306 t CELESTIAL DYNAMICS. 



tion of this subject by the great Laplace forms a bright mon- 

 ument in the department of exact science. 



These calculations are essentially conducted in the follow- 

 ing manner : In the first place, the time between two eclipses 

 of the sun, widely apart from each other, is as accurately 

 as possible expressed in days, and from this the ratio of the 

 time of the earth's rotation to the mean time of the moon's 

 revolution determined. If, now, the observations of ancient 

 astronomers be compared with those of our present time, the 

 least alteration in the absolute length of a day may be de- 

 tected by a change in this ratio, or in a disturbance in the 

 lunar revolution. The most perfect agreement of ancient rec- 

 ords on the movements of the moon and the planets, on the 

 eclipses of the sun, &c., revealed to Laplace the remarkable 

 fact that in the course of 25 centuries, the time in which our 

 earth revolves on its axis has not altered g^th part of a sexa- 

 gesimal second ; and the length of a day therefore may be 

 considered to have been constant during historic times. 



This result, as important as it was convenient for astron- 

 omy, was nevertheless of a nature to create some difficulties 

 for the physicist. With apparently good reason it was con- 

 cluded that, if the velocity of rotation had remained constant, 

 the volume of the earth could have undergone no change. 

 The earth completes one revolution on its axis in 86,400 si- 

 dereal seconds ; it consequently appears, if this time has not 

 altered during 2500 years to the extent of ^th of a second, 

 or 43 >000>000 th part of a day, that during this long space of time 

 the radius of the earth also cannot have altered more than 

 this fraction of its length. The earth's radius measures 

 6,369,800 metres, and therefore its length ought not to have 

 diminished more than 15 centimetres in 25 centuries. 



The diminution in volume, as a result of the cooling-pro- 

 cess, is, however, closely connected with the changes on the 

 earth's surface. When we consider that scarcely a day 

 passes without the occurrence of an earthquake or shock in 



