International projectionist (July-Dec 1934)

July 1934 INTERNATIONAL PROJECTIONIST and were we not to follow the rule of first completing the operations within the parentheses, we would square the 2, then doing the indicated multiplication, would multiply our 5x9 and our 4x3, to obtain an expression — 45+12+4 which would give us an answer of 61. However, if we correctly follow the rule to perform all operations within the parentheses first, we square the 2 and add the resulting 4 to the three within the parentheses, to obtain an expression 5x9+4x7, or 45 + 28. which is 73, the correct answer. It can be seen that the incorrect answer was obtained because we did not follow the rule of first completing all operations within the parentheses. In adding positive and negative numbers together, all the negative numbers are added together, and all the positive numbers added together, after which the smaller sum is subtracted from the larger — the final result taking the sign of the larger of the two sums. This rule is important, because upon it is based the entire procedure of algebraic subtraction. When we subtract one algebraic expression from another, we change the signs of all of the terms of the subtrahend (that being subtracted) and then add. For example, consider the expression (7a+5a — 6b) and subtract it from the expression (9a — 5a — 9b). Remembering the rule which states that all operations within the parentheses must be performed first, we simplify our two terms by adding the 7a and the 5a in the first to obtain 12a, making the expression (12a — 6b). the second becoming, after similar simplification. (4a — 9b). Changing the signs of all terms in the subtrahend, this becomes — 4a + 9b, and we then add: 12a— 6b— 4a + 9b, to obtain an answer of 8a+3b This result is in its simplest terms, of course, because, as was pointed out previously, it is impossible to add two unlike terms to obtain an expression simpler than the statement indicating the addition — i.e., two screens and three apples. In dealing with the multiplication and division of positive and negative numbers, there are only two fundamental rules which must be kept in mind: (1) That when two terms of an algebraic expression with like signs (either both positive or both negative) are multiplied or divided together, the result will be positive. (2) That when two terms of an algebraic expression with unlike signs (one positive and one negative) are PREFIXING NEEDED TO AVOID NEW FILM DAMAGE Trevor Faulkner S. M. CHEMICAL COMPANY, INC. THE photographic emulsion on newly developed film is very soft and therefore it is easily abraded. In order to have a steady image on the screen during projection, it is necessary that the film be held firmly over the aperture plate. Therefore, the film passes between the aperture plate and tension shoes, one on each the right and left sides of the aperture plate. The tension shoes are similar in construction to the runners of a sled and the amount of tension applied to the film is controlled by spring pressure which can be varied by adjustment. A similar condition also prevails at the sound gate. In the projectors almost universally used the tension shoes are held against the celluloid side of the film and the emulsion side is held firmly against the tracks of the aperture plate; also against the sound gate in the sound head. Since the aperture plate has the "spot" of the projection lamp concentrated on it and is stationary, it becomes heated to a relatively high temperature during the ten or eleven minutes required to project the average reel of film. Emulsion Depositing New film, not specifically treated, will leave a deposit of emulsion on the tracks of the aperture plate as it passes over them. This deposit soon bakes to a hardness sufficient to seriously damage the remaining portion of the film. This deposit has an action similar to that of a diamond glass cutter, since its "bite" into the film passing over it yields an added tension that may offer such a resistance to the free passage of film as to cause the teeth of the intermittent sprocket to pull or tear the perforations as it propels the film past the aperture. An emulsion deposit on the tracks at the sound gate will scratch the film as it does at the aperture plate: but a more far-reaching consequence is its interference with the necessary "direct right angle seat" of the film across the light beam as it passes from the exciter lamp to the photo-cell thereby disturbing the proper transmission of sound. "Motor boat" noises often result from such emulsion deposits at the sound gate because of the altered alignment of the film's passage; also the focus of the light beam is disturbed by the altered angle of the film seat on the sound gate or valve. Scratches or 'Rain The emulsion of new film will become scratched if brought into contact with any stationary dirt or grit or any part of the projector that has roughened surfaces, even of the slightest degree, or in rewinding the film for ensuing screenings, or in exchange inspection; unless it has previously been specifically treated to protect it. These scratches mar the screen presentation of the picture by the "rainy" effect in the projected image. Each scratch (Continued on page 25) multiplied or divided together, the result will be negative. A speciabzation of these rules which should be remembered is that the even powers of any number or letter (the second, fourth, sixth, eighth, tenth, twelfth, etc.) whether that number or letter be either positive or negative, will always be positive. The odd powers, however, (third, fifth, seventh, ninth, eleventh, etc.) will be positive if the original number be positive, and negative if the original number be negative. In other words, if we square (raise to the second power) either — 3 or +3, we obtain +9; but if we cube (raise to the third power) — 3, we obtain — 27; while cubing +3 gives us +27. Questions 1. Define the two parts of a logarithm. 2. Explain how a number may be raised to a power by the method of logarithms. 3. What gives the subject of logarithms their principal importance? 4. Solve the following problems, performing the indicated operations in their correct order : (a) 5 + 7+3 x 2 x 4+62— 23+V4= ? (b) 61— 52 + 7 x 8=? (c) 8—5 x 3+ (6+22 + 1)-? (d) V(4+5x2)+ll=? 5. Subtract : 21y+18b— 17 from 27y— 7b+3 6. Multiply : — 7 times 6; — 4 times — 5; 9 times 8 7. Divide : 81 by 9 ; 56 by —8 ; —44 by —8 8. Perform the following : Cube — 5 ; Square 4 ; Raise — 2 to the fifth power ; Raise — 2 to the fourth power ; Extract the square root of 16. (Answers to above on page 19)