3/4 On the Figure of the Earth. 



scribe round its axis of rotation will be the same in a given time, 

 as before. It is easy to conclude from this, that the angular ve- 

 locity of rotation will be augmented by a fifty thousandth. So 

 that, supposing the time of a rotation to be one day, or a hun- 

 dred thousand decimal seconds, it will be diminished two seconds 

 by the diminution of a degree in the temperature of the space. 

 If we extend this consequence to the earth, and also consider 

 that the duration of the day has not varied since the time of 

 Hipparchus, by the hundredth of a second, as I have shown by 

 the comparison of observations with the theory of the secular 

 equation of the moon, we shall conclude, that since that time, 

 the variation of the internal brat of the earth is insensible. It 

 IS true that the dilatation, the specific heat, the degree of per- 

 meability by heat, and the density of the various strata of the 

 earth being unknown, may cause a sensible difference between 

 the results relative to the earth, and those of the sphere we have 

 supposed ; according to which the diminution of the hundredth 

 of a second, in the length of the day, would correspond to a di- 

 minution of two hundredths of a degree of temperature. But 

 this difference could never extend from two hundredths of a de- 

 gree, to the tenth ; the loss of terrestrial heat corresponding to 

 the diminution of a hundredth of a second in the length of the 

 day. We may observe, even that the diminution of the hundredth 

 of a degree, near the surface, supposes a much greater one in 

 the internal strata; for it is known that ultimately the tempera- 

 ture of all the strata diminishes in the same geometric progres- 

 sion, so that the diminution of a degree near the surface, cor- 

 responds to a much greater diminution in the strata nearer to 

 the centre. The dimensions of the earth, therefore, and its in- 

 ertial movientum would diminish more than in the case of the 

 sphere we have sup))osed. Hence it follows, that if, in the course 

 of time, changes are observed in the mean height of the thermo- 

 meter placed at the bottom of the observatory caves, it must be 

 attributed not to a variation in the mean temperature of the 

 earth, but to change in the climate of Paris, of which the tem- 

 perature may vary, with many accidental causes. It is remark- 

 able that the discovery of the true cause of the secular equation 

 of the moon, should at the same time make known to us the in- 

 variability of the length of the day, and of the mean temperature 

 of the earth since the time of the most ancient observations; 



This phaenomenon induces a belief that the earth has anived at 

 that permanent temperature, which accords with its position in 

 space, and its relation to the sun. It is found by analysis, that 

 whatever be the specific heat, the permeability by heat, and the 

 density of the strata of the terrestrial spheroid, the increase of the 

 heat, at a depth very small, compared to th.e radius of that sphe- 

 roid, 



