TRANSACTIONS OF SECTION B. 585 



and, after complete settlement, filter. Starting with, say, 1000 grms. in the zero 

 bottle, transfer the filtrate to bottle —1 and the precipitate to bottle +1. Then 

 add another 1000 grms. to the bottle, and repeat the operations as in the folio-wing 

 table : — 



Ntjmbbes of THi: Bottles. 



E. 31 63 156 250 312 375 312 250 156 63 31 



F. 15 31 94 156 234 312 312 312 234 156 94 31 15 



After the sixth fractionation the 2000 grms. of earth are spread out amongst 

 13 bottles in the proportions represented in the bottom line. 



The separation of two earths by this plan is comparatively easy. The pre- 

 cipitation by ammonia depends not du-ectly on the affinities of the earths for the 

 acid, but rather on the excess of affinity of the precipitating ammonia. For if the 

 affinities of the two earths are represented by 100 and 101, aud that of ammonia 

 by 150, the affinities on which the precipitation depends would be represented by 

 150-100 = 50, and 150-101 =49, the difterence of which is 2 per cent, of the 

 larger. 



Now if a precipitant of which the affinity for the acid was only 110 were used, 

 the affinities in question would be 110-100 = 10, and 110-101 = 9, and the 

 diffiirence, 10-9 = 1, is 10 per cent, of the larger instead of only 2 percent. 

 Therefore if an alkali of which the affinity of the acid was only a little greater 

 than that of earths were used for precipitation, it is lihely that the differences 

 between the two earths would come out more strongly, and the labour of fractional 

 precipitation might be much reduced. Professor Stokes has suggested that some 

 of the compound ammonias might prove useful as precipitants instead of ammonia. 

 I have not, however, tested the suggestion. 



The amount of earths present has to be determined before each precipitation, 

 so as to know how much ammonia is to be added to get half precipitated. This is 

 done by standard solutions, and when everything is in good order it does not occupy 

 much time. Filtration is always the lion's share of the trouble. 



The above calculations have been based on the assumption that only two earths 

 are present. If more than two are present, the process fails in any reasonable 

 time to yield practically pure specimens of more than two out of a group of 

 closely allied earths. Thus, if there are as many as three earths, say A, B, and C, 

 whose positions in reference to the chemical process employed are in the order of 

 sequence in which they are written, we may get a specimen of A as nearly as we 

 please free from B and C, and a specimen of C as nearly as we please free from A 

 and B, but we cannot get a specimen of B practically free from A and C. The 

 law seems to be that to obtain practically pure spccime?is of three closely allied 

 earths, it is essential to have recourse to at least two different chetnical processes. 

 The mere continued repetition of the same process will not do, unless indeed the 

 operations are repeated such a vast number of times as to make the approximate 

 expressions no longer appUcable, even though the substances are chemically very 

 close. 



With a greater number of earths the same law holds good ; thus with n earths 

 closely aUied, to be separated we must have recourse ro n — 1 different chemical 

 processes. 



The acid in which the earths are dissolved is not a matter of indiflference. 

 There is an objection to sulphuric acid on the ground of its disposition to form 

 double salts, so that of the sulphates in solution a good portion might be double^ 

 sulphat&s, in which the two molecules of base combined with one of acid consisted. 



