The spectral types may be summed up in the following way:—
| White | stars:— | Secchi's | type | I:— | Harvard | B and A, |
| Yellow | " :— | " | " | II:— | " | F, G and K, |
| Red | " :— | " | " | III:— | " | M, |
| " | " :— | " | " | IV:— | " | N. |
The Harvard astronomers do not confine themselves to the types mentioned above, but fill up the intervals between the types with sub-types which are designated by the name of the type followed by a numeral 0, 1, 2, ..., 9. Thus the sub-types between A and F have the designations A0, A1, A2, ..., A9, F0, &c. Exceptions are made as already indicated, for the extreme types O and M.
11.
Spectral index. It may be gathered from the above description that the definition of the types implies many vague moments. Especially in regard to the G-type are very different definitions indeed accepted, even at Harvard.[6] It is also a defect that the definitions do not directly 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 [§9] that the light-radiation of a star is described by means of the total intensity (I), the mean wave-length (λ0) and the dispersion of the wave-length (σλ). λ0 and σλ 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 (λ = 530 μμ), 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 μμ. We found indeed that the visual intensity curve is extended, approximately, from 400 μμ to 760 μμ, a sixth part of which interval, approximately, corresponds to the dispersion σ 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 μμ, with a dispersion of 16 μμ, which is considerably smaller than in the visual curve.