865 



the conditions of climate, which are found to vary so greatly even 

 in the same latitude and at the same elevations, and affect so im- 

 portantly all organic creation. The generalization of a vast mass 

 of material has been ably carried out, and in the true spirit of Induc- 

 tive philosophy. 



The first volume of a great work by the distinguished philosopher 

 Dr. G. S. Ohm has just reached us : he calls it his Molecular Physics, 

 and dedicates it to the Royal Society as an acknowledgement of his 

 obligations to us, for that praise and encouragement which sustained 

 him in his arduous labours. He received the Copley Medal in 1841 . 



While science has progressed abroad, at home it has not remained 

 stationary. Sir William Hamilton's daring conception of a new 

 system of imaginaries, and the successful application which he has 

 made of it to the Geometry of three dimensions, have, as might have 

 been expected, given rise to other speculations of the same nature. 

 The first of these fruits of the theory of Quaternions was the triple 

 algebra of Professor De Morgan (Cambridge Philosophical Transac- 

 tions, 1847). The aim which the author proposed to himself was to 

 frame systems of imaginary trinomials, in which the rules of operation 

 should be the same as in ordinary algebra ; and accordingly he makes 

 it an essential condition that the commutation property of multipliers 

 (abandoned in the theory of Quaternions) should be maintained. 

 The memoir is highly suggestive. The general and analytical cha- 

 racter of the author's treatment of the subject adds much to its in- 

 trinsic interest. The subject is however regarded on the algebraic side ; 

 and the question of geometric interpretation is hardly considered. 



Professor Graves, on the other hand, has taken up the problem of 

 the imaginary trinomials in its geometrical aspect (Proceedings of the 

 Royal Irish Academy 1 845) ; his object being " to frame for the Geome- 

 try of three dimensions a theory strictly analogous to that by which 

 Mr. Warren has succeeded in representing the combined lengths and 

 directions of right lines in a plane." The new distribution symbols 

 of operation employed by Mr. Graves are imaginary cube roots of 

 positive unity. His system is closely allied to one of those proposed 

 by Professor De Morgan, but appears to lend itself more readily to 

 geometric interpretations. 



This part of the subject comes under the head of " Symbolical 

 Geometry," — a science, the first step of which was made by M. Ar- 

 gand, in the geometrical interpretations of the sign +, and which 

 Sir William Hamilton has done so much to mature and perfect, in 

 connection with his theory of Quaternions. 



A symbolical method differing in many of its details has been re- 

 cently proposed by Professor O'Brien (Cambridge Philosophical 

 Transactions, 1847), and exemplified in its application to the theory 

 of the vibratory motions of an elastic medium. 



The department of applied mathematics, which appears to have 

 made the most important advances within the last few years, is the 

 theory of the motions of fluids and elastic solids. The theory of 

 fluid motions had until recently been restricted by the hypothesis, 

 that the action of two adjacent elements was normal to the separating 



