OF ARTS AND SCIENCES. 



25 



The value of h cannot be determined directly, but must be deduced 

 from the times of internal and external contact. The interval be- 

 tween the internal contacts is assumed to be 24 minutes, or that 

 during which the satellite moves through 2° of longitude. In the 

 equation D- = a^ sin'^ w -\- b^ cos'^ to, we have for w = 1°, 



J) = (l—r)= 0.236, 



and as before for w =: 23°, 



J)=l -\-r = 1.7Gi. 



From these conditions the values of a and b given in the last column 

 of Table IX. are deduced. 



TABLE IX. — Elements of Orbits. 



"We must next compute the amount of obscuration at the end of 

 each half-hour, for the various values of r. The distance between the 

 centres is first computed by the equation D"^ = a^ — (a^ — b^) cos" w, 

 substituting successively, w = 2°. 5, 5°.0, 7°.5, 10.°0, 12°. 6, 15°.], 

 17°.6, and 20°.l. The first part of Table X. gives the values of B 

 corresponding to those assigned to rat the head of each column. The 

 triangles formed by the centres of the two bodies and one end of the 

 segment now become known, since their three sides equal 1, r, and D. 

 Calling the angle at the centre of the luminous body a, we have 

 r^=l'^ -\- D^ — 2 D cos a. From this we deduce cos « and versin «, 

 or the height of the segment bounded by the circle having a radius 

 unity. The height of the other segment will equal i? — J^ -\- ^os u, 

 from which the areas of the segment, and consequently of the uneclipsed 

 portion, may be deduced. This area is given in the second portion 

 of the table. For comparison the observed light is repeated, in the 

 last column from the last column of Table VIII. The residuals, or 

 the observed values minus those computed with each value of r, are 

 given in the third part of Table X. The residuals are all zero when 

 the time equals 0.0 or 4.6, and are therefore omitted. The average 

 residuals are given in the last line. 



