1363 
§ 26. We have now to calculate the left hand side of equation 
(10) for the case that o is the surface of an element (de, dr). 
For this purpose we shall each time take together two opposite 
sides, calculating for each pair the contributions due to the different 
terms on the right hand side of (22), or as we may say to the dif- 
ferent rotations yo, It is convenient now to denote by a, b,c the num- 
bers 1, 2,3 either in this order or in any other derived from it by 
a cyclic permutation, while the #-components of the vector we are 
calculating and which stands on the left hand side of (10) will be 
represented by X,,... X,. . 
a. Let us first consider that one of the sides (de, dez, dx.) which 
faces towards the side of the positive w,. The vector N drawn 
outward has the direction 4* and in §-units the magnitude = As the 
. 4 
direction ec corresponds to a”, D*, 4*, the rotation y,, gives with N 
a vector product represented by a vector in the direction c. The 
magnitude of this vector is in §-units 
and in natural units 
This must be multiplied by (qs, dva day de, the magnitude of the side 
; 1 ; 
under consideration in natural units, and finally by 7, to express the 
C 
vector product in v-units. Because of (24) we may write for the result 
Yab dra day dee, = Wes dea day de. 
The opposite side gives a similar result with the opposite sign (N 
having for that side the direction — 4*), so that together the sides 
contribute the term 
dw c4 
WwW 
0x, f 
to the component X,. For shortness’ sake we have put here 
da, dz, dx, dx, — dW. 
Finally we may take. c = 1, 2, 3. 
6. Secondly we consider a side (dq, des, da) facing towards the 
positive x. The vector N has now the direction — c*. We consider 
the vector products of this vector with the rotations y,, y,a and Y6q, 
which vector products have the directions a, 6 and 4. A calculation 
exactly similar to the one we performed just now gives the contributions 
to Xa, Xs, X,. For these we thus find the products of dea de, dx, by 
Proceedings Royal Acad. Amsterdam. Vol. XIX. Es 
