94 Mr. J. J. Waterston on certain Thermomolecular 



§ 35. The next step is to lay off these values of 7 on the re- 

 spective lines. This has been done on Plate III. and the points 

 marked 7. Considering that the distance of these points from 

 0° depends on the value obtained for P , which depends on the 

 integrity of the second differences of expansion, its mathematical 



d v 



expression being jj-t^ we have to judge whether, if perfect ex- 

 actness had been attained in it and direction of line of vapour- 

 density, they would have ranged in one line parallel to the axis 

 of temperature, except sulphide of carbou. In favour of this 

 there is to be added that if we compute 7 from Pierre's observa- 

 tions on a liquid (e. g. bromine, methyle-bromide, &c.) whose 

 vapour-line has not yet been determined, but which we may 

 judge from analogy is likely to trend to the ether-node, and 

 which we assume to do so by drawing a line from this node 

 through the boiling-point of the liquid and extending it upward 

 to 7, we find invariably that this point ranges along with the 



others. They are marked O7 on Plate III. 



§ 36. The dotted line IG is drawn parallel to the axis at a 

 distance, z l } equal to three times the distance of the ether-node, 

 zn. It will be remarked that it coincides with the average range 

 of the upper limiting points 7, y, &c. 



This closes the evidence of the law of saturated vapour-density 

 and of liquid expansion, — also of the ether nodal point, and of 

 the line of the upper limiting temperatures 7. We now come 

 to the 



Evidence as to Relations of Molecular Volume in different Liquids. 



§ 37. If we draw a line parallel to the axis of temperature 

 intersecting the vapour-lines in the respective points r, r, &c. 

 (Plate III.), it is evident that the molecular density of the re- 

 spective saturated vapours at those points is the same in all 

 (§ 4) ; i. e. the number of molecules in a cubic inch of each is the 

 same in all ; in other words, the volume of the aeriform molecule 

 is the same in all. If we now compute the volume of the liquid 

 molecule at these points or r temperatures, we shall find that 

 they also are quantitatively related to each other in a very in- 

 teresting way. 



§ 38. The vapour molecular volume of a body is the vapour- 

 deusity (i. e. hydrogen 1, oxygen 16, water 9, alcohol 23, &c.) 

 divided by the specific gravity of the saturated vapour at the 

 respective temperatures. The liquid molecular volume is the 

 same vapour-density of the body divided by the specific gravity 

 of the liquid at the respective temperatures. It has now to be 

 shown that in certain chemically allied bodies these latter volumes, 



