This mean temperature of the air at a fixed point, or at a group of contiguous points on the surface, is to a certain degree the fundamental element of the climate and agricultural relations of a district; but the mean temperature of the whole surface is very different from that of the globe itself. The questions so often agitated, whether the mean temperature has experienced any considerable differences in the course of centuries, whether the climate of a country has deteriorated, and whether the winters have not become milder and the summers cooler, can only be answered by means of the thermometer; this instrument has, however, scarcely been invented more than two centuries and a half, and its scientific application hardly dates back 120 years. The nature and novelty of the means interpose, therefore, very narrow limits to our investigation regarding the temperature p 176 of the air. It is quite otherwise, however, with the solution of the great problem of the internal heat of the whole Earth. As we may judge of uniformity of temperature from the unaltered time of vibration of a pendulum, so we may also learn, from the unaltered rotatory velocity of the Earth, the amount of stability in the mean temperature of our globe. This insight into the relations between the 'length of the day' and the 'heat of the Earth' is the result of one of the most brilliant applications of the knowledge we had long possessed of the planet. The rotatory velocity of the Earth depends on its volume; and since, by the gradual cooling of the mass by radiation, the axis of rotation would become shorter, the rotatory velocity would necessarily increase, and the length of the day diminish, with a decrease of the temperature. From the comparison of the secular inequalities in the motions of the Moon with the eclipses observed in ancient times, it follows that, since the time of Hipparchus, that is, for full 2000 years, the length of the day has certainly not diminished by the hundredth part of a second. The decrease of the mean heat of the globe during a period of 2000 years has not, therefore, taking the extremest limits, diminished as much as 1/306th of a degree of Fahrenheit.* [footnote] *Laplace, 'Exp. du Syst. du Monde', p. 229 and 263; 'Mecanique Celeste', t. v., p. 18 and 72. It should be remarked that the fraction 1/306th of a degree of Fahrenheit of the mercurial thermometer, given in the text as the limit of the stability of the Earth's temperature since the days of Hipparchus, rests on the assumption that the dilation of the substances of which the Earth is composed is equal to that of glass, that is to say, 1/18,000th for 1 degree. Regarding this hypothesis, see Arago in the 'Annuaire' for 1834, p. 177-190.