Mr. A. Griffiths on Diffusive Convection. 461 



of radii r and 8r, we obtain the equation 



- pa,x 2.,L, + (,L + -^ - *£) x HA 



\ 1 — e * ' 



=/)x27rror, ... (9) 



where v=the upward velocity, 



7) = the coefficient of viscosity, 

 /> = difference between the pressures at the lower 

 - and upper ends of the tube. 



Let jo = M + — h/L + P, /. e. P is the excess of pressure 



above that necessary to produce statical equilibrium. 



By algebraical transformation, neglecting the square and 



higher powers of -r- 9 equation (9) becomes 



Let 



&v 

 3r*' 



1 </TL _ -P 

 1 2 7jk i hr) 





1 #TL 

 12 ?;& _/ " 



(10) 



The solution of (10) is 



r-Mx^+M.a-A+^g. . . . (11) 



If there is no slipping at the walls of the tube v=Q, when 

 r = R, hence = M 1 e/» + M 2 e-^+=^; when 



r = 0, ^— =0, hence 

 Or 



= M 1 -M 2 . 



Ultimately (11) becomes 



12P*/- ^+e-^ 





U 7j = 0, it can be shown algebraically that 



12P£ 

 V =gTL>' 



What may be called the proportional-de>i*tion equals 



efz + e-f*' 

 Phil. Mag. S. 5. VoL 46. No. 282. Nov. 1898. 2 K 



