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108 STONEY—UNIVERSE OF REAL EXISTENCES,  [April3, 
ductions from data, in which simpler machinery is intentionally 
substituted for complex operations going on in objective nature. 
Thus, in computing the mutual perturbations of the planets, the 
planets are treated as though they were spheres, made up of untex- 
tured spherical shells, each of uniform density throughout ; and it 
is left out of account that they approach to being spheroids, with 
mountains on their surface, irregularities of a like kind at greater 
depths, rocks in those mountains, minerals in those rocks, a differ- 
ent molecular texture in each mineral involving numberless motions 
among and within the molecules; moreover with tidal strains, heat 
expansions by day, contractions by night, and so on; perhaps seas 
and an atmosphere, vegetation and animals, all in constant and 
complicated movement ; with a multitude of other details. Now 
it is legitimate to omit all these from our calculation, for though 
every one of them produces its effect in actual nature, the differ- 
ence between their joint operation and that computed from the im- 
mensely simplified hypothesis made by the mathematician, can be 
shown to be too small to make any approach to being detected by any 
human appliance. Hence, for any purpose which is of use to man, 
the approximation arrived at by the simpler problem is sufficient, 
wherever the errors are of such a nature that they are not cumulative. 
Nevertheless, tt should be clearly recognized that tt is a model of 
nature—a mechanism tllustrating nature—and not nature tself, that 
has been mathematically investigated. So it is with all dynamical 
1 This has been sometimes overlooked, A recent instance is in a determina- 
tion of the rate‘at which gases escape from atmospheres, based on the insufficient 
data commonly used in the mathematical investigation of such problems, and 
leading to a rate for the escape of helium from the earth’s atmosphere which is 
negatived by observation (see Bryan, on the Kinetic Theory of Atmospheres, 
Phil, Trans. of the Royal Society, vol. 196 A, 1901, p. 1; and Stoney, on the 
behavior of helium in the earth’s atmosphere, Astrophysical Fournal, vol. xi, 
1900, p. 369). 
In such cases it may be difficult, and is sometimes impossible, to put our finger 
on the oversight that has been made. In this instance it may be conjectured with 
some probability that the mistake has been in the tacit assumption that the par- 
tition of energy between the internal and the translational motions of the mole- 
cules takes place with a frequency which warrants our arguing from the supposi- 
tion, tacitly made in the mathematical investigation, that it goes on without inter_ 
mission, There seems reason to believe that this partition of energy actually 
takes place, not at every encounter, but only at encounters as infrequent from 
the molecular standpoint as those that make chemical reaction possible between 
the molecules of a mixture of suitable gases. Now this, in the case of a mixture 
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