Notices respecting New Books. 219 



elementary star-atlas, but that is hardly what is required so much as 

 a series of little simple diagrams giving all the brightest stars in 

 the various districts under examination with the relative positions 

 of the objects to which attention is called. Such diagrams as 

 those given of several of the constellations in Sir E,. S. Ball's 

 i Story of the Heavens ' are what are required, and could be easily 

 and cheaply supplied. "We trust Capt. Noble may see his way to 

 introduce something of the kind in a second edition ; he has 

 already provided for the study of the Moon by an excellent 

 reproduction of Webb's well-known map. 



The book is to a great extent a reprint of papers which 

 originally appeared in the columns of ' Knowledge,' and there are 

 occasionally references to the positions of the planets which were 

 appropriate enough at the time of writing, but which of course no 

 longer apply, and read rather strangely when published in this more 

 permanent form. There are one or two other incidental points 

 which might be criticised : it is to be hoped, for example, that the 

 student will not imagine that the rather rough and ready method 

 on p. 15 for computing the longitude of the Moon's terminator gives 

 it correctly to 0"*1, though certainly it would be excusable for him 

 to draw that inference. But these little flaws are not serious enough 

 to detract from the value of the work as a whole ; it is useful, 

 clear, and practical, and will be of the most essential service to many 

 a young beginner, and, without doubt, will, as its author hopes, 

 prove in many an instance a suitable introduction to works of a 

 more advanced character, such as Webb's ' Celestial Objects.' 



Algebra', an Elementary Textbook for the higher classes of Secondary 

 Schools and for Colleges. By Gr. Chrystal, M.A. Part I. 

 Edinburgh: A. & C. Black, 1886 ; pp. xx + 542. 

 This first part is composed of twenty-two chapters, which treat 

 of the subject of Algebra (and of allied subjects which do not 

 usually come into an Elementary Treatise) under the following 

 heads. 1. Eundamental Laws and processes of Algebra: a valuable 

 introduction which discusses the laws of Association, Commutation, 

 and Distribution, and the properties of and 1, and closes with an 

 interesting historical note. 2 treats of Monomials, the laws of 

 Indices and Degree. 3, with the heading " Theory of Quotients, 

 first principles of Theory of Numbers," lays open to view the 

 fundamental properties of Eractions, treats of prime and composite 

 numbers, and gives several theorems connected with factors and 

 primes. 4 is a most important chapter on distribution of Pro- 

 ducts, elements of the Theory of Rational Integral functions, 

 in which are explained the 2 and t Notations, the principles of 

 Substitution, Homogeneity, Symmetry, and the principle of Indeter- 

 minate Coefficients. This chapter was written "as a suggestion to 

 the teacher how to connect the general laws of Algebra with the 

 former experience of the pupil. In writing this chapter I had to 

 remember that I was engaged in writing, not a book on the philo- 

 sophical nature of the first principles of Algebra, but the first 

 chapter of a book on their Consequences." 5 discusses at some 



