10 Sir W. R. Hamilton o« Qimternions. 



tithonization is not a transient effect which at once passes away, 

 but is, on the contrary, a persistent change. 



I tithonized the chlorine and hydrogen contained in the in- 

 strument, and kept it in the dark for ten hours. On expo- 

 sure to the lamp rays it moved after a few seconds, showing, 

 therefore, that the change which had been impressed on the 

 chlorine was not lost. In the former case 600 seconds had 

 elapsed before any movement was visible. 



When, however, we remember that the invisible images on 

 Daguerreotype plates, and even photographic impressions on 

 surfaces of resin, and probably all other similar changes are 

 slowly effaced, it would be premature to conclude that titho- 

 nized chlorine does not revert to its original condition. I 

 have sometimes thought that there were in several of my ex- 

 periments indications that this was taking place, but would 

 not be understood to assert it positively. Whether it be so 

 or not, one thing is certain, that the taking on of this condi- 

 tion and the loss of it is a very different affair from any trans- 

 ient exaltation of action due to a temporary elevation of tem- 

 perature, or the contrary effect produced by cooling. 

 April 26, 1844. 



II. On Quaternions; or on a new System of Imaginaries in 

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

 P.R.I.A., F.R.A.S., Hon. M. It. Sac. Ed. and Dub., Hon. 

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

 tersburgk, Berlin, Turin, and Paris, Member of the American 

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

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

 the University of Dublin, and Royal Astronomer cf Ireland, 

 1. 1 ET an expression of the form 



-*^ Ql = w + ix -\-jy + kz 



be called a quaternion, when w, x, y, %, which we shall call 

 the four constituents of the quaternion Q, denote any real 

 quantities, positive or negative or null, but i,j, k are symbols 

 of three imaginary quantities, which we shall call imaginary 

 units, and shall suppose to be unconnected by any linear rela- 

 tion with each other; in such a manner that if there be an- 

 other expression of the same form, 



Q' = W)' + ix^ +jy' + kz', 

 the supposition of an equality between these two quaternions, 



Q = Q', 



* A communication, substantially the same with that here published, was 

 made bv the present writer to the Royal Irish Academy, at the first meet- 

 ing of tnat body after the last summer recess, in November 1843. 



