lOG REPORT— 1894. 



pound of steam removes (l — x) k lb. of salt, while each pound of feed 

 introduces s lb. of salt. In steady working when the limit is reached 



(1 -x) k~s 



Let kls=c, the ratio of concentration of the boiler water. Then, for 

 example, if the boiler water contains twenty times as much salt as the 

 feed, x=l —■^^j=0•95, or the steam contains 5 per cent, of priming water. 

 The method assumes that the feed contains a definite percentage of easily 

 soluble salt, and that the trial has continued till the maximum concentra- 

 tion is reached. 



But if the boiler is freshly filled it may be a long time before the 

 limiting condition is reached. Let W be the quantity of water in the 

 boiler in pounds, and F the quantity of feed per unit of time. Let k be 

 now the saltness of the boiler water at t from the beginning of the test. 

 In a short interval, dt, the quantity of salt Fndt enters the boiler with 

 the feed, and the quantity 'F{l—x)kdt is carried away in the priming 

 water. The increase of salt in the boiler is therefore 



Wdk=F {sdt-{l-x) Mt] . 



Let W/F=«. Then 



adk + (1 —x) kdt - sdt=0. 

 Integration gives 



k= ^ • "^ 



1—x 



l+x 



e 



The constant of integration is obtained by putting k=s when i=.0. 



1+x 

 Let also t=n. Then 



a 



c=*= 1 - (l-'L) 



s l-x\ e"J 



From this equation, c being ascertained by analysis of the boiler 

 water, x can be determined at any period of the test. As the equation is 

 not easily solved x may be approximated to thus. If c is the concentra- 

 tion after t hours' working, a first approximation to x is 



Xy=:-\ — c. 



Put this in the expression above for c ; a value Cj will be obtained 

 which would be the concentration in the time t,]ic were the limiting 

 concentration. Then assume 



£ ^max 



Cy C 



C2 

 Cmax — ^ 



