273 



in which C is the concentration of the saturated vapour. 



t\ • 

 Now we will suppose that the state is stationary, i. e. that — = 0. 



ot 



Then c satisfies the ecpiation : 



^ /d\ d'c d'c\ dc 



D[ . ^— -^— -— ae^ (//) 



ydx' ^ dy' ^ dz'J dy ^ ^ 



while y.t = y^ = and v,/ = az. In this equation we will further take 



d'c 



r — ^ 0. Of course this is only approximately true lor the values 



of X that concern points within the rectangle. For points beside the 



rectangle c will be verj' small only when \y^ ._ is small with res- 



y^ a 

 pact to the dimensions of the rectangle, which we will always suppose. 

 So we will treat the problem as a twodimensional one, i. e. as if 

 the i-ectaugle has an intinite breadth in the direction of A'*). So we 



will neglect - — . 

 ox" 



a d'o 



Finally we remark that being large, consequently D -— may 



1) * oy^ 



dc 

 be neglected with respect to (ï: —. One might object to this when 



oy 



c is zero or very small, but then is c = 6' or at least then c is 

 approximately a constant, so all terms of the differential equation 



are zero or very small, and so it will be allowed to omit — . That 



dy' 



^ d'c 



D T— may not be neglected, notwithstanding the small factor D, 

 oz"- 



is caused by the fact that the evaporated substance will be concen- 



trated in a thin layer, so that c varies rapidly with z; ^— and - — 



oz oz^ 



therefore are large. 



After these simplifications the differential equation for c becomes: 



b'^c a dc 



d?=7.% <^'^' 



As, in consequence of a sufficiently rapid stream, a diffusion 



1) When by the rapid evaporation an undersaturation arises, this will probably 

 be proportional to the speed of evaporation. 



^) Experiments with crystals that solve in a flowing liquid, have confirmed this 

 supposition. 



