370 A Short History of Astronomy [CH. xin. 



measured in terms of this unit. Delaunay, working inde- 

 pendently, arrived at like conclusions, and shewed that tidal 

 friction might thus be capable of producing just such ,an 

 alteration in the moon's motion as had to be explained ; if 

 this explanation were accepted the observed motion of the 

 moon would give a measure of the effect of tidal friction. 

 The minuteness of the quantities involved is shewn by 

 the fact that an alteration in the earth's rotation equivalent 

 to the lengthening of the day by T ^ second in 10,000 years 

 is sufficient to explain the acceleration in question. More- 

 over it is by no means certain that the usual estimate of 

 the amount of this acceleration based as it is in part on 

 ancient eclipse observations is correct, and even then a 

 part of it may conceivably be due to some indirect effect 

 of gravitation even more obscure than that detected by 

 Laplace, or to some other cause hitherto unsuspected. 



288. Most of the writers on lunar theory already men- 

 tioned have also made contributions to various parts of 

 planetary theory, but some of the most important advances 

 in planetary theory made since the death of Laplace have 

 been due to the French mathematician Urbain Jean Joseph 

 Leverrier (1811-1877), whose methods of determining the 

 distance of the sun have been already referred to ( 282). 

 His first important astronomical paper (1839) was a dis- 

 cussion of the stability (chapter XL, 245) of the system 

 formed by the sun and the three largest and most distant 

 planets then known, Jupiter, Saturn, and Uranus. Subse- 

 quently he worked out afresh the theory of the motion of 

 the sun and of each of the principal planets, and constructed 

 tables of them, which at once superseded earlier ones, and 

 are now used as the basis of the chief planetary calculations 

 in the Nautical Almanac and most other astronomical 

 almanacs. Leverrier failed to obtain a satisfactory agree- 

 ment between observation and theory in the case of 

 Mercury, a planet which has always given great trouble to 

 astronomers, and was inclined to explain the discrepancies 

 as due to the influence either of a planet revolving between 

 Mercury and the sun or of a number of smaller bodies 

 analogous to the minor planets ( 294). 



Researches of a more abstract character, connecting 

 planetary theory with some of the most recent advances 



