ANIMAL MECHANICS. 



181 



compare it with the inherent or potential work of the muscu- 

 lar fibres contracting separately. 



We may imagine a circle described round the point 0 

 with a radius assumed equal to unity, and such that the fibres 

 passing to their insertion completely fill the circumference of 

 the arc of this circle. If 0 denote (Fig. 28) the angle XOx, 

 made by any muscular fibre with the bisector OX, and / de- 

 note the force of contraction of the muscular fibres applied 

 perpendicularly to a unit length ; then fdO will be the force 

 acting in the line Ox, and the resultant of all these forces, 

 estimated in the direction OX, will be 



cos OdO = 2/ sin 9. 



AVhen the whole muscle AOB contracts, each fibre is short- 

 ened so as to allow the base AB to be drawn towards 0, in 

 the direction OX, remaining parallel to itself. If b denote 

 the bisector OX, and Zb be the amount of contraction, the 

 total work done by the triangular muscle will be — 



Work of triangular Muscle = ESb = 2fSb sin 0 = 2f8q, (30) 



where q denotes the perpendicular (IF) let fall from the 

 point X upon the side of the triangle. 



If we assume, that the cross section of a triangular muscle 

 is everywhere the same, this cross section may be conveniently 

 used as the unit to which / is applied, and we obtain the fol- 

 lowing important theorem : — 



The Work done by the contraction of any triangular muscle 

 is equal to the Work done by a prismatic muscle having the same 

 cross section and a length equal to twice the perpendicular drop- 

 ped on the side, from the foot of the bisector of the vertical angle 

 of the triangular muscle. 



