24 MACGEEGOE ON DENSITY AND 



slightly above 20°C. Wheu the solution had takeu the temperature of 20^* it was at once 

 poured iuto the specific gravity bottle, and the latter stoppered, dried and weighed. The 

 thermometer used had been provided with a table of corrections at Kow. . Weighings for 

 the determination of density were made in one pan only (always of course the same pan), 

 the double weighings for the determination of mass having shown that the ratio of the 

 lengths of the arms of the balance was practically constant. In calculating the densities 

 from the observations, the usual corrections were applied. 



In using tlie determinations of other observers, I fou.ud that in many cases they had 

 not stated whether their published percentages were percentages of anhydrous or of 

 crystallised salt in solution, and that in many cases also they had omitted to state whether 

 their specific gravities were referred to water at the same temperature as the solution, or to 

 water at some other temperature as C^C or 4°C. In the former cases, however, comparison 

 of the observations of différent men usually showed whether anhydrous or crystallised 

 salt was meant. In the latter it was often possible, especially when several observa- 

 tions of dilute solutions were given, to determine the temperature of the water which was 

 taken as the standard substance, by plotting a curve of concentrations against specific 

 gravities, and noting the point of its intersection with the axis of specific gravities. 



In the case of all salts for which the densities of sufficiently dilute solutions have 

 been determined, either by myself or by other observers, I find that up to certain con- 

 centrations, varying from 1 to 5 per cent, of anhydrous salt in solution, the excess of the 

 density of a solution over that of water at the same temperature as the solution, is directly 

 proportional to the percentage of salt in the solution. In symbols, if D^jd, are the 

 densities at the same temperature i of a solution and of water respectively, and if p is the 

 percentage of anhydrous salt in the solution, we have thus 



D,=^d,+ kp, 



where k is a constant for all sufficiently dilute solutions of any one salt. The value of the 

 constant k for any one salt haA'ing been determined, the densities (in grms. per cu. cm.), 

 obtained from the above formula, are found to agree with observed values to the fourth 

 place of decimals within the limits of concentration specified above. 



The following tables give the concentrations and observed densities of dilute solu- 

 tions of a number of salts, together with the densities calculated by the aid of the above 

 formula with the proper value of k. The fourth column gives the differences between 

 the observed and calculated values. The values of the density of water used in these 

 calculations are those given by Volkmann, ' which are based on the observations of 

 Hagcn, Matthiesseu, Pierre, Kopp and Jolly. 



' Wied. Ann. xiv (1881) p. 2C0. 



