Transactions of the Cambridge Philosophical Society, 67 
tions of the rules. If Prof. Miller would detach from these mathe- 
matical reasonings a body of Precepts, such as might enable the 
crystaUographer, from proper measurements, to determine the sym- 
bols of the faces of any proposed crystal, putting these precepts in 
such a form that they should be capable of being employed by any 
person conversant mth the processes and symbols of dgebra, he 
would render his work useful to a much wider circle of calculators 
than will, we fear, now venture to apjdy his processes. Nor would 
this addition to the work at all mar the great mathematical beauty 
of matter and style which aU competent judges wdll allow it to 
possess. 
We cannot conclude this brief notice without expressing our satis- 
faction, that this subject of crystallography ,’after being put in so many 
forms for the last half century, has here assumed a shape which, 
so far as mathematical simplicity and symmetry go, leaves us no- 
thing to desire, and therefore no reason for further change. 
Transactions of the Cambridge Philosophical Society, vol. vii. Part I. 
These Transactions have a claim upon our notice, not only from 
their general scientific importance, and especially from their con- 
taining the labours of several of our best British mathematicians, 
but also, in the part now before us, from the peculiar and compre- 
hensive interest of the problems to which most of the memoirs re- 
fer. There are three great problems which at the present time have 
a manifest right to the best exertions which mathematicians of the 
highest class can employ in favour of physical science ; and this 
claim has recently been allowed and acted upon to a great extent 
by the most eminent mathematicians of England, France, Germany, 
and Italy. These three problems are, the motion of waves in water ; 
the undulations of the fluid or fluids by w'hich light, heat, and si- 
milar phsenomena are supposed to be produced ; and the molecular 
forces by which the particles of bodies are held together ; and of 
these, the two latter ones are closely connected with each other. 
All the papers in the present Part of the Cambridge Transactions, 
with one exception (the elegant memoir of Mr. Holditch on Rolling 
Curves), refer to these three problems ; v/hich have also been the 
subject of several investigations in previous parts of the Transac- 
tions. 
On the subject of the first of these three problems, the motion of 
waves in water, we have a memoir by Mr. Green, who had in a 
previous memoir solved the problem of the motion of waves in a 
canal of small variable depth and width ; a case which we believe had 
not been before successfully attacked by any mathematician. In 
the present memoir Mr. Green employs himself upon two or three 
other cases of the general problem, and in particular on the motion 
of w'aves in a deep sea. After solving this case, he adds, “We shall 
be able to deduce a singular consequence which has not before been 
noticed, that I am aware of.” This consequence is, that any parti- 
cle of the fluid revolves continually, (he might have added uniformly ^ 
F 2 
