Changes of Curvature by Means of a Flexible Lath. 447 



cent., with a possible error of several units per cent., which 

 error would, however, be considerably diminished if we were 

 not using equations and curves of a complexity greater than 

 the results seem to justify. 



In the case of a feebly marked break of this sort, a single 

 equation will, naturally, bridge it over for a considerable 

 distance ; but the results in columns x. and xi. show that a 

 single curve of the same length as those which I consider re- 

 present the results cannot be applied to this part of the 

 figure without increasing the apparent error, and even if there 

 were no increase in such a case, it must be remembered that 

 this representation could not be accepted, for it would necessi- 

 tate the use of three equations to represent the whole of the 

 figure, whereas two are sufficient, and give results in good 

 accord with the experimental error. 



It may be mentioned that the position of this break (14*4 

 per cent.) corresponds to an exact molecular proportion, 

 3 H 8 2 : 6C 2 H 4 2 requiring 14'3 per cent. This is the only 

 break amongst those investigated in the present communi- 

 cation in which the proportion of dissolved substance is 

 sufficiently large to admit of any statement as to the indica- 

 tion of definite molecular proportions. 



Case III. 



The freezing-points of aqueous solutions of cane-sugar were 

 the subject of investigation in this case, and the experimental 

 values have already been published in the Berichte der deutsch. 

 chem. Gesel. (xxiv. p. 3333), together with some details of an 

 examination both by the graphic and mathematical methods. 

 The two methods were found to agree most fully in showing that 

 one parabolic or bent-lath curve cannot represent the results, 

 but that two such curves, meeting at 2 to 2*5 molecules to 

 100H 2 O (see E F, fig. 1), would do so. The experimental 

 error was found to be 0'023°, and the apparent errors of the 

 representation were as follows : — 



Graphic Method. Math. Method. 

 ... -058° -054° 



Drawn as 1 curve ^E 39-15° 9'5° 



Rel. error 1700 413 



{a 



e -0250° 



sE -0270 



meeting at 2*5 mols. j Rel> QIJ , QV w ^ 



2H2 



~ ( e \J60\J 



„ 2^curves * E . 027Q o . 0257 o 



