Notices respecting Neio Boohs. 151 



they are apt to regard a book like the present as containing little 

 more than a series of manipulations of symbols ; and it is greatly 

 to their advantage to see the results applied to concrete cases. 

 Thus Chap. X. is devoted to the question of approximate quadra- 

 ture in the case when it is effected by ordinates at unequal dis- 

 tances, so taken as to ensure the best result; at p. 128, there is 

 an application of Legendre's functions to the determination of the 

 temperature of a sphere cooling under assigned conditions ; and 

 Chap. XXV. is devoted to similar questions of a more general charac- 

 ter. Still, questions of this kind come in only incidentally, and 

 the student is cautioned that for applications he must look elsewhei'e. 

 The author states that his demonstrations have been carefully 

 chosen so as to bring under the attention of students some of the 

 most instructive processes of modern analysis ; and we may add 

 that students may consider themselves fortunate in having a guide 

 to these subjects who is not only intimately acquainted with them, 

 but willing to expound them in a form well suited to the needs of 

 the learner. 



Solid Geometry. By Peecival Frost, M.A., formerly Fellow of 

 St. John's College, Mathematical Lecturer at King's College. 

 Vol. I. 8vo, pp. 422. London: Macmillan and Co. 1875. 

 This work is the first volume of a second edition of the ' Treatise 

 on Solid Geometry ' published some years ago by Messrs. Frost 

 and Wolstenholme. Owing to the removal of the latter gentleman 

 from Cambridge, the preparation of the present edition has de- 

 volved on Mr. Frost, who has greatly altered the work both in 

 form and substance, and has made additions which bring the first 

 volume nearly up to the size of the original treatise. The subject is 

 one that may be studied either for its own sake by those who are 

 interested in pure Geometry, or for its use in physical investiga- 

 tion. The student who regards it from the latter point of view 

 will find nearly all that he needs in the volume before us, as well as 

 something more ; thus, he might omit the chapter on quadriplanar 

 and tetrahedral coordinates, that on the four-point coordinate 

 system, and a few connected subjects, which occupy in all about 

 one sixth part of the volume. In the remaining five sixths of the 

 volume the subjects are much the same as those contained in the 

 older books — such as were in use in Cambridge twenty or five-and- 

 twenty years ago. Bearing in mind that the volume before us is 

 only about half of the whole work, we obtain in some sort a mea- 

 sure of the enormous progress made by the science of pure Geo- 

 metry within the last three or four decades. 



If we compare what we may call the older part of the volume 

 with Leroy's ' Analyse appliquee a la Geometrie des trois dimen- 

 sions' — a work to which the writers of the older Cambridge books 

 were under great obligations — we shall find not only a great differ- 

 ence in the methods employed, but that incidentally much new 

 matter has been introduced. Thus, even in so elementary a part 

 of the subject as the chapter on planes, several points come under 



