ANIMAL MECHANICS. 



235 



XY and AB, there is no curvature and no force perpendicular 

 to the muscular fibres. 



In the simplest case of muscular skew surface that occurs 

 in nature, let AB and A'B\ Fig. 57, represent straight bones 

 which are the origin and insertion of the rectilinear muscular 

 fibres joining them. The curved surface formed by the mus- 

 cular fibres (vide Fig. 54) is a surface of the second order, 

 known as the Hyperboloid of one sheet, the direction of whose 

 centre may be found readily by means of the following simple 

 construction. 



Draw the diagonals AB and AB of the skew quadrilateral 

 ABB A, and bisect each diagonal in x and y, and join x and 

 y, producing indefinitely both directions ; the right line xy 

 passes through the centre of the hyperboloid. 



This construction may be thus proved — Fig. 58. Since 



Fig. 58. 



the bone AB, and the muscular fibre AA' both lie upon the 

 surface, the plane BAA is a tangent plane at the point A ; 

 and in like manner, the plane ABB is the tangent plane at 

 the point B '; and similaily the tangent plane at A is the 



