﻿312 WILCOCKS' REFLECTIONS ON THE 



The explanation offered by the schoolmen of Tycho's day was rejected by that 

 astronomer upon ground already stated. 



Upon this point Arago remarks, " that the phenomena did not imply motion in a 

 line mathematically straight; for by substituting a highly elliptical orbit for the 

 straight line, its conjugate axis might have been small enough to escape observation 

 from the earth. Tycho's objection had therefore no force." 



Arago further says : " If the Astronomers of the time of Tycho had understood the 

 velocity of light, and had been able in their observations upon parallax, to practice 

 the precision of which the moderns justly boast, they would from the hypothesis of 

 a change of distance, considered as a means of explaining the variations of the intensity 

 of the star of 1572, have drawn conclusions, before which, in my opinion, the most 

 daring would have recoiled. The reader shall judge." 



" The star of 1572 being in the region of the other stars, its distance from the earth 

 must have equalled at least that, over which light could travel in three years." 



" At the time of its sudden apparition, and for several months afterwards, the new 

 star surpassed in brilliancy the other stars of the first magnitude. For a star of the 

 first magnitude to become one of the second, by receding from the earth, it must (as 

 has been proved, Chap. 5, p. 361,) double its primitive distance. Thus the star of 

 the first magnitude of 1572 could not have faded to the second rank without having at 

 least receded the distance over which light could travel in three years." 



" Six years at least must have elapsed between the last day of the period in which 

 it shone in its full splendor, and the day when it should first appear of the second 

 magnitude, even if the velocity of the star equalled that of light." 



" Three years would have been acquired for the star to pass from its position in 

 the first rank, to that in the second, and three years for its light to pass from the 

 second position to the first." 



" Under the supposition that the star retains the same velocity, the transition from 

 the second magnitude to the third, would have required an interval of six years, and 

 so on to the seventh magnitude." 



" In short, the star of the middle of November, 1572, receding from the earth with 

 the velocity of light, could not pass from one magnitude to another, by means of its 

 increased distance, in less than six years; it would have required thirty-six years to 

 descend from the first to the seventh magnitude." 



" Let us compare these calculations with the results of observation." 



" In March, 1573, the new star in Cassiopeia was still of the first magnitude." 



"One month later, in April, 1573, it had already descended to the second magni- 

 tude." 



" To explain so rapid a variation of intensity by a simple change of distance, it is 

 vain even to give the star a velocity greater than that of light ; for example, with an 



