424 Mr. S. Lupton on the Reduction of 



where mean values must be taken for the differences of x, 

 which are usually small. 



These somewhat long preliminaries form a basis for the 

 discussion of the recent application of the graphical method 

 to the theory of solution. 



In an account of the nature of solution having special 

 reference to ethyl alcohol (Journ. C. S. 1887, p. 778), Mende- 

 leeff propounded the idea that, if solutions are regarded as 

 strictly definite atomic chemical combinations at temperatures 

 higher than their dissociation-temperatures, the expression for 

 density u as a function of the percentage composition x must 

 be a parabola of the second order, or it may be represented by 

 the general equation 



u = a + bx-rcx' 2 . 



Between two definite compounds, which exist in solution, we 



must expect that the differential coefficient -7- = b + 2cx will 



be a rectilinear function of x. This consequence can in the 

 first place be verified by experiment, and secondly <>ives the 

 means of ascertaining what are the definite combinations 

 existing in solution. The hypothesis has been proved to be 

 correct, and up to this time 1 have not met with a single ex- 

 ception. 



It seems then that Mendeleeff assumed a certain form 

 of equation; collected experimental results, from other ob- 

 servers in many cases, to determine the constants ; and 

 found that the equation fairly represented the results of 

 experiments. He then differentiated, replaced the differential 

 coefficient by a new ordinate, plotted the results, and found 

 that they were represented by straight lines. He assumed 

 that the intersection of these straight lines showed a change 

 in the nature of the dissolved substance which could only be 

 the formation of another hydrate. 



This method may be valid if the experimental results can 

 prove the equation to be absolutely and not only approximately 

 true. Mr. Pickering, however, made use of an entirely 

 different method, and says : — " My conclusions as to the 

 first differential of the densities are in direct opposition to 

 MendeleeffV (Journ. C. S. 1890, p. 79) ; and even more 

 emphatically in Phil. Mag. xxix. p. 433 : — " I altogether dis- 

 agree with Mendeleeff 's views as to the nature of the density 

 first differential." 



Considering that Mendeleeff 's results were not sufficiently 

 numerous or accurate to support such an important con- 

 clusion, Mr. Pickering undertook a laborious research on the 



