130 Mr. J. J. Waterston on the Expansion 



If q I is one-half Q L, the density is g^th, being the sixth 

 power of one-half. 



The proportionate increment of vapour-density for 1 degree is 



represented by the reciprocal of G L, because -r- = — -. Thus, 



suppose lq = ljQ, but^/=|GL, the proportionate increment of 

 density in the vapour represented by the line g I for rise of 1° is 

 double that of the vapour represented by G L, although their 

 densities are equal. 



§ 25. The simplicity of the relation between the proportionate 

 increments of density in the vapour and in the liquid is note- 

 worthy. In the vapour the proportionate increment of density 



is : in the liquid it is - . A numerical example will 



illustrate this. Let #=0° and 7 = 100°, and — =3, and sup- 

 pose £ = 50°. The proportionate increment of vapour-density 

 for 1° is — , or eighteen times that of the liquid ; the first being 

 3%ths, and the second being y^th. When they are equal, 



-(ry — t) = {t-g), or * = 94°-8. Thus, to find the point when 



P 



these proportionate increments are equal, the rule is to divide 



{y—g) by ( — hi J and take the quotient from 7. 



It is remarkable that in alcohol and ether this corresponds 



very exactly with the point of transition. Is the temperature of 



this point always to be thus found ? If so, what is the transition- 



6 48Q 



point of water? 7-^ = 489, -+1 = 20-26; so,^^=24, and 



7-24° = 388° C.A. = 399° CM. 



§ 26. As an example of the mode of laying down a line upon 

 the chart, chloroform may be taken. We have observations of its 

 vapour-tensions by Regnault, and of its expansion by M. Pierre. 



At 60° CM. = 60-48 C.A=f its tension is 738 miliims. 

 At 100° CM. = 100° CA. =t 1 its tension is 2354-6. 



The difference is 0*2178, which, divided by t x — 1 , gives 



