1889.] 



of three Ternary Quadrics. 



33 



Only one form of a given type is written down ; the others 

 may be obtained by interchanging the letters — the number of 

 forms so obtainable is given by the number in brackets which 

 follows. The forms are arranged in sets, as obtained, according to 

 their degrees. 



[1010] = (a'Py) b y Cpb a c a u a , (3) 

 The degree — class — order symbols of eighteen of the types are 

 placed in square brackets. This indicates that they are reducible 

 after multiplication by u x . Some of them are further reducible 

 on multiplication by u 2 : namely these are (501),; (710),; (801),; 

 (911) ; (1010). Allowing these reductions the system is expressible 

 by 13 kinds of forms, viz. by 



((abc) 2 ba a 2 a 2 (bcu)b x c x (bcu) 2 u a b a b x (abc) (bcu) a x 



{(a/37) 2 W (fiyx)upUy (pyx) 2 (a/3y)(Pyx)u a 



(bcu) (cau) (abu) (bcu)b a c a b a c a b x c x (bcu)b a c x u a (bcu)b y c x u y 



(fiyx) (afix) (yax) (Pyx)a p a y UpU y apa y (Pyx)apa x u y (Pyx)c x CpUp 



VOL. VII. PT. I. 3 



