214 M. Arago on the Thermometrkal State 



And this important result comprehends the solution of the 

 question before us. Few words will be required to prove this. 



The Alexandrian astronomy determined, by direct observa- 

 tions, the duration of its sidereal day, or of the rotation of the 

 earth. It allowed the moon to progress exactly throughout this 

 time, and noted the arc which it had run. The Arabian astro- 

 nomers proceeded in exactly the same manner, and such pre- 

 cisely is the method still followed by ourselves. Thus each as- 

 sumed the sidereal day of his own epoch. But since the moon, 

 as we have seen, always moves with the same velocity, the pro- 

 gress which she makes must depend solely upon the duration of 

 the time during which she pursues her course. If the sidereal 

 day, at the time of Hipparcus, had been longer than it now is, 

 the Greek astronomer would have observed the moon during a 

 longer time than modern observers ; the diurnal displacement 

 of this luminary would have been greater than it now is ; and 

 its velocity would have appeared to us to have diminished. But 

 the arc described in a day, is of precisely the same extent at all 

 the epochs ; therefore, including the most ancient observations, 

 the word sidereal day has invariably designated the same equal 

 space of time ; and therefore (as the sidereal day and the dura- 

 tion of the earth'*s rotation are synonymous), during 2000 years 

 the velocity of the rotation of our globe has continued the same ; 

 and, therefore, its volume is not changed ; and, therefore, final- 

 has, in reality, been continually increasing ; but tMs increase is of the nature 

 that, in astronomy, is denominated a perturbation. It depends on a diminu- 

 tion in the eccentriciLy of the ellipse which the earth annually takes round 

 the sun. When this eccentricity, which hitherto has been diminishing, shall 

 come to increase, the velocity of the moon will by degrees diminish, just as it 

 has hitherto increased, and thus it wiU alternatively continue. The unifor- 

 mity of the velocity then, announced above, is found only after correcting the 

 lunar observations, in relation to the perturbations which the movement of the 

 trarislation of the earth induces in the movements. 



When it was recently said that the movement of the moon was independ- 

 ent of the movement of the earth, it is to be observed that this has reference 

 only to our movement of rotation. If this remark was not supplied in this 

 place, it might be supposed there was a contradiction, which, however, does 

 not exist. 



It may also be noted, that to Laplace belongs the merit of all these disco- 

 veries upon the moon's motion, and of their application to the inquiry of the 

 invariability of the day, and of the temperature of the earth. 



