210 



ANIMAL MECHANICS. 



so that the surface possesses a convex curvature in one of 

 the regions formed by those intersecting lines, and possesses 

 a concave curvature in the other region. In the direction of 

 the intersecting lines themselves, the surface has no curvature 

 at all, for these lines divide the convex from the concave 

 portion of the surface. 



The lines drawn upon skew surfaces, along which the 

 surface is not curved, may become right lines, and, as the 

 surface itself is the aggregate of all the lines composing it, 

 we may have a skew curved surface composed altogether of 

 rectilinear fibres. This case frequently occurs in animal me- 

 chanics, the rectilinear generators being the actual fibres of 

 the muscles. 



As the ellipsoidal muscles are more easily understood than 

 the skew muscles (notwithstanding that they are composed 

 altogether of curved and not rectilinear fibres), I shall com- 

 mence my description of curved muscular surfaces, with that 

 of ellipsoidal muscles, and proceed afterwards to show the 

 properties of skew muscles. 



Ellipsoidal Muscles. — If a tangent plane be drawn at any 

 point of a convex or ellipsoidal surface, it will touch the sur- 

 face in one point only ; and if a plane be drawn parallel to the 

 tangent plane and very close to it, so as to intersect the sur- 

 face, this plane will cut the surface in an ellipse, or circle, 

 according as the principal curvatures at the point in question 

 are unequal or equal. If tangent planes be now drawn to the 

 surface along the elliptic curve of intersection, they will form 

 a tangent cone to the surface, and this cone will be a circular 

 or elliptic cone, according as the curve of intersection is a 

 circle or ellipse.* 



* The curve of intersection with a surface made by a plane very near and 

 parallel to a tangent plane is called by geometers the indicatrix curve. 



