FAR. 



MR J. Y. BUCHANAN ON THE 



PAGE 



vicinity of 1/32, and that they increase whether the concentration is increased or 

 diminished. In the ennead MR, the solutions of the caesium salts and the iodides 

 approach most nearly to conformity with the law of the first hypothesis. The solutions 

 of chlorides and salts of lighter molecular weight conform more nearly to the geometric 

 law of the second hypothesis. 



44. When the solutions of a salt follow strictly the law of the second hypothesis, the general 111 



expression for the displacement of a solution containing mMR in 1 kilogram of water 

 is Am = Aj"', where A^. expresses the displacement of the solution when m=l. When 

 the solution does not follow this law exactly, the displacement for any particular value 

 of m is expressed by A„i = Aj''. Then the degree in which the solution conforms to the 

 law is indicated by the difference x-m when in is greater than 1. For solutions where 

 m is less than 1, and is expressed by vulgar fractions, the expression a;-m is replaced 

 by 1/m - Yjx. 



45. The displacements of most of the solutions are treated in this sense in Tables I. to VII. 112 



Tables VIII. to X. give for a number of solutions the values of log A„i/iog A„ = a; ; or, 



~2 



the exponent of the displacement A,„ when the exponent of A is taken as unity. If 

 the solutions conform to the geometric law of the second hypothesis, the value of x is 2. 



SECTION VIII. 



Comments on the Chakgbs in the Values of (i A - u for Different Values of m in the 

 Case of Solutions op Individual Salts of the Type MR and MRO3. 



46. The increment of displacement {v) due to the dissolution of m gram-molecules of a salt in 1000 116 



grams of water may be looked on as being the result of two operations, namely ; (a) the 

 dissolution of m/2 gram-molecules of the salt in 1000 grams of water, which produces 

 the first increment of displacement ; and (b) the further dissolution of m/2 of salt in the 

 solution so formed, which produces the second increment of displacement. These incre- 

 ments of displacement are rarely alike ; the second portion of salt dissolved generally 

 produces a greater increment of displacement than the first, and this has been very 

 generally held to be the law. One of the principal motives for making this research 

 was to find oiit, by the use of the more refined hydrometric method, if there is any point 

 in the dilution of a saline solution at which further dilution is accompanied by expansion 

 in place of contraction. The general result of the Avork is to show that in the solutions 

 having the concentrations here used, where m is less than 1/16, cases of expansion on 

 dilution are not uncommon. A table gives the values of m for which the value of 

 c? A - w is positive and becomes negative for the next lower value of m. That is, the 

 value of cZA - w changes sign at some concentration lower than that indicated by m and 

 higher than that indicated by w2/2. 



47. The method of treating the displacements of the solutions of the salts of the enneads 117 



MR and MRO3 is described in the case of solutions of KCl. 



48. The influence of possible error in the determinations of specific gravity on the values of 118 



cZA - u is discussed. 



49. A table furnishes evidence of the agreement in the results obtained by different experi- 119 



menters at different dates and using different instruments. 



50. A specimen table indicates the stages in tlie calculations used in the discussion of the 121 



values of v and rZA in the case of solutions of KCl of different concentrations. 



