1365 
§ 28. Between the differentials of the original coordinates x, and 
the new coordinates 2a which we are going to introduce we have 
the relations 
Azn (BIRB DD tet ANGELO) 
and formulae of the same form (comp. $ 10) may be written down 
for the components of a vector expressed in v-measure. As the 
quantities q, constitute a vector and as 
vd — Pp Vn 
we have according to (28) *) 
ua ee WG = (b) Xba ws, 
or 
Wa =p = (b) Rha wb. 
Further we have for the infinitely small quantities &,*) defined 
by (19) 
ie 5 (6) Pha Sui. 
and in agreement with this for the components of a vector expressed 
in &-units 
c 
c 
hy 
Ba id (b) Pba bs 
\ 
so that we find from (25) *) 
Kab = = (ed) Pea Pab fed « 
Interchanging here c and d, we obtain 
Yar = Z(cd) pda Peb Ade = — B (cd) Pda Peb Led 
and 
Xiab = 4 Bcd) (Pea Pab — Pda Pct) Xed » + « « (31) 
The quantity between brackets on the right hand side is a second 
order minor of the determinant p and as is well known this minor 
ly Comp. 99) 6-15 
2) For the infinitesimal quantities a occurring in (19) we have namely (comp. 
(30) ) 
4 D= 2 (6) Tha Uh 
and taking into consideration (19) and (29), i e. 
Ga =S (OPI fb re Pa == (6) Von Eb 
and formula (7) l.c., we may write (comp. note 2, p. 758, I. c.) 
Be = Db) fab #5 = (bede) pia Pab Neb Jed Pe = 
= Lcd) pea Yea CA — =U (cdf) Pea Jed 1fd Sf = ZO) Pea Se - 
3) Put Zl Zp = Dan. Then we have 
Op = Bo! ZE = = (ed) pen par He! Ba! = & (cd) Pea pas Hed 
and similar formulae for the other three parts of (25). 
