of the Royal Observatories of Greenwich and Paris. 291 
As the rate of the Lignieres chronometer is irregular, it 
seems advisable to deduce the rate for reducing the obser¬ 
vations there by interpolation from the two nearest rates, 
supposing that each answers to the middle of its interval. In 
this manner are obtained the following rates for the observa¬ 
tions at Lignieres. 
July 18th. 4“* 3"'4i ; but as this differs considerably from 
the rate which the chronometer had on leaving Paris, the 
rate 4"“ s' sS, derived from the observations of the 18th and 
19th, has been retained, as being probably nearer the truth. 
19th. 4'" 
21st. 3"* 57"’6 s. 
22d. s'" 5 T' 4 < 9 - 
The rate of the Fairlight chronometer being sufficiently 
uniform, the mean of the whole, 3™ 56^-51, has been adopted 
for all the observations there, which cannot produce any 
sensible error. 
The diherence of meridians is now obtained from the 
following formula. 
Let P be the sidereal time at Paris, L the corresponding 
chronometer time at Lignieres, U and F, corresponding 
chronometer times at Lignieres and Fairlight, and F', chro¬ 
nometer time at Fairlight, and G the corresponding sidereal 
time at Greenwich; the intervals of chronometer times 
(L^ —L) and (F'-—F) must be reduced to intervals of 
sidereal time (/' — /) and (^f' — f) by the formulae given 
above. Then P -|- (/'— 0 “h Cf* — f) —G = difference 
of meridians required as is evident, 
