122 Dr. Frank Watson Dyson [April 24, 



stars are eliminated, and that the mean distance of the group can be 

 correctly inferred. 



9. During the last twenty or thirty years the proper motions of 

 many stars have been determined by comparison of modern with 

 earlier observations. Particularly, the reduction by Dr. xiuwers of 

 Bradley's observations made in 1755, led to the accurate determin- 

 ation of the angular movements of the brighter stars. The proper 

 motions of fainter stars have been found by comparison of recent 

 ol^servations with those made in the first half of the nineteenth 

 century. These have all been utilized to determine the direction and 

 angular amount of tlie drift produced in the stars by the motion of 

 the solar system through space. The results were very puzzling, 

 because different mathematical methods and different groups of stars 

 gave widely different directions for the solar motion. The cause 

 was discovered about ten years ago by Professor Kapteyn, who found 

 in the proper motions of the stars another indication of regularity — 

 or perhaps it might be called a systematic irregularity — smaller than 

 the one discovered by Herschel, but unmistakable when once pointed 

 out. He interpreted these systematic irregularities to mean that the 

 stars are divisible into two groups, streaming through one another 

 in opposite directions in space. Prof. Kapteyn's discovery has been 

 submitted to mathematical analysis by Prof. Eddington and Prof. 

 Schwarzschild. Their researches have illuminated the whole subject 

 of stellar motions, and, though they are not in entire agreement, they 

 leave no doubt of the existence of a preferential movement among 

 the stars towards the north part of Orion, and the diametrically 

 opposite direction in the constellation of the Serpent. 



10. We must next consider the motus pecuUares — the irregular 

 movements of the stars themselves. From observations of the 

 velocities of stars in the line of sight, especially from those made 

 at the Lick Observatory under Prof. Campbell's direction, it is known 

 that a few stars are moving with great velocity, such as 100 kilo- 

 metres a second, while others are moving very slowly. The follow- 

 ing analysis of Campbell's results for one class of stars (Table II.), 

 those of spectral type A (taken from a paper by Prof. Eddington), 

 shows the proportion of slow-moving, moderate, and quick-moving 

 stars. 



Comparison with the third column of the table shows that the 

 velocities are distributed in accordance with the law of errors. This 

 law is identical with that found by Maxwell for the velocities of the 

 molecules of a gas. In the case of a gas, this distribution of velocities 

 results from the frequent collisions. For the stars there is no 

 evidence that it has resulted from their interaction. It must be 

 regarded as an observational fact that the distribution of the velocities 

 of the stars is stated concisely by this simple mathematical formula. 



11. The three movements — the movement of the solar system in 

 space, the streaming of the stars, and their irregular movements — are 



