MECHANICS. 109 



The determination of the law observed by this action, 

 in the case of fluids, belongs to Hydrodynamics, and 

 will be explained under that head. There remains, 

 therefore, to be considered here only the law of ani- 

 mal force. 



180. The strength of men, and of all animals, 

 is most powerful when directed against a resist- 

 ance that is at rest : when the resistance is over- 

 come, and when the animal is in motion, its force 

 is diminished ; lastly, with a certain velocity, the 

 animal can do no work, and can only keep up the 

 motion of its own body. 



A formula having the three properties just mention- 

 ed, will afford an approximation to the law of ani- 

 mal force. Let P be the weight which the animal 

 exerting itself to the utmost, or at a dead pull, is 

 just able to overcome; W any other weight with 

 which it is actually loaded ; and v the velocity with 

 which it moves when so loaded ; c the velocity at 

 which the power of drawing or carrying a load en- 

 tirely ceases ; then W P (1 J is an equation 



that has all the three conditions mentioned above. 



Not only, however^ has the formula P (1 - j these 



conditions, but the square of it has the same, or, 

 indeed, any function of it which vanishes when 



1 - vanishes, that is, when v =r c. We are left? 

 c 



then* 



