394 M. H. Becquerel's Experimental Investigations 



If ft) = 0, then A = ; so that, corresponding to Cayley's 

 theorem, " An odd-ordered determinant which is skew with 

 respect to a zero diagonal vanishes/' we have an exact coun- 

 terpart, viz. "An odd-ordered determinant which is skew with 

 respect to a zero centre vanishes." The latter, too, may be 

 proved exactly like the former, viz. by multiplying the ele- 

 ments of every row by —1, and thus showing that A= — A. 



But, further, the product of the two determinants in (III.) 

 is equal to 



d\ — a 7 



(_1)3 6l _ 6 , 



C 1 —C 7 



a 2 — a 6 



«3 



-a 5 



a ± + a 7 



a 2 -\-a 



6 «3 + «5 



b 2 —b 6 



h 



-h 



\ + b 7 



b 2 +b 



3 h+h 



C2—C& 



c B 



— C5 



Ci +c 7 



c 2 +c € 



c 3 +C5 



y Zehfuss 



's 



theorem, is equal to 





a x a 2 





a s 



a 5 



a 6 



a 7 





h h 





h 



b 5 



h 



h 





C\ c-2 





C3 



c 5 



H 



«7 





C 7 Cq 





C5 



C3 



c 2 



«1 





b 7 b 6 





h 



h 



h 



h 





a 7 a 6 





a 5 



a 3 



a 2 



a x 



? 



i-iy 



that is to say, is equal to the centre-skew determinant obtained 

 from A by deleting the middle row and middle column. 

 Hence the theorem — A centre-skew determinant of odd order is 

 not altered by making all the elements of the middle row and 

 middle column zero with the exception of the centre element. 



Instead of deducing this from (III.) we might reverse the 

 order, viz. prove the theorem just enunciated by expanding A 

 according to binary products of the elements of the middle 

 row and middle column, and then by means of this theorem 

 establish (III.). 



Beeclicroft, Bishopton, N. B., 

 October 8, 1881. 



LI. Experimental Investigations on Magnetic Rotatory Polari- 

 zation in Gases. By M. Henri Becqueeel.^ 



[Concluded from p. 324.] 

 Discussion of the Sources of Error: Corrections. 



IN measurements so delicate as these about to be recorded, it 

 was of the highest importance that the effect of the various 

 disturbing causes proceeding from the apparatus itself should 

 be most carefully studied and measured. Although the 

 corrections which it was necessary to make in the results 

 observed were very small, yet, as they were of the same order 



