118 MR J. Y. BUCHANAN ON THE 



difference, ct?A, between consecutive increasing values of A. If we consider the pair of 

 solutions for which m = 1/8 and 1/16, we find that the dissolution of the quantity 1/1 6 KCl 

 in 1000 grams of water produces an increment of displacement v= 1*684 Grig.jo. When 

 ■ we dissolve a further 1/16 KCl in the solution, the displacement is increased by 

 dA^ 1-732 Gin-s-. The difference 1732 - 1 "684 = 0-048 is quite genuine. If we now 

 consider the pair of solutions for which m= 1/256 and 1/512, we have the displacements 

 A = 1000-098 and 1000'064 respectively. Here the dissolution of the first 1/512 KCl 

 causes an increment of displacement of 'y = 0064 Gi9-5=, while the dissolution of the 

 second 1/512 increases the displacement by only 0-034 G19.5 , showing that contraction has 

 taken place when the concentration of the solution has been increased from 1/512 to 2/512 

 gram-molecule per 1000 grams of water. From this it follows necessarily that the dilution 

 of 1/256 KCl + 1000 grams of water to 1/512 KC1+ 1000 grams of water is accompanied 

 by expansion. The specimen table for KCl in § 50 is constructed so as to show the 

 character of the change of displacement of a solution with change of its concentration. 

 The first line (n) gives the ordinal number of each column ; in the second line (m) we 

 have the quantity of salt, expressed in terms of the gram-molecule, dissolved in 1000 

 grams of water ; and in the third line (v) we have the increment of displacement in 

 terms of grams of water at the temperature of observation, G^. Then follow three 

 sub-tables [a, b, c). In sub-table a consecutive values of m, A, etc., are considered; 

 in sub -table b alternate values of 771, A, etc., are considered; and in sub-table c values 

 are given which represent the mean of those given in a and b. The last line in each 

 sub-table contains the values of the differences c?A — v, dA' — v', and dA" — v" , arrived 

 at in sub-tables a, b, and c respectively. 



§ 48. Before entering upon a detailed examination of the tables giving values of cZA 

 and V and their differences dA — v, we will consider the influence of change in specific 

 gravity on the value of the displacement, from which it will be possible to ascertain 

 how far the differences dA — v are to be accepted as independent of experimental error. 



For this purpose we will consider the effect of change of specific gravity on the 

 least concentrated solution of the salt KCl, the value of m being 1/512, and the 

 molecular weight of the salt being 74-6. 



The mean specific gravity is given in the table as 1*000082 ; the weight of soiutioi] 

 composed of 1000 grams of water and 1/512 gram-molecule KCl is 1000-1457 grams ; the 

 displacement is therefore 1000*064. The difference of displacement between the 1/256 

 and 1/512 gram-molecule solution is 0-034. 



We have seen (§ 35) that the mean probable error of the specific gravity of 

 any of the solutions entered in the tables. Class A, is ±3 in the sixth decimal place ; and 

 this is independent of the concentration of the solution. When the values of the 

 displacement are obtained by the use of any of these specific gravities, the probable 

 error is only increased by that due to the preparation of the solution, which may be 

 neglected (see § 49). The values of displacement so arrived at are affected by a 

 probable error which is also independent of the concentration. 



