574 
NAIURE 
[JULY 30, 1914 
THE STARS AROUND THE NORTH POLE. | 
N KNOWLEDGE of distances of the stars is of 
fundamental importance in any attempt to 
describe the stellar universe It is required, before 
answers can be given to questions on the average 
distances of stars from one another, their brightness 
compared with the sun, and the extent to which they 
reach in space. There are not more than 100 or 150 
stars of which the distances have been measured with 
any degree ot accuracy. Although this number is being 
steadily increased, it is only the stars which are com- 
paratively near to the sun whicn can be treated 
individually. For the greater number we have 'to be 
content with average values which apply to groups 
of stars. 
A map or a photograph of the stars gives only their 
bearings—that is to say, their directions as seen from 
the earth. It gives no information whatever about the 
distances. One star may be a hundred times as far 
away as its neighbour on the map. But if two maps 
are made, separated by a sufficient interval of time, 
some differences will be found in the relative positions 
of the stars. These indicate movements either of the 
stars themselves or of the point from which they are 
viewed. But the movements which are observed are 
merely changes of angular position. We cannot tell 
directly from them either the actual velocities or dis- 
tances of the stars, but only the ratio between these 
quantities. It is, however, from the geometrical study 
of these small angular motions, supplemented by the 
information obtained from the spectroscope as to the 
velocities of stars in the line of sight, that cur know- 
ledge of their distances is derived. 
The problem is in many ways analogous to one 
which has been completely solved. In the early days 
of astronomy the movements of the wandering stars 
or planets were noted. ‘The essential characteristics 
of the movements were embodied in geometrical 
formule by the Greeks. In the course of time 
Copernicus showed that these formula could be most 
simply interpreted on the assumption that the earth 
revolved round the sun. His purely geometrical 
arguments were, it is true, powerfully reinforced by 
the revelations of Galileo’s telescope. Nevertheless, 
the planetary system as formulated by Copernicus and 
Kepler resulted from the observation of the angular 
movements of the planets and the attempt to give them 
the simplest possible geometrical interpretation. 
Further study of the planetary system has been 
guided and controlled by the law of gravitation. But 
the observational data on which our very complete 
knowledge of the solar system is based, the distances, 
sizes, and movements of all its members, are a long 
series of measures of the angular movements as seen 
from the earth. Linear measurements are only re- 
quired to obtain the form and dimensions of the earth 
itself, and thus supply a base line to determine the 
scale of the system. 
The fixed stars present us with a very similar 
problem. From the study of their small angular 
movements, supplemented by spectroscopic observa- 
tions, it is required to construct as far as possible a 
model of the stellar universe. Such a model would 
give for each star :— 
(i) Its actual position in space, measured along three 
axes with the sun as origin. 
(ii) The velocity in kilometres a second in each of 
these directions. 
(iii) The brightness or luminosity, taking the sun as 
unit. 
(iv) The mass. 
(v) The size. 
(vi) The physical and chemical constitution. 
1 Dise urse delivered at the Royal Institution on Friday, April by 
Dr. F. W. Dyson. F.R.S. a Same > 
NO; 2335, VOL. 93] 
Of these elements the mass is at present only deter- 
muinable tor double stars, and the size for eclipsing 
variables. The physical and chemical constitution are 
known trom spectioscopic observations tor a consider- 
able number of stars. But the distance and absolute 
brightness can be tound only tor a limited number of 
the nearer stars. Average results can, however, be 
obtained for the more distant stars, which tell us :— 
(1) The number within certain limits of distance 
from the sun. 
(2) The mean velocities of these stars, and what per- 
centage are moving with given velocities, say, for 
example, between 10 and 20 kilometres a second. 
(3) Whether these velocities are irregular or show 
anything in the nature of streaming in particular 
directions. 
(4) What proportion of the stars are comparable with 
the sun in intrinsic brightness, and what proportion 
are ten times or one-tenth as bright, and so on. 
Such a description of the stellar system is, to a large 
extent, within the powers of astronomers, and we 
nurse the perhaps extravagant hope that generalisa- 
tions will be discovered which will lead to the formula- 
tion of dynamical laws on the constitution of the 
stellar universe. 
A small area round the pole has been chosen as a 
sample, because this part of the sky has been observed 
more fully than any other of equal extent. It forms a 
small cap extending to a distance of 9° from the pole, 
and covering about 1/160 of the whole sky. In the 
years 1855-6 Carrington, an English amateur 
astronomer, well known from his observations of 
sun-spots, using a very small transit instrument, 
observed the positions of all the stars in this part of 
the sky from the brightest down to very faint stars 
between the toth and 11th magnitudes. He thus 
constructed a catalogue, giving with great accuracy 
the positions of 3700 stars for the year 1855. About 
the year 1900 these stars were re-observed at Green- 
wich by a combination of visual and photographic 
observations. By comparison with the positions as 
given in Carrington’s Catalogue, the angular move- 
ment of each of these 3700 stars in forty-five years is 
determined. These angular movements, or ‘‘ proper 
motions ’’ as they are technically called, are the data 
available for obtaining the actuai positions and move- 
ments of the stars in space. We have to solve the 
geometrical problem of making these stars stand out 
in three dimensions, so that we may see them as we 
see a picture in a stereoscope. 
Now the proper motions of stars are very small. 
The star of largest proper motion moves only 870" 
a century. An idea of the smallness of this motion 
may be obtained from the tact that it will take two 
centuries to move a distance equal to the apparent 
diameter of the sun or moon. There is no star 
among those near the North Pole with a _ proper 
motion so great as this. The following table gives 
an abstract of the proper motions of the 3726 stars 
under consideration :— 
Taste I. 
Limits of Number 
Proner Motion. of Stars. 
> 40" a century a8 2 
20°—40" 4, , eae 39 
IO—20° we 134 
See os a sis 574 
34 ee wee 977 
Oi ea alae ‘ed 2,000 
It is clear that the stars with large proper motions 
must either be moving fast or must be comparatively 
near. These are the alternatives, but for an individual 
star it is impossible to decide between them. 
The table shows how largely the proper motions 
of stars vary in amount. They differ just as widely 
*thwe ee 
