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CALCULATING OBJECTIVE FOCUS is discussed elsewhere. But here the rule for determining the focal length of an objective and the other rules, which may be called variations of it will be given. They may also be expressed in formulas for those, who work by formulas. (1) To determine the focus of an objective lens to give a picture on the screen of a given diameter at a given throw or dis- tance; divide the throw in feet by the desired diameter in feet, and multiply the diameter of the aperture by the quotient. The result will be the focus in inch measurement. (2) To determine the diameter of a projection on the screen given by a lens of known focus at a given throw; multiply the throw in feet by the aperture in inch measurement, and divide by the focal length. (3) To determine the focus of a lens, by the size of picture projected at a known throw; divide the throw by the diameter of the projected picture and multiply the aperture by the quotient. This is a good way of measuring the focal length of a lens. To express the above in formulas, call the throw, T ; the diameter of the projected picture, D; the focus of the lens, F; and the diameter of aperture, A. Then for the rules, 1, 2, and 3, we have: T T T (1) F = — XA. (2) D = — XA. (3) F = —XA. D F D Examples of rules (1) and (2) have just been given. An example of rule (3) will be given here. A lens is found to project the standard aperture of 29/32 inch on a screen at twenty feet distance, with a diameter of four feet. What is the focus of the lens ? Divide the throw, 20, by the diameter of the projected picture, 4; the quotient is 5. Multiplying 29/32 by 5 gives 4.526, the focus of the lens. It may be easy to substitute an exact inch aperture for the focal measurement by this method to avoid fractional diameter of the aperture entering into the calculation. This method can be carried out in a room with any reasonably strong source of light, and with a hole cut in a card as the aper- ture. The card must be brought as close to the lens as possible, so long as a sharp image of the aperture is produced. The largest image must be projected to make the method correct. The image must be a true projection. 161