1865.] Mr. Cay ley on the Theory of Matrices. 543 



n 1 (if n be the order of the equation in x), is not really more general 



V 

 than the transformation wherein y is put equal to any rational function ^ 



whatever of x ; such rational function may, in fact, by means of the given 

 equation in x, be reduced to a rational and integral function of the order 

 n 1 ; hence in the present case, taking V, W to be respectively of the 

 order nl, =3, it follows that the equation in y obtained by the elimina- 

 tion of a; from the equations 



V=(a, b, c, d, ejjc, 1) 4 =0, 

 _(a,/3, r .a;fo, I) 3 



is a mere linear transformation of the equation AU-r-BII=0, where A, B 

 arc functions (not as yet calculated) of (a, b, c, d, c, a,, /3, y, <$, a', (3', y , 5') 4 . 



II. " A Supplementary Memoir on the Theory of Matrices." By 



ARTHUII CAYLEY, F.R.S. Received October 24, 1865. 



(Abstract.) 



M. Ilermite, in a paper "Sur la thcorie de la transformation des 

 fonctions Abeliennes," Comptes Rendus, t. xl. (1855), establishes inci- 

 dentally the properties of the matrix for the automorpbic linear trans- 

 formation of the bipartite quadric function xw -\-ys' zy wx', or trans- 

 formation of this function into one of the like form, XW+YZ' ZY' 

 WX'. These properties are (as will be shown) deducible from a general 

 formula in my " Memoir on the Automorpbic Linear Transformation of a 

 Bipartite Quadric Function," Phil. Trans, t. cxlviii. (1858), pp. 39-46 ; but 

 tbe particular case in question is an extremely interesting one, the theory 

 whereof is worthy of an independent investigation. For convenience the 

 number of variables is taken to be four ; but it will be at once seen that as 

 well the demonstrations as the results arc in fact applicable to any even 

 number whatever of variables. 



III. " On the Existence of Glycogen in the Tissues of certain Entozoa." 

 By MICHAEL FOSTER, M.B. Communicated by Professor 

 HUXLEY. Received November 4, 1865. 



Although glycogen has been found by various observers in the tissues 

 of many of the Invertebrata, no one, as far as I know, has noticed the 

 very remarkable amount which may be obtained from some of the Entozoa. 

 I first came across this fact while working upon a tape-worm ; unfortu- 

 nately I neglected to determine the quantity of glycogen I obtained, and 

 have not since had an opportunity of repeating the observation. The fol- 

 lowing remarks apply only to the round worm (Ascuris luiubricoides ?) 

 which dwells in the intestines of the common piu;. 



