

Nature of Solutions. 429 



It was found impossible to draw any of the figures obtained 

 with the help of a bent ruler, except in different sections. In 

 some cases these sections cut each other on prolongation, 

 this is so with the heat of dissolution and the expansion- 

 results ; in others they meet tangentially, this is so with the 

 first differentials of the densities and conductivities ; while in 

 one case, that of the heat-capacities, they do not meet at all. 

 But this want of continuity is probably only apparent. In all 

 cases therefore, except the last mentioned, the whole figure is 

 continuous. The fact that it can only be drawn in separate 

 sections does not prove that it is made up of so many separate 

 curves. This is only rendered probable by the fact that each 

 section is shown by subsequent differentiation to be within 

 experimental error a parabolic curve, and is proved by the 

 fact that all the very different figures representing the differ- 

 ent properties all require to be drawn in the same number of 

 sections, and give the same number of lines for the second 

 differentials, thus showing changes of curvature in the original 

 figures at the same points. 



Prof. Arrhenius attacks me on the subject of this smoothing 

 of the curves, remarking that if "Mr. Pickering had f smoothed ' 

 his curve properly he would evidently have removed these 

 angular points or sudden changes of curvature." The ques- 

 tion hinges on the interpretation of the word "properly." 

 Prof. Arrhenius seems to think that the " proper " amount of 

 smoothing to be made is such that all sudden changes of curva- 

 ture should be obliterated ; and this, too, in an investigation the 

 sole object of which is to ascertain whether there are such sudden 

 changes or not. I must beg to differ from him. The " proper " 

 amount of smoothing I take to be such as w r ill allow but little 

 more error in the experimental points than the known errors 

 of the determinations, or than that which seems to be the 

 probable error according to the irregularities of consecutive 

 points in the figure. If with such smoothing we are led to 

 conclusions which are obviously false, or which are at variance 

 with the results obtained from independent sources, then and 

 then only must we admit some further unknown source of 

 error, and increase the smoothness of our drawings. 



Even excessive and unwarrantable smoothing will not help 

 us in reducing the whole figure to one regular curve, but 

 results only in emphasizing the more marked changes of cur- 

 vature as the less marked ones disappear. This was found to 

 be so even in the case of the curve for the heat of dissolution 

 of solutions from 5 per cent, in strength upwards ; a curve 

 which, of all the instances examined, was that in which the 

 changes were the least marked, and in which the figure 

 presented the greatest seeming regularity. 



