442 Royal Society : — 



plane trigonometry, and algebra. We venture to assert, that' 

 amongst students alread}' acquainted with its merits, this is one o* 

 their favourite text-books ; for the treatment throughout is admirably 

 clear, strict, and elegant,— in fact, such as can be achieved only by 

 one who, besides that perfect mastery of the subject which can only be 

 acquired by original research, possesses also that unacquirable talent 

 of lucid exposition, and is guided by that knowledge of the difficulties 

 usually encountered by students, which experience only can give. 



This third edition is revised and enlarged, and contains many 

 improvements upon the former two, with respect to its type, arrange- 

 ment, and its well-chosen and numerous selection of examples. The 

 student will do well to work all these conscientiously, and to pay 

 particular attention to those interesting chapters on " abridged nota- 

 tion." The last chapter contains a short but clear account of the 

 most important modern geometric methods, amongst which is that 

 beautiful method of reciprocal polars first introduced by Poncelet, an 

 acquaintance with which may be said to form an epoch in the history 

 of every young mathematician. 



The importance of these methods may be estimated from the fact, 

 that in the hands of a Steiner, with scarcely any help from algebra, 

 they have become the most powerful instruments of discovery, and 

 have given him a wonderful insight into the nature and properties 

 of curves ; an insight which is, perhaps, more thorough and direct 

 than any attainable by one who is accustomed to call in the more 

 mechanical aid of algebraic calculation. 



We do not wish here to revive the old and useless discussion on 

 the comparative merits of the algebraic and geometric methods; 

 both have undoubtedly their advantages, and both are indispensable. 

 In the greater part of the present treatise, however, the former of 

 these methods is adopted ; and in drawing attention to the import- 

 ance of the last chapter, we would mei'ely remark, that if his ol)ject 

 be to obtain a thorough knowledge of the properties of conies, the 

 student will do well to combine the two methods to a greater extent 

 than is here done ; for the fact cannot be disputed, that the very 

 facility with which results can be obtained algebraically, may indi- 

 rectly prevent that intimate acquaintance with the properties of 

 curves which a rigid geometrical investigation always secures. 



LXIV. Proceedings of Learned Societies. 



ROYAL SOCIETY. 

 [Concluded from p. 389.] 

 June 21. — The Lord Wrottesley, President, in the Chair. 



THE following communications were read : — 

 " On the Existence of a Magnetic Medium. By T. A. 

 Hirst, Esq. 



In a note on the above su1)ject, communicated to the Royal So- 

 ciety on March 16, 1855, Professor Williamson objects to a certain 



