86 Colorado College Studies. 



by Cauc-liy, connecting the pressures in differet directions in 

 any fluid, to show that the tangential force in any direction 

 along a plane is proportional to tlie sliding along the same 

 plane resolved in the same direction. He published tliis 

 theory in 1843. 



In 1845 G. G. Stokes derived the same equations as Poisson, 

 but found that A=SB. He based his investigation upon 

 three princiijal hypotheses: "First, that the difference between 

 the pressures on a plane in a given direction passing through 

 a given point P of a fluid in motion and the pressure which 

 would exist in all directions about P if the fluid in its neigh- 

 borhood were in a state of relative equilibrium depends only 

 on the relative motion of the fluid immediately about P; that 

 the relative motion due to any motion of rotation may be 

 eliminated without affecting the differences of the pressures 

 above mentioned." (Stokes.) He then arrives at the con- 

 clusion that the stresses due to viscosity are functions of the 

 rates of strain. After speculating as to the molecular consti- 

 tution of the fluid, he arrives at the hypothesis that these are 

 linear functions. This is his second hypothesis. For gases 

 he introduces a third: " When a gas is expanding equally in 

 all directions, the stresses P, Q and R are the same as if the 

 fluid were frictionless." * * * * In his report to the 

 British Association in 1846 "On Kecent Researches in Hy- 

 drodynamics," Stokes claims that the principal feature of his 

 investigation consists in eliminating from the relative motion 

 of a fluid about any particular point the relative motion which 

 corresponds to a certain motion of rotation and examining 

 the nature of the relative motion which remains; and that 

 the method employed does not necessarily require the con- 

 sideration of the ultimate molecules. 



The second assumption of Stokes is not altogether satis- 

 factory, since it rests upon the supposition that the velocity 

 is small. 



In 18()1 O. E. Meyer derived the ordinary equations if 

 B=0, which, according to other investigators prior to this 

 time, are true only for an incompressible fluid. 



