8 Gwyther, Specification of Stress. 



Transformation from surface integrals to volume integrals, which 

 is the basis of the theorem connected with Green's name, may be 

 looked upon as the mathematical correlative to Faraday's con- 

 ception of a Field of Force, and I propose to make use of the 

 Transformation in that sense in the paragraphs which follow. 

 I shall regard the " body " as made up of particles which are 

 possessed of a molecular structure, in consequence of which the 

 particle may be supposed to possess an internal angular 

 momentum, which we may figure to be lof a gyrositatic type, ano 1 

 that this angular momentum is capable of variation by a suitable 

 couple. I shall also suppose that a closed surface can be drawn 

 in the body, which can move so that no mass is carried across this 

 surface, either from within outward, or from the outside inwards. 

 I shall assume that the ordinary processes of mathematics, and 

 the conditions for the employment of Green's Transformation 

 apply to the case. 



Taking I, m, ' n as the direction-cosines of a normal to 

 the surface measured outwards, and using \dS and \dV to 



denote integration over the closed surface, and over the in- 

 cluded volume respectively, we shall have relations such as : 



I. The rate of change of momentum in the direction of the axis 

 of x of the matter within the surface 



/ 



(P/+ Urn + Tn - t 3 « + W 2 n)d S 



&£+ infill §4^ +»*W 



8* 8y 8z 8y 8s > 



II. The rate of change of angular momentum about the axis 

 of x 



= the moment of the rate of change of linear momentum 

 about the axis of x 



+ j-qr l dK 



The usual method of supposing the surface to be indefi- 

 nitely contracted only serves to hide the fact that an assumption 

 has to be mad'e at this stage. I propose to formulate an 

 assumption that the body is made up of particles as already 

 described, and that the particles are in a field of stress, the 

 elements of stress at any particle being a function of [the co- 

 ordinates of that particle, and that the force acting on that 

 particlei is ^he force resulting from such a distribution or field 

 of stress. 



