854 
This formula is also given by Born. It may be found, without 
deduction however, in a paper by Lorentz’). 
5. The second variation is easily found, without calculation, by 
submitting the first variation in turn fo the operation which we had 
to apply to Not in order to find dNw*. So we get without difficulty 
Oe 
d.d Nwt = & (b) 5, {Ora dNw? — Orb dNwt}, 
v 
0 
Oae 
It is, however, important to remark that this formula implies the 
accurate definitions of the displacements as given in § 2. This can 
be verified by a direct deduction, following throughout the same 
line of argument as in the case of the first variation. We may 
refrain from reproducing the calculus, but it will be good to point 
out, that one has to develop the Jacobian with the required exactness 
up to the terms with 67, and, above all, that at the last step to be 
taken one has to be careful to choose the right starting-point from 
where the displacements will carry the particles to the point under 
consideration, viz., 
0 0 
JS Nwt = & (be) TE jor [Ort Na red [OraNwe-ôre Nw] °. 
Ore 
wt — Grt + 10E (Ore, 
Òze 
and not «*—Awt, as we might be tempted to take. 
Next, we have to give an interpretation of our mathematical 
result in physical terms such as polarization and magnetization. 
The Simultaneous Displacements. 
6.1. Before turning to the physical interpretation we must look 
closer into the nature of our displacement vector r¢ and the under- 
lying assumptions. 
We are to assume, that the trails of the electrons can be found 
from the trails of the nuclei with the aid of the vectors 7% in the 
indicated manner. First of all, we have taken these to be continuous 
functions of the coordinates. This implies that neighbouring atoms 
are supposed as having their electrons at similar distances in similar 
directions, the positions of the electrons relative to the nuclei varying but 
extremely slowly from one atom to the next. Of course this will not 
1) H. A Lorentz, Haminton’s Principle in Einstein's theory of Gravitation, 
Proc. R. Ac. of Amsterdam, 19, p. 751, 1915. 
