New Method of determining the Longitude. 111 
very great, the correction resulting from that part of the 
formula immediately connected with these signs, (depend- 
ing on the variation in the semi-diameter and declination 
of the moon,) may be neglected, and the equation becomes 
simply 
w==(t—t) x [ ave &e. 
The values of ¢ and + are obtained by observation, and 
those of ¢ and h might easily be deduced therefrom, if ob- 
servers record their observations entire ; since, the sidereal 
time of the transits being given, we might easily compute 
the apparent time to the nearest minute, which will be 
quite sufficient. The values of +, g, d, and 4, may be ta- 
ken from an ephemeris, and computed for the apparent 
times of observation as shown at the meridian for which 
such ephemeris is calculated ; and the values of a and 6 
may be obtained from the same ephemeris by second dif- 
ferences. See p.9. 
‘| have already remarked that these formule are adapt- 
ed to sidereal time only: if therefore the clock, by which 
any of the comparisons are made, should be adjusted to 
mean solar time, the observed interval, denoted by ¢ or’, 
must be multiplied by 1,0027379.” p. 10. 
first border of the moon and three stars were observed 
March 3d, 1822, by M. Nicolai at Manheim, and by M. 
Struve at Dorpat, as follows : 
1822, Stars. Manheim. Dorpat. Difference. 
= 7 =e —F)= 
March 3.309 Mayer-+13” 18%, 30-+-10" 17', 56-+3" 0*,74 
2Gemin.+8 9,43+ 5 8, 55+3 0,88 
w Cancri—9 41,11-—12 41, 894+3 0,78 
Mean +3 0,80 
The times of the moon’s culmination are not here given, 
and it becomes necessary to take them from an ephemeris. 
By the Con. des Tems it appears, that the moon passed the 
meridian of Paris March 3d, at 8h. 51m. apparent time ; 
and as the estimated longitude of Manheim is 0h. 24m. 315. 
