60 Cambridge Philosophical Society. 



portant characteristic which it has now acquired of being a true 

 theory, inasmuch as, being framed to suit one class of comets, viz. 

 round telescopic ones, it is found, without any addition, to apply to 

 a class at first sight totally different, viz. the tailed comets, of which 

 the great one of 1 843 is so extreme an example. 



Not only then does there now seem to be a chance, by pursuing 

 the usual method of astronomical inquiry (comparing prediction with 

 numerical observation), of ascertaining the laws of these apparently 

 most capricious pha?nomena, but even of proving whether, though 

 so diverse from everything else in our system, they are regulated by 

 the theory of planetary gravitation. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



[Continued from vol. xxvii. p. 229.] 



April 14, 1845. — On the Theories of the Internal Friction of 

 Fluids in Motion, and of the Equilibrium and Motion of Elastic 

 Solids. By G. G. Stokes, M.A., Fellow of Pembroke College. 



The theory of the equilibrium of fluids depends on the funda- 

 mental principle, that the mutual action of two contiguous portions 

 of a fluid is normal to the surface which separates them. This prin- 

 ciple is assumed to be true in the common theory of fluid motion. 

 But although the theory of hydrostatics is fully borne out by expe- 

 riment, there are many instances of fluid motion, the laws of which 

 entirely depend on a certain tangential force called into play by the 

 sliding of one portion of fluid over another, or over the surface of a 

 solid. The object of the first part of this paper is to form the equa- 

 tions of motion of a fluid when account is taken of this tangential 

 force, and consequently the pressure not supposed normal to the 

 surface on which it acts, nor alike in all directions. 



Since the pressure in a fluid, or medium of any sort, arises di- 

 rectly from molecular action, being in fact merely a quantity by the 

 introduction of which we may dispense with the more immediate 

 consideration of the molecular forces, and since the molecular forces 

 are sensible at only insensible distances, it follows that the pressure 

 at any point depends only on the state of the fluid in the immediate 

 neighbourhood of that point. Let the system of pressures which 

 exists about any point P of a fluid in motion be decomposed into a 

 normal pressure p, alike in all directions, due to the degree of com- 

 pression of the fluid about P, and a system S of pressures due to the 

 motion. The author assumes that the pressures belonging to the 

 system S depend only on the relative velocities of the parts of the 

 fluid immediately about P, as expressed by the nine differential co- 

 efficients of u, v and w with respect to x, y and z. [The common no- 

 tation is here employed.] He assumes, further, that the relative 

 velocities due to any arbitrary motion of rotation may be eliminated 

 without affecting the pressures of the system S. Choosing for the 

 motion of rotation that for which the angular velocities are 



-— ( -t^ — — j about thfi axis of x, with similar expressions for the 



