262 _- REPORT—1862. 
a whole, or in other words the mean motion, in any direction, of the molecules 
in the neighbourhood of a given point, must not be confounded with the 
motion of the molecules taken individually. The medium being continuous, 
so far as anything relating to observation is concerned, the former will vary 
gontinuously from point to point. But it by no means follows that the motion 
of the molecules considered individually should vary from one to another 
according to some function of the coordinates. The motion of the individual 
molecules is only considered for the sake of deducing results from hypotheses 
as to the molecular constitution and molecular forces of the medium, and in 
it we are concerned only with the relative motion of molecules situated so 
close as to act sensibly on each other. It would seem to be very prebable, 
a priori, that a portion by no means negligible of the relative displacement 
of a pair of neighbouring molecules should vary in an irregular manner from 
pair to pair; and indeed if the medium tends to relieve itself from a state of 
constrained distortion, this must necessarily be the case; and such a re- 
arrangement must assuredly take place in fluids. The insufficient generality 
of Cauchy’s equations is further shown by their being absolutely incompatible 
with the idea of incompressibility. We may evidently conceive a solid which 
resists compression of volume by a force incomparably greater than that by 
which it resists distortion of figure, and such a conception is actually realized 
in such a solid as caoutchouc or jelly. 
I have not mentioned the hypothesis of what may be called, from the 
analogy of surfaces of the second order, a central arrangement of the molecules, 
that is, an arrangement such that each molecule is a centre with respect’ to 
which the others are arranged in pairs at equal distances in opposite directions, 
because the hypothesis was merely casually introduced as one mode of making 
eertain terms vanish which are of a form that clearly ought not to appear in 
the expressions relating to the mean motion, with which alone we are ulti- 
mately concerned. 
The arguments in favour of the existence of ultimate molecules in the case 
of ponderable matter appear to rest chiefly on the chemical law of definite 
proportions, and on the laws of crystallography, neither of which of course 
can be assumed to apply to the mysterious ether, of the very existence of 
which we have no direct evidence. If, for aught we know to the contrary, 
the very supposition of the existence of ultimate molecules as applied to the 
ether may entail consequences at variance with its real constitution, much 
more must the accessory hypotheses be deemed precarious which Cauchy 
found necessary in order to be able to deduce any results at all in proceeding 
by his method. There appears, therefore, no sufficient reason @ priort for 
preferring the more limited equations of Cauchy to the more general equations 
of Green. 
‘.. Green, on the other hand, takes his stand on the impossibility of perpetual 
motion, or in other words, on the principle of the conservation of work, which 
we have the strongest reasons for believing to be a general physical princi- 
ple*. The number of arbitrary constants thus furnished in the case in which 
the undisturbed state of the medium is one of freedom from pressure is, as 
has been stated, twenty-one. Professor Thomson has recently put this 
result in a form which indicates more clearly the signification of the con- 
stantst, and at the end of his memoir promises to show how an elastic solid, 
* Whether vital phenomena are subject to this law is a question which we are not 
here called upon to discuss. 
_+ “Elements of a Mathematical Theory of Elasticity,” Phil. Trans. for 1856, p. 481. 
Read April 24, 1856, . Z 
