OF GASES AT HIGH EXHAUSTIONS. 
433 
cooling, an increase of exhaustion from 20 M to 2 M retarding the carriage of heat 
more than all the previous exhaustion from 760 millims. to 20 M. 
716. I have shown elsewhere'" that the property of gaseity is pre-eminently a 
property dependent on collisions. A given space full of air at the ordinary pressure 
contains millions of millions of molecules rapidly moving in all directions, each molecule 
momentarily encountering millions of other molecules in a second. In such a case 
the length of the mean free path of the molecules is exceedingly small compared 
with the dimensions of the containing vessel, and those properties are observed which 
constitute the ordinary gaseous state of matter—-properties which depend upon 
constant collisions. 
The gaseous state continues so long as the collisions are almost infinite in number 
and of inconceivable irregularity. But in such high vacua as I now describe the free 
path of the molecules is made so long that the hits in a given time may be disregarded 
in comparison to the misses, and the average molecule is allowed to obey its own 
motions or laws without interference ; and when the mean free path is comparable to 
the dimensions of the containing vessel, the properties which constitute gaseity are 
reduced to a minimum, and the matter then becomes exalted to an ultra-gaseous state. 
In the ultra-gaseous state properties of matter which exist even in the gaseous state 
are shown directly, whereas in the state of gas they are only shown indirectly, by 
viscosity and so forth. 
717. The ordinary laws of gases are a simplification of the effects arising from the 
properties of matter in the ultra-gaseous state; such a simplification is only permissible 
when the mean length of path is small compared with the dimensions of the vessel. 
For the sake of simplicity we make abstraction of the individual molecules, and feign 
to our imagination continuous matter of which the fundamental properties—such as 
pressure varying as the density, and so forth—are ascertained by experiment. A gas 
is nothing more than an assemblage of molecules contemplated from a simplified point 
of view. When we deal with phenomena in which we are obliged to individually 
contemplate molecules, we must not speak of the assemblage as gas. 
718. An objection has been raised touching the existence of ultra-gaseous matter 
in highly exhausted electrical tubes, that the special phenomena of radiation and 
phosphorescence which I have considered characteristic of this form of matter can be 
made to occur at much lower pressures than that which exhibits the maximum effects. 
For the sake of argument let us assume that the state of ultra gas with its associated 
phenomena is at the maximum at a millionth of an atmosphere. Here the mean free 
path is about 4 inches long, sufficient to strike across the exhausted tube. But it has 
been shown by many experimentalists that at exhaustions so low that the contents 
of the tube are certainly not in the ultra gaseous state, the phenomena of phospho¬ 
rescence can be observed. This circumstance had not escaped my notice. In my first 
paper on the “ Illumination of Lines of Molecular Pressure and the Trajectory of 
* Proc. Roy. Soc., No. 205, 1880, p. 469. 
