404 M. Laplace on the Figure of the Earth. [Dec. 



that after a long time the temperature of the space diminishes 

 one degree ; the sphere will ultimately assume this new degree 

 of temperature ; its mass will not be altered ; but its dimensions 

 will diminish by a quantity which I suppose a hundred thousandth 

 part, as is nearly the case with glass. In virtue of the principle 

 of areas, the sum of the areas, which each molecule of the sphere 

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

 same as before. It is easy to conclude from this, that the 

 angular velocity of rotation will be increased a 50 thousandth 

 part. Therefore supposing the duration of rotation to be orte 

 day, or 100,000 decimal seconds, it will be diminished two 

 seconds by the diminution of one degree in the temperature of 

 the space. If we extend this consequence to the earth, and if 

 we consider that the length of the day has not varied since 

 Hipparchus so much as the hundredth of a second, as I have 

 shown by a 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 heat of the earth is insensible. 

 It is true indeed that dilatation, specific heat, the greater or 

 smaller permeability to heat, and the density of the different 

 strata of the terrestrial spheroid, all of them unknown, may 

 occasion a sensible difference between the results relative to the 

 earth and those of the sphere which we have just considered, 

 according to which a diminution of the hundredth of a second 

 in the duration of the day answers to a diminution of a two 

 hundredth of a degree in the temperature. But this difference, 

 corresponding to the diminution of an hundredth of a second in 

 the length of the day, can never raise the loss of terrestrial heat 

 from the two hundredth of a degree to a tenth. We see even 

 that the diminution of a hundredth of a degree near the surface 

 supposes a greater diminution in the temperature of the inferior 

 strata ; for we know that at length the temperature of all the 

 strata diminishes in the same geometric progression ; so that 

 the diminution of a degree near the surface corresponds to 

 greater diminutions in the beds nearer the centre. The dimen- 

 sions of the earth and its vis inertias diminish, therefore, more 

 than in the case of the sphere which we have imagined. It 

 follows from this, that if in the course of time we observe any 

 change in the mean height of the thermometer placed at the 

 bottom of the caverns below the observatory, we must ascribe 

 it not to any variation in the mean temperature of the earth, but 

 to a change in the climate of Paris, the temperature of which 

 may vary from many accidental causes. It is remarkable that 

 the discovery of the true cause of the secular equation of the 

 moon makes us acquainted at the same time with the invariabi- 

 lity of the length of the day, and that of the mean temperature 

 of the earth, from the epoch of the most ancient observations. 



This last phenomenon leads us to think that the earth has 

 mow come to the permanent state of temperature which cone- 



