Coiidactlult)/ of a Solution of Copper Sulphate. 189 



From this table it will be seen that a. and /3 are fairly 

 constant for all solutions, though perhaps a increases slightly 

 with the concentration. The errors in ^ aie too great and 

 too irregular to indicate any law of variation. Assuming 

 then that a and /? are constant, we find the mean values are, 

 a = 022!) ; (i = 000121. In a the probable error of the 

 result is -OOOo^, or a little less than 2| per cent, of the whole. 

 Although the values of a and /S thus found give the conduc- 

 tivity with ftiir accuracy, yet they fail in one particular. It 

 will be seen on examining the results in the case of the last 

 two solutions, that there is a temperature of maximum con- 

 ductivity somewhere between 90 and 100° C. In previous 

 experiments, however, I got maxima between 90 and 100°, 

 with solutions of 3 and per cent., it being very marked in 

 the latter case. It is possible that there may be a maximum 

 in every case, but generally above 100° C, and that its 

 position may vary considerably with veiy small impurities 

 in the solution, though I do not know what impurity I could 

 have introduced in the one case and not in the other, as in 

 each case I used water distilled in the same way, and salt 

 from the same vessel. 



I should remark that, in calculating a and (3 in the case of 

 the solutions that have a maximum under 100°, I only used 

 the results between 20° and 80°. 



It now remained to determine the law connecting con- 

 ductivity and concentration {k and n). After trying various 

 formuhe and plotting sevei-al functions of k and n, I at last 

 suspected that k varied as some powei- of n, and on taking 

 logai-ithms and plotting them, I found the resulting curve 

 very nearly a straight line, the deviations from it being sucli 

 as might arise from errors of observation. Putting tc ^ a n'', 

 we have log A; = log a + h log n. This is a very simple 

 form to work out by "least squares," and I found the 

 constants were a = -OOiOS, b = -700, the avei-age error 

 being 34 per cent. The general expression for the conduc- 

 tivity thus becomes k = -00403 X ii^'^ (1 + -0229 t - 

 •000121 t^). The curves I, II, and 111 show the relations 

 between the conductivity and temperature for three different 

 solutions, and may be taken as typical. The curves them- 

 selves are plotted from the mean values of the temperatuie 

 coefficients, and the crosses show the actual observations. 

 As I remarked previously, the coefficients are probably some 

 function of the concentration, but my results are not accurate 

 enough to determine it. Curve IV shows the logarithms of 



