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entire base of this cone and by just as much as this magnification of the source fails to cover the cone by that same proportion does our hght through the objective and therefore on the screen fall below the amount possible with the illuminant aperture and objective used. Now to cover this cone we must have certain conditions fulfilled. In the first place, it is obvious the condenser must be as large as the cone at the point at which the condenser is placed, and that any area of the condenser outside this cone is entirely useless. In the second place, and here comes the point in the paper to which all this serves but as preamble, the entire area of the condenser seen through the aperture from every point of the objective opening must appear illuminated, that is, every straight line on which points of the objective and points of the aperture both lie is an actual path of light.
If we consider a corrected condenser it is easily seen that this condition is fulfilled, if, and only if, some section of the cone in front of the aperture or beyond the objective shall be entirely covered by an image of the source. Between the aperture and objective the image must cover the area indicated by lines diagonal on our section from the top and bottom of the objective opening to the top and bottom of the aperture opening respectively. We see then that any position from the condenser to the screen, of the image of the source by the condenser is capable of giving the maximum light possible with the objective, provided only the cone is completely filled. For the best position, therefore, of the image we must look to some other factor than simply the maximum possible illumination, always keeping in mind, however, the two requirements already found.
The natural direction to look is toward efficiency. At which one of all these image positions can we get this maximum quantity of light through the objective with the least power consumption — that is, the smallest area to be illuminated to the intrinsic brilliancy determined by the nature of the illuminant? We see at once that we shall need a smaller area of source if we so choose the focal length of our condenser that the image will fall at the aperture plate than at any position in front of this with a given minimum distance between source and condenser — generally determined by practical limitations of temperature. For positions of the image beyond the aperture plate we easily see that if Do is the effective diameter of the objective, Fo its equivalent focus, the diameter (or diagonal) of the aperture and its distance from the optical center of the condenser, the necessary source area is still a minimum with the image at the aperture plate unless
in which case we can use a smaller source with it focused in the objective than would be necessary for maximum illumination if the image were focused on the aperture. This condition is usually fulfilled in lantern slide but not in motion picture projection.
As for the distance from the condenser to the aperture it may be selected at will, subject of course to the condition that the
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