286 NEW formullE relative to comets. 



There is but one remark to be made relatively to the numerical con- 

 version of these and the auxiliary quantities ^, y!, &c. and a, s. The 

 intervals t\ t" and also t' — t\ given in days, must be expressed in 

 terms of mean solar time, and in parts of radius, by multiplying them 

 by the diurnal factor •01720213, which corresponds to the solar arc 

 59' 8"'2, and of which the logarithm is 8-2355821. 



The preceding formulae (A) are we believe the most convenient 

 and the most accurate that have appeared for the determination of the 

 component velocities of a comet, observed in three positions at compa- 

 ratively small intervals. The factors ^. //, &c. have here been first 

 noticed ; they give every requisite degree of precision to the values of 

 a;,, y,y z,. The computation we have reduced to uniformity and faci- 

 lity by means of the three arcs a-\-l — L, « + /' — L, « + /"— L, 

 of which the several angular quantities a, a', &c. are functions ; and 

 which take place of nine arcs hitherto employed. The particular form 

 given to D is also advantageous. It directly leads to the value of this 

 factor, by the three previously determined quantities A, A', A". 



When the observations can be taken so that the intervals /', t" may 



be equal, the factors ^',(ti", v will each be expressed by 1 — — -. The 



term which depends on /' — /" will then vanish, and we shall have 

 the more simple expressions : 



X, 



91^' /' \' I \''ii . ^^' 



= X. + ^(AV-AV + ^') 



2, = ^^(Ay-AV); 



in which the quantities A, A', A" and D have the same forms as be- 

 fore ; but instead of (24), we have 



a =: cos (/ — L), /? =1 sin (/ — L), y =z tan X, 



and similar values for a', a", &c. 



