of Water and other Liquids. 401 



or not, consisted in applying to the experimental points of 

 which it was composed a ruler bent by the hands, and ascer- 

 taining whether the whole figure could be drawn in one 

 section, or whether it could only be drawn in several inde- 

 pendent sections. The mere fact of the latter being the case 

 did not prove that there was any real change of curvature at 

 the point where two sections met, it simply suggested the 

 possibility of this being the case : this possibility was, how- 

 ever, converted, in my opinion, into certainty, by finding that 

 each of these sections was a simple parabola (although a ruler 

 may be bent to form curves of a non-parabolic nature) ; by 

 finding that some seven or eight different curved figures of 

 totally different characters, and representing, either different 

 properties, or the same property under different conditions, 

 all gave indications of changes of curvature at the same points; 

 and by finding that these points certainly corresponded to 

 definite hydrates, wherever the solutions were strong enough 

 to permit of such evidence being obtainable. 



The culminating proof, however, of these changes of cur- 

 vature, and of the hydrates which they represent, has been 

 obtained from the law of the freezing-points which I have 

 formulated, and which has reduced the proof of their existence 

 to a mere question of mathematics (Chem. Soc. Proc. 1889, 

 p. 149). So far as I have gone at present, every one of the 

 hydrates which the changes of curvature indicated has been 

 established beyond all reasonable doubt. 



Such results afford conclusive proof of the validity of the 

 method which I used to recognize these changes of curvature, 

 and justify me in publishing the results of a similar treatment 

 of the curves representing the density of water at different 

 temperatures, although the changes shown by them are much 

 more doubtful than in the majority of the cases previously 

 examined, and although there is little or no evidence from 

 any other source available for confirming their existence. 



In an examination of the effect of temperature on the densi- 

 ties of sulphuric-acid solutions (Journ. Chem. Soc. 1890, p. 120), 

 I determined the value of the water-contents of a 25 cubic 

 centim. bottle at every 2° between 6° and 38° (for the method 

 see ibid. p. 69) . The results, which are given in Table I., when 

 plotted out (fig. 11, Plate VII., which, however, does not show 

 the whole of them), suggested the existence of some change of 

 curvature at about 18° : on differentiating the experimental 

 values, a differential (dwjdt in Table 1.) was obtained which also 

 suggested a change at this temperature, though a change of a 

 very doubtful nature : this differential is shown in fig. 1, 

 Plate VII., and appears to consist of two nearly straight 



