1914] on The Stars around the North Pole 110 



that these formulae could be most simply interpreted on the as- 

 sumption that the earth revolved round the sun. His purely geo- 

 metrical arguments were, it is true, powerfully reinforced by the 

 revelations of Gahleo'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 required to obtain the form and dimensions of 

 the earth itself, and thus supply a base line to determine the scale of 

 the system. 



4. The fixed stars present us with a very similar problem. From 

 the study of their small angular movements, supplemented by spectro- 

 scopic observations, it is required to construct as far as possible a 

 model of the stellar universe. Such a model would give for each 

 star — 



{a) Its actual position in space, measured along three axes with 

 the sun as origin. 



{b) The velocity in kilometres per second in each of these 

 directions. 



(c) The brightness or luminosity, taking the sun as unit. 



{d) The mass. 



{e) The size. 



(./') The physical and chemical constitution. 



Of these elements, the mass is at present only determinable for 

 double stars, and the size for eclipsing variables. The physical and 

 chemical constitution are known from spectroscopic observations for 

 a considerable number of stars. But the distance and absolute 

 brightness can be found only for a hmited number of the nearer 

 stars. Average results can, however, be obtained for the more distant 

 stars which tell us — 



{a) The number within certain limits of distance from the sun. 



[h) The mean velocities of these stars, and what percentage are 

 moving with given velocities, say, for example, between 10 and 

 20 kilometres per second. 



(c) Whether these velocities are irregular or show anything in the 

 nature of streaming in particular directions. 



{cl) 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, 

 Avithin the powers of astronomers, and we nurse the perhaps extrava- 

 gant hope that generalizations will be discovered which will lead to 



