480 



THOMAS MUIH ON BIPARTITE FUNCTIONS. 



for examination how the matter of the iwcariance of the discriminant will look 

 from the new point of view. 



Instead of the special symmetric form which represents a quadiic, let us 

 rather take the quite general bipartite of the third degree 



X 



y 



z 



<h 



«2 



a 3 



h 



b. 



h 



«1 



c 2 



c 3 



calling the determinant of it its square array A , and perform the two sets of 

 substitutions 



y = Pig + fa + &f 

 * = yii + y 2 v + yd 



%'= in t £ + "^2'i + " l d 

 y' = n i£' +nrf+na? 

 *' =*v? + 'W +'' 3 r 



calling the determinant of the first substitution Ai and of the second A- 2 

 The mere substitution changes the bipartite into 



which 



O-l U'i 



a 

 t 



(Si 



p, 



I5 3 



£ 



72 



n 



ys 



£ » 



£ 



*] 



r 



a, 







at 







a z 





&i 







h 







K 





c . 







c. 







Cj 





£ 



9 f 



«i &i 





«, 



a 2 a 3 



Ci 



a 



ft A 



« 2 i 2 



C J 



y> 



y* y 3 



a s &, 



c 3 



?«,, 



m 2 



m s 



f 



>/ 



t 



91, 



Jl2 



>h 



? 



'/' 



t 



V, 



r i 



r 3 



£' >; c ' 



(§22) 





£■ 

 n 



A-AA, 



r 



(§43) 



