528 Mr. A. Griffiths on the Source of 



can be made negligible by taking g very large, in -which case 

 the weakened solution rises very rapidly. 



If d=l-\-t (where G?=density and t = concentration), it can 

 readily be shown that the heat generated equals the weiglit 

 transmitted into the bottom of the tube by diffusion multiplied 

 by the rise of the weakened solution. 



The apparatus sketched in the preceding section will now 

 be studied. 



The quantity transmitted through L x into the upper com- 

 partment equals 



^AT 



_ bLi * 



1 — e ~*~ 



The heat produced by the fall of the substance transmitted 

 to the bottom of the upper compartment equals 



vATga x 

 1 — e ~* 



The quantity transmitted into the bottom of L x by diffusion 

 equals 



*AT A _ »AT«"V 



vAT: 



1 — e ~~k 1 — e "*" 



The energy produced by the rise of the diluted solution 

 equals 



vATge 



-*h\ 



_vli l 



l-e T J 



by 



Proceeding in this way, and making some algebraic trans- 

 formations, it can readily be shown that the heat produced in 

 this way when we consider the two tubes equals 



I l-e T 



vAT 



l—e~* 



k a. -f o 2 ejj^ I 



vh 2 C 



One effect of the operations just considered is to reduce 

 the quantity of the dissolved substance at the top of the lower 

 compartment by a certain amount, and to place the same 

 amount at the bottom of the upper compartment. 



The potential energy gained per second is the product of 

 the weight of the total amount transmitted and the thickness 

 of the diaphragm. Thus the potential energy gained per 



