90 PROFESSOR TAIT ON THE 



It is treated, in fact, just as it would then be if all the others were reduced to 

 massive points. 



The value of the term in the virial is 



1 ns2(R) 



because, though every particle suffers the above average number of collisions, 

 it takes two particles to produce a collision. This is equal to 



— np7rs' i = —6p (sum of volumes of spheres) ; 



so that the virial equation becomes 



o 



nVv-/2 = — p(V— 4 (sum of volumes of spheres)). 



which, inform at least, agrees exactly with Amagat's* experimental results for 

 hydrogen. 



These results are closely represented at 18° C. by 



p(V- 2-6) = 2731; 

 and at 100° C. by 



^(V-2-7) = 3518. 



The quantity subtracted from the volume is sensibly the same at both 

 temperatures. The right-hand members are nearly in proportion to the absolute 

 temperatures. The pressure is measured in metres of mercury. Hence the 

 volume of the gas, at 18° C. and one atmosphere, is (to the unit employed) 



2-6 + 2731/0-76 = 3596 nearly. 



Thus, by the above interpretation of Amagat's results, we have at 18° C. 



nirs* = 3-9/3596. 



Clerk-Maxwell, in his Bradford Lecture, \ ranks the various numerical 

 data as to gases according to " the . completeness of our knowledge of them." 

 The mean free path appears in the second rank only, the numbers in which are 

 regarded as rough approximations. In the third rank we have two quantities 

 involved in the expression for the mean free path, viz., the absolute diameter 

 of a particle, and the number of particles per unit volume (s and n of the pre- 

 ceding pages). 



To determine the values of s and n separately, a second condition is 

 required. It has usually been assumed, for this purpose, that the volume of a 

 gas, " when reduced to the liquid form, is not much greater than the combined 

 volume of the molecules." Maxwell justifies this assumption by reference to 

 the small compressibility of liquids. 



* Annates de Chunk, xxii. 1881. f Phil. Mar/., 1873, ii. 453. See also Nature, viii. 298. 



