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the labours of the mathematicians appear of late to have been cul- 

 tivated almost exclusively by our own countrymen, — 1 refer to the 

 Calculus of Operations and the Theory of Imaginaries. Two im- 

 portant papers on the former subject have lately appeared in our 

 Transactions, and have earned for their authors the Medals of the 

 Society. In the latter field, Mr. De iVIorgan, Mr. John Graves, 

 Mr. Charles Graves, and Mr. Kirkman, have succeeded in obtain- 

 ing many curious and interesting results; but the most valuable 

 seems to be those which have been arrived at by Sir William Rowan 

 Hamilton in his Theory of Quaternions: his late application of it 

 to the geometry of three dimensions, and to questions in optics and 

 astronomy, evidently prove the power of this Calculus as an instru- 

 ment of invention and research. 



I regret to say, that since our last Meeting we have lost many 

 eminent men ; the obituary memoirs, however, seem to me to call 

 for no particular remark, with one exception, that of the distin- 

 guished chemical philosopher Gay-Lussac. That memoir has been 

 prepared by M. Biot, and I am sure you will concur with me in 

 thinking, that in performing that duty he has conferred a great 

 obligation on the Royal Society and on all men of science ; the 

 memoir will be read, uninjured by translation, just as we have re- 

 ceived it. 



Col. Sabine, 



I have the honour of presenting to you the Copley Medal in 

 charge for Professor Hansen. It has been awarded to him for his 

 discoveries in Physical Astronomy. 



To have contributed even a little to the advancement of that 

 science, as it exists at the present day, would have been no mean 

 achievement. Hansen has done much more ; his contributions are 

 of a very high order. Previously to the appearance of Hansen's 

 memoirs, two methods had been employed in the determination of 

 the planetary perturbations. One of these, known by the name of 

 the method of variation . of elements, besides being exceedingly 

 beautiful in theory, is peculiarly well adapted to the determination 

 of the secular variations and the inequalities of long period. 

 It has the disadvantage, however, that the number of elements 

 whose perturbations we are thus required to calculate, is twice as 

 great as that of the coordinates, the perturbations of which are the 

 final objects of investigation ; and also that the former perturbations 

 are frequently much greater than the latter. In order to take into 

 account the square of the disturbing force, which is quite necessary 

 in the present state of astronomy, we must find the change intro- 

 duced into the perturbation of each element of the disturbed planet, 

 by the perturbations of each several element both of the disturbed 

 and disturbing planets. Consequently, unless we content ourselves 

 with the selection of a few of the most important terms, the calcu- 

 lations become extremely long and laborious. 



In the second of the methods above alluded to, the perturbations 



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