ANIMAL MECHANICS. 



459 



the arm, is a point of inflexion on the curve where the cur- 

 vature changes sign, and the curve becomes asymptotic to 

 the line OX. 



The following are the values of the abscissae and ordinates 

 at these important points : — 



Om' = - On' - a 



(,32) 



mm = — nn — — - 

 2a $a 



The tangent drawn at the point of inflexion cuts off an 

 abscissa on the axis OX equal to 4a, The readiest mode of 

 approximating to the best numerical values of A and a, is by 

 comparing the co-ordinates of the maximum effect (m) with 

 the equations (132). 



In Fig. (106) I have drawn, on a larger scale, the por- 

 tion of the cuspidal cubic (131) corresponding to positive 

 values of w and t, and have also shown the actual observations 

 by means of the small circles. The agreement between theory 

 and observation is very satisfactory. 



Fig. 106. 



