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CALCULATING SIZE OF IMAGE corresponding diameter of the original on the film, the ratio of its distance from the center of the objective to the distance of the film picture therefrom. He takes the gate diameter as one inch, and divides the distance of the screen in feet by the focal distance in inches. The quotient would be correct for a diameter of one inch; it is then to be corrected by multiplication by the fraction expressing the real diameter of the gate opening which is the diameter of the film picture as projected. EXAMPLE OF CALCULATION OF SIZE OF SCREEN IMAGE Let the gate opening be 29/32 inch, and the focus of the lens 5 inches and the distance of the screen from the center of the lens be 60 feet. First divide 60 by 5 giving 12 feet. This would be correct for a one inch gate. Then multiply 12 by the fraction 29/32 and we obtain 10.87 feet or a little over 10 feet 10 inches. It seems incongruous to divide feet by inches. The operation could be done equally well by dividing the same quantities, ex- pressed in inches by their ratios, into each other as done above, mul- tiplying by the diameter of the gate, expressed as it always is in inches or rather in fractions of an inch. This gives the diameter of the picture on the screen in inches, and can be reduced to feet by dividing by twelve. The trouble of this division is avoided by the dividing of the feet by the inches in what at first sight may seem an incorrect way of calculation. Thus: 60 feet is equal to 720 inches. Dividing this by 5, which figure is the focal distance of the objective in inches, we obtain, 144 inches as the diameter of the screen image in inches, and this is equal to 12 feet as before, and 12X29/32 gives 10 feet 10 inches. Another way of calculating the focus of an objective for a given throw and a given size of picture on the screen, is to divide the throw by the diameter of the screen picture desired, and to multiply the diameter of the opening in the aperture plate or gate by this quotient. The result will give the focal length of the objective required in inches. Assume a throw of ninety nine feet, and that a diameter of screen picture required is sixteen feet. If we divide 99 by 16 we obtain as quotient, 6.1875. Then multiplying the aperture, which we will take as 29/32 inch, which is the standard now, the product is 5.6, almost exactly. 159