SODIUM CHLORIDE BERTHOLLET'S LAWS 419 



gravity of water is 9998'7 and 9585) this augmentation is expressed if 

 7.V 1 and 65-7 be substituted for 71 '17, and 0-31 and O72 for 0'428. 

 In this manner the specific gravity 19 at 



when water at 0= 10000. 20 



p p.c. of salt, then by mixing, for instance, equal weights of water and the solution, we shall 

 obtain a solution containing %p of the salt, and if it be formed without contraction, then its 



211 



specific gravity x will be determined by the equation - = . -\ , because the volume is 



x S (> S 



equal to the weight divided by the density. In reality, the specific gravity always comes out 

 greater than that calculated on the supposition of an absence of contraction, as may be 

 shown by substituting S by its parabolic expression, S = S + Ap + Bp 2 , and x by S + A^p + 

 B\p^. By this means it may be easily shown that the contraction, c, in the formation 

 of 100 grams of solution, is not in so simple a relation to the composition of the solution 

 as G. T. Gerlach (1888) takes it, on the supposition that c = Ap (100 j?), where A is a con- 

 stant for all solutions of a given substance. The magnitude of c is evidently determined 

 by the equation p,'B + (100 p)/S H = 100/S + c, where B is the specific gravity of the sub- 

 stance dissolved, on the supposition of its being in a liquid state. If for sodium chloride 

 at 15 with ^ = 10 and ^ = 20, the mean observed specific gravities be taken as 10726 and 

 11501, then (as S = 9991'6) ^4 = 2851 x 10-', and 5 = 17476, and therefore for p = 5, the 

 calculated specific gravity will be 10377, and the observed is 10353, with a probable error 

 of not more than 2 : hence the difference greatly exceeds the possible error. A similar un- 

 adaptability of the above-mentioned supposition is evinced in the investigation of all other 

 solutions. The hypothesis under consideration resembles in this respect the hypothesis of 

 Michel and Crafts or Grosjean, which are examined in my work on the specific gravities of 

 solutions. In a first rough approximation solutions may be regarded as mechanical aggre- 

 gates, and then a general law of their formation may be looked for, but a detailed study 

 of the subject necessitates the search for chemical reactions in them, and such a repre- 

 sentation of the nature of solutions leads to the conclusions enunciated in the first chapter 

 and more fully developed in my above-mentioned work. This naturally does not exclude 

 the desire to find laws to which solutions may be subjected, but under the inevitable 

 condition of the consideration of their chemical composition. Such are, for example, the 

 deductions of Van't Hoff, who does not, however, touch on the specific gravity of solu- 

 tions. With respect to the sp. gr. of weak solutions of metallic chlorides, it may, for 

 instance, be supposed that, having a composition RC1 + 200OHo, they would all have a 

 specific gravity at 15/4 C , approaching to 9951 + 2'585-M, where M is the molecular weight 

 of the metallic chloride dissolved. For instance, for SrCl. 2 , M=158, and the formula gives 

 S = 10861, and experiment 10364 ; for LiCl, M=42'5, and 5 = 10061, and experiment 10060. 

 But similar rules, without the existence of a complete theory of solutions, can only serve 

 as material for the construction of a theory, and too great an importance should not be 

 attached to them. 



19 Generally the specific gravity is observed by weighing in air, dividing the weight 

 in grams by the volume in cubic centimetres, found from the weight of water displaced, 

 divided by its density at the temperature under which the experiment is carried on. If 

 we call this specific gravity S t , then as a cubic centimetre of air under the usual condi- 

 tions weighs about 0'0012 gram, the sp. gr. in a vacuum 8=81^ 0'0012 (S^-l), if the 

 density of water = 1. 



20 If the sp. gr. S 2 be found directly by dividing the weight of a solution by the 



E E 2 



