JSoticcs respecting New Boohs, 499 



As has been said, five consecutive terms, viz. Aa, Ab, B, 

 Bb, and Be, have been exhaustively treated, and each one has 

 been proved to be incapable of being resolved into fractions 

 with different boiling-points. We believe that the conclusion 

 cannot be resisted that the kerosene series of hydrocarbons 

 mounts by increments of 7 instead of by increments of 14, 

 and we hold that the real atomic weight of carbon is 6 and 

 not 12. 



Laboratory, New Maiden, Surrey. 

 14th April, 1894. 



L. Notices respecting New Books. 



Uniplaxab, Algebra. : being Part I. of a Propedeutic to the Higher 

 Mathematical Analysis. By Irving Stridor" am, Ph.D., Professor 

 of Mathematics in the University of California. San Francisco, 

 the University Press. 



" HPHE logical grounding of Algebra," writes the author in his 



-*- preface, " may be essentially arithmetical or geometrical. I 

 have chosen the geometrical form of presentation and develop- 

 ment." " The point of departure is Euclid's doctrine of pro- 

 portion, the fundamental propositions of which are enunciated 

 and proved in an Introduction (pp. 1-20) in which I have followed 

 the method recommended by the Association for the Improvement 

 of Geometrical Teaching." 



With Chap. I. commences the explanation of the " Laws of 

 Algebraic Operation " as affecting real, or magnitudes involving 

 only the idea of length ; imaginary, including also the idea of 

 turning through a right angle, and complex, embodying length and 

 rotation through any angle. The product is obtained as a fourth 

 proportional to the unit, or " idemf actor " (Peirce), and the factors 

 of that product ; the quotient as a fourth proportional to the 

 unit, the dividend, and the reciprocal of the divisor. Indeter- 

 minate Forms are here introduced, their evaluation being treated of 

 lower down ; combinations of signs, the Associative, Commutative, 

 and Distributive Laws are successively treated of and proved. 

 Logarithms are defined in Napier's manner, treated so as to intro- 

 duce the conceptions of the modulus and base as well as expo- 

 nential, whose Laws — of Involution and the Index — are proved. 

 The law of the interchange of indices and coefficients in Log 

 Operations is called by the distinct name " Metathesis." To con- 

 clude the chapter, Indeterminate Exponential forms are touched 

 on, and a useful synopsis of the matter of the chapter added. 



Chap. II. contains an introduction to the circular hyperbolic 

 and Gudermannian functions, with proofs of some fundamental 

 limits. 



Chap. III. is occupied with " Complex Quantities," represented 



