Stability of Flow of an Incompressible Viscous Fluid. 81 



(3) An explanation of this effect is suggested, based on the 

 assumption of a non-uniform distribution of the ionization 

 produced by Rontgen rays, the final values of a corresponding 

 to an effectively uniform distribution. 



(4) The value of a. is shown to fall off as the pressure of 

 the gas is reduced. 



I wish to express my gratitude to Prof. E. M, Wellisch 

 for suggesting these experiments, and for his very helpful 

 interest throughout the work. 



Sloane Laboratory, 



Yale University. $ 



Augrust, 1912. 



VIII. The Stability of Flow of an Incompressible Vvscous 

 Fluid. By Professor A. H. Gibson, JD.Sc, University 

 College, Dundee *. ■'. > 



AS a result of experiment Osborne Reynolds f concluded 

 that the conditions tending to stability of flow, i. e. to 

 stream-line as opposed to sinuous flow, of an incompressible 

 viscous fluid are : — 



(1) Free (exposed to air) surfaces. 



(2) Converging boundaries. 



(3) Curvilinear motion with the velocity greatest at 



the outside of the curve. 



(4) An increase in viscosity. 



(5) A diminution in density. 



From an examination of the equations of motion he also 

 showed t that conditions (4) and (5) might be predicted 

 from theoretical considerations. 



As regards conclusion (3), recent experiments by the 

 author § indicate that for increased stability in curvilinear 

 motion the greatest velocity should be at the inside, not at 

 the outside of the curve, and the object of the present paper 

 is to point out that this, as well as the truth of conclusions 

 (1) and (2), might also be inferred from the general equations 

 of motion. 



* Communicated by the Author. 



t Proc. Royal Institution of Great Britain, 1884. 



t Phil. Trans. 1883. 



§ Memoirs Manchester Lit. and Phil. Soc. vol. lv. (1910-11), ii. 



Phil. Mag. S. 6. Vol. 25. No. 145. Jan. 1913. G 



*w 



