Lectures on Stellar Statistics | Page 8

B0 and M there corresponds a certain spectral index s. The
extreme types O and N are not here included. Their spectral indices
may however be determined, as will be seen later.
Though the spectral indices, defined in this manner, are directly known
for every spectral type, it is nevertheless not obvious that the series of
spectral indices corresponds to a continuous series of values of some
attribute of the stars. This may be seen to be possible from a
comparison with another attribute which may be rather markedly
graduated, namely the colour of the stars. We shall discuss this point in
another paragraph. To obtain a well graduated scale of the spectra it
will finally be necessary to change to some extent the definitions of the

spectral types, a change which, however, has not yet been
accomplished.
12. We have found in §9 that the light-radiation of a star is described
by means of the total intensity (I), the mean wave-length ([lambda]0)
and the dispersion of the wave-length ([sigma][lambda]). [lambda]0
and [sigma][lambda] may be deduced from the spectral observations. It
must here be observed that the observations give, not the intensities at
different wave-lengths but, the values of these intensities as they are
apprehended by the instruments employed--the eye or the photographic
plate. For the derivation of the true curve of intensity we must know the
distributive function of the instrument (L. M. 67). As to the eye, we have
reason to believe, from the bolometric observations of LANGLEY
(1888), that the mean wave-length of the visual curve of intensity
nearly coincides with that of the true intensity-curve, a conclusion
easily understood from DARWIN's principles of evolution, which
demand that the human eye in the course of time shall be developed in
such a way that the mean wave-length of the visual intensity curve does
coincide with that of the true curve ([lambda] = 530 [mu][mu]), when
the greatest visual energy is obtained (L. M. 67). As to the dispersion,
this is always greater in the true intensity-curve than in the visual curve,
for which, according to §10, it amounts to approximately 60 [mu][mu].
We found indeed that the visual intensity curve is extended,
approximately, from 400 [mu][mu] to 760 [mu][mu], a sixth part of
which interval, approximately, corresponds to the dispersion [sigma]
of the visual curve.
In the case of the photographic intensity-curve the circumstances are
different. The mean wave-length of the photographic curve is,
approximately, 450 [mu][mu], with a dispersion of 16 [mu][mu],
which is considerably smaller than in the visual curve.
13. Both the visual and the photographic curves of intensity differ
according to the temperature of the radiating body and are therefore
different for stars of different spectral types. Here the mean
wave-length follows the formula of WIEN, which says that this
wave-length varies inversely as the temperature. The total intensity,

according to the law of STEPHAN, varies directly as the fourth power
of the temperature. Even the dispersion is dependent on the variation of
the temperature--directly as the mean wave-length, inversely as the
temperature of the star (L. M. 41)--so that the mean wave-length, as
well as the dispersion of the wave-length, is smaller for the hot stars O
and B than for the cooler ones (K and M types). It is in this manner
possible to determine the temperature of a star from a determination of
its mean wave-length ([lambda]0) or from the dispersion in [lambda].
Such determinations (from [lambda]0) have been made by SCHEINER
and WILSING in Potsdam, by ROSENBERG and others, though these
researches still have to be developed to a greater degree of accuracy.
14. Effective wave-length. The mean wave-length of a spectrum, or, as
it is often called by the astronomers, the effective wave-length, is
generally determined in the following way. On account of the
refraction in the air the image of a star is, without the use of a
spectroscope, really a spectrum. After some time of exposure we get a
somewhat round image, the position of which is determined precisely
by the mean wave-length. This method is especially used with a
so-called objective-grating, which consists of a series of metallic
threads, stretched parallel to each other at equal intervals. On account
of the diffraction of the light we now get in the focal plane of the
objective, with the use of these gratings, not only a fainter image of the
star at the place where it would have arisen without grating, but also at
both sides of this image secondary images, the distances of which from
the central star are certain theoretically known multiples of the
effective wave-lengths. In this simple manner it is possible to determine
the effective wave-length, and this being a tolerably well-known
function of the spectral-index, the latter can also be found. This method
was