Notices respecting New Books. 475 



rubidium, and under Amides we miss a good many newly discovered 

 " polyammonias." At page 214, however, a paragraph, apparently 

 inserted at the last moment, refers us to Light for a description of 

 the methods of spectrum-analysis ; so that we may hope that other 

 opportunities will be found for supplying, in the course of the work, 

 all similar omissions. 



In conclusion, we have only to say that Mr. Watts is producing 

 a work of which the value will be at once apparent to every chemist, 

 and one which is admirably adapted for use as a book of reference 

 by those who, though not constantly occupied with chemical pur- 

 suits, nevertheless require from time to time to consult some trust- 

 worthy and nearly complete authority on particular points ; while, 

 from the clearness of the style and the fulness of information on 

 many subjects that are hardly treated at all in the common text- 

 books, many parts of his Dictionary may be read with great advan- 

 tage by every chemical student who has already mastered the first 

 rudiments of his science. 



Dual Arithmetic, a New Art. Invented and developed by Oliver 

 Byrne. London: Bell and Daldy, 1863. 



No greater service can be rendered to mathematical science than 

 the facilitation of its ultimate reduction to numerical measurement. 

 Notwithstanding all that has been done to ease calculation, still the 

 actual work of arithmetic remains the great incubus. All prac- 

 tical mathematics resolve themselves ultimately into numbers, and, 

 sooner or later, every practical mathematician has to face the arith- 

 metical labour ; yet there still remains, as a reproach to science, the 

 difficulty of saying whether this ultimate reduction is most feared by 

 those who , to avoid it, take refuge in analysis or in geometry, or by 

 those to whom a superior energy or a different taste gives a mastery 

 over its laborious detail. 



We receive with a satisfaction, altogether independent of its suc- 

 cess, any attempt like the present to place arithmetic on a more 

 compact basis. 



Mr. Byrne has done himself a great injustice by neglecting to place 

 prominently before his reader a distinct and logical statement of the 

 intention and objects of his method, and of the means by which he 

 attains them. We conceive that we shall be doing a service to him, 

 as well as to our readers, by endeavouring partially to supply this defect. 

 We say partially, because we feel that our perusal of a work, the 

 completion of which is avowedly reserved for future treatises, can 

 but imperfectly replace the clear and symmetric idea which exists in 

 the author's mind, and of which, as we must be permitted to say, it 

 is his part to present a clear and symmetric statement to the public. 

 If we fail in reproducing his meaning with exactness, the blame 

 must fall on him, for presenting us with a chaos of rules, examples, 

 and notes, without any logical guide beyond a table of contents. 



Retaining the ordinary decimal system of the Arabic numeration, 

 Mr. Byrne superadds the expression of the whole or a portion of a 



