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probably find the proper lens and best lamp-house position, but the easier plan is to advance the arc a little when an approximately correct lens and lamp-house position is found, and this is usually done.
When the lamp-house is moved back for the long "throw" it is not unusual to change the arc lens to a 7^^ lens, making the combination two 7>^ lenses. The resultant light loss is considerable, however, 50 per cent, perhaps. This loss of light has given rise to an erroneous idea that the longer throw requires a correspondingly greater amount of current for a given size screen. Another plan is to let the 6^^ arc lens alone, and substitute an Sj^ lens for the 7>4 converging lens. This will give the same amount of light on the same screen at the longer distance, without increasing the current consumption. A 6^inch and 8 3^ -inch lens combination has practically the same equivalent focus as two 7y2" lenses, though the reciprocals are not exactly identical in both cases. However, the distortion of poor lenses sometimes prevent getting an even, white-lighted screen.
This brings us very naturally to the consideration of a better lens arrangement for the lens next the arc, for, if this can be made a fixed factor, then the matter of adjustment for different lengths of throw is simplified.
Taking up the consideration of the arc and the theoretically best adjacent lens-surface it is at once apparent that if a curved surface could be employed, the same safe distance might be maintained between the arc and the lens at its center, while the outer edge of the lens, by reason of its enveloping curvature, would gather very much more light. But to make a single lens of this conformation having the same 6^ -inch focal length as the plano-convex usually employed gives the opposite or convex surface of the lens a disastrous curvature. A better plan is, not to attempt the total light refraction with the one lens, but set another close thereto having such a curvature that the sum of the two will give the focus desired. A lens of — ly^ and + 6/^ (dioptric measurement), say 8" focus, in combination with a 10-inch, either bi-convex or a plano-convex, is about correct for a three-inch arc location and is an ideal arrangement, but unfortunately, it is only ideal. A meniscus of six-inch focus would have to be about a -f 7 which, obviously, is not practical. The use of a — 1}^ and -f 5>^ lens, about 10" focus, in combination with either a bi-convex or plano-convex lens of 10-inch focus, is good, being approximately the equivalent of a 5" lens. This combination used with a 7}^, 8 or 8^ -inch plano-convex, seems to make a very satisfactory three-lens meniscus set.
There is still another factor to be taken into consideration — namely, the liability of condenser breakage. But, as has been explained, if the arc can be kept close to the lens very much less current is required for the same screen illumination. And right here a Kelvin law helps us very materially, i. e., *'the light of an arc lamp increases directly as the increase in current, while the heat increases as the square." Obviously, therefore, if we can employ such an arrangement as will require but half as much current as another we get but onefourth as much heat.