some observations made with chronometers. 363 
anchor in Dover roads, it was thought useful to connect Ports- 
mouth with Falmouth in the same manner. The following 
are the days on which the observations for ascertaining time 
were taken, from which the results were derived : 1823. 
1. July 30, Dover. 2. August 4, Falmouth. 3. August 6, 
Dover. 4. August 11, Falmouth. 3. August 6, Dover. 
6. August 24, Portsmouth. 7. August 30, Falmouth. 8. Sep- 
tember 2, Portsmouth. 9. September 7, Falmouth. 10. Sep- 
tember 11, Portsmouth. The difference of each chronometer 
from the mean time of the respective places being therefore 
known on these days, there may be employed two modes of 
calculating the difference for an intermediate moment, viz. 
the rate between every two successive differences belonging 
to the same place may be considered as uniform, and the 
intermediate term is accordingly found by simple proportion 
from two terms only ; or the intermediate term may be de- 
rived by interpolation from all the terms, provided that in 
the whole interval no external cause have acted on the chro- 
nometers so as to produce a sudden change in their rates. 
Thus if d' } d", d!" represent the difference from the mean time 
of the same place at the moments t', t", t'" 3 this difference will 
be for the moment t = d + d + 
d!" . Each of the above days, except the first 
and last, respectively combined with two, or all the days 
belonging to the other place, will therefore give a result. 
Having thus explained the method which I have used, it will 
be sufficient to give the mean results of the chronometers, out 
of which one only was rejected on account of its irregular 
rate. 
