86 Mr. J. J. Waterston on certain Thermomolecular 



of pyroxylic spirit and methoxylic ether; there is also evidence 

 that other bodies of a special character belong to it. 



§ 12. There are sixteen bodies, chemically pure, whose lines 

 of expansion, as well as of saturated vapour-density, have been 

 determined. In nine the upper limiting temperature (G), de- 

 rived from the expansion-observations being laid off on the 

 vapour-line, are found to range parallel to the axis of tempera- 

 ture. In three of the sixteen the observations are confined to 

 too small a range and are too irregular to give G with certainty ; 

 but the average of several trials makes it likely that they also 

 conform. Of the remaining four, mercury has its upper limit 

 four times as far removed from the axis as the preceding. 



§ 13. The line of alcohol- vapour does not trend to either node ; 

 it is specially related to the line of water-vapour by crossing it 

 near where it meets the axis. At this p^oint also the lines of 

 sulphuric-acid vapour and hydrates intersect ; hydrated alcohol 

 also. These are the only cases of such axial relation yet deve- 

 loped. The position of the upper limit of expansion of these 

 bodies has not yet been determined. 



§ 14. It is remarkable that zl (fig. 1) is just three times zn. 

 What recondite principle determines this ratio of 1 to 3 ? Why 

 is the vapour-line determined by the sixth root of density? 

 Space has three rectangular dimensions and six rectangular di- 

 rections ; and these ratios continually make their appearance in 

 the dynamical theory of gases, in consequence of the relation of 

 space to resolved forces. It is natural to think that this is the 

 parent of the triad in both cases. 



§ 15. Another relation, differing from the above, is exemplified 

 in two analogous chlorides. The vapour-line of the trichloride 

 of phosphorus, Cl 1 ^ P* (boiling-point 74°), trends to the ether- 

 node (Plate III.) . If the vapour-line of the trichloride of arsenic, 

 CI 1 * As* (boiling-point 134°), trends to the same, we have two 

 lines related as those in fig. J ; but the volume of the liquid mo- 

 lecule of one measured at A is equal to that of the other measured 

 at a instead of being as h : h'. 



Evidence of the Law of Saturated-vapour Density. 



§ 16. The law has reference to density, not pressure, and 

 does not appear subject to deviation. To obtain density from 

 pressure we have to divide the pressure by the temperature 

 reckoned from the zero of gaseous tension, —274°; that is, in 

 cases where the deviation from the laws of Mariotte, Dalton, 

 and Gay-Lussac is too small to be noticed, as it is assumed to be 

 in Hegnault's observations of pressure under the boiling-point. 

 Each observed pressure in millims. was divided by its tempera- 



