Remarks on the Lunar Theory, 



411 



most evidently that the true motions of the sun and moon's 

 apogee and node must agree at and after such an interval, or 

 such phaenomenu could not take place. 



It appears, sir, to this gentleman, of little conseqaence, whether 

 the ]) is distant from her node ten degrees on the one side, or 

 ten degrees on the other; or whether the ]) is within 90 degrees 

 of her perigee, it appears to be a circumstance which he has not 

 given himself the trouble to ascertain. Where eclipses are ob- 

 served in various parts of the globe, it is necessary to reduce the 

 time to one meridian ; and also to apply the equation of time 

 before the interval between the eclipses can be truly ascertained. 

 The difference of longitude of the O and J must also he taken 

 into the account; the ]) must likewise be divested of the equa- 

 tions which regulate the inequalities in her motion, and the cor- 

 rection for the acceleration applied before her mean motion in 

 longitude, or her mean synodic revolution, can be correctly as- 

 certained. 



The acceleration of the ]) is a periodical equation (as indeed 

 are all the equations v%hich regulate her motion); its period is very 

 long, and is equal in length to that of the variation of the pccen- 

 tricitv of the earth's orbit, on which it depends ; its period in- 

 cludes millions of years ! It will be accelerated and retarded by 

 the same quantity ; and therefore if the mean motion be taken 

 for the whole tinie of the acceleration, or retardation, it will be 

 found never to vary: the mean motions of the perigee and nodes 

 of the lunar orbit'are also subject to secular equations, being 

 always proportional to that of the ]) 's longitude. In conse- 

 quence of the duration of this period being at present unknown, 

 and also the time when the acceleration will attain its maximiun, 

 we are not enabled to apply this cc|uation to its corresponding 

 ejioch. This equation, as given by Laf)!ace, in its present form 

 will for ever increase, which cannot be the case. But it may be 

 extended back to the most ancient observations of the D , and 

 probably for many centuries to come, without any sensible error. 



That Dr. Maskelvne ever ventured to obtrude such roviavtic 

 specidalions o\\ the public, is not disputed; the duties of his office 

 as Astronomer Royal, and his superintcndance of the calculations 

 of the Nautical Almanack, were sufficient to occupy his time; 

 and which have immortalised the memory of that illustrious 

 astronomer : l)nt, although he did not launch into such specula- 

 tions, the elements on which they are founded were strictly ap- 

 plied under his directions by the computers of the above work. 

 To render the theory of the moon perfect, researches as extensive 

 as those which have already been made are recpiired. Observa- 

 tions made at remote periods, in conjunction with theory, are 

 3 F 2 requisite 



