68 Royal Society : — 



original equation ; that it was thus possible to form two functions 

 connected by a certain relation between their coefficients, and such 

 that, when both functions were linearly transformed, the same rela- 

 tion should continue to exist between their coefficients. Functions 

 so related have been called co-variants. The geometrical importance 

 of this theory is now manifest. When we are given the equation 

 of any curve or surface, the theory of linear transformations at once 

 presents us with equations representing other curves and surfaces, 

 and possessing permanent relations to the given one, which will be 

 unaffected by any change of the axes of coordinates : and in like 

 manner the same theory presents us with certain functions of the 

 coefficients of the given equation, the vanishing of which must 

 express a property of the given curve or surface wholly independent 

 of the choice of axes. Besides these geometrical applications, the 

 theory has other important uses, which I shall not stop to enume- 

 rate. That so valuable a theory is not yet as well known in this 

 country as it deserves to be, must arise from the difficulty of becom- 

 ing acquainted with it. I am sure that there are many mathema- 

 ticians who find with regret that the more recent memoirs on this 

 subject are unintelligible to them in consequence of their having 

 overlooked the earlier memoirs, of the importance of which they 

 were not aware at the time that they were published. And I feel 

 that such persons will be ready to welcome an elementary guide to 

 this branch of Algebra." — Preface, p. vi — viii. 



From this book of Mr. Salmon, taken in conjunction with Mr. 

 Spottiswoode's on ' Determinants,' and the work of Brioschi (trans- 

 lated from the Italian into French by Combescure), any one may 

 learn enough of the subject to qualify him for reading the original 

 memoirs of Messrs. Cayley, Sylvester, &c. 



XIII. Proceedings of Learned Societies, 



ROYAL SOCIETY. 



[Continued from vol. xvii. p. 442.] 



Jan. 27, 1859. — Sir Benjamin C. Brodie, Bart., Pres., in the Chair. 



'' I TIE following communications were read : — 



*- "Researches on a New Class of Organic Bases, conducted 



by Charles S. Wood, Esq." By A. W. Hofmann, LL.D., F.R.S. 



In his remarkable memoir* on the action of reducing agents on 

 nitro-compounds, in which Zinin first pointed out the formation of 

 organic bases by the substitution of hydrogen for oxygen, some expe- 

 riments are recorded on the deportment of dinitronaphtaline (nitro- 

 naphtalesc) with sulphuretted hydrogen. Zinin states that this pro- 

 cess gives rise to the formation of a basic compound crystallizing in 

 delicate copper-red needles, and yielding with acids white scaly salts. 

 In a subsequent paper f Zinin returns to the action of sulphuretted 



* Bulletin Scicntifiqtie de St. Petersburg, x. 18. 

 t Journ. fiir Prakt. Chein. Bd. xxxiii. 29. 



