40 Prof. 0. Reynolds. On the Dynamical [May 24, 



also proposed. This differs from Maxwell's theory in that tlie latter 

 merely postulates changes of specific resistance and specific induc- 

 tive capacity from point to point of the dielectric, while our theory is 

 distinctly chemical. We consider that our results on mixed films are 

 best explained by the theory we propose, though the difficulty of dis- 

 proving Maxwell's theory is almost equal to the difficulty of establish- 

 ing it, and we do not wish to imply that some sort of explanation on 

 this theory may not be constructed to fit in with our observations. 

 This is a point, however, on which we are still engaged. The matter 

 may, perhaps, be best summed up in the statement that the evidence 

 we have against Maxwell's theory is nearly worthless; but that we 

 do not consider this theory necessary if our theory of conduction be 

 accepted. 



II. " On the Dynamical Theory of Incompressible Viscous 

 Fluids and the Determination of the Criterion." By 

 OSBORNE REYNOLDS, F.R.S., &c. Received April 25, 1894. 



(Abstract.) 



The equations of motion of viscous fluid (obtained by grafting on 

 certain terms to the abstract equations of the Eulerian form so as to 

 adapt these equations to the case of fluids subject to stresses depend- 

 ing in some hypothetical manner on the rates of distortion, which 

 equations Navier* seems to have first introduced in 1822, and which 

 were much studied by Cauchyf and PoissonJ) were finally shown 

 by St. Yeuant and Sir Gabriel Stokes, || in 1845, to involve no other 

 assumption than that the stresses, other than that of pressure uniform 

 in all directions, are linear functions of the rates of distortion with a 

 co-efficient depending on the physical state of the fluid. 



By obtaining a singular solution of these equations as applied to 

 the case of pendulums in steady periodic motion Sir G. Stokes^f was 

 able to compare the theoretical results with the numerous experi- 

 ments that had been recorded, with the result that the theoretical 

 calculations agreed so closely with the experimental determinations 

 as seemingly to prove the truth of the assumption involved. This was 

 also the result of comparing the flow of water through uniform tubes 

 with the flow calculated from a singular solution of the equations so 

 long as the tubes were small and the velocities slow. On the other 



* ' Mem. de 1' Academic,' t. ri, p. 389. 



t ' Mem. des Savants Etrangers,' t. 1, p. 40. 



J ' Mem. de 1' Academic,' t. \, p. 345. 



' B.A. Keport,' 1846. 



|| ' Cambridge Trans.,' 1845. 



H ' Cambridge Trans.,' vol. ix, 1857. 



