304 Scientific Proceedings, Royal Dublin Society. 
or analogous to those that prevail in the part of nature which is 
illustrated by them. Of this kind is that most useful and simplest 
wave-theory of light which represents it by an undulation of mere 
transverse vibrations. Of the same kind are the various attempts 
to represent the ‘texture,’ which must prevail in the luminiferous 
ether.’ And somewhat akin to these are those instructive 
analogies which can be traced out between different sciences, 
wherever in both the same differential equation governs the 
progress of events. Thus, when a current of electricity is turned 
on to a circuit, the current penetrates the wire from its surface 
towards its core, by the same law as that by which heat would, by 
conduction, be carried inwards from the surrounding dielectrie— 
a process already familiar to us, and which, therefore, makes the 
sequence of events in the other case easily conceived. 
Again it must be remembered that in every dynamical investi- 
gation, what the mathematician really investigates is not the 
problem presented by nature, but some simplication of it. The 
legitimacy of this process and its value depend upon the important 
circumstance that, in dynamics, a slight change in the data leads 
only, at least for a time, to a slight change in the result. Thus in 
computing the mutual perturbations of the planets, the planets — 
may be treated as though they were spheres, made up of untex- 
tured spherical shells each of a uniform density throughout; and 
it may be 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 different molecular texture in each mineral, 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 numberless 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 
difference between the outcome of their joint operation and that 
computed from the greatly simplified data of the mathematician 
is too small to make any approach to being perceived by any 
human agency. Hence, for any purpose which is of use to man, 
1 See these Proceedings, vol. vi. p. 392, or ‘‘ Philosophical Magazine’’ for June, 
1890, p. 467. 
