474 Dr. Gr. J. Stoney on Texture in Media, and on the 



of solids, such as their power of propagating tensile, compres- 

 sive, shearing, and twisting stresses, are an outcome of what 

 I have called the texture of the medium ; and only appear 

 between blocks so large that, in considering the effect of one 

 of these large blocks upon its neighbours, we need only take 

 account of the general outcome that emerges when vast num- 

 bers of the individual events that are actually going on are 

 combined, and their general drift obtained by a statistical 

 method. 



It is especially instructive in this connexion to consider 

 the problems of that branch of dynamics which is called Rigid 

 Dynamics — such as the investigation of the motions of a top, 

 or hoop, or of the precessional motion of the Earth. In these 

 inquiries the integral calculus is employed. But the integra- 

 tions are all such that the calculated motions of such bodies 

 would come out almost precisely the same, whether the abso- 

 lute limit, as furnished by the integrals, be taken, or a sum- 

 mation for which the volume of the rigid body is regarded as 

 divided into blocks as large as the smallest specks visible in the 

 microscope. It is desirable, however, that we should bear in 

 mind that there is the ividest difference between the physical 

 assumptions underlying these two methods of procedure. 



If we proceed by integration, it is tacitly assumed that the 

 stresses characteristic of a solid body prevail between elements 

 of the volume however small, and differ, according to the law 

 laid down as the law prevailing in the medium, at situations 

 in the body however near. This is not true. 



On the other hand, if we proceed by summation, it is 

 assumed that the forces acting on each little block are distri- 

 buted equally and without any variation of direction to the 

 several equal portions into which its little mass may be con- 

 ceived to be divided, however minute this subdivision may be. 

 If this were the case, the internal stresses of a rigid body would 

 be powerless to induce rotation in any one of these blocks, or to 

 alter any rotation that may have pre-existed in it. Accordingly 

 each of these blocks would not rotate round the instantaneous 

 axis : it would merely revolve round it*. These, which are 

 the real physical meanings of the assumptions made in the two 

 cases respectively, are specially instructive. 



About fifty years ago Professor MacCullagh announced his 

 great discovery that the phenomena of light could be accounted 

 for, if we suppose light to be an undulation in an incompres- 



* The proper inference from this is that our equations have only taken 

 into account a part of the forces that are really acting : and this is true. 



