1892.] Stability and Instability of Viscous Liquids. 273 



The physiological differentiation we can trace when we see that 

 the eosinophile cell has accentuated the glandular and protective cha- 

 racter of the primitive cell; while in its attack by direct contact 

 brought about by pseudopodial activity we see the remnant of the 

 direct pseudopodial and ingestive attack of the primitive cell. 



The hyaline cell, or permanently free phagocyte, represents the 

 specialisation of the direct pseudopodial ingestive activity of the 

 primitive cell. 



While, lastly, the absorptive powers of the primitive cell are repre- 

 sented by the rose- staining cell of the more differentiated animal 

 forms. 



II. "Stability and Instability of Viscous Liquids." By A. B. 

 BASSET, M.A., F.R.S. Received October 10, J892. 



(Abstract.) 



The principal object of this paper is to endeavour to obtain a 

 theoretical explanation of the instability of viscous liquids, which was 

 experimentally studied by Professor Osborne Reynolds.* 



The experiment, which perhaps most strikingly illustrates this 

 branch of hydrodynamics, consisted in causing water to flow from a 

 cistern through a long circular tube, and by means of suitable appli- 

 ances a fine stream of coloured liquid was made to flow down the 

 centre of the tube along with the water. When the velocity was 

 sufficiently small, the coloured stream showed no tendency to mix 

 with the water ; but when the velocity was increased, it was found 

 that as soon as it had attained a certain critical value, the coloured 

 stream broke off at a certain point of the tube and began to mix with 

 the water, thus showing that the motion was unstable. It was also 

 found that as the velocity was still further increased the point at 

 which instability commenced gradually moved up the tube towards 

 the end at which the water was flowing in. 



Professor Reynolds concluded that the critical velocity W was 

 determined by the equation 



< w, 



where a is the radius of the tube, p the density, and ft the viscosity of 

 the liquid, and n a number; but the results of this paper show that 

 this formula is incomplete, inasmuch as it does not take any account 

 of the friction of the liquid against the sides of the tube. 



In the first place, if the surface friction is supposed to be zero, so 

 that perfect slipping takes place, the motion is stable for all veloci- 



* ' Phil. Trans.,' 1883, p. 935. 



