THE ORBIT OF NEPTUNE. 



39 



The constants being so taken that the perturbations, and also the differential 

 coefficient of Si, shall all vanish at the ejDOch 1850.0. These perturbations are 

 given for the beginning of every tenth year, from 1600 to 2000, in the following 

 table : 



Secular and Long-Period Perturbations of the Elements of Neptune from 



1600 TO 2000. 



Date 



<5^ 



S log a 



dh 



dh 



5p 



H 



Sp' 



8q' 





n 





n 



n 



n 



„ 



II 



„ 



1600 



— 149.21 



— 473 



+ 22.33 



— 45.28 



— 4.68 



+ 0.79 



+ 8.58 



— 116.52 



10 



137.63 



455 



21.18 



43.85 



4.48 



0.79 



8.29 



111.82 



20 



126.50 



437 



20.05 



42.39 



4.29 



0.78 



7.99 



107.12 



30 



115.83 



418 



18.94 



40.90 



4.10 



0.77 



7.69 



102.42 



40 



105.62 



400 



17.85 



39.37 



3.90 



0.76 



7.39 



97.73 



50 



— 95.88 



— 381 



+ 16.77 



— 37.81 



— 3.71 



+ 0.75 



+ 7.09 



— 93.04 



60 



86.60 



362 



15.71 



36.22 



3.52 



0.73 



6.78 



88.36 



70 



77.78 



344 



14.67 



34.60 



3.32 



0.71 



6.47 



83.68 



80 



69.42 



325 



13.65 



32.94 



3.13 



0.69 



6.15 



79.00 



90 



61.52 



307 



12.66 



31.25 



2.94 



0.67 



5.83 



74.33 



1700 



— 54.09 



— 288 



+ 11.69 



— 29.53 



— 2.75 



+ 0.64 



+ 5.50 



— 69.66 



10 



47.13 



269 



10.74 



27.77 



2.56 



0.61 



5.17 



64.99 



20 



40.65 



250 



9.81 



25.99 



2.37 



0.58 



4.84 



60.32 



30 



34.65 



231 



8.90 



24.17 



2.18 



0.55 



4.49 



55.66 



40 



29.13 



212 



8.01 



22.33 



2.00 



0.52 



4.14 



51.01 



50 



— 24.09 



— 193 



+ 7.14 



— 20.45 



— 1.81 



+ 0.48 



+ 3.79 



— 46.36 



60 



19.52 



174 



6.30 



18.54 



1.62 



0.44 



3.43 



41.71 



70 



15.43 



154 



5.48 



16.60 



1.44 



0.40 



3.08 



37.06 



80 



11.81 



135 



4.69 14.63 



1.25 



0.35 



2.71 



32.42 



90 



8.68 



115 



3.93 



12.62 



1.07 



0.30 



2.34 



27.79 



1800 



— 6.03 



— 96 



+ 3.20 



— 10.59 



— 0.89 



+ 0.25 



+ 1.96 



— 23.15 



10 



3.86 



77 



2.50 



8.53 



0.71 



0.20 



1.58 



18.52 



20 



2.17 



57 



1.83 



6.44 



0.53 



0.15 



1.20 



13.88 



30 



0.96 



38 



1.19 



4.32 



0.35 



0.10 



0.81 



9.25 



40 



— 0.24 



— 19 



+ 0.58 



— 2.17 



— 0.17 



+ 0.05 



+ 0.41 



— 4.63 



50 



0.00 







0.00 



0.00 



0.00 



0.00 



0.00 



0.00 



60 



— 0.24 



+ 19 



— 0.54 



+ 2.20 



+ 0.17 



0.06 



— 0.41 



+ 4.62 



70 



0.96 



88 



1.04 



4.42 



0.34 



0.11 



0.82 



9.25 



80 



2.17 



57 



1.51 



6.68 



0.51 



0.17 



1.24 



13.87 



90 



3.86 



77 



1.93 



8.96 



0.68 



0.23 



1.67 



18.48 



1900 



— 6.03 



+ 96 



— 2.32 



+ 11.26 



+ 0.85 



— 0.29 



— 2.10 



+ 23.09 



10 



8.68 



115 



2.67 



13.59 



1.01 



0.35 



2.54 



27.70 



20 



11.81 



133 



2.98 



15.94 



1.17 



0.42 



2.98 



32.30 



30 



15.44 



152 



3.25 



18.31 



1.33 



0.49 



3.43 



86.90 



40 



19.53 



171 



3.47 



20.70 



1.48 



0.56 



3.89 



41.49 



50 



— 24.10 



+ 190 



— 3.65 



+ 23.11 



-1-1.64 



— 0.63 



— 4.35 



+ 46.09 



60 



29.14 



209 



3.79 



25.54 



1.80 



0.70 



4.81 



50.69 



70 



34.66 



227 



3.89 



27.99 



1.95 



0.77 



5.28 



55.28 



■80 



40.66 



246 



3.94 



30.46 



2.11 



0.84 



5.75 



59.88 



90 



47.13 



265 



3.94 



32.95 



2.26 



0.91 



6.23 



64.47 



2000 



— 54.09 



+ 284 



— 3 89 + 35.46 



+ 2.42 



— 0.98 



— 6.71 



+ 69.06 



^j> and hq refer to the fixed ecliptic of 1850.0, Zp and 5(/to the movable eclijitic 

 of the date, the motion being that adopted in Hansen's " Tables du Soleil," and 

 concluded from the seculp-r diminution of the obliquity there given. 



The corrections to the true longitude, latitude, and radius vector derived from 

 the pure elliptic elements require corrections for these perturbations as follows : 



