194 cosmos. 



the whole structural configuration of the universe, lends a pe- 

 culiar charm to those investigations which relate to the dis- 

 tances of the fixed stars. 



Human ingenuity has invented for this class of investiga- 

 tions methods totally different from the usual ones, and which, 

 being based on the velocity of light, deserve a brief mention 

 in this place. Savary, whose early death proved such a loss 

 to the physical sciences, had pointed out how the aberration 

 of light in double stars might be used for determining the 

 parallaxes. If, for instance, the plane of the orbit which the 

 secondary star describes around the central body is not at 

 right angles to the line of vision from the earth to the double 

 star, but coincides nearly with this line of vision itself, then 

 the secondary star in its orbit will likewise appear to describe 

 nearly a straight line, and the points in that portion of its 

 orbit which is turned toward the earth will all be nearer to 

 the observer than the corresponding points of the second half, 

 which is turned away from the earth. Such a division into 

 two halves produces not a real, but an apparent unequal 

 velocity, with which the satellite in its orbit recedes from, 

 or approaches, the observer. If the semi-diameter of this 

 orbit were so great that light would require several days or 

 weeks to traverse it, then the time of the half revolution 

 through its more remote side will prove to be longer than the 

 time in the side turned toward the observer. The sum of 

 the two unequal times will always be equal to the true pe- 

 riodic time ; for the inequalities caused by the velocity of light 

 reciprocally destroy each other. From these relations of du- 

 ration, it is possible, according to Savary's ingenious method 

 of changing days and parts of days into a standard of length 

 (on the assumption that light traverses 14,356 millions of 

 geographical miles in twenty-four hours), to arrive at the 

 absolute magnitude of a semi-diameter of the earth's orbit , 

 and the distance of the central body and its parallax may be 

 then deduced from a simple determination of the angle under 

 which the radius appears to the observer.^ 



In the same way that the determination of the parallaxes 

 instructs us as to the distances of a small number of the fixed 

 stars, and as to the place which is to be assigned to them in 

 the regions of space, so the knowledge of the measure and 

 duration of proper motion, that is to say, of the changes which 

 take place in the positions of self-luminous stars, throws some 



* Savary, in the Connaissance des Temps pour 1830, p. 56-69, and 

 p. 163-171 ; and Struve, ibid., t>. clxiv. 



