ANIMAL MECHANICS. 449 



IFior. I0 2. Curve of useful work, n = ^ II< *' 7 ( 



K + g q- 3.9) 



and have shown the actual useful effects of each weight, by 

 means of the centres of the small circles corresponding to each 

 weight. This Figure conveys to the eye a complete idea of the 

 accuracy of the Law of Constancy of Work, and of its agree- 

 ment with observation. 



The upper line in the Figure shows the horizontal asymp- 

 tote, towards which the ordinate continually approaches, and 

 both the curve itself and the observations show that the 

 useful effect increases with the weight employed. 



Equation (116) may be thus written, 



wv 1 + av % - constant; 



in which wv" 1 represents the useful work, and av 1 the work 

 done by the arm; in this equation, a is a constant, being 

 the weight of the arm, and v grows less as the weight thrown 

 increases; hence the work expended on the arm is less as 

 the weight is greater, and therefore the useful work must 

 increase continually with the weight, and reaches a maximum 

 when the weight is infinite. 



In Figure 102, the useful work is represented by the 

 ordinate of the hyperbola, and the work done on the arm is 

 represented by the intercept of the ordinate between the 

 curve and its asymptote, which diminishes continually as the 

 weight (abscissa) increases. 



The coordinates of the centre of the hyperbola (120) are 



a = - q, 



0- P, 



and the equation of the curve, referred to its asymptotes, is 



Zri + pq = o. 

 2 G 



(121) 



