258 
The two series of giant and dwarf stars appear once 
more; the giants are all of about the same brightness, 
except that those of Class B are brighter than the 
rest; the dwarf stars diminish in brightness by about 
two ‘magnitudes for each spectral class; the two series 
overlap up to Class G and ‘separate at Class K, and 
so on. We have clearly come, for the third time, 
and again from independent data, upon the same 
phenomena as before; and, with the more extensive 
observational material, some of the characteristics 
and relations of the two groups are shown better than 
ever. 
But this new evidence does much more than to con- 
firm that which we have previously considered—it 
proves that the distinction between the giant and 
dwarf stars, 
ness and spectral types, do not arise (primarily at 
least) from differences in mass. Even when reduced 
to equal masses, the giant stars of Class K are about 
one hundred times as bright as the dwarf stars of 
similar spectrum, and for Class M the corresponding 
ratio is fully tooo. Stars belonging to the two series 
must therefore differ greatly either in surface bright- 
ness or in density, if not in both. 
There is good physical reason for believing that 
stars of similar spectrum and colour-index are at 
least approximately similar in surface brightness, and 
that the surface brightness falls off rapidly with in- 
creasing redness. Indeed, if the stars radiate like 
black bodies, the relative surface brightness of any 
two stars should be obtainable by multiplying their 
relative colour-index by a constant (which is the ratio 
of the mean effective photographic wave-length to the 
difference of the mean effective visual and_photo- 
graphic wave-lengths, and lies usually between 3 and 
4, its exact value depending upon the systems of 
visual and photographic magnitude adopted as 
standards). Such a variation of surface brightness 
with redness will evidently explain at least the greater 
part of the change in absolute magnitude among the 
dwarf stars (as Hertzsprung and others have pointed 
out), but it makes the problem of the giant stars 
seem at first sight all the more puzzling. 
The solution is, however, very simple. If a giant 
star of Class K, for example, is one hundred times as 
bright as a dwarf star of the same mass and spec- 
trum, and is equal to it in surface brightness, it must 
be of ten times the diameter and 1/1000 of the density 
of the dwarf star. If, as in Class M, the giant star 
is one thousand times as bright as the dwarf, it must 
be less than 1/30,000 as dense as the latter. Among 
the giant stars in general, the diminishing surface 
brightness of the redder stars must be compensated 
for by increasing diameter, and therefore by rapidly 
decreasing density (since all the stars considered have 
been reduced to equal mass). 
But all this rests on an assumption which, though 
physically very probable, cannot yet be said to be 
proved; and its consequences play havoc with certain 
generally accepted ideas. We will surely be asked, 
Is the assumption of the existence of stars of such 
low density a reasonable or probable one? Is there 
any other evidence that the density of a star of Class 
G or K may be much less than that of the stars of 
Classes B and A? Can any other evidence than that 
derived from the laws of radiation be produced in 
favour of the rapid decrease of surface brightness 
with increasing redness ? 
We can give at once one piece of evidence bearing 
on the last question. The twelve dwarf stars of 
Classes K2 to M, shown in Fig. 2, have, when re- 
duced to the sun’s mass, a mean absolute magnitude 
of 7-8—three magnitudes fainter than the sun. . If of 
the sun’s surface brightness, they would have to be, 
NO. 23225 VOL: .93)| 
NATURE 
and the relations between their bright- } 
[May 7, 1914 
average, cf one-fourth its radius, and their’ 
mean density would be sixty-four times that of the 
sun, or ninety times’ that of water—which is 
altogether incredible. A body of the sun’s mass and 
surface brightness, even if as dense as platinum, 
would only be two magnitudes fainter than the sun, 
and the excess of faintaess of these stars beyond this 
limit can only be reasonably ascribed to deficiency in 
surface brightness. For the four stars of spectra 
K8 and M, the mean absolute magnitude of which, 
reduced to the sun’s mass, is 9:5, the mean surface 
brightness can at most be one-tenth that of the sun. 
(To be continued.) 
on the 
UNIVERSITY AND EDUCATIONAL 
INTELLIGENCE. 
CAMBRIDGE.—The office of superintendent of the 
museum of zoology will shortly become vacant by the 
resignation of Dr. Doncaster. The stipend at pre- 
sent attached to the office is 200]. per annum. 
Applications to occupy the University’s table in the 
Zoological Station at Naples, and that in the labora- 
tory of the Marine Biological Association at Plymouth 
should be addressed to Prof. Langley, The Museums, 
Cambridge, on or before June 4. 
Mr. C. G. Darwin, eldest son of the late Sir George 
Darwin, has been appointed mathematical lecturer 
at Christ’s College. 
GiLascow.—lIt is announced that honorary degrees 
are to be conferred on Dr. Archibald Barr, late regius 
professor of civil engineering and mechanics in the 
University, Colonel Sir William B. Leishman, 
BeR-S., ese: of pathology in the Royal Army 
Medical College, and Sir Ernest Hi. Shackleton;: 
C.V.O. The degrees will be conferred on Com-’ 
memoration Day, June 23, when an oration on Lord 
Lister will be delivered by Sir Hector C. Cameron. 
Lonpon.—The Page-May Memorial Lectures for 
the current session will be delivered by Dr. Keith 
Lucas, whose subject will be ‘‘ The Conduction of the’ 
Nervous Impulse.’’ The course will be held at Uni- 
versity College, on Fridays, beginning on May 15. 
The lectures are open to all internal students of the’ 
University of London and to such other persons as 
are specially admitted. Applications should be ad- 
dressed to the secretary, University College, London 
(Gower Street, W.C.). 
OxrorD.—Congregation on May 5 passed a statute 
authorising the establishment of an additional pro- 
fessorship in chemistry, to be called Dr. Lee’s Pro- 
fessorship of Chemistry. In the same Congregation 
the statutes providing for the establishment of Dr. 
Lee’s Professorships of Anatomy and Experimental 
Philosophy, in place of the existing Lee’s Readerships, 
passed their first stage. Should these statutes be 
finally approved, the University will be relieved of its 
present contribution of 1470l. towards the stipends of 
the professors of human anatomy and experimental 
philosophy, and will gain an additional professor of 
chemistry, the consequent charges being borne in all 
these cases by Christ Church. 
The Halley Lecture for 1914 will be delivered by. 
Colonel C. F. Close, director of the Ordnance Survey, 
at the Examination Schools at 8.30 p.m. on May 20. 
Subject, ‘“‘The Geodesy of the United Kingdom.” 
The celebration of the seven hundredth anniversary 
of the birth of Roger Bacon will be held on Wednes- 
day, June to. 
Rhode Island, is to receive a 
H. Bragg, 
Brown UNIVERSITY, 
visit in “November next from Prof. W. 
