of Substances in Solution. 129 



freezing-point measured being thus about o, l. The water 

 into which the diffusion had taken place would at the end of 

 the experiment contain only about 4 molecules of the sub- 

 stance to every 100,000 H 3 0. These proportions had neces- 

 sarily to be modified in several instances, and in such cases it 

 was assumed that, in accordance with Graham's results (in 

 support of which some of the present results may also be 

 adduced), the rate of diffusion varied directly as the number 

 of molecules present in a given volume of solution, or, more 

 roughly, in a given weight of water. 



The determinations were made in two separate series, 

 marked (1) and (2) respectively in Table I., which contains 

 the results. In the first series the temperature varied from 

 12°'l to 15°'3, the time allowed being probably 18 days, 

 the record of the exact time having been unfortunately lost : 

 in the second series the temperature was 16 o, to 18°' 2, and 

 the time was 25 days. Various steps were taken to estimate 

 the magnitude of the probable errors. In the first place, the 

 error due to any disturbance occurring in removing and 

 replacing the glass plate from the inner jar Was found to be 

 inappreciable. A blank experiment in which these opera- 

 tions were performed showed that the solution of cane-sugar 

 wdiich the inner jar contained gave exactly the same freezing- 

 point before and after the operations, i. e. within the 

 estimation-figure of the thermometric reading, which was 

 0*05 millim. or o, 0005. Secondly, in the first series dupli- 

 cate determinations were made with each of the substances 

 cane-sugar, acetic acid, and urea: the differences in the freezing- 

 points of the solutions obtained in each pair were '0011°, 

 •0062°, and '0026° respectively, mean 0-0033°, or about 3 per 

 cent, of the actual decrease measured, a quantity fully 

 accounted for by the difference in size of the jars. Three per 

 cent, in the actual decrease, however, represents only 1*24 

 per cent, in the proportional decrease (or actual decrease 

 -r- mean freezing-point), which is the quantity which is 

 taken to represent the rate of diffusion v ; and an error of 

 1*24 per cent, here will represent an error of 2*4 per cent, on 

 the values of the supposed constant mv 2 . Thirdly, glycerine 

 solutions of the same strength were used in both series, and 

 so also were cane-sugar solutions of nearly the same strength : 

 the relative values for mv' 1 in the two series were 1 : 2'dS6 in 

 the case of glycerine, and 1 : 2"567 in the case of cane-sugar, 

 the difference between the two ratios amounting to only 0*3 

 per cent. 



The results of the diffusion-experiments are given in 

 Phil. Mag. S. 5. Vol. 35. No. 213. Feb. 1893. " K 



