FREE AND PERFECTLY ELASTIC MOLECULES IN A STATE OF MOTION. 57 
on the chart to the abscissa t . The curve traced out by these coordinates is one leg 
of a species of hyperbola. The apex of this hyperbola has its ordinate F'F' (see chart) 
ecpial to the element F in the equation, and the corresponding abscissa is G, which is 
equal to «Jt at this point which is the zero of the vapour. It makes — - — - = 0, 
As the tension of a vapour is excessively small for a considerable range of tempera¬ 
ture above its zero point, the curve, which begins at F', does not sensibly leave the 
tangent at its vertex, F'E,—which is also parallel to the axis at the distance from it, 
F,—for some distance beyond the point of contact. It then takes a sudden bend, 
having the greatest curvature at the point where the tension of the vapour is nearly 
one half the tension of the air, and ascends along the line of vapour converging towards 
it as an asymptote. This curve answers very well to the general run of the experi¬ 
ments on aqueous vapour at low temperatures, and those of Professor Magnus that 
have recently appeared in the 14th number of the ‘Scientific Memoirs’ correspond 
with it almost exactly. 
Are we then to infer from this coincidence that the general divergence from the 
straight at low temperatures is the effect of a minute portion of air that clings to the 
water, in spite of all the precautions taken to prevent it, and that it only becomes 
sensible when the tension of the vapour, per se, has descended to the same attenuated 
proportion ; or is the law that is represented by the general equation of Note B, 
defective to this trifling extent ? 
Although no attempt has yet been successful to give a physical interpretation of 
the function of the temperature that represents the density of a vapour, yet it must 
be considered as a circumstance favourable to the possibility of doing so on the vis 
viva theory, that it corresponds so far with several of the laws of gases or media as 
like them to involve the sixth power of an element of the temperature. Thus in 
XYI. (§ 22) it was shown that when a medium was compressed the vis viva increased 
as the mean molecular distance diminished, or, what is the same, that the sixth power 
of the molecular velocity increased in the same ratio as the density. This actually 
enables the condition of a gas in respect to density and temperature, while dilating or 
being compressed, to be represented on the chart of vapours, and has already been 
referred to in Note B. The physical demonstration of this peculiarity of function 
depends ultimately (as shown in Section III.) on the six rectangular directions of 
space. It seems highly probable, therefore, that the same primary cause shapes the 
function in the case of vapours, and we may thus be led to hope that in the liquid 
condition of bodies their molecules are arranged upon a plan more simple and less 
interwoven with the essential nature of the molecular forces than might otherwise 
have been anticipated. 
In the upper curve, FCS, the ordinates represent the sixth root of the respective 
MDCCCXCII.—A. 
