$ 239-241] Lun.ir Theory 309 



This may be otherwise expressed by saying that the length 

 of the month diminishes by about one-thirtieth of a second 

 in the course of a century. Moreover, as Laplace shewed 

 ( 245), the eccentricity of the earth's orbit will not go on 

 diminishing indefinitely, but after an immense period to be 

 reckoned in thousands of years will begin to increase, and 

 the moon's motion will again become slower in consequence. 



Laplace's result agreed almost exactly with that indicated 

 by observation ; and thus the last known discrepancy 01 

 importance in the solar system between theory and observa- 

 tion appeared to be explained away ; and by a curious 

 coincidence this was effected just a hundred years after the 

 publication of the Principia, 



Many years afterwards, however, Laplace's explanation 

 was shewn to be far less complete than it appeared at the 

 time (chapter xin., 287). 



The same investigation revealed to Laplace the existence 

 of alterations of a similar character, and due to the same 

 cause, of other elements in the moon's orbit, which, though 

 not previously noticed, were found to be indicated by 

 ancient eclipse observations. 



241. The third volume of the Mecanique Celeste con- 

 tains a general treatment of the lunar theory, based on a 

 method entirely different from any that had been employed 

 before, and worked out in great detail. " My object," says 

 Laplace, " in this book is to exhibit in the one law of 

 universal gravitation the source of all the inequalities of 

 the motion of the moon, and then to employ this law as 

 a means of discovery, to perfect the theory of this motion 

 and to deduce from it several important elements in the 

 system of the moon.'' Laplace himself calculated no lunar 

 tables, but the Viennese astronomer John Tobias JBurg 

 (1766-1834) made considerable use of his formulae, 

 together with an immense number of Greenwich observa- 

 tions, for the construction of lunar tables, which were sent 

 to the Institute of France in 1801 (before the publication 

 of Laplace's complete lunar theory), and published in a 

 slightly amended form in 1806. A few years later (1812) 

 John Charles Burckhardt (1773-1825), a German who had 

 settled in Paris and worked under Laplace and Lalande, 

 produced a new set of tables based directly on the formulae 



