454 Notices respecting Neiv Boohs. 



combined with an amount of turning " (A, axis a), viz. a = a a, 

 index A. It " may be expressed as the sum of two components 

 one of which has an indefinite axis and the other the same 

 axis as the Quaternion": viz. if A is less than a quadrant, 

 a=« (cos. A. a, index O + sin. A. a, index ir/2). Here it may 

 be of interest to recall Hamilton's original definition as given 

 in the Phil. Mag. for July 1844, viz.: Q,=w + ix+jy + Jcz, where 

 i 2 = — 1 . . . ij= —ji=Tc . . . and no linear relation connects i, j, Tc. 

 The later definition (adopted in the ' Lectures ' and ' Elements ') 

 of a Quaternion as the operator which changes one vector into 

 another, is not the same thing exactly, Prof. Macfarlane explains, 

 as the quotient of two vectors. Sums and Products of Quaternions 

 are then dealt with and " Quaternion Exponentials." " Scalar 

 Differentiation,"" Matrices," " Vector Differentiation," and " Gene- 

 ralized Addition " occupy the concluding fifteen pages of what is 

 thus a tolerably complete monograph on the bases of the Calculus 

 written from the poiut of view which commends itself to the 

 author. That all his readers will be prepared to adopt these 

 views can scarcely be hoped — quot homines, tot sentential being 

 apparently the rule here too. But Prof. Macfarlane has con- 

 tributed an interesting and well thought-out essay to the small 

 stock of Quaternion literature. J. J. W. 



Watts' Dictionary of Chemistry. By H. Eoestee Morley, M.A., 

 D.Sc, and M. M. Pattison Muir, M.A. Vol. III. London : 

 Longmans, Green, & Co., 1892. 

 This third volume of the new edition of Watts' Dictionary of 

 Chemistry, by Dr. Morley and Mr. Muir, shows no falling off 

 in quality as compared with the preceding volumes, which have 

 already been noticed in the pages of this Magazine. The work 

 extends to 856 pages, and comprises references and articles under 

 the letters I to P inclusive. Among the longer articles, that on 

 Iron, by Mr. Muir, occupies 14 pages, and is followed by a useful 

 article on the Iron Group of Elements by the same author, who 

 summarizes the chief properties and relationships of Iron, Man- 

 ganese, Cobalt, and Nickel in the course of 3 pages. 



The subject of Isomerism is treated of by Dr. Armstrong in 

 about 9 pages, an amount of space w 7 hich hardly enables the 

 author to do full justice to this all-important topic. It is to be 

 regretted that under this restriction so much space is devoted to 

 the historical treatment. The author has, however, managed to 

 compress a very large amount of information into the space allotted 

 to him. He criticises adversely the recent stereochemical develop- 

 ments of the theory of isomerism by Wislicenus and others. None 

 of the objections urged against these views appear to us, however, to 

 be fatal, and whatever decision may be arrived at as the result of 

 future investigation it cannot be denied that the extension of the 

 Le Bel-Van't Hoff hypothesis, by Wislicenus, Victor Meyer, &c, 



