1819.] M. Laplace on the Figure of the Earth. 405 



sponds with its position in space, and relatively to the sun. We 

 find by analysis that whatever be the specific heat, the permea- 

 bility to heat, and the density of the strata of the terrestrial sphe- 

 roid, the increase of heat at a very small depth when compared 

 with the radius of that spheroid, is equal to the product of this 

 depth by the elevation of the temperature of the surface of the 

 earth above the state of which 1 have just spoken, and by a 

 factor independent of the dimensions of the earth, which depends 

 only on the qualities of its first stratum relative to heat. From 

 what we know of these qualities, we see that if this elevation 

 amounted to several degrees, the increase of heat would be very 

 sensible at the depths to which we have penetrated, and where, 

 however, observations have not enabled us to discover it. 



Note by M. Arago. 



We conceive that our readers will not be displeased to find 

 here some details respecting the method by means of which ~M. 

 Laplace has established the constancy of the duration of the 

 day. 



A mean solar day is equal to the time which the earth 

 employs to make a complete revolution on itself, increased by 

 the mean apparent motion of the sun in the same interval. 

 Theory has proved that the mean apparent motion of the sun, as 

 that of all the planets, is constant. The length of the solar day 

 then can vary only by a change in the velocity of the rotation 

 of the earth. 



We call lunar month the interval of time which the moon 

 employs to return to the same position relatively to the sun ; to 

 its conjunction, for example. This interval is evidently inde- 

 pendent of the velocity of the rotation of the earth. Even 

 though our globe were to cease altogether to turn on its axis, 

 the movement of translation of the moon would experience no 

 alteration. From this Hows a very simple method of discovering 

 if the duration of the solar day has changed. 



Suppose that we determine at present by direct observations 

 the duration of a lunar month ; that is to say, how many days 

 and fractions of a day the moon employs to return to its con- 

 junction with the sun. It is clear that by repeating this obser- 

 vation at another epoch, we should find a different result, if the 

 length of the day has not been constant, even though the 

 velocity of the moon has not changed during the interval. The 

 month, for example, would appear longer if the duration of the 

 day had diminished ; and shorter, on the contrary, if the day 

 had become longer. Tiie constancy of the lunar month will be 

 a proof of the invariability of the duration of the day. 



But all the observations concur to prove that from the Chal- 

 deans to our time the duration of the lunar month has been 

 gradually diminishing. Hence it follows from what has been 

 b j id, either that the velocity of the moon has accelerated, or that 



