236 



ANIMAL MECHANICS. 



plane of the bone AB', and of the muscular fibre AA ; and 

 the tangent plane at B is the plane ABB'. Draw any number 

 of chords ab', ab',&c, parallel to the diagonal AB' ; since 

 these are all chords of the common surface, their points of 

 bisection all lie upon a diametral plane By A' of that surface, 

 and passing through y, the point of bisection of the diagonal 

 AB. In like manner, if a number of chords a'b, a'b, &c, be 

 drawn parallel to the diameter A'B, their points of bisection 

 will also lie upon another diametral plane AxB', and passing 

 through x, the point of bisection of the diameter A'B, The 

 common line of intersection xy of these two diametral planes 

 By A' and AxB', will, therefore, pass through the centre of 

 the skew surface, or hyperboloid. 



We are now in a position to determine the mechanical 

 conditions of equilibrium 

 of such a muscle. Let 

 XY and AB, Fig. 59, de- 

 note the directions of the 

 two generating lines at 

 any point 0, and let pa- 

 rallel planes be drawn 

 at equal small distances 

 above and below the tan- 

 gent plane ; and let their F 'g- 59- 

 indicatrix hyperbola be projected, as in the figure upon the 

 tangent plane. Then, if a and b. denote the lines Oct and Ob, 

 the equations of the indicatrix hyperbolas, which are con- 

 jugate to each other will be, if referred to the axes Oa and 

 Ob, 



6 2 



(42) 



All that has been previously stated respecting the tangent 

 cone and indicatrix ellipse, in convex muscular surfaces, holds 



