68 Notices respectiny New Books, 



him up to easy problems producing simple equations. For instance, 

 such a question as the following occurs very early in the book : — 

 " A and B began to play with equal sums ; A won 30 shillings ; and 

 then 7 times A's money was equal to 13 times B's : what had each 

 at first ? " But before letting the learner try such questions, he is 

 set a number of exercises like the following : — If x stand for a num- 

 ber of shillings, and if A has 13 shillings and B has 21 shiUings, 

 (I) what will A have after spending x shillings? (2) What will B 

 have if he receive twice as many shillings as A has spent ? (3) If A 

 receives x shillings from B, how many will each have ? and so on. 

 On the whole the book seems very well done ; and the large number 

 of examples which it contains will doubtless make it useful to 

 learners, who are at first mainly concerned to acquire a sort of me- 

 chanical ease in manipulating algebraical expressions. 



A Treatise on Attractions, Laplace's Functions, and the Figure of the 

 Earth, By John H. Pratt, M.A., F.R.S., Archdeacon of Cal- 

 cutta, Fourth edition. London and New York : Macmillan and 

 Co. 1871. Crown 8vo. Pp. 245. 



The third edition of this book was the subject of a rather long 

 notice in our pages (vol. xxxi. pp. 144-149); we shall therefore limit 

 our notice of the present edition to making mention of the chief 

 points in which it differs from its predecessor. These are three in 

 number: — (1) The chapter which treats of the Attraction of Table- 

 lands, Mountains, &c. has been greatly enlarged. The author 

 has introduced a discussion of certain formulae for calculating the 

 effect of variations in the density of the earth's superficial mass, which 

 formed t]]e subject of a pamphlet written by him in 1868. (2) The 

 chapter which treats of the Earth considered as a Fluid Mass has 

 been modified to bring it into accordance with the author's recogni- 

 tion of the fact that the variations of the force of Gravity on the 

 Earth's surface are not in themselves sufficient to prove that the 

 earth was originally fluid. (3) In the section on the determination 

 of the mean figure of the earth, supposing it to be spheroidal, the 

 author gives at much greater length than in the earlier edition his 

 views of the best method of deducing the mean value of the Axes of 

 the Earth from the principal measured long arcs, viz. the Anglo- 

 Gallic Arc, the Kussian Arc, and the Indian Arc. The substance of 

 this addition appeared in our pages (vol. xxxiii. p. 10). Besides 

 these there are several minor alterations, the result of the whole 

 being to increase the volume by 83 pages. The preface is dated 

 Calcutta, November 8, 1871, not long before the author's death; 

 this date, compared with that of the second edition of the author's 

 Treatise on the Mathematical Principles of Mechanical Philosophyj 

 (October 5, 1841), shows that his life in India extended over more 

 than thirty years ; and when we remember that his scientific pursuits 

 were entirely additional to his professional duties, that they were 

 pursued under the disadvantage of the climate of Calcutta, involved 

 laborious calculations, and were continued up to the end of his life, 

 we cannot but regard the composition of the volume before us as a 

 striking instance of devotion to science. 



mam 



