[ 342 j 



XL I. On Steady Motion in an Incompressible Viscous Fluid. 

 By Thomas Craig, Ph.D., U.S. Coast and Geodetic Survey, 

 formerly Fellow of the Johns Hopkins University, Baltimore, 

 \Md., U. S. A.* 



IN the following paper an attempt has been made to give 

 the theory of steady motion in an ordinary viscous fluid, 

 and the results of the general investigation applied to the case 

 when there is a solid body of given form immersed in the 

 fluid, and the fluid moves subject to the condition that at infi- 

 nity all the flow is parallel to the axis of z. 



The general equations of motion of an incompressible viscous 

 fluid are well known to be 



Du v dp _ 2 



Dw rj dp , „ 



pm = p z -cu +flVw \ 



maintained, and actually is maintained in the universe, would become 

 strictly true, in so far as the limits within which such uniformity of 

 temperature is non-existent would be (relatively speaking*) indefinitely 

 small. 



The late Prof. Clerk Maxwell remarks ('Theory of Heat,' p. 163) :— 

 u The transference of heat, therefore, from one body of the system to 

 another always increases the ' entropy ' of the system. Clausius ex- 

 presses this by saying that the entropy of the system always tends 

 towards a maximum value." It appears, therefore, that, on the above 

 view that the universe is already in a state of equilibrium of temperature, 

 the " entropy " of the universe would already have reached a maximum 

 value, which continually tends to be maintained. The theory of finality 

 in the universe seems to have been discussed with considerable interest 

 in Germany. A critical notice of this subject may be found in Lange's 

 Geschichte des Materialismus (of which I believe an English translation 

 now exists). 



It should be mentioned [as also noticed in my previous essays] that 

 Dr. Croll, in the Phil. Mag. for May 1868 and July 1878, also Mr. Johnstone 

 Stoney (Proceedings of the Royal Society 1868), have published papers 

 dealing with the eventuality of encounters among the stars, and suggested 

 views which may, as far as they go, be regarded as consistent with the 

 development of an encircling theory suggested in this and my former 

 essays. Also the fact of the present theory having beeu arrived at before 

 seeing the papers above cited, naturally tended rather to afford some 

 confidence in the result. 



The entertaining of the above theory would be no more than admitting 

 the possible application of the principle of evolution to universal changes 

 as well as to planetary changes : the birth and death of worlds compa- 

 rable to the birth and death of individuals. Or the secular fluctuations 

 of life in the cosmical units of the universe would be paralleled by those 

 of the individuals of a planet — while the conservation of life has its cor- 

 relative in the conservation of energy and of matter. 



* Communicated by A. G. Greenhill, Es.q. 



