1870.] On the Muscular Forces employed in Parturition, 257 



March 10, 1870. 

 WARREN DE LA RUE, Esq., Vice-President, in the Chair. 

 The following communications were read : — 



I. " On some Elementary Principles in Animal Mechanics. — 

 No. III. On the Muscular Forces employed in Parturition/'' 

 By the Rev. Samuel Haughton, M.D., Fellow of Trinity Col- 

 lege, Dublin. Received January 31, 1870. 



In the first stage of natural labour, the involuntary muscles of the uterus 

 contract upon the fluid contents of this organ, and possess sufficient force 

 to dilate the mouth of the womb, and generally to rupture the membranes. 

 I shall endeavour to show, from the principles of muscular action already 

 laid down, that the uterine muscles are sufficient, and not much more than 

 sufficient, to complete the first stage of labour, and that they do not pos- 

 sess an amount of force adequate to rupture, in any case, the uterine wall 

 itself. 



In the second stage of labour, the irritation of the fcetal head upon the 

 wall of the vagina provokes the reflex action of the voluntary abdominal 

 muscles, which aid powerfully the uterine muscles to complete the second 

 stage by expelling the foetus. The amount of available additional force 

 given out by the abdominal muscles admits of calculation, and will be found 

 much greater than the force produced by the involuntary contractions of 

 the womb itself. 



The mechanical problem to be solved for both cases is one of much 

 interest, 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 

 Lagrange (Me'canique Analytique, p. 147) in all its generality. In the 

 most general case of the problem, the following beautiful thereom 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 1 inch 

 broad ; let P denote the pressure resulting from all the forces in action, 

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

 one square inch ; and let p 1 and p 2 denote the two radii of principal curva- 

 ture of the membrane at the point considered. Then we have the follow- 

 ing equation : — 



P=Txfi + l\ 



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

 curvatures become equal, and the equation becomes 



P= 2T . 

 P ' 



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



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