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316 ARTHUR C. HARDY [j. s. M. p. E.
in the preceding section. In a similar way, the proper diameter for the condenser is determined by finding the position and size of its image formed by the projection lens. It may be worth while to remark that the adjustment of the arc is less critical if the diameter of the projection lens is slightly larger than required to produce the desired screen illumination.
PRACTICAL CONSIDERATIONS
The foregoing treatment of this subject has been kept as free as possible from practical details in order that the attention might be focussed exclusively on the underlying principles. No mention has been made of the pull-down mechanism or the arc control mechanism, which may prevent the condenser from being placed in the most favorable location. Also, it was not thought desirable to distinguish between condensing systems employing lenses and those using a mirror. Both types are characterized by the common property of forming an image somewhere in space and of a certain size. Also, both mirrors and lenses have rims in common which may restrict the light beam unless the diameter is properly chosen. As the fundamental requirements are the same in both systems, the design procedure is identical in the two cases and is greatly facilitated by the concept of an ideal system, which for our purpose is assumed to operate without losses.
By way of conclusion it is interesting to return again to equations (2) and (3) and to reconsider the assumptions upon which they depend. It will be recalled that the source was assumed to be uniform and of constant brightness from every direction of observation. In other words, the source was assumed to obey Lambert's law of emission, which states that the intensity varies as the cosine of the angle from the normal. An examination of the intensity distribution curves of some of the sources in common use for motion picture projection shows a decided tendency for them to obey Lambert's law of emission except for shadows cast by the negative carbon or the arc control mechanism. Although this decreases the available illumination, it does not otherwise vitiate any of the conclusions reached in this paper. It will also be recalled that the lenses in the system were assumed to obey the so-called sine condition. Unless the projection lens obeys this condition, the definition at the margin of the screen will suffer. Since aberrations in the condensing system do not affect the definition on the screen, the lenses employed in that part of the system need not fulfill the sine condition to the same degree. In view of the well-known