513 



A very remarkable fact is that in a rabbit in which the spinal 

 cord is in a normal condition, and in which the toes, after partial 

 amputation as in the preceding experiments, are about losing the 

 last appearance of sensibility, I find that there is a rapid and 

 very notable return of this vital property if I divide the posterior 

 columns of the spinal cord in the dorsal region. These experiments 

 show that when sensibility seems to be lost in a part deprived of 

 circulation , it is not completely so, but that the transmitted excita- 

 tion which causes sensation is too slight to produce it, and that if in 

 its way to the sensorium this excitation meets with a cause of increase, 

 then sensation can be produced by it. 



II. " On Quaternary Cubics." By the Rev. GEORGE SALMON. 

 Communicated by ARTHUR CAYLEY, Esq. Received June 

 14, 1860. 



(Abstract.) 



In this paper quaternary cubics are discussed under the canonical 

 form first given by Professor Sylvester, 



where 



The writer shows how, when quantics are thus expressed with a 

 supernumerary variable, it is possible to form contravariants also 

 expressed with a supernumerary variable, and such that for the vari- 

 ables, either in covariant or contravariant, we may substitute differ- 

 entials with regard to the variables of the other. By the help of 

 this principle, covariants, contravariants, and invariants of the cubic 

 are formed with great facility. It is proved that a quaternary cubic 

 has five fundamental invariants of the degrees respectively 8, 1 6, 24, 

 32, 40, as well as an invariant of the degree 100, whose square can 

 be expressed in terms of the five fundamental invariants. The discri- 

 minant is also expressed in terms of the four first of these in variants. 

 It is remarked that in the same manner as the theory of ternary 

 cubics is analogous to the theory of binary quartics, so there are 

 many analogies between the theory of quaternary cubics and that of 

 binary quintics. 



Four covariants are noticed of the first degree in the variables, by 

 the aid of which expressions for the cubic can be obtained analogous 



2N2 



