THE MUSCULAR MOTOR AND ALIMENTATION 131 



the volumes. Therefore ^ = r 3 . If the materials are not 



., ,. . m 

 identical = (x. 



M 



The idea of similitude extends also to the movement of 

 machines. Between the " durations " / and T necessary to de- 



scribe two similar figures, there is the relation = = 9. In the same 



way, the " speeds" u and U being, by definition, u = -, U = - 

 u IT u 1 r 



U = E X 7 or u = rx e = e- 



Finally, the " accelerations " y and a, which express - and ~ 

 will be to each other as : 



U Y 



Thus, if two similar parts of the machine, and its reduced model , 

 take the accelerations, y and Q, by the action of the forces /and F, 



one would have ~ = by definition ( 18) ; whence : 



f r f r 



F = * X & or F == 9 = * ei' 



This last relation is called Newton's law of similitude. Its 

 applications are very easy : 



The speeds of the model, and of the machine are to each other 

 as the durations ^ == 9. 6 is deduced from Newton's formula 



presuming identical materials. Then ~ = r 3 and y. = r 8 ; whence 



**=&> or Q = 



the ratio of the speeds is equal to the " square root of the ratio 

 of the dimensions." Therefore : 



For example, the speeds of the contraction of the muscles, or 

 the " rhythm " ( 91), of an adult of 1'69 metres high, and a child 

 of 1*44 metres high will be in the relation : 



iS=- 923 - 



