( 117 ) 



Analogously we find quite simply as second derivative the scalar : 



~ ABC 2^ ÖW 



According to the usual way of expressing, the first derivative is 

 the rotation vector and the second tiie divergency. 



II. If X is to be a ^_X, i. e. a second derivative of a pLanivector 

 i, we must have: 



_ 1 iö(r.i?) ö(r,.Q) 



BC \ öif ÖÜ ( 



and it is easy to see that for tljis is necessary and suflieient 



III. If X is to be a o-^, i- e. a first derivative (gradient) of a 

 scalar distribution y, we must have : 



X — — — X = — — X — ^^ 



.4ÖU ' ' Bdv Cdw 



and it is easy to see, that to this end it will be necessary and 

 sufficient that 



Y=0. 



IV. It is easy to indicate 'comp. Schering, Göttinger Nachrichten, 



1870) the (jX, of wjjich tlie divergency is an isolated scalai' value in 

 the origin. 



It is directed according to the radius vector and is equal to : 



1 

 sinh'^r 

 when we put the space constant = 1 '). 





Ö..-. 



V,+ 1='^'-^P+1 



^p+1 



7 — 'V P~^ ^ 



q 

 g p n 



These last definilions include the well known divergency of a vector, and the 

 gradient of a potential also as regards the sign ; hence in the following we shall 

 start from it and we have taken from this the extension to non-Euclidean spaces. 

 -) For another space constant we have but to substitute in the following formulae 

 r 

 R '°' '■• 



