THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



SUPPLEMENT to VOL. XXV. THIRD SERIES. 



LXXVIII. On Qiiatcrnions; or on a new System of Imaginaries 

 in Algebra. By Sir William Rowan Hamilton, LL.D., 

 P.R.LA., F.R.A.S., Hon. M. 11. Soc. Ed. and Dub., Hon. 

 or Corr. M. of the Royal or Imperial Academies of St. Pe- 

 tersburghf Berli?i, Turin, and Fan's, Member of the Americati 

 Academy of Arts and Sciences, and of other Scientific Socie- 

 ties at Home and Abroad, Andrews' Prof, of Astronomy in 

 the Utiiversity of Dublin, ajid Royal Astronomer if Ireland. 



To the Editors of the Philosophical Magazine ajid Journal. 

 Gentlemen, 



I HAVE been induced to think that the account contained 

 in the following letter, of the considerations which led 

 me to conceive that theory of quaternions, a part of which you 

 have done me the honour to publish in two recent Numbers 

 (for July and October) of your Magazine, might not be without 

 interest to some of your readers. Should you think proper to 

 insert it, a public acknowledgement (very pleasing to my own 

 feelings) will have been rendered, on the one hand to the Rev. 

 Mr. Warren, whose work on the Geometrical Representa- 

 tion of the Square Roots of Negative Quantities (printed at 

 Cambridge in 1828) long since attracted my attention and 

 influenced my thoughts ; and on the other hand to the gen- 

 tleman (John T. Graves, Esq.), to whom the letter was ad- 

 dressed, and with whom I had been engaged, at intervals, for 

 many years in a correspondence, very instructive and sug- 

 gestive to me, on subjects connected therewith. Nor am I 

 without hope that Mr. Graves may thus be led to communi- 

 cate through you to mathematicians some of the extensions 

 which he has made of results of mine, with some of those 

 other speculations which are still more iully his own. On 

 some future occasion I may perhaps be allowed to mention 

 any other quarters from which I may be conscious of having 

 derived more recent assistance, in my investigations on the 

 Phil. Mao. S. 3. No. 169. Stcppl. Vol. 25. 2 K 



