42 



same in both cases. From this it follows inevitably that it is the 

 sun's transit, indicated by the passage of the point a ov b across 

 the radius-vector, and not the transit of any star over any given 

 meridian of the earth's surface, that is the true measure of the 

 earth's rotations, or at least that would be so, were the earth's 

 orbit a perfect circle, along which she moved with uniform ve- 

 locity. 



Suppose the earth, instead of rotating 365 or 360 times in 

 each orbital revolution, were to rotate only once. By rotating 

 once, however, be it observed, 1 do not mean that she should keep 

 the same point of her circumference constantly on the radius- 

 vector, looking to the sun ; on the contrary I really mean to say 

 what the word expresses, that she should indeed turn once round 

 about on her axis like a wheel, carrying every point of her cir- 

 cumference past the radius- vector, and across the orbit. Of 

 course, as already remarked, and as admitted by all astronomers, 

 the results would be precisely the same, whether the star revolve 

 round about the heavens from east to west while the earth stands 

 still at N, or the earth move round in the contrary direction, from 

 west to east, while the star stands still. Let the earth, there- 

 fore, for the present be considered as standing still at N, and 

 let the star revolve to the right, or from east to west. By the 

 time the star reaches the first degree to the right of N, the earth 

 will have turned on her axis one degree in the opposite direction, 

 making together a difference of two degrees ; and this being re- 

 peated at each degree, the star will make its transit over the 

 same meridian which it left behind at N, when it has only gone 

 round half its circuit of the heavens, and the earth has turned 

 only half round on its axis. After a similar process, during 

 the other half of the star's revolution and the earth's rotation, 

 the star will make a second transit over the same meridian, or 

 in other words, the star and that meridian will again be in one 

 at N, after completing their respective circuits. But it must be 

 perfectly obvious, that in this process the earth has turned round 

 on its axis only once, and measured its complete rotation by car- 

 rying every point of its circumference, without exception or short- 

 coming, past the radius- vector and the sun ; and consequently 

 that the radius-vector and the sun's transit are the sure and only 

 measures and indications of complete rotation, while on the con- 

 trary, the star and its sidereal day falls short of that complete 

 measure by no less than a half rotation in this particular case. 

 If the earth were to rotate twice, the star would have three tran- 

 sits ; and, in short, for every number of the earth's complete ro- 

 tations in a year, the star will make one transit more, which is 

 just the proportional value of its shortcomings with respect to 

 the rotations. Let the star now stand still at N, while the earth 



