806 Professor Dr. J. C. KafpUyn [May 22, 



The motion may be preferentially in a horizontal plane or alono^ a 

 determined line, say along the longer axis of the pond, provided only 

 that the motions in any two opposite directions are equally frequent. 



Not only that : even if the cloud, as a whole, is not immovable, 

 we are not necessarily helpless. For, if the insect-cloud and the 

 photographer were both on a sailing vessel, circumstances would be 

 the same as on the mainland, though now the cloud is in motion. 

 Only, instead of the absolute displacement of the photographic 

 apparatus, we must know the displacement relative to the ship, or 

 rather relative to the insect-cloud. This, then, finally is the real 

 thing wanted. We may obtain the distance of the insect-cloud, or 

 what comes to the same, the average distance of its members, as soon 

 as we are able to find out the displacement of our point of view with 

 regard to the centre of gravity of the cloud. 



Our case is much the same in the world of the stars. 



We shall be able to determine the average distance of the 

 members of any arbitrary group of stars, provided that we can find 

 the motion of the solar system, both in amount and in direction, 

 relative to the centre of gravity of the group. 



Now, astronomical observations such as those which led the elder 

 Herschel to his discovery of the solar motion through space enable 

 us to determine the direction of tlie sun's motion relative to such 

 groups as the stars of the 3rd, 4th, etc., magnitude. Spectroscopy 

 enables us to determine the cimonnt of that motion. 



We must be al)le, therefore, to find out the average distance of 

 the stars in these groups. For other groups, such as the stars having 

 an apparent centennial motion of 10", 20", etc., there is a difficulty. 

 Still, however, we have succeeded in overcoming this difficulty by a 

 somewhat indirect process, and pressing into service the stars of 

 which the individual distances are known. Tliis, then, is the upshot 

 of astronomical work on the distances. 



What we know about Star-distance. 



By direct measurement ive know the distance of some hundred 

 individual stars. 



For the rest we know the average distance of any fairly numerous 

 group of stars of determinate apparent magnitude and apparent motion.* 



* At the present moment some objection might certainly still be made 

 against the generality of this statement. In fact, the scarcity of spectroscopic 

 data is the cause that, though the determination of the solar motion separately 

 for such groups as the stars of determinate magnitude and proper motion is 

 quite possible, it has not yet been carried through. As a consequence the 

 results used in what follows still rest on the assumption that the centres of 

 gravity of all the groups considered are at rest relative to each other. That 

 this assumption must be probably true, follows from the near identity of the 

 direction of the sun's motions, furnished by the several groups. 



