128 SCIENCE PROGRESS 



to the method which was used to demonstrate the presence 

 of the hydrates. In order to bring out the changes of cur- 

 vature due to hydrate formation, Mendeleef had introduced 



the method of plotting the first differential co-efficient -^ of the 



dp 



density 5 against the percentage composition p. The result, in 



the case of sulphuric acid, was a series of five straight lines 



of varying inclination, which did not intersect but "jumped" 



at the points corresponding with the composition of the four 



hydrates. But as Arrhenius pointed out {Phil. Mag. 1880, 28, 



33), the same differential co-efficients had; been plotted by 



Mendeleef himself two years previously {Ber. 1886, 16, 386) 



as a pair of intersecting curves. It was therefore natural to 



conclude that the existence of the breaks was to a large extent 



a matter of opinion. 



This impression was considerably strengthened when 



Pickering, using fresh experimental data, was led to deny 



altogether the existence of the five straight lines on which 



Mendeleef had relied for the proof of his theory, and plotted 



the first differentials as a single curve, continuous from end to 



end. By differentiating this curve a second time he obtained, 



however, a second set of points which he considered might be 



represented by a series of eleven straight lines. This second 



differentiation was made the subject of very severe criticism. 



Owing to the existence of experimental errors it could only be 



carried out after " smoothing " the curve formed by the first 



differentials — a process that was evidently accompanied by 



considerable risk and a certain amount of arbitrariness. 



Moreover, even when the second differentials were plotted, 



many of the " breaks " were so insignificant that it would have 



been easy in many cases to join by a single curve points which 



were supposed, in accordance with the hydrate theory, to 



lie on a series of straight lines. It was therefore possible 



that the breaks in the curve of the second differentials, like 



those in Mendeleefs curve of the first differentials, were due 



to errors of measurement which might be eliminated by 



further improvements in the experimental methods. Nernst, 



indeed, in a contemptuous criticism of the " so-called " hydrate 



theory {Theoretical Chemistry, p. 445), went so far as to say 



that the readiness with which breaks were found was dependent 



mainly on the inaccuracy of the observations, and that the 



