NEW WA YS OF MEASURING THE SUN'S DISTANCE. 73 



fixed images. This movement gives us a second measure 

 of the distance, which, however, may be regarded as only a 

 reversed repetition of the preceding. But now, carrying on 

 Jhe reverse motion, the moving images of star and asteroid 

 separate from their respective fixed images, the moving 

 image of the star drawing near to the fixed image of the 

 asteroid and eventually coinciding with it Here we have a 

 third measure of the distance, which is independent of the 

 two former. Reversing the motion, and carrying the moving 

 images to coincidence with the fixed images, we have a 

 fourth measure, which is simply the third reversed. These 

 four measures will give a far more satisfactory determination 

 of the true apparent distance between the star and the 

 asteroid than can, under any circumstances, be obtained in 

 the case of Mars and a star. Of course, a much more exact 

 determination is required to give satisfactory measures of the 

 asteroid's real distance from the earth in miles, for a much 

 smaller error would vitiate the estimate of the asteroid's 

 distance than would vitiate to the same degree the estimate 

 of Mars's distance : for the apparent displacements of the 

 asteroid as seen either from Northern and Southern stations, 

 or from stations east and west of the meridian, are very much 

 less than in the case of Mars, owing to his great proximity. 

 But, on the whole, there are reasons for believing that the ad- 

 vantage derived from the nearness of Mars is almost entirely 

 counterbalanced by the advantage derived from the neatness 

 of the asteroid's image. And the number of asteroids, with 

 the consequent power of repeating such measurements many 

 times for each occasion on which Mars has been thus ob- 

 served, seem to make the asteroids so long regarded as 

 very unimportant members of the solar system the bodies 

 from which, after all, we shall gain our best estimate of the 

 sun's distance ; that is, of the scale of the solar system. 



Since the abdve pages were written, the results deduced 

 from the observations made by the British expeditions for 



