Notices respecting New Books. 213 



The absolute differences may be entirely referred to possible 

 errors in the weighing. We may observe that the values of the 

 chemical equivalents themselves are not determined with greater 

 accuracy, for if we only admit 395 "1 as the equivalent of cop- 

 per instead of 395*6, the law is mathematically verified by the 

 average of these experiments. 



Conclusion. — The weights of copper, hydrogen and silver, 

 separated by the same electrical current, are in proportion to the 

 chemical equivalents of these bodies, and Faraday's law is veri- 

 fied within the hmits of errors of observation. 



XXVI. Notices respecting Neiv Books. 



A Treatise on the Calculus of Operations. By the Rev. Robert Car- 

 MicHAEL, A.M., Fellow of Trinity College, Dublin, and Member of 

 the Royal Irish Academy. London : Longman, Brown, Green, 

 and Longmans. 1855. 



''PHIS is a work which will be welcome to every mathematical 

 -*- student, for it will, in a great measure, supply a want which 

 has long been felt. The Calculus of Operations ranks amongst the 

 most important improvements which modern mathematicians have 

 introduced. It originated in a profound investigation of the essential 

 nature of all existing operations, whereby it was found, that, although 

 they differ considerably in their objects, they have nevertheless so 

 much in common that the results obtained by one operation may, 

 with a few modifications, be translated into the language of another ; 

 that each, in fact, is a particular interpretation of far more general 

 results, which are susceptible of an unknown number of interpre- 

 tations. 



A wide field of discovery is thus opened to the mathematician. 

 Not only are operations in differential calculus, in integral calculus, 

 and in the calculus of finite differences, in some cases, immensely 

 facilitated, but an intimate relation between these operations is esta- 

 blished, and the key obtained to still higher and more complicated ones. 



Such being the importance of the subject, no doubt can be enter- 

 tained that the calculus of operations might be introduced into our 

 elementary course of instruction at a far earlier period than it is at 

 present; but in order to do so, its elementary principles must be 

 first demonstrated with all that lucid precision and completeness 

 which is necessary to interest and carry conviction to the young 

 student, and thus enable him to employ the calculus with confidence 

 and facility. This is scarcely the object of the book under review. 

 The author has furnished an admirable text-book to those who are 

 already, to some extent, acquainted with the calculus. He has stu- 

 diously avoided "all prolixity of detail as alike unnecessary and 

 ■wearisome " to them, but we may add, important and not neces- 

 sarily wearisome to the less advanced student. To such intentions, 



