254 
NATURE 
[May 7, 1914 
It is also clear that the naked-eye stars, studied 
by Boss, Campbell, and Kapteyn, are, for the. most 
part, giants. With this in mind, we are now in a 
position to explain more fully the differences between 
the results of these investigators. 
All the stars of Class B are giants, and, so far as 
we may judge from the Scorpius cluster, they do not 
differ from one another very greatly in absolute 
brightness. It is therefore natural that the results 
of all three investigators are 
in this case fairly similar, B A 
though Campbell, in em- 
ploying stars that averaged 
brighter to the eye than 
did the others, has evidently 
been working with — stars 
that are really brighter. In 
Class A the giants and 
dwarfs differ so little, and 
are so. thoroughly _ inter- 
mingled, that the situation 
is about the same. In 
Class M, even the nearest 
and brightest of the dwarf 
stars are invisible to the 
naked ‘eye :. “hence: the 
stars of this class studied 
by the three investigators 
are all giants, and once 
more their results agree. 
A number of the dwarf 
stars of Class K are visible 
to the naked eye; _ but 
these all lie very near us, 
and have such large proper 
motions that they are ex- 
cluded as ‘abnormal’ by 
both Campbell and_ Boss. 
The results of the two agree 
in indicating that the stars 
studied by them are typical 
giants. The few dwarfs, 
however, have such large 
parallaxes and proper-motions 
that their inclusion more 
than doubles the mean 
proper-motion, and presum- 
ably, also, the mean parallax 
of the whole, as shown by 
Kapteyn’s figures in Table 
WUE For eeGlass Gy «the 
dwarf stars average much 
brighter, and a much greater 
number of them is~ visible 
to the naked eye. These 
have large parallaxes and 
proper-motions, and raise the 
average for all the stars 
of this class to greater 
values than for any other. 
But Boss’s rigorous limita- 
tion to small proper-motions 
weeds them practically all 
out, leaving giant stars 
once more. Campbell’s less drastic procedure 
omits only the nearer of the dwarfs (to be 
precise, those with the larger proper-motions), 
and his result lies about half-way between the others. 
In ‘the case of Class F, the dwarf stars are still 
brighter—intermingling, in fact, with the giants. 
We can therefore see them farther off, and we get 
more of them in our catalogues, in proportion to the 
giants, than in any other class. Their mean parallax 
NO. 232357 VOL@.03 | 
is, however, smaller than for the dwarfs of Classes G 
and K, and hence the mean proper-motion and 
parallax of all the stars of this class is less than 
for Class G. Campbell’s criterion here excludes very 
few stars, and even Boss’s admits a good many of 
the remoter and slower moving dwarfs, causing his 
mean parallax and proper-motion to be considerably 
greater for this class than for any other. 
It should finally be added that Kapteyn’s discussion 
F G K M N 
shows that the siars of Class N are exceedingly 
bright, possibly surpassing any of the other giant 
stars. 
We are now in a position to define more precisely 
the brightness of a typical giant or dwarf star of a 
given class of spectrum, and also to obtain a measure 
of the degree of divergence of the individual stars 
from this typical brightness. Taking first the stars 
of Class B and the dwarf stars of the other classes, 
