PROCEEDINGS 



OF 



THE ROYAL IRISH ACADEMY. 



1844-45. No. 48. 



November 11, 1844. 



SIR Wm. R. HAMILTON, LL.D., President, in the 

 Chair. 



His Grace the Duke of Leinster, Most Noble the Marquis 

 of Downshire, Baron Farnham, and Baron Wallscourt, were 

 elected Members of the Academy. 



The Chair having been taken, p7'o tempore, by the Rev. 

 J. H. Todd, D.D., V.P., the President gave an account of 

 some additional researches in the theory of Quaternions, or of 

 a new system of Imaginaries in Algebra. 



In the theory which Sir William Hamilton submitted to 

 the Academy in November, 1843, the name quaternion was 

 employed to denote a certain quadrinomial expression, of 

 which one term was called (by analogy to the language of or- 

 dinary algebra) the real part, while the three other terms 

 made up together a trinomial, which (by the same analogy) 

 was called the imaginary part of the quaternion : the square 

 of the former part (or term) being always a positive, but the 

 square of the latter part (or trinomial) being always a nega- 

 tive quantity. More particularly, this imaginary trinomial 

 was of the form ix +jy + kz, in which x, y, z were three real 

 and independent coefficients, or constituents, and were, in se- 

 veral applications of the theory, constructed or represented by 



VOL. HI. B 



