DISTANCES OF THE ai'ARS. 189 



nissima ad alcima dclle viaggiori, e che pcro quell a fussc al- 

 tissima, jwlfcddc accadcrc che qicalche sotsibil mutazione 

 succcdcsse tra di loroy " 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 dis- 

 tances from a coimnon center ; 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 in- 

 troduction of the Copernican system imposed, as it were, the 

 necessity of numerically determining, by means of measure- 

 ment, 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 determina- 

 tions, of which Kepler so successfully availed himself, do not 

 manifest any perceptible change arising from parallax in 

 the apparent positions 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 (lG5i mill- 

 ions 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 par- 

 allax 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 distance of the fixed stars must be more than 3438 

 times the earth's mean distance from the sun, or semi-di- 

 ameter of its orbit. '^' This loivcr limit of distances rose to 

 206,265 semi-diameters when certainty to a second was at- 

 tained in the observations of the great astronomer, James 

 Bradley ; and in the brilliant period of Frauenhofer's instru- 

 ments (by the direct measurement of about the tenth part 

 of a second of arc), it rose still higher, to 2,062,648 mean 

 distances of the earth. The labors and the ingeniously con- 

 trived zenith apparatus of Newton's great cotemporary, Rob- 

 ert Hooke (1669), did not lead to the desired end. Picard, 

 Horrebow (who worked out Romer's rescued observations) 



" Besael, in Schumaclier's Jahrb. fur 1839, s. 511. 



