596 
io VEER = VA i == ie We (Wa ig) Oes ca (6) 
or also to 
pul WE VERS SUG oo Bus Gore (YY) 
hence to 
NG Rl eae ee ees (A) 
In this equation the auxiliary vectors v and w occur no more. 
It is the required condition that the ,v-field may be V-creating. 
As: 
we -{V 1 (vi vj} = we- (a. V) (a! (Vi — vj) ®) = 
= (a. V)iwea? (vi — v,)}) —(a.V) we fat (vi vj} —= = (11) 
= (vi > vy)? V Wi, 
(A) is equivalent to 
(vi — vj) 2 V >We), LT Ge cae SV (12) 
and as } 
Ln —p 
Vn pW = AW We (QV) Wie Witten Wimpy eo (13) 
k 
also to 
DVCAM, ne) on aks ol te ere) 
(B) can be deduced from (A) without returning to the auxiliary 
vectors v; and wz. We can show also independently of (A) the 
necessity of (B). For, when ,_,w is V,-normal, we always have 
an) 
n—pW = À (VA) 50 6 (7 fn—p)} Re (14) 
in which 2 is a function of the place. Hence 
ni SDN de so Wife) 6 vere er (LB) 
from which (B) is a direct result, because every v is 1 V fs. 
When p=n—1, we see from (B), or clearer from (15), that 
V — w is a simple bivecior. From this we may deduce the following 
theorem. When a field w is V_{-normal and w is interpreted as 
1) The forms (10) and (12) of the condition are identical with those occurring 
in E. von Weser, Vorlesungen über das Pfaffsche Problem (TEUBNER, 1900) 
page 99 and 100. 
3) (A) and (B) were already given without proof in J. A. ScHoureN, Over het 
aantal graden van vrijheid van het geadetisch meebewegende assenstelsel. Versl. 
der Kon. Ak. v. Wet. 27 (18) 16—22. 
3) The differentiating effect of a differential operator extends to the first coming 
closing bracket. 
4) This term is zero, because wj,Lv; and LV, 
