74 



J. G. MACGEEGOE ON THE DENSITY AND THEEMAL 



On Plate I curves will be found, whose abscissae and ordinates are the temperatures 

 and densities, respectively, of the above tables. They are drawn on a somewhat large scale, 

 and are crowded together that all may be given on one page. To find the density indi- 

 cated by a point on any curve, the ordinate of the point must be added to the number at 

 the left-hand end of the curve. The number at the other end indicates the composition of 

 the solution. The Roman numerals refer to the above tables. By means of these curves 

 the density of any solution at any temperature within the limits of the above experiments 

 maybe approximately determined. I have not thought it worth while to deduce formulae 

 for that purpose. 



The third columns of the above tables shew that (1) the ratio of the densities of any 

 solution of copper suljihate and of water respectively, at the same temperature, diminishes 

 with the temperature ; (2) in the case of some solutions it attains a constant value within 

 the temperatvxre limits of the experiments ; and (3) in the case of others its rate of change 

 with temperature diminishes as the temperature rises, so that it seems as if for them also 

 it would become zero at higher temperatures. These results may be paraphrased thus : — 

 (1) The density of a solution of sulphate of copper diminishes with increase of temperatu.re 

 at low temperatures at a greater rate than that of water ; or the thermal expansion of such 

 a solution is at low temperatures greater than that of water. (2) The higher the tempera- 

 ture the smaller is the difference between the rates of diminution of density with tempera- 

 ture, or the thermal expansions, of the solution and of water. (3) At sufficiently high 

 temperatures, certainly for some solutions and probaljly also for all solutions, the rates of 

 diminution of density with temjierature, or the thermal expansions, of the solution and of 

 water respectively, are the same. 



From the curves of Plate I we can easily determine, by graphical methods, approxi- 

 mate values of the rate of change of the density of a sohition of given constitution with 

 temperature at different temperatures ; and we find that the rate of change of density with 

 temperature increases with the temperature. Thus, taking the solution containing 19.92 

 per cent, of the crystallized salt, we get the following corresponding values : — 



We may also determine, by similar methods, the values of the rate of change of 

 density with temperature for given temperatures and for solutions of different degrees of 

 concentration. Thus, for 20" and 30° C. we have the values of the following tables : — 



