tly give _quantitative_ characteristics of the spectra. None the
less it is possible to substitute for the spectral classes a continuous
scale expressing the spectral character of a star. Such a scale is
indeed implicit in the Harvard classification of the spectra.

Let us use the term _spectral index_ (_s_) to define a number expressing
the spectral character of a star. Then we may conveniently define this
conception in the following way. Let A0 correspond to the spectral index
_s_ = 0.0, F0 to _s_ = +1.0, G0 to _s_ = +2.0, K0 to _s_ = +3.0 M0 to
_s_ = +4.0 and B0 to _s_ = -1.0. Further, let A1, A2, A3, &c., have the
spectral indices +0.1, +0.2, +0.3, &c., and in like manner with the
other intermediate sub-classes. Then it is evident that to all spectral
classes between 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 Sec.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 unders