THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 107 



4)(4,*)(,)(7, 3.858530.0 2.500161 



+2(7,5)( S ,4)(4,7)(6,6)= 0.182088.0- 0.503701 



6)( e ,;)(5,7)(4,4)= 0.050095.0 0.376332 



4)(4,6)(6,7)(a,a)= 0.011756.0- 0.218615 



-f- ( S ,4)(4,.)(7,o)(e,7)= + 15.268077 



_)- (6,6)(S,6)(7,4)(4,7) = -f 0.001670 



4- (o,4)(4,e)(7,8)(e,7)= -f 0.001014 



2(7,4)(4,.)(S,8)(6,7)= 0.319377 



2(7,s)( 5 ' 4 )( 4 ' 8 )( 6 - 7 )= 0.248866 



2(7, 4)(4 , )( , )(a , 7)= 0.002603 



Sum of preceding terms = 135.5553368.0 2 472.626581.0 249.878554 



4 +29.5227974.0 3 +230.6343243.0 2 +523.7682780.0+250.403089 

 Sum is value of equation (54). 

 Whence we get 



(f 29.5227974.0 3 +95.0789875.2 2 \ , (3 ~ Q . 



+51.141697.0+0.524535 j = 



Equations (55-64) reduced to numbers are as follows, in which the numbers 

 inclosed in brackets are logarithms. 



JT =[0.5618811] lDL = rp.8861924]^lJi-; (371) 



D Jj 



^"=[1.0276376] ^!^b^' = [0.2498875] ^f^- ; (372) 



^'"=[9.2072145] - .y =[0.3092759] - ZgL. (373) 



[9.4381189] Df [9.1138076] Df m m . 



~[9.1 138076] AD [9.4381 189] AD ' 



[8.9723624]J>/ W [9.7501125]jy . ,^^ 



~[9.7501125]^"Z)" [8.9723624]A'Z> ' 



[0.7927855]Z>'/ r [9.6907241]Z>/ /r . (3 ~ 6) 



~ [9.6907241] AD [0.7927855]^"!)"' 



N r =[0.4566913] - llY tv 1 [0.5650289] -^ ^ 2 ; (377) 



^"=[1.2562282] ^^!^ = [9.2757168] A * N ~; (378) 



JV r "=[8.4485146] ^i lv tV 6 ^[0.5373636] f M '~; (379) 

 Ar , r _[9.5433087]A/ 2 -[9.4349711]A/ 1 . (38Q . 



^ ~~m AiUf\nii-\ A T\ pn a Af>r>t\OT\ A n ' V ' 



A7/r _[8.7437718]D,/ 4 -[0.7242832]A/3. / 381) 



[0.7242832] A S D 3 [8.7437718]^^' 



