716 

ments are, they are too coarse to tell us much about 
the distances of the stars. 
Let us consider several 
measures :— 
(1) Van Maanen’s list of five stars is as follows :— 
recent sets of parallax 
Star Parallax Probable error 
“ “ 
96 mae 0:026 +0:007 
672 — 0:009 0-004 
1549 0-001 0-002 
2921 0;078 0-006 
3233 0:003 0-010 
(2) In two recent lists we find parallaxes for 61 
Cygnus, the star for which Bessel first found a 
parallax. Q 
Authority Parallax Probable error 
a“ 
Miller, 24-in. telescope, Sproul 
Observatory me Sob AO: 2 01 + 0-010 
Slocum and Mitchell, 40-in. tele- 
scope, Yerkes Observatory 0:272 0:005 
The negative parallax in Van Maanen’s list would 
mean that the star was actually more distant than its 
comparison stars, which is at least unlikely, and in 
two other cases it will be seen that the parallaxes 
found are smaller than their probable errors. Some- 
what similarly, in the case of 61 Cygnus, although 
the two parallaxes found agree very well, they differ 
by much more than their probable errors. 
(3) In the recent most considerable list of stellar 
parallaxes published (Slocum and Mitchell, Popular 
Astronomy, March, 1914), out of twenty-eight results, 
eight are negative parallaxes and another four are 
smaller than their probable errors; yet the list is one 
of stars selected for large proper motion or some other 
peculiarity which indicated a measurable parallax. 
These three sets show us that, valuable as the photo- 
graphic method is, it is to be feared that it will also 
soon work out its rich lodes. So it does not take us 
much further. In this way the direct attacl< by parallactic 
displacement will reveal perhaps some one or two 
hundred parallaxes; but we would learn nothing as to 
the distances of the great mass of stars, except what 
we already know, namely, that the distances are 
tremendous. 
Fortunately there is an indirect method of attack 
which, in the course of time, will tell us the distances 
of all the stars. 
Basically this method depends upon a knowledge of 
the proper motions of the stars. If by its annual 
motion around the sun, the earth causes the stars to 
be displaced, it is obvious that the progressive motion 
of the sun through space must cause a progressive 
displacement. If for the moment we assume the stars 
to be at rest, they will seem to suffer two displace- 
ments—one purely periodic in a year, the other pro- 
gressive, due respectively to the earth’s orbital motion 
and the sun’s motion through space. 
The earth’s orbital motion being periodic has no 
cumulative effect, but the sun’s progressive motion 
is. cumulative. The amplitude of the earth’s periodic 
motion is about 300,000,000 Kilometres, and all the 
best and most recent results show that the sun is 
moving through space with a velocity of about 18 kilo- 
metres a second; hence in a year the sun, and with 
it, of course, the earth and the rest of the solar system, 
move over a distance of 550,000,000 kilometres; 
roughly this is already twice the earth’s annual dis- 
placement, and, as already stated, it is cumulative; 
thus, in six years, the progressive displacement is 
already eleven times the earth’s periodical displace- 
ment, and the gain is continuous. Hence the mere 
lapse of time will tell us the distance of the stars, but 
the problem is complicated because the proper motions 
NO. 2391, VOL. 95] 
NATURE 




[AUGUST 26, I915 
of the stars are not mere reflexes of the sun’s proper 
motion; the stars themselves are also in motion, so 
that a process of unravelling is necessary. Without 
any unravelling, but by simple averaging, the elder 
Herschel found that the sun was travelling in the 
direction of the constellation Hercules. At Capetown, 
in 1905, Prof. Kapteyn announced his discovery that 
the proper motions of the stars divided themselves into 
two distinct drifts. The elder Boss found that the 
proper motions of a widely-spread group of stars con- 
verged to a point. The same astronomer also found, 
from a study of the proper motions, that there was a 
marked relation between the amount of proper motion 
and a star’s spectrum. 
Investigations based upon proper motions—the 
thwart or across the line of sight motions—were 
powerfully aided by spectroscopic results, and 
especially by the application of the Doppler principle, 
which tells us almost directly the radial velocity of the 
star, or its motion in the line of sight. The inter- 
pretation of stellar spectra is far from complete, and 
its problems will not be discussed to-night. The broad 
facts are that stellar spectra, with a few exceptions, 
fall into four great classes, which may be called the 
helium stars, the hydrogen stars, the metallic stars, 
and the carbon stars, in which the gradation from 
one class to another is so well marked that it is very 
plausibly assumed that a star of one class can in the 
course of time change into its contiguous class, and 
from that into its next class. At present it is assumed 
that the helium class is degrading or cooling into the 
hydrogen class, and that the hydrogen class is similarly 
approaching the metallic class (in which our sun is), 
and that later the metallic class will degrade into the 
carbon class, and that, finally, the carbon class will 
cool down and become dark stars. This continuous 
degradation is a convenient memoria technica, but it 
is not based upon any facts. Sir Norman Lockyer, 
by a closer study of spectra, asserts that there is both 
a descending and an ascending scale. The assumption 
that there are the dark stars above referred to is unsup- 
ported by any fact. But to-night we are only con- 
cerned with spectrum analysis as an aid to interpret- 
ing the proper motions of the stars. Radial velocities 
fully confirm the motion of the sun through space as 
disclosed by the proper motions. The recent spectro- 
scopic determinations of the direction and amount 
of the solar motion made by Dr. Campbell in 
America and by Messrs. Hough and Halm at the 
Cape, agree within a reasonable margin with the 
determinations of Newcomb and Boss, which are 
based on proper motions. Further, as with the proper 
motions, it is found that as the stars degrade from 
helium to hydrogen to metallic to carbon spectra, their 
velocities increase. Prof. E. C. Pickering and others 
have shown how certain species of stars aggregate in 
certain parts of the skv. Thus the helium stars are 
only found near the Milky Way, that great girdle of 
stars which is the framework of the sidereal system. 
The direct measurement of parallaxes, and the small- 
ness of their proper motions, both indicate that the 
helium stars are enormously distant; and conversely, 
that stars near us are generally of the metallic spec- 
trum class. Besides the Taurus group of converging 
stars found by Boss, several other groups, with mem- 
bers spread all over the sky, have been found. The 
stars in these groups appear to be moving with nearly 
equal and parallel velocities through space. It is 
evident that once a star is grouped correctly, and the 
parallax or distance and velocity of any one star in 
its group is known, we can also determine its distance. 
Unfortunately the Doppler principle, by which astro- 
nomers determine the radial velocities of the stars, is 
somewhat limited in its application. In the helium 
and hydrogen classes the lines of the spectrum are 
