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ON THE SPECTRUM OF HYDROGEN

these systems. No one has ever seen a Planck's resonator, nor
indeed even measured its frequency of oscillation; we can observe
only the period of oscillation of the radiation which is emitted. It
is therefore very convenient that it is possible to show that to
obtain the laws of temperature radiation it is not necessary to
make any assumptions about the systems which emit the radiation
except that the amount of energy emitted each time shall be equal
to Kv, where h is Planck's constant and v is the frequency of the
radiation. Indeed, it is possible to derive Planck's law of radiation
from this assumption alone, as shown by Debye, who employed a
method which is a combination of that of Planck and of Jeans.
Before considering any further the nature of the oscillating systems
let us see whether it is possible to bring this assumption about the
emission of radiation into agreement with the spectral laws.

If the spectrum of some element contains a spectral line corre-
sponding to the frequency v it will be assumed that one of the
atoms of the element (or some other elementary system) can emit
an amount of energy hv. Denoting the energy of the atom before
and after the emission of the radiation by E_l and E% we have

t-* or » = -
fi

.(5)

During the emission of the radiation the system may be regarded
as passing from one state to another; in order to introduce a name
for these states, we shall call them "stationary" states, simply
indicating thereby that they form some kind of waiting places
between which occurs the emission of the energy corresponding to
the various spectral lines. As previously mentioned the spectrum
of an element consists of a series of lines whose wave lengths may
be expressed by the formula (2). By comparing this expression

with the relation given above it is seen that—since v = -, where o

is the velocity of light—each of the spectral lines may be regarded
as being emitted by the transition of a system between two stationary
states in which the energy apart from an additive arbitrary
constant is given by —chF_r(n^) and —chF_s(n₂) respectively. Using
this interpretation the combination principle asserts that a series
of stationary states exists for the given system, and that it can