Boiling-point as related to Chemical Corjiposition. 175 



y - ft*-*) 

 ,y I+7O — c) 9 



where c is the value of x to which 0° C. in either case corre- 

 sponds. 



4. If in this equation we make x exceedingly large, the 



8 



value of y will become - , a definite quantity, being the melt- 

 ing-point or boiling-point of the infinite olefine of the series. 



In a memoir on Cumulative Resolution * I have already 

 pointed out that the only series in which Kopp's, or the linear, 

 law of boiling-point can have any chance of rigorously hold- 

 ing good is in that of the olefines. It will be found in the 

 sequel that that law does not in fact hold good for the only 

 actual olefines at present admitting of seriation as to boiling- 

 point. As is, however, common with the points at infinity 

 of chemical curves, the infinite olefines are characterized by 

 great simplicity in their physical relations; not only their 

 boiling-points, but their melting-points also are multiples by 

 whole numbers of certain fundamental constants. 



In the following sections reference is made to those series 

 alone which end in infinite olefines. For this reason various 

 aromatic series (which as a rule terminate w T ith infinite methyl) 

 are not considered. 



5. The work of actual calculation of the numerical con- 

 stants in the equations adduced below calls for no special 

 remark. It may, however, save trouble to subsequent com- 

 puters if I point out the means of obtaining the important 

 constant c. This is often reasonably obvious on inspection. 

 A value thus surmised is accordingly substituted for c, a new 

 constant ot added to the numerator of the equation; and, from 

 three or more points, the values of a, /3, and 7 are determined. 

 The numerator is next equated to 0, and the value of x thus 

 found is used instead of e in a second approximation. 



Three or four approximations are in general sufficient to fix 

 the value of c, thereby reducing that of a to zero. 



When it is hardly possible by inspection to frame a pre- 

 liminary opinion as to the position of c, Taylor's series will 

 be found very useful in starting the approximation. 



Melting-point. 



6. The melting-points selected for treatment have all been 

 taken from easily available sources, and are most of them very 

 well known. I have therefore not thought it advisable to 



* Phil. Mag. [5] iii. p. 498. 



