152 



Astiviiomical and Nautual Collections. 



p', p", f", the curtate distance of the comet from the earth. 



x, x", x", the distance of the comet from the sun reduced to the 

 direction of the vernal equinox. 



y', y", y", the distance of the comet from the line of the vernal 

 equinox, reduced to the plane of the ecliptic, rec- 

 koned eastwards. 



z', z", z!" , the distance of the comet northwards from the plane of 

 the ecliptic. 



/, r", r", the distance of the comet from the sun. 



k', the chord of the comet's orbit between the \st and 2d ob- 

 servation. 



k", between the \st and Zd. 

 It is obvious that 



a; = p cos. « — R cos. A. 



2/ = § sin. a — R sin. A. 



z =: P tang. &. 



r = vr^' + 2/' + 2';- 



*'= V ([x- — xy + [y — i/r + [z' ' - z'} '). 

 k" = ^ ax'" - xj + [y'"- yj + [z"-zj). 



[Note 1 . These equations may be more readily understood 

 with the assistance of a figure. The lines not in the plane of 

 the ecliptic are dotted, and the characters relating to them en- 

 closed in parentheses, the line z becoming always a point in an 

 orthographical projection. Tr.] 



