330 HISTORY OF CHRONOPHOTOGRAPHY. 



In the former case photographs are taken at the rate of 40 or 50 to 

 the second and are projected in three or four times the original time. 

 We can thus show a horse galloping or a bird fl3^ing so slowly that 

 the eye can follow the motions of the limbs. In the other case the 

 photographs are taken at very long intervals and are projected in 

 rapid succession. For this purpose the writer's chronophotograph 

 (fig. 19, PI. II) is furnished with an arbor upon which, if the crank is 

 fitted, the efi'ect is that only one photograph is taken at each turn. 

 The slowest, almost imperceptible motions of clouds, taken at long 

 intervals and rapidly projected, are translated into a rapid and strik- 

 ing agitation. 



What is generally important in the study of a motion is to obtain a 

 geometrical drawing of it. Chronophotography upon a fixed plate 

 gives such a drawing to scale exactly. Chronophotography on a 

 movable film may do so by the aid of certain devices which will be 

 described below. Chronophotography on a fixed plate has furnished 

 the experimental solution of many problems of geometry, mechanics, 

 physics, and physiolog}^ that no other method could so readily have 

 solved. 



Geometry. Formation in sjyace of geometrical figures of three dimen- 

 sions. — Geometers define this sort of figures by saying that they are 

 generated by straight lines or curves of difi'erent forms displaced in 

 different ways. Chronophotography realizes this conception com- 

 pletely. Before the pitch-dark field a white rod, lighted up and sub- 

 jected to a displacement in space, leaves on the photographic plate the 

 vestiges of its successive positions. It generates on the plane of the 

 plate the projection of the figure in three dimensions which it has 

 formed. In that way has been obtained (fig. 21, PI. Ill) the projection 

 of a sphere on a plane. A band of paper, white on one side, l)lack on 

 the other, was curved into a semicircular form and rotated about its 

 chord. The figure so formed would have altogether the appearance 

 of a solid sphei'e if a greater f requeue}" of the illuminations had pre- 

 vented the discontinuity of the surface generated. 



Fig. 22 (PI. Ill), the projection of a [one-sheeted] hyperboloid of 

 revolution, was generated by a string placed oblique to the vertical 

 axis round which it turned. 



If figures with their relief are sought, the photographs should be 

 taken with a stereoscopic apparatus. Fig. 23 (PL III) shows in this 

 way an hyperboloid with its asymptotic cone. These examples, taken 

 from very simple cases of geometry, enable us to imagine what variety 

 of forms would be obtained with complex curves subjected to varied 

 motions. There would be \exy simple experimental solutions of prob- 

 lems of geometry sometimes most complicated. 



Mechanics. — Mechanics is founded on the laws of motion, laws of 

 spaces described, of velocities, and of accelerations. The difficulties 



