Powers of a Determinant. 231 



and, if this change were made, we might contrast them by saying 

 that while the one reduces to zero 3^ elements in the last three 

 columns, the other does the same in the first three rows. 



5. The third paper which concerns our subject emanated from 

 the same city as the second, viz., Buda-Pest, its author being 

 Hunyady, and its title " Beitrag zur Theorie des Flachen zweiten 

 Grades."' It appeared in Crelle's Journal, LXXXIX., pp. 47-69, 

 about the beginning of 1880, but is dated July, 1879, so that it must 

 have been written about a year after the publication of Scholtz's 

 results. It is in part merely the natural extension to three- 

 dimensional space of Scholtz's theorems in plane geometry, and 

 there are features of it which suggest acquaintance with what 

 Scholtz had done, but, although references to previous workers are 

 numerous, the name of Scholtz is not anywhere mentioned in it. 



The determinant, Aio say, to which Hunyady was, of course, 

 led, is 



2rtia3 2aia4 2a2as 2«2^4 2a^a^ 



This he treats in exactly the same manner as Scholtz had treated 

 Afi, the penultimate equation of the process being 



Aio- ! 62f3<^4 i • 1 (J2^Yh ! • I (^2bslfi i . I ^72636-4 I = — I ^162^3^/4 I ^.P, 



where P stands for the determinant 



which he says can be shown to be equal to 



I 62C3C/4 j . I a2Czdi I . I rt2^3^^4 I • I «2^3Q I 



