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316 PRINCIPLES OF CINEMATOGRAPHY
so that it is only 2/5ths that of the 35-mm sprocket and then, although both sprockets will rotate an equal number of turns per minute, the actual footage passed by each will be in proportion to their respective diameters.
The second alternative is to maintain the sprocket wheels at equal diameters this may be necessary in order to retain the films at similar curvatures because of some optical requirements and also since most printers expose the films while they remain in contact with these sprocket wheels. If this is done the worm reduction gear at position 'C must be 2-5 times greater than that at position 'B' and will, therefore, be a ratio of 180:1 and, in consequence, the 16-mm sprocket will only rotate at a speed of 8 revolutions per minute as compared with the 20 revolutions per minute made by the 35-mm sprocket wheel at position 'B\
The third alternative is, of course, to accommodate part of the film speed reduction by a suitably chosen worm gear at position 'C and to accommodate the remainder by a small change in the 16-mm sprocket diameter. On first consideration this arrangement may seem to be an unnecessary complication but, in some designs, it has proved to be a distinct advantage. The curvature placed upon a 35-mm film in a direction along its length need only be relatively slight in order to prevent 'bowing' or curvature across the film width. As the width of the film decreases it may be necessary to increase this longitudinal curvature somewhat in order to prevent bowing across such a narrow strip and, therefore, the 16-mm film is most likely to remain fiat at the exposing aperture if the sprocket wheel is of a smaller diameter than that used to drive the 35-mm film. However, at certain printing speeds, it may not be possible to reduce the diameter of the 16-mm sprocket by the full amount necessary to provide the complete reduction ratio since, under these conditions, the longitudinal curvature would be so severe that image definition would be poor at the upper and lower edges of the exposing aperture. Under such circumstances the only course open to the designer is to accommodate part of the reduction ratio by the gear reduction and the remainder by a change in the 16-mm sprocket diameter.
Constant Film Speed
In a straight-line driving mechanism such as that seen at 'A', Figure 139, three main sources of error may effect the uniformity of film motion past the scanning points. Firstly, the speed of the motor shaft may vary within small limits; secondly, the accuracy with which the worm gearing is made may transmit a 'gear tooth