GENERAL PRINCIPLES 



deduce, if possible, a formula, which will satisfy all the values 

 of the independent variable x and its function y, obtained by 

 experiment. 



Thus, let us write y = / (x) as the law of the propagation of 

 light, x being the distance and y the quantity of light received 

 on a plane surface. Experience gives 



At a distance 1, a quantity of light ... 1 



2, ... J=(J)| 



**> " 9 == (~5) 



There is no doubt, therefore, that y is the inverse of the square 

 of x, or thatjy = 



is the form of the function desired. 

 x 2 



In the same way, in the case of falling 

 bodies, y = ft 2 . The diagram given by this 

 equation is an arc of parabola OP passing 

 through the origin (fig. 12), which demon- 

 strates to the eye the more rapid increase of 

 space than of time. 



5. Graphic Method, Instead of making graphs from the 

 results of experiments, a method has been devised by which 

 they are directly traced by the moving point. Let us take again 

 as an example the fall of a body, and take a 

 registering point to which is attached a piece of 

 lead, which hangs in front of a cylinder covered 

 with paper. The cylinder 

 can turn on its own axis. 

 Let us suppose it station- 

 ary, and let the tracing 

 point fall from M to M'j; 

 we note the duration t, 

 and the space traversed 

 s = MM' ; which tells us 

 nothing of the variation 

 of space in relation to time 

 (fig. 13) ; but let us turn 

 the cylinder on its axis by 

 a clockwork movement at 

 a known and steady speed ; 

 we shall have, in develop- 

 ing the graph on paper 

 (fig. 14) the spaces tra- 

 versed in equal times. In 

 short, the times, 1, 2, 3 ... seconds will be abscissae, the 



1234 



M' 



FlO. 



Fio. 15. 



