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Art. VII. — On the Measurement of the Progress of an Eclipse 
of the Moon with a Seoctant , or Reflecting Circle. By T. E. 
Bowdich, Esq. Communicated by the Author. 
JlT is impossible to observe the beginning of an eclipse of the 
Sun or Moon on shipboard, with precision, but by measuring 
the progress of either with a sextant, at intervals of five minutes. 
Advantage may still be taken of these phenomena, for the deter- 
mination of the longitude. 
This method offers the great advantage of multiplying the 
angles, and consequently of diminishing the errors by which the 
partial observations may be affected. 
It was first proposed for eclipses of the Sun by Wales, who 
thus observed that of 1774. King, who accompanied Captain 
Cook in 1777, also availed himself of it; but, in both instances, 
the mere observations are recorded, without calculation, formula, 
or result. 
Kohler appears to have been the first who recommended, and 
Humboldt the first who put in practice, the application of this 
method to eclipses of the Moon. The latter thus determined 
the longitude of Ibague within |th of a degree; but as Oltmans, 
who calculated this observation, has merely given us the result, 
without the formula, and as I do not know of any formula be- 
ing in print, I thought it might be useful, as well as interesting, 
to submit the following, which is general, until a neater one may 
be discovered. 
Let A = longitude }) — long. 0 — 180°. 
\ — latitude of }). 
A / = augmentation of the relative longitude of }). 
a, == movement in latitude of }). 
$ — semi-diameter of 0. 
S’ = do. )). 
p =. parallax of 0. 
p' do. ]). 
s = enlightened part of }) in minutes. 
t — the time before or after the instant of calculating the long, of }). 
T = time for which the above elements (from the Naut. Alman.) are calcu* 
lated. 
T' = mean time of the observation. 
