5° 



AI.MAK NÆ.S.S. 



M.-N. Kl. 



the cross as Ix IV)rc d'iuitinj^ tlic space cf)iii|jlfm(-nt of two vectors. Krom 

 this ef|iiatir)n wc ,i^( I lix ordinary curl of a \'ector as a particular case 

 (vi/. // ; 31, rmil \vc will also call (3) the curl of a. 



We will (leri\e a lew properties of this quantit\-: 



It is a tensr)r (polyadic) of order n — 2, thus a vector only in .S'.j. 

 From § 9 (10) we immediately get: 



(4) 



V X a = - 



e, e,. e» 



e, e._, e« 



C, • C, ■ C;;- 



9 a c a ■? a 



5 .V, 3 .\-., d x„ 



But as: 



(5) 



3 .V,- 



.V,- 



<^ Xi c X, 



(4) evidentlv can be written: 



(6) 



V X a =-- 



Ci e., e„ 



e, e,. e„ 



3 3 3 



9 .Vj 9 .Vo 9 .\„ 



(U Oc, a„ 



of which the well-known formula in three-space: 



(7) 



curl a 



f 



? 



3.V 3v 3- 

 (I, a o i^-A 



is a particular case. 



When — as in (6) — one or moie rows of a determinant consist ol 

 operators, it is always understood that these are to be applied to the 

 quantities in all of the following rows, i. e. : to the determinants formed 

 from the matrix of the following rows. 



