288 



ANIMAL MECHANICS. 



from which it appears, that the semi-axis major of the ellipse, 

 whose centre is C (Fig. 76), is 3.138 inches. 



Equation (63) denotes an ellipse or hyperbola, according 

 as y 2 is negative or positive ; — that is, according as the equili- 

 brium of the bones is unstable or stable. Making y 2 negative, 

 we have 



y 2 = - sin j3 sin j3' {Lx 2 + Mx + iV), 



and this expression will become a maximum, and equal to the 

 square of the semi-axis minor, when 



s M 

 x = 0 = - — £ = - £.70 inches, 



which corresponds with C, the centre of the conic. 

 Writing the equation (63) 



- y l = -. — — ^ = Lx 2 + Mx + N, 

 sin (5 sin (5 



we have, for the semi-axis minor of the ellipse formed by 



y' = V - {LI 2 + MB + N) = 1.424 inches. 



The ellipse (y\ x) drawn to scale is shown in Fig. 76 ; and 

 ts equation, referred to C as origin of coordinates, is 



The work done by the muscle, causing the bone A B to 

 rotate round any two chords PQ and ST, is proportional to 

 the squares of those chords ; and we may, therefore, compare 

 the actual work done round the chord, £T, with the calculated 

 maximum round the chord PQ. 



