col*. 
[358 
le by 
358] ADDITION TO THE MEMOIR ON TSCHIRNHAUSEN’S TRANSFORMATION. 
453 
But we have (see Table No. 72 in my “Seventh Memoir on Quantics,” Philosophical 
Transactions, vol. cli. (1861), pp. 277—292, [269]) 
I (aTJ + 6/377) = (/, 18/, 3/^a, /3) 2 , 
J(aU + 6/3H) = (/, P, 97/, -/ 3 +54/^a, j3f; 
so that, writing a=U', /3 = §0', we have 
I* = I{TJ'U+№'H), 
/* = /(£Tt7+40'77); 
or the function (1, 0, (£, 2), l) 4 obtained from Tschirnhausen’s transformation of 
the equation U = 0 has the same invariants with the function U'U+ 4©'77; or, what 
is the same thing, the equation (1, 0, (S, 3), 1) 4 = 0 is a mere linear trans 
formation of the equation U'U + 40.77 = 0 ; which is the above-mentioned theorem. 
T\