Stonry— Of the Kinetic Theory of Gas. 355 
the approximation arrived at by the simpler problem is sufficient, 
wherever the errors are of such a nature that they are not cumula- 
tive. Nevertheless, it should be clearly recognized that it is a 
mechanism illustrating nature, and not nature itself, that has been 
mathematically investigated. So it is with all dynamical investi- 
gations: the data of nature have to be simplified to bring the task 
within the range of man’s power over mathematical analysis ; and 
the result is satisfactory because of the important fundamental 
principle referred to above, that in dynamics a slight modification 
of the data furnished by nature may be safely made, because it 
leads only to there being a small difference between the calculated 
result and that which occurs in nature—of course care being taken 
in each case that the approximation of the computed result to 
what occurs in nature shall be sufficiently close for the object we 
have in view. 
These criticisms need to be pressed with special emphasis when 
we are examining investigations into the dynamical condition of 
gases. Here we have to substitute for the data of nature others 
which differ from them in undesirable ways and to an undesirable 
extent, in order to arrive at data simple enough to be available as 
a basis for mathematical deductions. Nevertheless, some of the 
results are not appreciably affected by this too great simplification 
of the data: for instance, those which are consequences of such 
general facts as that the molecules spend most of their time in 
travelling about in straight lines like missiles, without a prepon- 
derance of the kinetic energy of the motions in any one direction ; 
and the further fact that the interchange of energy which occurs 
during the encounters, and the immense number of these encounters, 
leads to a rapid distribution to other motions of any excess of 
energy which any one motion of any one molecule may possess, 
and thus both equalises the pressure throughout the gas, and 
establishes the prevalence of a constant average ratio between that 
portion of the energy which manifests itself in the journeyings of 
the molecules, and that which is occupied in internal motions of 
the Ba class. 
In order to make this language intelligible it is necessary to 
explain that in treating of gases it is convenient to use the word 
motions in a generalized sense, so as to include both motions 
proper and all other events which are brought about by imparting 
