410 M. J. A. Groshans on the Specific Gravity of certain 



by a greater quantity than the water which has been added ; 

 (a + /3) would be less than unity. 



Space does not allow of our saying more about the sum 



Instead of considering solution as a combination of one 

 gramme of the soluble body with aq grammes of water, 

 one often prefers to consider it as a diffusion of a molecule 

 part of the soluble substance, or a grammes (a being the 

 molecular weight of the substance in solution) through n 

 molecules of water ; instead of n we will employ the letter A. 

 In this case we can make use of the same interpolation-for- 

 mula, after having modified it in the following manner : — 



Since A = a/18 aq., we multiply both terms a and /3 by 

 a /18 ; the fraction remains unchanged ; and the new inter- 

 polation-formula becomes 



in which v =a/18 «, and X = a/18#. 



(v + \)18/a = a + £. 

 With this formula we have calculated the density of the solu- 

 tion of sugar, C^H^Oji, a = 342, according to the experiments 

 of Gerlach. For the integral values (in round numbers) of 

 A, we have taken, as the basis of our calculations, the two 

 following experiments of Gerlach : — 



Percentage p 

 of sugar. aq. 

 5 19 



A. 



361 



Densities 

 17°-5/17°-5. 

 1-019686 



40 1-5 



28-5 



1-179358 



From which we have 







v = 7-3526 



logv 



= 0-8664411 



X= 12-494 







v + X=19-8466 « + /3= 1*043 



Table F. 

 Solution of Sugar; Gerlach's experiments at 17 c, 5, and 

 Marignac's at 20°. 



Molecules of 

 H a O. 



A. 



Gerlach, 



calculated 



density. 



«!£» 



17°5 



Marignac, 

 observed 

 density. 



d 2 A°. 



20° 



Difference. 

 G-M. 



25 



50 



100 



200 



400 



1-19610 

 11 1765 

 1-06536 

 1-03460 

 101782 



1-19448 

 1-11699 

 106517 

 1-03444 

 1-01770 



+000162 

 000066 

 0-00019 

 000016 

 0-00012 



