855 
exactly or even nearly exactly correspond to reality. But we can 
commit no essential error by assumiug the atoms as behaving in 
such a continuous way. 
Secondly. we must observe, that the only reality we are concerned 
with is the aggregate of trails of nuclei and electrons, and that the 
choice of the vectors r* is entirely arbitrary provided they furnish 
us with the right motion of the electrons relative to the nuclei. 
Obviously the choice can be made in a great many different ways. 
Sometimes it will be suitable to choose the 7* such that the time- 
component 7 vanishes in all points where matter is in a station- 
ary State. We need not specify a particular choice. 
6.2. As yet the displacements considered have been accompanied 
by a shift in time. In view of the physical interpretation of the 
formulae obtained, it will however be necessary to realize the 
simultaneous positions of the electrons relative to the nuclei. 
Now, in a first approximation, we find the electron belonging to 
the nucleus, which at the instant 2@) is in the point 2, x®, x), 
shifted to the point 
ci) + Ord), wl?) + Or), a) + Gri) 
at the instant 
a4) + Orl4) . 
Thus we see that its position at the time «© will be given by 
alt) + 9G), 2® + (2), 29) + 08), 
where 
oe — Art — wt Ord) : 
For an obvious reason gt — 0. 
_ Next, to obtain the second approximation, consider the nucleus 
at the instant 
a ( : Or) Ort) 
a4) — Ort) — & (c) 44 6? re ——— we Ord) ——_ 3, 
( de dae 
when its coordinates are 
k { _ _Ori4) Ord | dwt 
ma wa Ord) — wt > (c) | 4 Or — we Ord) — —+- 4 A? rrd, 
| Ou! Owe { ~ da) 
This line implies the preceding as a special case, for a =d. 
Then the displacements of the electron will be 
dr Ore 
Ort + 40% & (c) pe 08 D (c) we Le = 
so that its actual position will be given by 
