AT HUDSON OBSERVATORY. 153 



The first six of the following equations are dependent upon the longitudes, 

 and are severally multiplied by the cosine of the corresponding latitude. 



^ = — 32.625 8 + 6.603* +30.109rt —32.467;' + 40.720 1 — 4.672 s 



i; = — 23.385 — 0.510 +10.100 —28.875 +36.707 — 5.400 



^ = — 17.756 — 4.192 — 1.295 —25.476 +27.782 — 3.631 



JS = — 14.750 — 6.078 — 7.428 — 22.914 + 20.407 — 1.879 



^ = — 12.881 — 7.296 —11.611 —20.726 +13.814 — 0.186 



^ = — 11.604 — 8,241 —15.225 —18.389 + 6.335 + 2.002 



i; = + 24.462 — 34.932 — 64.694 + 22.945 + 19.768 — 34.780 



^ = _}. 16.770 —35.444 —61.086 +30.666 — 1.309 —26.121 



£: = + 7.2i>V .-> • .135 — 51.018 + 32.773 — 8.379 — 14.846 



E = + 1.240 —.7.124 —43.649 +32.861 — 8.888 — 6.763 



E = — 3.118 —23.649 —38.145 +32.375 — 7.202 — 0.600 



E = — 7.146 — 20.085 — 33.374 + 31.510 — 3.734 + 5.529 



From these equations I obtained the following elliptic elements : 



Perihelion passage, Berlin mean time, March 13. 158768. 

 Longitude of perihelion, . . . . 80° 12' 3".52 



" ascending node. 



Inclination of orbit, .... 

 Log. of perihelion distance, . 



Eccentricity, 



Semi-axis major, . . 180.383 

 Periodic time, . . . 2422.6 years. 



The errors of this orbit are as follow : 



Longitude. Latitude. Total Error. 



January 31, + 0".6 + 1".8 1".9 



February 12, + .4 — 3 .9 3 .9 



23, — 2 .6 + 2 .0 3 .3 

 March 3, + .1 +0.6 .6 



12, + .5 + 1 .1 1 .3 



24, + .9 — 1 .5 1 .7 



The total error of four of the observations is less than the limit of probable 

 error before determined, and that of the other two is greater. The excess and 

 defect are nearly equal. On the whole, then, the accordance is highly satis- 

 factory. The sum of the squares of the errors in the elliptic orbit is 34.62; in 

 VIII. — 2 



236 50 34 .67 

 59 12 36 .14 

 0.0865202 

 0.99323412 



