122 MR J. Y. BUCHANAN ON THE 



Vn and Vn+i, the difference of these quantities as given in sub-table h, line j, includes a 

 value for dA which is approximately three times greater than that obtained by taking 

 consecutive values v^+i and v^ as in sub-table a. 



Hence one-third of the difference of displacement {line k, sub-table b), added to the 

 lower value v„_i employed for the purpose of obtaining the difference, gives a new 

 interpolated value v' for the solution of m (see line m, sub-table h). 



From this series of interpolated values of v^ a corresponding set of values, clA' (see 

 line I, sub-table b), is obtained by taking the difference of consecutive values of v', 

 and the differences of these values, dA' and v', give a new series of values, dA' — v\ set 

 out in line n, sub-table b. 



A comparison of the values of dA' — v' (sub-table b) with those of dA — v (in sub- 

 table a) shows the same general character of the change of values and of sign from 

 m= 1/8 to m= 1/512, only that the reversal of sign takes place at m= 1/128 instead of 

 at 771 = 1/256 as in sub-table a. 



A third series of values is derived by using the mean of corresponding values of 

 V and v', namely, ^{v + v') = v" , and obtaining the difference dA" — v" in the same way 

 as the corresponding values of dA — v and dA' — v' were obtained. 



An inspection of these new values shows that the character of the decrease of the 

 positive value is the same as in the other two cases, but the reversal of sign remains at 

 7n= 1/128 as in sub-table b. The magnitudes of the values d/\" — v" when w<l/32 

 are, however, so small that they would indicate no comparative change of volume wlien 

 successive small increments of salt were added to these dilute solutions. 



These calculations serve to indicate the character of the relative changes of volume 

 occurring when successive dilutions are effected. 



The results of the treatment of the values of v in the case of KCl justifies a similar 

 treatment of the values of v in the solutions of the other salts included in the series of 

 tables. Class A, and the results for the salts of the types MR and MROg are given in 

 § 5 1 in a series of tables of Class F for each salt, similar to the specimen table given 

 above, and arranged in triads of the salts having the same acid radical, R or ROg as the 

 case may be. 



