Sir W. Rowan Hamilton on Qtiaternions* 511 



The bitartrate of ammonia may be readily made by dissol- 

 ving tartaric acid in water, saturating one-lialf of the solution 

 with ammonia or its carbonate, and adding to this the remain- 

 ing half of the liquid tartaric acid; the bitartrate of ammonia 

 immediately precipitates. 



For pyrotechnical purposes, the chlorates of baryta, stron- 

 tia, lead, &c. may be made without alcohol. With combus- 

 tibles containing hydrogen, the chlorate of baryta produces a 

 green flame of surpassing brilliancy ; and the chlorate of 

 strontia, although somewhat deliquescent, is much superior as 

 a crimson to the nitrate of that earth. 

 I am, Gentlemen, 



Your most obedient Servant, 

 Byker Bar, Newcastle-on-Tyne, Lewis Thompson. 



October 14, 1847. 



LXXV. On Qiiaternions ; or on a New Si/stem of Imag manes 

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

 V. P.R.I. A., F.R.A.S., Corresponding Member of the In sti' 

 tute of France^ S^c., Ajidrews' Professor of Astronomy in the 

 University of Dublin j a?id Royal Astronomer of Ireland. 

 ■[Continued from p. 293.] 

 51. TT has been shown* that if the two symbols «, x denote 

 J- certain constant vectors, perpendicular to the two 

 cyclic planes of an ellipsoid, and if v, t denote two other and 

 variable vectors, of which the former is normal to the ellipsoid 

 at any proposed point upon its surface, while the latter is tan- 

 gential to a line of curvature at that poin^, then the directions 

 of these four vectors », x, v, t are so related to each other as to 

 satisfy the condition f 



S . VT»Tx = (49.), article 47 ; 



S being the characteristic of the operation of taking the scalar 

 part of a quaternion. And because the two latter of these 

 four directions, namely the directions of the normal and tan- 

 gential vectors v and t, are always perpendicular to each other, 

 this additional equation has been seen to hold good : 



S.vT=0 (36.), article 45. 

 Retaining the same significations of the symbols, and carrying 

 forward for convenience the recent numbering of the formulae, 



* See the Philosopliical Magazine for October 1847; or Proceedings of 

 the Royal Irish Academy for July 1846. 



t Inadvertently transcribed as S . vtikt^O, towards the end of the last 

 communication to this Magazine: but correctly printed in the formula 

 (49.) here referred to. 



