62 Notices respecting New Books, 



where at the very outset there are numerous shoals and reefs to be 

 carefully avoided, and the success of the voyage depends greatly upon 

 the manner in which it is commenced. To junior masters and pupil- 

 teachers, therefore, Mr. Smith's book will be both acceptable and 

 valuable : alone it will by no means fit them for their duties, but as 

 a guide in the preparation of their own lessons it may be of great 

 utility. 



Of Motion. An Elementary Treatise by John Robert Lunn, M.A., 

 Fellow and Lady Sadleir's Lecturer of St. John's College. Cam- 

 bridge : Deighton, Bell and Co. 1859. 



Mr. Lunn, in his Preface, says, — " My object in the following 

 pages has been to put forth the principles of the science of motion 

 in their true geometrical form, postponing the consideration of 

 force (the properties of which are presumed to have been fully inves- 

 tigated in statics) until the reader may be able to separate in his 

 mind the geometrical ideas from the mechanical. To the fact that 

 these ideas are not kept separate at the outset, I apprehend that the 

 want of clearness in the student's mind about the real investigation 

 that does take place in any case may be attributed." 



We very much doubt whether the difficulties encountered by those 

 who are commencing the study of dynamics are — to any great ex- 

 tent — assignable to the cause here alleged. Nor do we understand 

 how " the properties of force " can be " presumed to have been fully 

 investigated in statics," — seeing that in " statics " only some of the 

 properties of force, and those the least important, are investigated. 

 Nevertheless we doubt not that Mr. Lunn's mode of treating the 

 subject will be useful to some readers, whilst his numerous problems 

 and their solutions will certainly be so to all. 



A Treatise on the Calculus of Finite Differences. By George Boole, 

 D.C.L., Professor of Mathematics in the Queens University, 

 Ireland. Cambridge : Macmillan and Co. 1860. 

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

 Earth. By John H. Pratt, M.A., Archdeacon of Calcutta. Cam- 

 bridge : Macmillan and Co. 1860. 



The name and character of Professor Boole are too well known 

 to our mathematical readers to render it necessary for us to do more 

 than announce this new work of his ■ On the Calculus of Finite 

 Differences.' As an original book by one of the first mathematicians 

 of the age, it is out of all comparison with the mere second-hand 

 compilations which have hitherto been alone accessible to the 

 student. We heartily wish that our elementary books on mathe- 

 matics were more frequently written by men of the rank of Prof. 

 Boole, instead of being left to mere book-makers. 



The work of Archdeacon Pratt " is in part a republication of those 

 portions of" his " work on ■ Mechanical Philosophy ' which treat of 

 Attractions, Laplace's Functions, and the Figure of the Earth ; " but 

 very greatly enlarged and improved. The reader will find new and 

 interesting matter, both in the purely analytical portion and in the 

 physical applications. " It has been my endeavour," says the author, 

 " to put the well-known difficulty in Laplace's analysis, arising from 



