1366 
is related to a similar minor of the determinant of the coefficients 
nas. If a'b' corresponds to ab in the way mentioned in § 25, and 
c'd in the same way to cd, we have 
Pea Pdb — Pda Pcs =P (Hea Hdb — da’ Ne'b')s 
so that (31) becomes 
Yab =p =. (cd) (%e'a’ HL 
According to (27) this becomes 
TT da! Te'b’) X ed: 
Way =p = (ed) (roa Tay — Ada HL) Wan 
for which we may write 
Was = tp = (ed) (Tea ds — Haa Heb) Wed: 
Interchanging c and d in the second of the two parts into which 
the sum on the right hand side can be decomposed, and taking into 
consideration that | 
Wade = — Weds 
as is evident from (26) and (27), we find *) 
Was =p = (cd) A a Mad Wed- 
$ 29. Finally it can be proved that if equation (10) holds for 
one system of coordinates #,,.... + v,, it will also be true for 
every other system z',,...-: v',, so that 
f [Re NJ + [Ra «_N] wao =iftaas. et eee 
To show this we shall first assume that the extension 2, which 
is understood to be the same in the two cases, is the element 
(Es tine aig) 
For the four equations taken together in (10) we may then write 
fm dor, a. fr, do =r, an ele ter zn (33) _ 
and in the same way for the four equations (32) 
fe do = v', d&,. Je i= 0 052"... Raet GE 
We have now to deduce these last equations from (33). In doing so we 
must keep in mind that w,,.... wu, are the #-components and 
uw, .... Ww, the z-components of one definite vector and that the 
same may. be said of pst tee Ve and De aks Oe 
Hence, at a definite point (comp. (30)) 
Da (0) Oh ae ee 
We shall particularly denote by 2,5, the values of these quantities 
belonging to the angle P from which the edges dz,,. . . . de, issue 
4 
1) Comp. (28) 1. ¢. 
