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 m 3 s ‘41 ; but as this differs considerably from 
the rate which the chronometer had on leaving Paris, the 
rate 4 m 2 S, 3S, derived from the observations of the 18th and 
19th, has been retained, as being probably nearer the truth. 
19th. 4 m i s '38. 
21st. 3 m 57 s '63. 
22d. 3 m 5 7 s ‘ 49 * 
The rate of the Fairlight chronometer being sufficiently 
uniform, the mean of the whole, 3 ra 56*51, has been adopted 
for all the observations there, which cannot produce any 
sensible error. 
The difference of meridians is now obtained from the 
following formula. 
Let P be the sidereal time at Paris, L the corresponding 
chronometer time at Lignieres, L ' 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) by the formulae given 
above. Then P -f- — /) -f- (/' — f) — G = difference 
of meridians required as is evident. 
