with respect to the JE titer. 421 



Tims if e represents the all-round probable value of the 

 «rror %, + f.s- for a single eclipse, we shall have 



p.e. in a= y-1 S | i)', tnf 2ij? \ > 



^eV-HZr^-Zvt-ZvOh ■ • • (9) 



as is found on expanding and simplifying. The probable 

 •errors in b and c can of courses be similarly expressed. 



12. In order to obtain a preliminary notion of the con- 

 ditions of the problem without undue labour, T have considered 

 a simplified system which is not strictly speaking ; L dynami- 

 cally possible one, but which represents the actual system 

 sufficiently nearly for the purpose in view. The observer is 

 supposed to be carried uniformly round the sun in a circular 

 orbit whose radius II is equal to the mean radius of the earth's 

 orbit, the time of revolution being one year. The Jovian 

 system is supposed to move in a very slightly elliptic orbit, 

 with the sun at the centre of the ellipse, the inclination, </>, 

 of this orbit to that of the observer being 1° 18' 41 ' r , which 

 is the actual inclination of Jupiter's orbit to the plane of the 

 ecliptic. The excentricity of the modified orbit of Jupiter 

 is such that its projection on the plane of the observer's orbit 

 is a circle, this circle being uniformly described in 11 years 

 315 days, and having a radius R/ equal to the mean radius 

 •of Jupiter's actual orbit. To take account of the fact that 

 eclipse observations are impracticable for some time before 

 and after Jupiter is in conjunction, an eclipse is considered 

 as possibly observable only when the angle earth-sun-Jupiter 

 lies between the limits ±yfr (yjr— 102°, say). Between these 

 limits, eclipse observations are taken to be uniformly frequent 

 and uniformly weighty. With, the axis of .<• through the 

 node of Jupiter's (modified) orbit, the axis of y in the per- 

 pendicular direction in the plane of the ecliptic, and the axis 

 of z perpendicular to the ecliptic, the results found arc 



(p.e. in a) =-lT" B»-2R'Riint/*+B w 



2V 4 e 2 1 

 (p.e. in />)-= . — . v . (10) 



(p.e.inc) 2 = 



R 2 - 2R'R sin f /yfr + R' 2 

 'sin-(/)R c2 Ji'-(l- sin 2 Wf 2 ) 



13. In these expressions R=148 X 10 s kilom., R'/R=5*2, 



V = 3 x 10' kilom. per second, <£ = 1° 18' 41"; n, the number 



