ANIMAL MECHANICS. 



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true in the skew surface for its tangent cone and indicatrix 

 hyperbola. Thus, the tensile strain in the tangent plane at 

 0, will vary in any azimuth as the square of the perpendicular 

 let fall upon the tangent to the hyperbola, or as the radius of 

 curvature of the section of the surface passing through that 

 perpendicular. Let us trace the variation in the tensile strain 

 round the point 0. In the direction Oa the strain is propor- 

 tional to a 2 , and diminishes from Oa to OY, varying always as 

 the square of the perpendicular let fall from 0 upon the tan- 

 gent to the hyperbola YaB; in the direction OY, this per- 

 pendicular vanishes because OY is the asymptote, and the 

 tensile strain and curvature vanish with it. When we pass 

 OY, the tensile strain increases from zero to b 2 , in going from 

 OY to OB; varying now according to the square of the per- 

 pendicular let fall upon the tangent to the hyperbola YbA, 

 from the centre 0, and so on. Thus the tensile strain has 

 two maxima, a 2 , and 5 2 , corresponding to the axes Oa and Ob 9 

 and vanishes between these maxima, in the directions XY 

 and A B y the asymptotes of the indicatrix hyperbolas. In 

 the convex muscular surface, on the contrary, the tensile 

 strain ranged from a maximum a 2 to a minimum b 2 , and never 

 vanished at all. The perpendicular pressures, produced by 

 the tensile strains in the skew surface, are in opposite direc- 

 tions inside the angular spaces containing the two hyperbolas, 

 because the curvatures of the surface have opposite signs in 

 these two regions. 



The joint effect of the tensile muscular forces in a closed 

 convex surface is to compress the contents enclosed within 

 it; but in the muscular skew surface, which is an open surface 

 and cannot be made to enclose a space, the joint effect of a 

 contraction of all its fibres results in an effort made by the 

 surface to destroy its own curvature and return into the con- 

 dition of a plane surface. Thus, if one of the bones AB be 



