1562 
In the following calculations the vector N has one of the directions 
1*,...4*, As this is also the case with the vectors Bax and Bis, 
the vector product occurring in (22) can easily be expressed in &- 
units. After that we may pass to natural units and finally, as is 
necessary for the substitution in (10), to z-units. 
In order to pass from S-units to natural units we have to multiply 
a vector in the direction a* by a certain coefficient 2a, and a part 
of the extension a*, 6*, c* by a coefficient As. These coefficients 
correspond to Z, (§ 10) and (ys. ($12). The factors 2,7 e.g. can he 
expressed by means of the minors I, of the determinant y of the 
quantities ys. If this is worked out and if the equations 
Gis Fab 
Yab = ’ Jab = 
g 
gy=1 
are taken into consideration, we obtain the following corollary, 
which we shall soon use: 
Let a, 6,¢,d and also a',d'c',d' be the numbers 1, 2, 3,4 in any 
order, a being not the same as a, then we have, if none of the 
two numbers « and wu’ is 4, 
bed Aveta’ 
bat da 
and if one of the two is 4 
ENE nt ia eee en 
lye Aved 
la! da 
EN or ov ee 
§ 25. We shall now suppose (comp. § 24) that in &-units the 
vector B,« has the value + 1, and we shall write 4,5 for the value that 
must then be given to Bs. If the S-eromponents of the vectors Al | 
ete. are denoted by 4&,!,... See etc., we find from (21) 
fad = (ELEN ENE) (EZ RIV Zl) | (25) 
This formula involves ae ; 
Vig YE ee et hn ee 
It may be remarked that y,, is the value that must be given to 
the vector 4,+ if Bj* is taken to be 1. 
The quantities ys may be said to represent the rotations | Bas . Bys|. 
At the end of our calculations we shall introduce instead of y,, the 
quantities w,, defined by 
War = La'b' (a —_ b) ¢) Waa — 0 eri cy ae la ee (27) 
In the first of these equations a, 6, a', b' are supposed to be the 
numbers 1, 2,3,4, in an order obtained from 1, 2,3,4 by an even 
number of permutations. 
