238 



ANIMAL MECHANICS. 



fixed, and A'B free to move (Fig. 54), the contraction of the 

 fibres will bring A'B' into the same plane with AB, making 

 ABA'B' a plane quadrilateral ; this reduction of the skew 

 quadrilateral to a plane quadrilateral being accompanied by a 

 peculiar twisting motion of the entire sheet of muscle varying 

 with the nature of its curvatures at each point. 



Let us now consider, in detail, the action of a quadrilateral 

 skew muscle, in which one bone, AB, or A'B' is fixed, and 

 the other is either altogether free, or subject to various con- 

 ditions in its motion, the most usual of which is, that it is 

 compelled to turn always round some fixed socket or joint, 

 whose position, as well as that of the fixed bone, is known 

 and given. As the muscle may be supposed to perform its 

 work by two distinct motions, one of which reduces the skew 

 quadrilateral to a plane, and the other is confined altogether 

 to that plane, it will be convenient to divide the propositions 

 relative to skew quadrilateral muscles into two parts, viz. — 



1. Action of a quadrilateral muscle in a plane. 



2. Reduction of a skew quadrilateral muscle to the corre- 



sponding plane muscle. 

 The following postulate is necessary in order to solve the 

 problems that present themselves, and will be admitted by 

 some readers as an a priori truth, and by others as an induc- 

 tive truth demonstrable by instances. 



Postulate. 



The Framer of the Universe (Arffiiovpyog row koct/ulov) has 



constructed all muscles on the principle that each shall perform 

 the maximum of Work possible for it under the given external 

 conditions. 



From this postulate, the following results appear : — 

 Proposition A. (Problem.) 



Given a fixed bone A'B', and a perfectly free bone AB, 

 lying in the same plane, forming the origin and insertion oj a 



