Relations of Liquids and their Saturated Vapours. 83 



of the quotient of the corresponding pressure by z S. The other 

 observations of pressure (under the boiling-point) of hydrobromic 

 ether treated in the same way give points which lie in a straight 

 line AB. Similarly the pressure-observations of hydriodic ether 

 give points which lie in a straight line a b ; and these lines pro- 

 duced meet at n, which is in the line nzl } & perpendicular to z S 

 (the axis of temperature) passing through z. 



§4. In a chart thus constructed, the pressure corresponding 

 to a given point B is equal to the sixth power of B T (the ordi- 

 nate of that point) multiplied by z T its abscissa, and, comparing 

 two points B and b equidistant from the axis, the density is the 

 same at each if the vaporous body is the same ; or the number 

 of molecules in a volume is the same if the vaporous body is dif- 

 ferent. Hence if, in two lines A B, a b, points are taken equidis- 

 tant from z T, the volume of a molecule at one is equal to the 

 volume of a molecule at the other. 



It is also evident, since the lines meet at —274°, that the 

 temperatures of those points, reckoning from z } are in a constant 

 ratio ; e. g., A a being parallel to B b, we have 



cA : ca = aB : db = lG : /G' = tan AGnl : tan ZGW=159 : 177, 



which are the numerical values of the tangents for these ethers. 

 They are denoted generally by the symbol h. 



§ 5. This ratio also dominates over the volumes of the liquid 

 molecules at these respective temperatures ; e. g. the liquid 

 volume of a molecule of the hydrobromic ether at B (being the 

 quotient of its vapour-density by the specific gravity of the liquid 

 at that temperature, and represented by the symbol jjl) is to the 

 liquid volume of a molecule of the hydriodic ether at b as dB to 

 ^ = 159:177. 



§ 6. It has now to be explained how these lines represent the 

 expansion of the respective liquids throughout their range of 

 temperature. 



Suppose we had complete Tables of the expansion of these two 

 liquids, the first having reference to a volume considered as a 

 unit at A, and the second having reference to a volume considered 

 as unity at a ; also let the volumes for each degree in the case 

 of the first liquid be given, and in the second the volumes for 

 each 441 degree be given. The Tables will be found to be 



1 o 9 u . 



identical; and computing the upper limit of temperature for each, 

 it is found that, reckoned from —274°, they are in the ratio of 

 159:177 = A:tf. 



§ 7. It follows also that if =p-r represent the rate of expansion 



1 11. 



per degree at A, jTttd * s tne rate a ^ B, and — = p-r- is also the 



G2 



