ANIMAL MECHANICS. 



331 



I have ^already proved that the work done in rotating A'B' 

 round the intersection of these planes will be a maximum, 

 when the angle between the planes is a right angle. Hence, 

 in order to obtain the maximum effect, we must make the 

 two planes (81) intersect at right angles. The angle 0, 

 between the planes is found by the equation 



n i - m 2 + AA' ; . . 



cos 9 = - — " (82) 



V^ + mM 1 v \ 4 m 2 + 1 



when 9 = 90 0 , cos 9 - o, hence we have the condition 



A A' = m* - 1. (83) 



If we now eliminate the parameters A, A', from the equa- 

 tions (81) and (83), we obtain the following locus of intersec- 

 tion of planes at right angles to each other, passing through 

 the bones AB and A'B' 



(f - m*x*) + (1 - m 2 ) (z 2 - c 2 ) = o. (84) 



This represents an Hyperboloid of one sheet, having its 

 Ellipse de Gorge in the plane of ?/, z ; and IP one of its axes ; 

 and the rectilinear generators of this hyperboloid are the 

 intersections of the rectangular planes passing through the 

 bones AB and A'B'. 



In order, therefore, that the maximum work shall be done 

 by the muscle AB A'B', it is necessary that the axis of rota- 

 tion shall coincide with some one or other of the generators 

 of the hyperboloid (84); but this is not sufficient, for my 

 Postulate (p. 238) requires, in addition, that of all the 

 generators of the hyperboloid, that particular generator shall 

 be chosen as axis of rotation, which shall give us the maximum 

 maocimorum of work done. We must, therefore, in the first 

 place, discover which, of all the generators, possesses this 

 property, and then, by measurements on the dead subject, 



