112 On the Figure of the Earth . 



theory of the secula;* equation of the moon, we shall conclude, 

 that since that time, the variation of the internal heat of the earth 

 is insensible. It is true that the dilatation, the specific heat, 

 the degree of permeability by heat, and the density of the va- 

 rious 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 dimi- 

 nution of the hundredth of a second, in the length of the day, 

 would correspond to a diminution of two hundredths of a degree 

 of temperature. But this difference could never extend from two 

 hundredths of a degree, 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 di 

 minution of the hundredth of a degree, near the surface, sup- 

 poses a much greater one in the internal strata ; for it is known 

 that ultimately the temperature of all the strata diminishes in the 

 same geometric progression, so that the diminution of a degree 

 near the surface, corresponds to a much greater diminution in the 

 strata, nearer to the centre. The dimensions of the earth, there- 

 fore, and its inertial momentum would diminish more than in the 

 case of the sphere we have supposed. Hence it follows, that if, 

 in the course of time, changes are observed in the mean height 

 of the thermometer placed at the bottom of the observatory 

 caves, it must be attributed not to a variation in the mean tem- 

 perature of the earth, but to change in the climate of Paris, of 

 which the temperature may vary, with many accidental causes. 

 It is remarkable that the discovery of the true cause of the se- 

 cular equation of the moon, should at the same time make 

 known to us the invariability of the length of the day, and of the 

 mean temperature of the earth since the time of the most ancient 

 observations. 



This last phenomenon induces us to suppose that the earth 

 has arrived at that permanent temperature, which accords with 

 Hs position in space, and its relation to the sun. It is found by 

 analysis, that whatever the specific heat, the permeability by 

 heat, and the density of the strata of the terrestial spheroid, 

 flie increase of the heat, at a depth very small, compared to the 



