Boiling-Points of Homologous Compounds. 377 



fourth column. Finally, for the sake of comparison, are 

 added in the last column the residuals which follow similarly 

 from Young's own formula 



AT = 144-86 T-° ,0148VT . 



The author's differences (being G — 0) have been reversed 

 in sign and also altered by the addition of a small constant 

 (O 0, 4) in order to make their mean value zero, an adjustment 

 practically equivalent to a small change in the initial point 

 assumed. 



A comparison of the fourth, eighth, and ninth columns of 

 Table VII. shows that the representation by three distinct 

 methods is not only equally good, but that after the first 

 term or two it is almost identical in detail. Strictly within 

 the range considered the three formulse are virtually the 

 same, aud it would appear that the common residuals do 

 represent approximately the actual errors of observation 

 reduced to a homogeneous system. On the other hand, the 

 facility w r ith which the series of numbers can be represented 

 in ways mathematically different, makes it impossible to lay 

 stress on any particular functional form or to pass beyond 

 the precise limits covered by the experiments. 



6. It is useful to consider the locus of the points x=n, 

 ?/ = T, as a curve. According to Kopp this curve is a 

 straight line, but the truth of this is at best limited. 

 According to the formulae found in this paper, the curve is 

 more generally parabolic in shape. Again, the locus of the 

 points #=T, y = AT may be considered as a curve. For 

 the normal paraffins it has been shown that this curve may 

 be treated as hyperbolic. Now, according to Young, this 

 curve is approximately the same for all substances which 

 are not associated, so that AT is a function of T only, 

 independent of the particular substance. Let the curves be 

 T=f(n) and AT — $(T), and consider the / curves of two 

 different series. By a displacement parallel to the axis 

 of x (or n) they may be brought into coincidence at some 

 point T. But by Young's law AT, being a function of T 

 only, is the same for both curves. Hence the curves will 

 coincide at the next point, and the next, and so on. Thus the 

 two curves will coincide altogether, and it follows that if 

 the equation of one in its original position is T=f(n), the 

 equation of the other must be T=/(w + a), where a is a 

 constant. This principle should be very useful, but it proves 

 not to be so. The reason for this is that comparatively small 

 errors in AT, if systematic, are fatal to the satisfactory 

 representation of f(n) . The law, though confessedly only 



