110 OUTLINES OF NATURAL PHILOSOPHY. 



then, at liberty to choose any of these functions, 

 and would assume the formula above as the sim- 

 plest, if another condition did not seem necessary 

 to be included. It is certain, that in all cases, 

 when v approaches to r, or when the speed becomes 

 great, a small variation in the weight is accom- 

 panied with a great variation in the velocity. The 

 simplest formula that corresponds to this condition, 



is, when 1 is raised to the square. 



181. Therefore, till experience has led to a more 

 accurate result, we may suppose the strength of 

 animals to follow the law expressed by the formu- 

 la, W = P (1 - 



This equation, supposing W and v variable, is an 

 equation to a parabola, the construction of which 

 will serve to represent this law more clearly to the 

 imagination. 



A formula for expressing the law of animal action, 

 was first proposed by EULER, in a Dissertation on 

 the Force of Oars. Mem. Acad. de Berlin, 1747. 



That which he employed was W = P (1 Y> 



C s 



different from both those we have mentioned, but 

 a function of the first, such as to become 0, when 

 v c. EULER, however, changed this to another, 

 Mem. Acad. de Berlin, 1752, and Nov. Com. Pe- 

 1 trop. 



