ANIMAL MECHANICS. 



333 



posed of any number of fibres, anyhow placed, may be thus 

 deduced. 



If we write 



(i) A "" S S, 



, , > ( g 9) 



then we find 



Work = 2—} = 4 — / = 7 = = (go) 



W *\/X 2 +m 2 +i VX 2 + n? + i 



and the equation of condition becomes 



cm (X 2 + m 2 + i) (A' 2 + m 2 + i) jXV - IX| (91) 

 = (m 2 + 1) { mc ( XX + X'X) + K\ (A 2 - A' 2 ). 



This equation admits of a solution on inspection, viz., 



x = a; 

 x = x\ 



which implies that if the fibres were so arranged as to make 

 X = X', then the generator A = X', which makes equal angles 

 in space w T ith the two bones AB and A'B\ is the required 

 maximum. I have not, as yet, found any skew muscle whose 

 fibres give X = X', and therefore we must set aside the most 

 obvious particular solution of our equation of condition, and 

 seek its general solution. If we eliminate X' by means of the 

 relation 



XX' = m 2 - 1, 



and expand (91), arranging by powers of X, we find, after a 



