124 Dr. J. J. Hood on the 



for some minutes after mixing ; indeed the precipitate may be 

 delayed for a considerable time by using solutions sufficiently 

 dilute. But it would seem from the above equations that the 

 ratio of the materials in the precipitate is independent of the 

 time taken to form, and whether the precipitant is added all 

 at once, or in small successive quantities. 



If the fraction of the total material in solution that is pre- 



A + B 



cipitated be — - — = # + ?/, and the ratio of the two salts in 



A 



solution be v, and in the precipitate /u., or A=vB, and x=fiy, 

 then equation (4) may be written 



( 1 -^^) = ( 1 ~MXW)) '' ■ • ' (5) 



from which it may be seen that the ratio of the less to the 

 more basic material increases the smaller the fraction preci- 



e 

 pitated, and that the maximum value of this ratio will be — -, 

 for an infinitesimal precipitate (X=go ). 



If the ratio ~j differ but little from unity, the separation of 



two such bodies by many repetitions of the process on each 

 precipitate obtained would be very tedious ; in the extreme 

 case of € = €', then |^ = v, or the ratio of the two materials in 

 the precipitate will be the same as in the original solution, 

 and no separation of the two constituents could be effected. 

 Consequently the complex nature of a body might never be 

 detected, at least by the application of such a process of sepa- 

 ration ; nor can the negative results obtained by Marignac* 

 for some of the commoner elements be looked upon as deciding 

 their homogeneous character. 



The following experiments by Mills and Bicketf are of 

 interest as showing the validity and application of the equation 



(>- 1)"- ('-l)' 



Iii each experiment the volume of the solution was 100 cubic 

 centimetres, the same quantity of precipitant (Na 2 C0 3 ) being 

 added to each. 



* Ann. Ch. et Phys. 1884. 

 f Phil. Mag. [5] vol, xiii, 



