DISTANCES OF THE STARS. Ibll 



niibsima ad alcuna delle maggiori, e die pero quella fussc al- 

 tissima, j^otrebbe accadere che qualche sensibil niutazione 

 succedesse tra di loro.'^ " Wherefore I do not "believe," saya 

 Galileo, in liis third discourse (Giornata terza), ''that all the 

 stars are scattered over a spherical superficies at equal dis- 

 tances from a common center ; but I am of opinion that their 

 distances from us are so various that some of them may ha 

 two or tln^ee times as remote as others, so that when som-i 

 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 liimself, 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 (1651 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 A-ery 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 343 S 

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

 ameter of its orbit.* This loicer limit of distances rose to 

 206,265 semi-diameters when certainty to a second M'as 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, Hob- 

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

 florrebow (who worked out Romer's rescued observations). 



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



