of the Rate of Diffusion of Solids dissolced in Liquids. 535 



Section IV. — Errors due to Changes of Temperature of 

 Apparatus as a whole. 



Apart from the effects of any differences of temperature 

 which may exist between the tubes themselves, there will in 

 general be a flow set up along them one way or the other 

 when the apparatus as a whole is heated. 



If the upper and lower compartments were of equal volume 

 and the coefficients of expansion and the compressibilities of 

 water and solution were the same, there would be no move- 

 ment along the tubes ; the liquid would simply be compressed 

 slightly. The actual motion could only be calculated from a 

 knowledge of the various coefficients of expansion and the 

 compressibilities. The author has not the data for an accurate 

 calculation, but to give an idea of the order of magnitude of 

 the error, the case will be considered in which the taps of the 

 upper compartment are open. 



Let V = volume of lower compartment. 



a — coefficient of cubical expansion of liquid. 

 = rise in temperature per second. 



It will be assumed that the temperature increases at a 

 constant rate, and that the steady state has been attained. 



Let v = velocity up the tubes per second. 



L = length of each tube. 



™ V*0 



lnen v = — r— . 



A 



The quantity of dissolved substance transmitted per second 

 (see Diffusive Convection, Sec. IV.) equals, when YL/k is 

 small, 



~L\ i"F/ approx,? 



ue - -tt( 1+ *-af> 



As an example, let the rise of temperature be 2° C. per 

 week; let a=0*00015, L = 4 cm., V = 40 c.c, A=0'I, 

 and # = 3xl0- 6 . Then VL«0/2A& equals O033 ; and the 

 error due to the flow produced by the expansion is more than 

 3 per cent. 



It may be mentioned that if a bubble of air is present in 

 the lower compartment, it increases the flow, and the corres- 

 ponding error, considerably. 



Even if the upper taps are not left continuously open, 

 there is an error corresponding to the above ; for opening 



202 



