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Notices respecting New Books. 4<31 



might have been expected from such an author, this " Elementary " 

 work abounds in matter which could only have been produced by a 

 mathematician of the highest rank. The nature of the book is clearly 

 stated in the Preface : — " I have endeavoured, in the following 

 Treatise, to convey as complete an account of the present state of 

 knowledge on the subject of differential equations as was consistent 

 with the idea of a work intended primarily for elementary instruc- 

 tion. It was my object, first of all, to meet the wants of those who 

 had no previous acquaintance with the subject ; but I also desired 

 not quite to disappoint others who might seek for more advanced 

 information. These distinct, but not inconsistent aims determined 

 the plan of composition. The earlier sections of each chapter con- 

 tain that kind of matter which has usually been thought suitable for 

 the beginner, while the latter ones are devoted either to an account 

 of recent discovery, or to the discussion of such deeper questions of 

 principle as are likely to present themselves to the reflective student 

 in connexion with the methods and processes of his previous course." 



We should have been glad if Professor Boole had entered more 

 fully into the difficulties which occur in the application of what are 

 called " Symbolical " methods, and especially in Partial Differential 

 Equations. Considering the very important place held by equations 

 of this class in physical inquiries (those of sound and light, for in- 

 stance) ; considering, moreover, that in the application of symbolical 

 methods to the solution of these equations we meet with some of 

 the most interesting and instructive views of the real nature of these 

 methods, — we cannot but regret that more space has not been devoted 

 to this part of the subject by one who is so well qualified to handle 

 it. We would suggest to tlie author the publication of a supple- 

 mentarj' volume appropriated to " Symbolical Methods " alone, and 

 going fully into the difficulties connected with their application ; 

 not that we expect a complete solution of all such difficulties even 

 from Professor Boole, but because we feel certain that their collec- 

 tion and comparison would bring into notice their mutual depend- 

 ence, and diminish the apparent number of obstacles to be overcome, 

 though unable to conquer them all. In the meanwhile we thank the 

 author most sincerely for placing in the hands of students and teach- 

 ers a treatise so incomparably superior to that of ' Hymers,' or any 

 other elementary book on the same subject with which we are ac- 

 quainted. 



In a future edition the author will doubtless correct a number of 

 errata which occur in the solutions to the ' Examples ; ' but to pre- 

 vent any embarrassment to students who read the book without a 

 tutor, it would be well to supply a list of these errata to purchasers 

 of the present edition. 



