522 



Gentlemen, had the pleasure of seeing this autumn in England, 

 should not be still among us, that I might have the opportunity of 

 bestowing it in person. 



Mr. Daniell, 



I beg to present to you the Copley Medal for your friend Signor 

 Matteucci, which has been awarded to him by the Council of 

 the Royal Society for his important discoveries in the magnetic 

 electricity of animal nature. 



These discoveries, so singular and so new in themselves, appear to 

 promise results of the highest importance, not only in theoretical 

 science, but also in its practical application to the relief of pain and 

 the cure or alleviation of disease. Whatever may, however, be their 

 ultimate result, the scientific world must ever retain the liveliest 

 sense of the merits of Signor Matteucci, and must ever consider him 

 as adding new lustre to the glory that a Galvani has already given 

 to their common country. 



Mr. Christie, 



I have to beg that you wall take charge of the Medal for Mr. 

 Boole, awarded to him for his important papers on a General Method 

 of Analysis, published in our Transactions for the present year, con- 

 taining matter as useful as it is original, and classifying and com- 

 prehending analytical operations*. That Mr. Boole will continue 



* The object v/hich the author proposes in this paper is to illustrate 

 the importance of conducting processes of redaction through the medium 

 of separation of sj'mbols by the assumption of an exponential form for the 

 principal quantity operated on. The method, therefore, consists in the 



transformation of given forms, from x to d, by means of the relation x = i' 

 and operating on the results by certain refined processes. Although the 

 facilities which the exponential form afl'ords, under certain circumstances, 

 have long been known to analysts, in no investigation does the importance 

 of this form appear in the manner in which it is exhibited in this paper. 

 Here the author has shown a method which classifies and comprehends 

 operations, and which has the advantage (in some cases at least) of show- 

 ing their limits. 



The author appHes his method to the solution of differential equations 

 and of equations of diff"erences. In the finite solution of difi'erential equa- 

 tions, the beauty and utility of the method are strikingly exhibited. Certain 

 forms of equations, the solutions of which have been efi^ected by transfor- 

 mations or by a happy assumption, are made, by the author's method, to 

 exhibit their solutions in dependence on a law. Both the processes by 

 which the transformations are effected and the results obtained by them are 

 of the highest interest and importance ; and this part of the paper is so 

 valuable, that, alone, it would entitle the author to honorary distinction. 



In the application to equations of difi'erences, under which head are in- 

 cluded generating functions, series, and the author's miscellaneous theorems, 

 the advantages of a general method must likewise be fully recognised ; and 

 the Council are satisfied that the author has done good service in the appli- 

 cations which he has made of his method in this branch of analysis. 



Anticipating that Mr. Boole's method will find a permanent place in the 

 science, the Council have not hesitated to award to him the Royal Medal. 



