1904.] Catalysis by Colloidal Metals and similar Substances. 365 



FR -, 



xswnp(x-r)dx - sin ^ (R - r) - R cos n*(R - r) + r 



n - p J r n 1 n p 



a i> ~ fR = Co - - -y 



sitfn p (x-r)dx n P $(R-r)- siri 2n p (R-r) 



Jr 4% 



This system of equations is simplified, and the dimensions of the 

 quantities occurring in them made clear by introducing in place of a 

 and n the quantities a and v defined by the relations : 



n (R - r) = v and a p /n p = a p C (R - r) 2 . 



These quantities a and v are functions only of the non-dimensional 

 number e defined by the equation 



R-r' 



After several transformations the final system of equations is 

 arrived at. 



CCo (R r) r Kt j'l 2 . x r _/ v 2 2 x r 

 \c(.\v\e (R_ r \2 sin vj 4- aovog / R _ r \2 sin vo 



x R-r R-r 



+ ;] (15), 



the quantities v being found as the successive roots of the equation 



V ' ^-i+. o), 



and the quantities a by the equation 



2e 



Values of time always exist for which the infinite series can practically 

 be replaced by its first member. If e be small the values for v x 2 and ^ 

 arising out of Equations 16 and 17 may be taken as 



vj 2 = 3e, i = - , 

 3e 



and the whole expression simplified to 



c = Co ^LZTV^e'/iA 

 x 



The concentration varies with distance from the small sphere in the 

 identical manner we found previously in Equation 8, and we have 

 already proved that this being so the average concentration C may 

 without appreciable error be assumed to be equal to the upper con- 

 ceivable limit of c. We thus have 



C = OQI 



an equation which by a slight transformation becomes identical with 

 Equations 12 and 14. 



2 E 2 



