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180 PRINCIPLES OF CINEMATOGRAPHY
cross-shaft and, of course, will rotate one-quarter of a revolution each time the driving pin engages with the cross.
If a curve is drawn showing the velocity of the film moving through the projector gate, plotted against the angle through which the driving pin is rotated in order to so move the film, it will be seen that the area enclosed by such a curve is quite symmetrical and that the rate of film acceleration is equal to the rate of deceleration. This graph is shown in the lower left-hand corner of the figure. In practice it is desirable to accelerate the film slowly so that the friction in the tensioned gate will be gradually overcome and the life of the film will therefore be prolonged. It is also an advantage to bring the film to rest as quickly as possible to leave a certain amount of time during which it may settle down before the shutter is opened. This may be done by using a cross cut as shown on the right of the figure. Here the slots are cut tangentially to the path of the pin at the point of entry, and the velocity-acceleration curve is shown in the graph below the mechanism. This modified cross was introduced in America in about the year 1920. It is, of course, quite possible to so design the size of the pin wheel that tangential entry may be achieved when a cross with radial slots, as shown on the left of the figure, is used. However, the two main requirements, namely tangential entry to minimise noise and wear as the pin engages with the cross, and slow film acceleration to increase the film life, should be obtained and, therefore, the second design has obvious advantages. It should nevertheless be realised that the earlier mechanism is capable of rotation in either direction with equal success, whereas the improved cross will only operate quietly in one direction. It will travel in both directions, but in the reverse direction the driving pin will cause very heavy wear at the walls of the slots in the cross, and the film will moreover receive a greater acceleration than it would if the pin rotated in the correct manner. Of course, this objection is relatively unimportant since it is very unusual to require a projector to run in the reverse direction.
It will be remembered that the 'pull-down' must take place within 90° of the complete cycle so that two shutter blades, each 90° in size and interlaced by two open sections of equal size, produce a flicker frequency of 48 per second with alternate dark and light periods of equal duration. The four-sided cross shown in the figure certainly operates within 90° but usually requires a shutter of slightly larger angle, say 100°, and to overcome this some projectors employ a six or eight-sided cross which, while still maintaining the tangential pin entry, will operate with a pin