228 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1925 



Thus, thou'rh at first the number of fractions keeps on augmenting, 

 there is soon reached a stage of constant fractionation, for it is best 

 to eliminate from time to time the poorest solutions and the richest 

 solutions as indicated in the diagram; for instance, in the fifth 

 series of fractionations there is removed from the series of operations 

 62.5 grams of crystals in a concentration of 2.7 milligrams. These 

 residues will later reenter into the procedure. 



At the fourth fractionation crystals are obtained having practi- 

 cally the concentration of the original salt. We may at this stage 

 profit by introducing a certain quantity of the original salt into the 

 ensemble as indicated in the figure. This artifice lias the added 

 advantage of increasing the mass of certain fractionations. At the 

 seventh fractionation this process may be repeated. 



We can couipute the number of series of fractionations necessary 

 to obtain a given concentration. Let us suppose that we start out 

 with a chloride solution containing in the dry state 0.76 milligrams 

 of radium per kilogram and that we wish to attain a concentration 

 of 20 milligrams of the radium. After a fractionation the concen- 

 tration of the richer portion is 0.76X1-6; the second series will give 

 for the richer portion 0.76X(l-6)-; after n series we will have 

 0.76X ( 1-6) ". Accordingly, 



0.76X(1.,6)"=20 



whence we obtain n equals 7. 



It is best now to continue the fractionation after tran&formation 

 of the chlorides into bromides. If we now wish to attain a concen- 

 tration of 1 per cent in radium, it will be necessary to make n series 

 of fractions, n being given by the relationship: 



(2.2 )"==: (10,000/20) 



whence n equals 8. 



Now let us consider the results of a fractionation starting with 

 134.25 kilograms of anhydrous chlorides containing 102.8 milligrams 

 of radium and carried to a concentration of 1.1 per cent of radium. 

 We have: 



Milligrams 



Radium in the initial chlorides 102.80 



Radium eliminated in tlie chloride fractionation 2.29 



Radium eliminated in the bromide fractionation .47 



Radium carried down with the precipitation of lead 1. 70 



Radium in the final salt at 1.1 per cent 96.04 



In order to obtain a like result, it would be necessary in the frac- 

 tionation of bromide, for example, to take out the rich portion at the 

 eighth crystallization and then to continue the progressive enrich- 

 ment, with the elimination of the rich fractions so as to condense 

 the greater part of the radium into the enriched quota. This en- 



