116 Mr. J. J. Sylvester on the Algebraical Theory of 



be meanwhile represented as — 



.••H 

 C-O-OH 



••H 

 p.-O-OH 



p.-O-OH 



0-OH 

 H 



0-OH 

 H 



.0-OH 

 C'-H 

 •O-OH 



c; 



0-OH 

 0-OH 



the acids. Glucose 



c: 

 c::; 



It will thus be seen that these combinates all belong to the 

 type nCM'*. 



Many others might be added. For instance, tartaric acid : — • 



-O-OHn 



-02 I 



...H 



•O-OH 

 • O. 



H-:OH 

 ^••0 OHJ 



And the bibasic 

 acid produced 

 from it by the 

 action of heat 

 will be perhaps 



r.,-0-.OH 



C...H 

 i^-O-OH 



tartrelie 

 acid. 



It is my intention to consider, in a future communication, the 

 second type, and to apply my views to the cyanogen combi- 

 nates, &c. 



XIII. Note on the Algebraical Theory of Derivative Points of 

 Curves of the Third Degree. By J. J. Sylvester, Professor 

 of Mathematics in the Royal Military Academy*. 



TWO years and upwards have elapsed since I discovered the 

 extraordinary theorem in the doctrine of cubic forms which 

 I am about to state, but which has never yet been published by 

 me, although communicated in confidence to a few friends, inclu- 

 ding Mr. Cayley. It arose out of purely arithmetical specula- 

 tions relating to such forms, to some of which I may make a 

 brief allusion in the course of this note. 



If we suppose the general homogeneous equation of the third 



* Commuaicated by the Author. 



