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



resistance proportional to the velocity and in exact accordance with 

 the theoretical results obtained from the singular solution of the- 

 equation, when direct motion changes to sinuous, i.e., when 



In the same paper it was pointed out that the existence of this; 

 sudden change in the law of motion of fluids between solid surfaces 

 when 



proved the dependence of the manner of motion of the fluid on a 

 relation between the product of the dimensions of the pipe multiplied 

 by the velocity of the fluid and the product of the molecular dimen- 

 sions multiplied by the molecular velocities which determine the 

 value of fju for the fluid, also that the equations of motion for viscous 

 fluid contained evidence of this relation. 



These experimental results completely removed the discrepancy 

 previously noticed, showing that, whatever may be the cause, in those- 

 cases in which the experimental results do not accord with those 

 obtained by the singular solution of the equations, the actual motions. 

 of the water are different. But in this there is only a partial 

 explanation, for there remains the mechanical or physical significance 

 of the existence of the criterion to be explained. 



In the present paper the author applies the dynamical theory to- 

 the motion of incompressible viscous fluids to show 



(a.) That the adoption of the conclusion arrived at by Sir Gabriel 

 Stokes, that the dissipation function represents the rate at which 

 heat is produced, adds a definition to the meaning of u, v, 10 the 

 components of mean or fluid velocity which was previously 

 wanting ; 



(6.) That as the result of this definition the equations are true, and 

 are only true, as applied to fluid in which the mean-motions of the 

 matter, excluding the heat motions, are steady ; 



(c.) That the evidence of the possible existence of such steady 

 mean-motions, while at the same time the conversion of the energy of 

 these mean-motions into heat is going on, proves the existence of 

 some discriminative cause by which the periods in space and time of 

 the mean-motion are prevented from approximating in magnitude to 

 the corresponding periods of the heat motions ; and also proves the 

 existence of some general action by which the energy of mean-motion 

 is continually transformed into the energy of heat-motion without 

 passing through any intermediate stage ; 



That as applied to fluid in unsteady mean-motion (excluding; 



