50 
PROFESSOR CAYLEY’S NINTH MEMOIR ON QIT ANTICS. 
indirect and artificial in the employment of such a property ; one sees no reason why, 
when a system of irreducible covariants is once written down, it should not be possible 
to show that the derivatives of F(U) with the original quantic f are each of them F(U), 
instead of having to show this in regard to the derivatives of F(U) with the several cova* 
riants % : as regards the quintic, where there is a single covariant %, the quadric function 
i, there is obviously a great abbreviation in this employment of i in place off ; but for 
the higher orders, assuming that the proof could be conducted by means of the quantic 
f itself, it does not appear that there would be even an abbreviation in the employment 
in its stead of the several covariants The like remarks apply to the proof in the last- 
mentioned paper. I cannot but hope that a more simple proof of Professor Gokdan’s 
theorem will be obtained — a theorem the importance of which, in reference to the whole 
theory of forms, it is impossible to estimate too highly. 
