Lectures on Stellar Statistics | Page 6

the colour through
the mean wave-length (and not conversely) or the effective wave-length
as it is most usually called, or from the colour-index. We shall revert
later to this question. There are, however, a great many direct
eye-estimates of the colour of the stars.
Colour corresponding to a given spectrum.
Sp. Colour Number B3 YW- 161 A0 YW- 788 A5 YW 115 F5 YW, WY-
295 G5 WY 216 K5 WY+, Y- 552 M Y, Y+ 95 -----------------------------
Sum ... 2222
Spectrum corresponding to a given colour.
Colour Sp. Number W, W+ A0 281 YW- A0 356 YW A5 482 YW+, YW-

F3 211 WY G4 264 WY+, Y- K1 289 Y, Y+ K4 254 RY-, RY K5 85
-------------------------------- Sum ... 2222
The signs + and - indicate intermediate shades of colour.
The preceding table drawn up by Dr. MALMQUIST from the colour
observations of MÜLLER and KEMPF in Potsdam, shows the
connection between the colours of the stars and their spectra.
The Potsdam observations contain all stars north of the celestial
equator having an apparent magnitude brighter than 7m.5.
We find from these tables that there is a well-pronounced regressionin
the correlation between the spectra and the colours of the stars. Taking
together all white stars we find the corresponding mean spectral type
to be A0, but to A0 corresponds, upon an average, the colour
yellow-white. The yellow stars belong in the mean to the K-type, but the
K-stars have upon an average a shade of white in the yellow colour.
The coefficient of correlation (r) is not easy to compute in this case,
because one of the attributes, the colour, is not strictly graduated (i.e. it
is not expressed in numbers defining the colour).[5] Using the
coefficient of contingency of PEARSON, it is, however, possible to find
a fairly reliable value of the coefficient of correlation, and
MALMQUIST has in this way found r = +0.85, a rather high value.
In order to facilitate the discussion of the relation between colour and
spectrum it is convenient to deal here with the question of the spectra
of the stars.
10. Spectra of the stars. In order to introduce the discussion I first give
a list of the wave-lengths of the FRAUENHOFER lines in the spectrum,
and the corresponding chemical elements.
FRAUENHOFER line Element [lambda] A 759.4 B 686.8 C([alpha])
H (hydrogen) 656.3 D1 Na (sodium) 589.6 D3 He 587.6 E Fe (iron)
527.0 F([beta]) H 486.2 ([gamma]) H 434.1 G Ca (calcium) 430.8
h([delta]) H 410.2 H([epsilon]) Ca(H) 396.9 K Ca 393.4

The first column gives the FRAUENHOFER denomination of each line.
Moreover the hydrogen lines [alpha], [beta], [gamma], [delta],
[epsilon] are denoted. The second column gives the name of the
corresponding element, to which each line is to be attributed. The third
column gives the wave-length expressed in millionths of a millimeter as
unit ([mu][mu]).
On plate III, where the classification of the stellar spectra according to
the Harvard system is reproduced, will be found also the wave-lengths
of the principal H and He lines.
By the visual spectrum is usually understood the part of the radiation
between the FRAUENHOFER lines A to H ([lambda] = 760 to 400
[mu][mu]), whereas the photographic spectrum generally lies between
F and K ([lambda] = 500 to 400 [mu][mu]).
In the earliest days of spectroscopy the spectra of the stars were
classified according to their visual spectra. This classification was
introduced by SECCHI and was later more precisely defined by
VOGEL. The three classes I, II, III of VOGEL correspond
approximately to the colour classification into white, yellow, and red
stars. Photography has now almost entirely taken the place of visual
observations of spectra, so that SECCHI's and VOGEL's definitions of
the stellar spectra are no longer applicable. The terminology now used
was introduced by PICKERING and Miss CANNON and embraces a
great many types, of which we here describe the principal forms as they
are defined in Part. II of Vol. XXVIII of the Annals of the Harvard
Observatory. It may be remarked that PICKERING first arranged the
types in alphabetical order A, B, C, &c., supposing that order to
correspond to the temperature of the stars. Later this was found to be
partly wrong, and in particular it was found that the B-stars may be
hotter than those of type A. The following is the temperature-order of
the spectra according to the opinion of the Harvard astronomers.
Type O (WOLF-RAYET stars). The spectra of these stars consist
mainly of bright lines. They are characterized by the bright bands at
wave-lengths 463 [mu][mu] and 469 [mu][mu], and the line at 501
[mu][mu] characteristic of gaseous nebulae is sometimes present.

This type embraces mainly stars of relatively small apparent brightness.
The brightest is [gamma] Velorum with m = 2.22. We shall find that