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NOTE ON CLEBSCH'S THEOEEM EEGARDING THE SECOND 
SET OF JACOBIANS DERIVED FROM n + 1 HOMOGENE- 
OUS INTEGRAL FUNCTIONS OF 71 VARIABLES. 
By Thomas Mum, LL.D. 
(Received June 25, 1913. Read July 16, 1913.) 
1. The theorem in question, which was originally published in CreZ/e's 
Journ., Ixix., pp. 355-358, and Ixx., pp. 175-181, was enunciated by its 
author in the following form : If Uj, u^, U3, ... be n + 1 homogeneous integral 
functions of the mth degree in the n variables x^, X2, x., ... ; and Vj, V2, 
Ya+i ^6 of Jacobians formed from the u's : a7id Wi, Wg, w,j+i be the 
set similarly formed from the v's ; then the w's differ from the u's by a 
common factor only — that is to say 
iu^^Mai^, i02 = W.u^y = M. 
Clebsch's mode of establishing it was to show that for any values of the 
a's and //s the determinant 
'dx^ 
~dXn 
a, b. 
t^k^h ^b,,7Cj, 
vanishes identically : that consequently 
%b^Ui, . ^aj,ic,, - %aj{ii,, . ^b,w„ = 0 ; 
