on the Rotation of the Planets , &c* 
*3 r 
Third monthly period, 
D. II. M. s. 
May 13 ii 25 51 
June 17 9 9 20 
34 revol. 34 21 43 29 
1 revolution = 24b. 38' 20 ",3 
This laft is, perhaps, as likely to be near the truth as any, 
fince the fame fpot was here obferved for the third time, and 
therefore its motion become more familiar. 
Here we have three longer periods that agree to fifteen 
feconds, which is quite fufficient for extending the interval of 
time to thofe obfervations that were made in the year 1777. 
But as thefe are the fynodical revolutions, it will be necelfary 
firfi: to reduce them to fydereal rotations. 
In figure 24. let us fuppofe the orbit of Mars, mabc, 
to be in the fame plane with the orbit of the earth, edfg ; 
and the axis of Mars to be perpendicular to his orbit. Let 
m, e, w, e , be the fituations of Mars and the earth on the 
13th of May and 17th of June ; then will the line em, that 
connects the centers of Mars and the earth, point out the geocen- 
tric place of Mars on the 13th of May; and the line em , the 
geocentric place of the fame planet on the 17th of June. Draw 
er and ms parallel to er ; then will er point out the geocentric 
place of Mars on the 13th of May ; and the angle sme is equal 
to the angle mer. Now, by an ephemeris * the geocentric 
place of Mars, May 13. at 11 h. 26' was 7 f. 20 d. 59' 21"; 
* The Nautical Almanac gives the geocentric place of Mars only to every lixth 
day ; for which reafon I ufed white’s Ephemeris, where it is given for every day, 
though perhaps not with fo much e^actnefs as I could wiftn 
S 2 
and 
