Stoney — Appreciation of Ultra- Visible Quantities. 533 



■measure by taking into account the degree in which the gas falls 

 «hort of being " perfect, " i. e. of accurately fulfilling the law 



pv_ _ _T_ 

 p^'~Y' 



where p is pressure, v volume, and T absolute temperature. 

 Judged in this and other ways, it appears that the average interval 

 between the molecules of any of the more perfect gases, when at 

 atmospheric pressures and temperatures, is something like the 

 ordinate of our gauge at the distance of one centimetre from its 

 apex. ^ If the vacuum in a Sprengel pump be carried so far as to 



be effected by expanding tlie gas, and will decrease if S (the distance within which the 

 molecules sensibly act on one another) is increased, which may be effected by exchanging 

 one gas for another. It is, in fact, a function of these two quantities and of others, 

 viz. of the velocities of the molecules (the mean of the squares of which is known from 

 the pressure and density of the gas), of the events that occur in the struggle of two 

 molecules with one another during their brief encounters, and of the time occupied by 

 these struggles. 



The events that occur during the encounters and the time they last are not suffi- 

 ciently known for the actual equation to be set down : but hypotheses can be framed in 

 regard to them — as for instance that the molecules when they encounter simply rebound 

 like hard elastic globes — which enable us to ascertain -what function c/a would be of 

 Sj<T if the hypothesis were true, and thus enable us to judge what kind of magnitudes 

 S and a- are. 



The quantities A. and S vary within wide limits from gas to gas ; but it is one of the 

 elementary propositions in the kinetic theory of gases that <r (which may be called the 

 average spacing of the molecules) is nearly the same in all nearly "perfect" gases 

 when compared at the same pressure and temperature. This is, in fact, the truth that 

 underlies and gives its value to Avogadro's erroneous hypothesis that at the same 

 temperature and pressure the size of the gaseous molecules of all substances is the same. 

 In the present state of science it is desirable that every practicable effort should be 

 made to determine with more exactness the value of this important physical quantity. 



1 Fhilosophieal Magazine, August, 1868, p. 140. If we assume, as in the text, that the 

 molecules of a gas at, say, 21° C. and 760 mm. pressure, are as numerous within a given 

 ■space as would be a number of points cubically disposed at intervals of a ninthet-metre 

 asunder (this being the ordinate of our gauge at the distance of one centimetre from its 

 apex) ; then the number of molecules of the gas in every cubic millimetre of its volume 

 is a uno-eighteen — the number represented by 1 with eighteen O's after it. Hence, in a 

 litre of the gas there will be a million times more, i.e. a uno-twentyfour of molecules. 

 Now at the above-mentioned temperature and pressure a litre of hydrogen weighs just 

 one-twelfth of a gramme ('083'). Hence the mass of each molecule is the twenty- 

 f ourthet of this (i.e. the fraction represented by 1 in the numerator, and 1 followed by 

 twenty-four O's in the denominator), i.e. it is = 8-3' xxvi^'^ of a gramme; and accord- 

 ing to this computation the chemical atom of hydrogen, being the semi-molecule, has 

 as its mass 4*16' xxvi^*^ of a gramme. This is probably somewhere in the neighbour- 

 hood of the true value ; so that we may regard the mass of a chemical atom of hydrogen 



2T2 



