Substances in the Solid State and in Aqueous Solution. 409 



considerable degree of accuracy by the formula 



-i * 



d = l+ — To 

 aq+p 



(a and /3 are two constants given by two experiments). 



Table E shows the agreement of the results obtained by the 



use of the interpolation-formula with the results of direct 



experiment. This table is copied from a publication of a 



research by Dr. Gr. Th. Gerlach*. 



Table E. 

 Experiments of Gerlach on a Solution of Crystallized Citric 

 Acid; t= 15°. 



Weight p in 

 100 parts 



of the 

 dissolved 



body. 



Aq. 

 100— p 



P 



(observed). 



Density 

 (calculated). 



Difference 

 between 



calculated 

 and 



observed 

 result. 



10 

 20 

 30 

 40 

 50 



9 

 4 

 2| 



1-5 

 1 



103916 

 1-08052 

 1-12439 

 1-17093 

 1-22041 



1-080569 

 1-124467 

 1-170950 



0-00005 

 0-00008 

 000003 



We see that the results obtained by use of the interpolation - 

 formula leave nothing to be desired. The three results of the 

 formula in the table have been calculated from two experi- 

 ments, the first and the fifth, which give: — 



a =0-380966 log « = 9-5807654 



= 0-72844 



a +0=1*10941 



The sum (« + /3) has some importance. Suppose that a 

 weighed quantity, say 10 grammes, of pure water, of which 

 the volume at 4° = 10 cubic centimetres and at t° a little more, 

 is added to a concentrated solution. Theoretically three cases 

 can occur: — 



1. The increase of volume of the solution can be exactly 

 equal to the added volume of the pure water : in this case we 

 should have (a + 0) = l. 



2. The increase of volume can be less than the added water; 

 this is the ordinary case. It is then said that the solution is 

 accompanied by "contraction;" in this case we find (a-f/3) 

 greater than 1 ; in general the sum (a + /5) is between 1 and 2. 



3. In the third case the volume of the solution is increased 

 * Specijische Gewichte der gebrauchlichsten Salzlosungen (Freiberg, 1859). 



Phil, Mag. S. 5. Vol. 18. No. 114. Nov. 1884. 2 E 



