502 Calculation of the Coefficients of the Lunar Inequalities. 





Inequalities of p. 



. 1 

 Inequalities of v. 



When/=l 

 1=2 



f-3 



-•00000547 cos 2c x t 

 f +-00002832 i^+cjt 

 \ -00045522 {c x -c 2 )t 

 J --00014364 (c x +c z )t 

 \ - -01681 440 (c x -c 3 )t 



+ -00000482 sin 2c x t 

 r -00003950 (c x +<?,)/ 

 t + 00065920 (c x -tf a )/ 

 j +-00015830 (\+c,)rf 

 \+-03728454 (^-Cg)! 



Again, substituting in the formulae (C), we find 



-•00001464 

 +•00000104 

 + 00000131 

 -00015273 

 +•004 16537 

 + -00000080 

 +•00000101 

 +•00000003 

 +•00008269 

 -00007368 

 -00011712 

 + 00319411 

 + •00008212 

 - -0000731 7 

 -00149753 



cos 2c,t 

 (c x +c 2 )t 



(Pi-c z )t 



(c 2 +c,)t 



{c 2 -C x )t 



2cJ 



(o 2 +\)t 

 (c 2 -c 3 )t 



(c 3 - Cl )/ 



(*3 + * 2 )' 



2e Q * i 



+ 00003771 



- -00000221 



- -00000270 



+ -00040253 



- -00872359 



- -00000163 



+ -00000200 



-00000020 



-00016601 



-•0001 4805 



J + -00028875 



t + -00675538 



/ - -0001 6486 



\ + 0001 4 702 



+•00375768 



sin 2c\t 

 ( Cl +c 2 )t 



(ci-e 2 )t 



(Ci + C 3 )t 



(ci~c 3 )t 

 (c 2 +c{)t 

 (c 2 -c x )t 



2cJ 

 (o 2 +c 3 )t 



(e 2 -c 3 y 



(o 3 - Cl )t 

 (c 3 +c 7 )t 



Lastly, the value of -^ contains one inequality of the second 



order, viz. + ^ef cos 2c q t ; or substituting for e t its value -016764, 

 we have |^ 2 = + -001264. Substituting this in the formulae (A), 

 we find 



Inequality in p= + -00000363 cos 2c 2 /, 

 Inequality in v = — -00004853 sin 2c 2 t. 



13. Collecting, therefore, the coefficients of like arguments, 

 remembering that cos (— «2?) = cos# and sin ( — #) = — sin#, we 

 obtain finally the following 



Inequalities of the Second Order. 



Argument. 



Value of 

 argument 

 according 

 to common 

 notation. 



Inequalities 

 of p. 



Inequalities of v. 



In partes radii. 



In seconds. 



2c 3 t 



(c x -b 2 )t 

 2c 2 t 

 2c, t 



(c 3 +c 2 )t 

 (c 3 -c 2 )' 



2()-0)-A 



2A 



2(>-©)+A 



2()-0)-A' 



2A' 



40-0) 



2()-0) + A / 



A+A' 



A-A' 



-00945492 

 - -00149753 

 - -00041349 

 - -00045290 

 + •00000366 

 -00002011 

 +•00003016 

 + •00016481 

 -00014685 



+ 02180557 

 + 00375768 

 + 00084958 

 + 00065450 

 -00004873 

 + 00004253 : 

 - -00004334 . 

 -00033087 = 

 + -00029507 ■ 



= +449772* 

 = + 775-08f 

 = + 175-24 

 = + 13500 

 = - 1005 

 = + 8-77 

 = - 8-94 

 = - 68-25 

 = + 60-86 



* Evection. 



t Second term of equation of the centre. 



