ANIMAL MECHANICS. 



255 



by bones and muscles selected at random. Let us suppose 

 that S, 0, Q,M, and X, or everything relating to the shoulder 

 joint, be given ; it is required to contrive for the Tiger an 

 olecranon and triceps, which shall enable all the muscles of 

 shoulder and elbow to act simultaneously, and to the greatest 

 advantage. 

 Let 



SO = a CI = x (unknown olecranon). 

 SC = b 01 '= y (unknown triceps). 

 OSC = <j> 



The angle 0 is given, because it is the angle whose cosine is 

 found from the relation 



^ SQ 289 

 cos 0 = — - = — ^ 



SX 1 6 1 2 



<j> = 79 0 40', 



because XQ is a tangent to the circle described by Q, round 

 the centre S. 



It is easy to see that the olecranon and triceps are given 

 by the equations 



x = a - b cos $ 

 y = b sin 



If the values of a, b 9 and 0, above given, be substituted in 

 these equations, they will determine the lengths of olecranon 

 and triceps, which (and which only) will enable all the muscles 

 of the shoulder and elbow in the Tiger to act simultaneously 

 to the greatest advantage. 



Whenever, as in the case of the triceps longus, a muscle 

 passes over two joints, a considerable amount of rotation 

 round both joints is possible, without requiring the fibres of 

 the muscles to be lengthened or shortened. Thus, in the 

 quadrilateral figure OSC1, the sides OS, SC, and C7, are 

 absolutely constant ; and it may be shown that the arm may 



