494 UNIVERSITY OF VIRGINIA PUBLICATIONS 



Hence, X = §9~^7^^ = 3.75 X lO"*^ = .00000375 



This value is obviously too small to have any significance; and as all 

 succeeding terms are very much smaller and alternating in sign, we can 

 with perfect safety discard all after the first two. 



Computing the amlnint of diffusing substance in either layer after lapse 

 of time t. Let Fq be the amount of iodine (say) originally put into the 

 cylinder, ¥2 the amount left in the lower layer after time t, Vi that found 

 in the upper layer after time t. Obviously, 



■'^ I . ,. , . -^'-kt 



r>x=r, 



72 = 0- u ■ dx = 2(7 ■ uq- r{l/B>-]- 1 V • e ~i^ 



J.T = 



(Where a is the cross section.) Also 



Fo = i 0- ■ Mo ■ ?■ 



Therefore, 



Or 



470-1 1'8+ IV • e^' I 



Put F2 = Fo - 7i, and solve for k 



7.--''' .^ j' Fo-2Fi ,r^l_ r^- f F„ 8l 



^H ■ '"H V, 8 J tH' '\\\ - 2V\ ■ ^j 



"^-2.30 X log ^^ ^'^ 



ttH " ^ U' ■f^o - 2Fi 



= ^0.233 X login! 0.8106 ^?~- 

 ^rt I I'o — 21 1 



This last is the formula used in all cases for computing k by the two 

 layer method. 



