388 Mr Hill, Note on the use of the experimental 



Multiplying h} 

 and a, we have 



TATTOO 



Multiplying by sin , and integrating between the limits 



Cv 



f ^ TlTCC f ^ 



= 2/0 sin --— + ^ J 



.0 «. Jo 



. „ rirx 



sin^ 



a 



a 



rira ^ 



cos cos 



a 



A ^^ 



rir 

 when r is even .4,. = 0, 



when r is odd J.,. = . — Vo • 2 = — ~ , 



a rir'-^ rir 



y = 2/0 i 1 - 4 S r^ ^^— e «- sm ^ — \ . 



"^ "^ ( 1 (2n-l)7r a j 



Hence we may draw two conclusions. 



(1) To make results with the instrument easily and 

 directly comparable it is advisable to keep ^ , the amount of 

 gelatine used, the same in different experiments. 



(2) With this condition if kt in one experiment =k't' in 

 another, the concentration at any point P is the same in either 

 experiment. Hence if we compare the times at which equal 

 concentrations are reached these must be inversely proportional 

 to the diffusion constants of the two salts. With a series of 

 observations therefore at equal intervals of time the concentrations 

 can be plotted and the curve compared with the standard curve 

 obtained for one salt whose diffusion constant is known. The 

 ratio of the times to equal concentrations can be compared at 

 several points of the curve : this ratio should be found nearly 

 constant, and its mean value for several concentrations will give 

 the ratio of the diffusion constants very accurately. 



If we suppose the conductivity to be directly proportional to 

 the amount of salt between the two electrodes we shall have the 

 conductivity 



A P (i A.K 1 -k^^^t . (2n-l)'7rx\. 



^ = f^yo i 1 - 4 2 ^ =^ e « sin -^ } dx, 



^^Jp\ i(2w-l)7r a ] ' 



where p and q are the values of x for the ends g, h, and G, H, of 

 the electrodes, and jjl is some constant, depending on the conduc- 

 tivity and the size of the plates. 



^ 1 {zn — lfir^ [ a 



(2n — 1) 7rq\ 



A = /x2/o 



— cos- 



