Sir George Gabriel Stoles. 201 



symmetrical with respect to an axis. For many years the papers, now 

 under consideration, were very little known abroad, and some of the 

 results are still attributed by Continental writers to other authors. 



A memoir of great importance on the " Friction of Fluids in 

 Motion, etc.," followed a little later (1845). The most general 

 motion of a medium in the neighbourhood of any point is analysed 

 into three constituents a motion of pure translation, one of pure 

 rotation, and one of pure strain. These results are now very familiar ; 

 it may assist us to appreciate their novelty at the time, if we 

 recall that when similar conclusions were put forward by Helmholtz 

 twenty-three years later, their validity was disputed by so acute 

 a critic as Bertrand. The splendid edifice, concerning the theory of 

 inviscid fluids, which Helmholtz raised upon these foundations, is 

 the admiration of all students of Hydrodynamics. 



In applying the above purely kinematical analysis to viscous fluids, 

 Stokes lays down the following principle : " That the difference 

 between the pressure on a plane passing through any point P of a 

 fluid in motion and the pressure which would exist in all directions 

 about P if the fluid in its neighbourhood were in a state of relative 

 equilibrium depends only on the relative motion of the fluid imme- 

 diately about P ; and that the relative motion due to any motion of 

 rotation may be eliminated without affecting the differences of the 

 pressures above mentioned." This leads him to general dynamical 

 equations, such as had already been obtained by Navier and Poisson, 

 starting from more special hypotheses as to the constitution of 

 matter. 



Among the varied examples of the application of the general 

 equations two may be noted. In one of these, relating to the motion 

 of fluid between two coaxial revolving cylinders, an error of Newton's 

 is corrected. In the other, the propagation of sound, as influenced by 

 viscosity, is examined. It is shown that the action of viscosity (/<) 

 is to make the intensity of the sound diminish as the time increases, 

 and to render the velocity of propagation less than it would otherwise 

 be. Both effects are greater for high than for low notes ; but the 

 former depends on the first power of /, while the latter depends only 

 on /* 3 , and may usually be neglected. 



In the same paragraph there occur two lines in which a question, 

 which has recently been discussed on both sides, and treated as a 

 novelty, is disposed of. The words are "we may represent an 

 arbitrary disturbance of the medium as the aggregate of series of 

 plane waves propagated in all directions." 



In the third section of the memoir under consideration, Stokes 

 applies the same principles to find the equations for an elastic solid. 

 In his view the two elastic constants are independent and not reducible 



A 2 



