188 



ANIMAL MECHANICS. 



Let AOB, Fig. 33, be a triangular fan-shaped muscle, and 

 let OF be the bisector of the vertical angle, and its length 



0 



Fig- 33. 



equal b. Since the line of insertion, AB, remains constant in 

 length, when the muscle contracts, the line AB will move, 

 parallel to itself in the direction YO, into a position A'B', 

 and the fibre OF will contract to its full amount of inherent 

 work, through a space AA' = BB' = $b ; if we take any other 

 fibre, Ox = /, and draw xx' parallel to 0 F, and with 0 as 

 centre describe the circle x'p, then xp will be the space 

 through which the fibre I contracts ; but this space is less 

 than xa = SZ, which bears to I the same ratio that AA = Sb 

 bears to b. Hence the fibre /, in contracting, only gives out 

 the work 



fdO x xp = f$b . cos Odd, 

 instead of the work 



which is inherent in it. 



If we suppose (Fig. 34) AB and A'B' of indefinite length, 

 and draw xy parallel to OY'm such a manner that Ox= 0y\ it 

 is easy to see that all the fibres lying to the left of xy will be 

 shortened by the transference o£AB to A'B\ while all the fibres 



