DISTANCES 01' THE STAltS. 257 



pero quella fusse altissima, potrebbe accadere che qualche sen- 

 sibil mufdzione succedesse tra di loro" "Wherefore I do 

 not believe," says Galileo, in his third discourse (Giornata 

 terza), " that all the stars are scattered over a spherical 

 superficies, at equal distances from a common centre ; but I am 

 of opinion that their distances from us are so various that 

 some of them may be two or three times as remote as 

 others, so that when some minute star is discovered by 

 the telescope close to one of the larger, and yet the 

 former is highest, it may be that some sensible change 

 might take place among them." The introduction of the 

 Copernican system imposed, as it were, the necessity of nume- 

 rically determining, by means of measurement, the change 

 of direction occasioned in the position of the fixed stars by 

 the earth's semi-annual change of place in its course round 

 the sun. Tycho Brahe's angular determinations, of which 

 Kepler so successfully availed himself, do not manifest any 

 perceptible change arising from parallax in the apparent posi- 

 tions of the fixed stars, although, as I have already stated, 

 they are accurate to a minute of the arc. For this the 

 Copernicans long consoled themselves with the reflection, that 

 the diameter of the earth's orbit (165J millions of geographical 

 miles) was insignificant, when compared to the immense 

 distance of the fixed stars. 



The hope of being able to determine the existence of parallax 

 must accordingly have been regarded as dependent on the 

 perfection of optical and measuring instruments, and on the 

 possibility of accurately measuring very small angles. As long- 

 as such accuracy was only secure within a minute, the non- 

 observance of parallax merely testified to the fact, that the dis- 

 tance of the fixed stars must be more than 3438 times the earth's 

 mean distance from the sun, or semi-diameter of its orbit. 17 



17 Bessel, in Schumacher's Jahrb.fur 1839, s. 511. 



VOL. III. S 



