Transactions of the Camhi^idge Philosophical Society . 67 



tions of tlie rules. If Prof. Miller would detach from these mathe- 

 matical reasonings a body of Precepts, such as might enable the 

 crystallographer, 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 with the processes and symbols of algebra, he 

 would render his work useful to a much wider circle of calculators 

 than will, we fear, now venture to apply his processes. Nor would 

 this addition to the work at all mar the great mathematical beauty 

 of matter and style which all competent judges will 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 which light, heat, and si- 

 milar phaenomena 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 

 Curv'es), refer to these three problems ; which 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 waA-es in a deep sea. After solving this case, he adds, "We shall 

 he 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, 



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