ANIMAL MECHANICS. 



233 



four corresponding points on the other bone ; and the corre- 

 sponding points on the two bones are supposed to be joined 

 by straight muscular fibres capable of contraction. 



The surface formed by these muscular fibres is a skew 

 surface, of a simple kind, called the Hyperboloid of one sheet. 

 It may be regarded as formed from the Quadrilateral muscle, 

 p. 195, by placing the origin and insertion of the muscular 

 fibres AB and A'B', in different planes, so as to form a skew 

 quadrilateral instead of a plane quadrilateral. 



A skew surface, of which the Hyperboloid of one sheet is 

 one of the simplest examples, may be readily imagined from 

 the shape of a saddle ; and at each point it possesses curvatures 

 which are not all in one direction, as in the convex or ellip- 

 soidal surface. If a tangent plane be drawn to the skew 

 surface at any point, this plane, instead of touching the sur- 

 face at a single point, will cut the surface along two inter- 

 secting right lines, which divide the surface at the point of 

 contact into two regions, in one of which the curvatures are 

 convex, and in the other concave, while along the right line 

 themselves, as is evident, there is no curvature at all. 



If a plane be drawn parallel to the tangent plane, 

 very near it, it will inter- A 

 sect the surface in a hy- 

 perbola and not an ellipse. 

 Let this hyperbola, or 

 indicatrix, be represented 

 in Fig. 55, its asymptotes 

 X Y and AB, are parallel 

 to the two right lines, 

 along which the tangent Fig. 55. 



plane intersects the surface, and the indicatrix plane meets the 

 surface inside the angles XOA and YOB, but does not meet 

 the surface inside the angles XOB and YOA. If, however, 



and 



Y 



