ANIMAL MECHANICS. 



209 



abdominal muscles to exert their full force in expelling the 

 contents of the uterus and vagina. 



Muscular Fibres forming curved Surfaces. 

 In all the preceding cases, we have supposed the sheet 

 formed by the muscular fibres to form a plane, but this 

 condition is rarely fulfilled with mathematical exactness. 

 The muscular sheets, in general, form surfaces more or less 

 curved, and it becomes necessary to take into consideration 

 the various curvatures of the several surfaces formed by the 

 sheets of the muscular fibres. 



Surfaces are divisible into two classes — viz., those whose 

 curvatures at any point are in the same direction, and those 

 whose curvatures at any point have opposite directions. The 

 first class of surfaces may be called convex, or ellipsoidal sur- 

 faces ; the second class may be called skew surfaces.* 



If we imagine a convex surface, like an egg, uterus, or 

 bladder, and at any point taken on the surface draw a line per- 

 pendicular to it, and imagine a plane passing through this 

 line to turn round upon it, this plane in each of its positions 

 will intersect the surface in a certain curve. In the convex 

 surface, the curvatures of all these curves at the point in ques- 

 tion will be all convex or all concave together, in the same 

 direction. 



If we imagine a skew surface, like a saddle, or dice box, 

 and draw a perpendicular to it at any point, the plane re- 

 volving round this perpendicular will intersect the surface in 

 certain curves, some of which are convex, and some concave ; 

 and the convex curves are separated from the concave curves 

 by two lines intersecting upon the surface at the given point ; 



* This term is here used in a sense slightly different from its meaning when 

 employed by geometers. 



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