Meanwhile it may be pointed out that the individual energies of the quanta reaching us from the nebulae are altered by red-shifts, quite-apart from the question of recession. In view of the fundamental relation previously mentioned,

the mere presence of red-shifts, the observed increase
in wave-lengths, necessarily implies a reduction in the
energies. This *energy effect* operates regardless of the
interpretation of red-shifts. It must be applied as a
matter of course to all measured luminosities before
distances can be estimated.

The calculation of the energy effect starts from the
fact that the fractional red-shift
*d* /
is constant
throughout a given spectrum. Each wave-length is increased, and,
consequently, the energy in each quantum
is reduced, by the constant factor
1 + *d* /
. We might
naturally conclude that the total luminosity, the sum
of all the individual energies, would be reduced by the
same factor. The conclusion, in fact, is valid in the
particular case of the `bolometric' luminosity, which is
the total radiation, integrated over all wave-lengths,
as it would be measured in empty space outside the
earth's atmosphere. But we are concerned with the
photographic luminosity. Hence the effect must be
traced through the, atmosphere, the telescope, and the
photographic film. The procedure is complicated because the energy
effect is selective (varying through the
spectrum). The distortions magnify the original factor
1 + *d* /
to a factor that
approaches
1 + 3*d* /
. More
precisely, the photographic magnitudes, to use the
technical measure of apparent faintness, are increased
by the increment,

This is the correction for the energy effect which is
valid regardless of the origin of red-shifts,
^{2} and which
is applied as a matter of course to all measures of apparent luminosity
used for the estimation of distances.

^{2} Since
*E* = constant =
*h* / *c*, the above statement assumes that
the relation between Planck's constant *h* and the velocity of
light *c*
is essentially the same for light from the distant nebulae as in light
from laboratory sources. The assumption has been tested by measuring
red-shifts both with a grating spectrograph and a prism
spectrograph. The fact that the shifts are the same in both cases seems
to confirm the constancy of *h* / *c*.
(*Annual Report of the Mount Wilson Observatory,* 1935-6.)
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