424 



pelled into the more posterior parts of the tubular prolon- 

 gations, and into the oval bodies in which these terminate. 

 Mr. Bergin had pointed out to Dr. Allraan the existence of 

 muscular fibres in the walls of the oval dilatations. The 

 contraction, therefore, of these muscles, will cause the con- 

 tained fluid to impinge upon the inverted extremity of the 

 proboscis, which will thus be forced outwards, and the pro- 

 boscis injected with the fluid. The source of this fluid would 

 appear to be in the oval bodies themselves, whose structure 

 is, in all probability, glandular, and which, besides possessing 

 a contractile power, by which the contents of their cavities 

 are expelled, would seem also to be the secerners of the fluid 

 which plays so important a part in the protrusion of the 

 proboscides. 



The Chair having been taken pro tern, by the Rev. H. 

 Lloyd, D. D., Vice-President, 



The President read a paper on a new Species of Imagi- 

 nary Quantities, connected with a theory of Quaternions. 



It is known to all students of algebra that an imaginary 

 equation of the form 2^ r= — 1 has been employed so as to 

 conduct to very varied and important results. Sir Wm. Ha- 

 milton proposes to consider some of the consequences which 

 result from the following system of imaginary equations, or 

 equations between a system of three different imaginary quan- 

 tities : 



P=f = F'=-\; (A) 



V = ^> jk-i, hi —j ; (b) 



ji = — k, kj = — i, ik = ~j ; (c) 



no hnear relation between i,j, k being supposed to exist, so 

 that the equation 



Q — q', 

 in which 



Q = «? 4- ia; +jy + A», 

 q' — w •{■ ix' -^jy' -f kz', 



