258 Mr. Teschemacher on Gun-Cotton. 



three of the seven quantities which do not form a triplet, then 



[i i.).i =—i Ji.i ). 



Thus, for instance, 



but _ _ i^{l^t^) = i^.i^ = !^, 



and similarly for any other such combination. When ?^, ?' , i 



form a triplet, the two products are equal, and reduce them- 

 selves each to — 1, or each to + 1, according to the order of 

 the three quantities forming the triplet. Hence in the octuple 

 system in question neither the commutative nor the distribu- 

 tive law holds, which is a still wider departure from the laws 

 of ordinary algebra than that which is presented by Sir Wm. 

 Hamilton's quaternions. 



I may mention, that a system of coefficients, which I have 

 obtained for the rectangular transformation of coordinates in 

 n dimensions (Crelle, t. xxxii. Sur qicdques proprietes des De- 

 tcrminans gauc/ics), does not appear to be at all connected with 

 any system of imaginary quantities, though coinciding in the 

 case of 71 = 3 with those mentioned in my paper " On Certain 

 Results relating to Quaternions," Phil, Mag. Feb. 1845. 



58 Chancery Lane, March 2, 1847. 



XLIII. On Gun-Cotton. 

 By E. F. Teschkmacher, Esq.^ 

 TN consequence of the discovery by Professor Schonbein of 

 -*- gun-cotton, and of the possibility of its substitution in 

 many cases for gunpowder, I have been induced to enter into 

 an examination of the mode of its formation and of its syn- 

 thetical composition, principally with a view of ascertaining 

 how far it would be likely to alfect an important branch of 

 trade — the production and value of saltpetre and nitrate of 

 soda. The examination was not commenced with the view 

 of publishing it, but some of the facts brought to light ap- 

 peared to possess sufficient interest to lay before the Society. 

 1 must premise that the experiments relate oidy to the gun- 

 cotton prepared by the process recommended by Mr. T. Tay- 

 lor. Equal measures of nitric acid of sp. gr. 1'509, and of 

 sulphuric acid sp. gr. r840, were mixed together, and consti- 

 tuted (No. 1) the acids used in these exjierimcnts. I dried 

 50 grs. of South American cotton (from La Guayra) over a 

 water-bath, and found the cotton gave off 3*40 grs. of hygro- 

 metric water. The 46'60 grs. of cotton which remained after 

 drying, I steeped in 487^ grs. oi the mixed acids No. 1 ; the 



* Coiiiiminiciited bv tlie Chemical Society; having been read Nov. 2, 

 184G. 



