary to slide the movable scale to the right, the answer will contain (to the left of the decimal point) one less than the sum of the figures to the left of the point in the / Z 3 4 ■* 6 7 8 9 1 1 1 1 1 1 1 1 1 II! 1 2 3 4 5 I 1 1 1 7 89 Figure 5 four figures ahead of the decimal point. We have seen that multiplication operations can be readily performed on the slide rule. Division may be thought of, for the purposes of this lesson, merely as a reverse multiplication operation, and as such may be done on the slide rule with comparable ease. Division by Slide Rule Referring again to Figure 3, let us consider for a moment the division of 9 by 3. If we place the scale of the movable member of the rule so that the 3 is directly over the 9, we are able to read the answer, 3, on the stationary scale directly under the left-hand index. In the same figure, if we are dividing 6 by 2, we read the answer 3 under the left-hand index in the same way. In Figure 5, if we are desirous of dividing 30 by 5, we read the answer 6 directly under the right-hand index on the stationary scale. The rules governing the placement of the decimal point in a division operation are as follows: When the figures are such that the movable scale is slid to the left, the answer will contain a number of digits to the left of the decimal point equal to the difference of the number of digits in the two numbers being operated upon. However, when the figures are such that the movable scale is slid to the right, the answer will contain a number of digits to the left of the decimal point which is equal to the difference in the two numbers being operated upon, plus one. These rules, however, are not nearly as complicated as they seem, and with a little practice in the manipulation of the slide rule will be found to be extremely simple and practical. With the simpler multiplication and division operations, decimal placement is a matter of observation, and while the above rules hold, of course, one will not find it necessary to physically calculate the number of figures in each number and actually make the indicated additions or subtractions. Answers to Problems, Article III VK/TTH but two exceptions the answers ** to the questions accompanying Article III of the series "Mathematics for the Projectionist" are so uniformly poor that they merit precious little comment herein. Out of nearly 100 papers, only the answers of two old stand-bys are correct in every particular. It is true that the problems appended to Article III were the most difficult to date, and it is barely possible that the problems posed evidence a tendency on the part of the author to hurry his "class" along. Still, every phase of the problems has been covered in the last several issues, and it is significant that a majority of the errors which showed up in the papers are traceable directly to carelessness— such as the substitution of a minus for a plus sign or a failure to recognize the simple and plainly expressed instructions. As much for the benefit of those who submitted answers to Article III as for the prestige of I. P., it appears desirable that the entire group of questions be reprinted this month, and an invitation extended to the "class" to try again. Meanwhile, a sheaf of representative answers will be forwarded to the author, Gordon Mitchell, for review with an eye to writing a special paper pointing out the common errors that were made. The problems, presented for the second time, follow: 10. In the following, solve for the unknown, showing each step in order to indicate the proper order of separation. (a) x=10-7— 78+1400+32— 49+20 20 (b) y=20 + 7 + (7+2)— (4— 2)' 11. Subtract: (—10 + 1—2 + 5) from (7 + 10—3+2) 12. (a) Multiply: —5 by 7. (b) Divide: —32 by —4. 13. Solve the following equation to obtain the value of "x": 4x+7 = 2x— 3 JONES ADVANCED BY RCA The RCA Victor Co. has announced the appointment of Harry W. Jones as sound supervisor in charge of all the company's film recording operations in New York. Mr. Jones was formerly sound engineering advisor to Photophone sound licensees in New York and Hollywood and has been associated with sound motion pictures since the early developmental days of 1919. He has had considerable practical experience with the company's High Fidelity system of recording. SHAUGHNESSY AND MARTENS AGAIN HEAD L. U. 650 James Shaughnessy and Arthur Martens have been unanimously re-elected president and business representative, respectively, of LA. Local Union 650 (Westchester County, N. Y., projectionists), and both have been named as delegates to the next LA. Convention. The entire executive board supporting these men, both of whom have been officers of the Local since its inception, were also voted into office.