152 



ANIMAL MECHANICS. 



of much interest and some difficulty, as it is the celebrated 

 problem of the equilibrium of a flexible membrane subjected 

 to the action of given forces. It has been solved by La- 

 grange (Mecajiique A nalytique, p. 147), in all its generality. 

 In the most general case of the problem, the following beau- 

 tiful theorem can be demonstrated: — Let T denote the tensile 

 strain acting in the tangential plane of the membrane, applied 

 to rupture a band of the membrane one inch broad ; let P 

 denote the pressure resulting from all the forces in action, per- 

 pendicular to the surface of the membrane, and acting on a 

 surface of one square inch ; and let p x and p 2 denote the two 

 radii of principal curvature of the membrane, at the point 

 considered. Then we have the following equation : — 



p=tJ- + ±) (, 9) 



If the surface, or a portion of it, become spherical, the two 

 principal curvatures become equal, and equation (19) be- 

 comes 



P=— (20) 

 9 



In the case of the uterus and its membranes, the force P arises 

 from hydrostatical pressure only, and is therefore easily mea- 

 sured, and the supposition of spherical curvature is approxi- 

 mately admissible. 



The natural position of the gravid uterus is shown in 

 Fig. 21, in which OP is the axis of the uterus, and AB a ver- 

 tical line drawn through G, the centre of gravity of the foetus ; 

 this vertical line must pass through F, the centre of floatation 

 of the foetus, or centre of gravity of the liquor amnii displaced 

 by the foetus. 



In the first stage of labour, the contraction of the muscu- 

 lar walls of the uterus compresses its liquid contents, and the 



