62 
Mr Bowdich on the Measurement of an Eclipse 
A\ 
the time of the middle of the eclipse, or t = T -f ^ J, will he 
given by the value of D, derived from the equation 
2 
(-J 
n- — a 5 
Lastly, any enlightened quantity of the Moon, or any distance 
of the horns, will be given by the formula 
T + 
WG) 
X) 2 — A A* 
B 
observing, that, in the former case, D — r — S' -f g, 
in the latter, D 2 = A' + B' + ^VA'B', 
' A' = (r + c) (r — c) B' = (S' + c) (f — c ) ; 
thus we may have the time t expressed in function of g, or in 
function of c. 
The longitude of the place will be expressed in time by the 
formula L — t — in which t' represents the time of the obser- 
vation of « or c; the longitude being east or west, according as 
L is positive or negative. 
Finally, substituting the value of t , we have the longitude 
expressed in time by the formula, 
Long. =T-t+ Q)± 7(17 
D 2 A 2 A 2 
B 
I have calculated M. de Humboldt’s observation at Ibague * 
by this formula, and the result would no doubt accord precisely 
with that in the text, were the elements it contains free from 
errors ; for, after correcting the most palpable, my result differs 
but 27" from that of M. Oltmans. The following errors cannot 
be disputed, and other lesser ones certainly exist. 
It is impossible that 21 h 20' 45" can be the mean time at 
Paris, since the elements are calculated very near the opposition, 
and this happened, according to the text, at 19 h 26' 41". If we 
suppose, for a moment, that this latter element is inexact, we 
may still convince ourselves that 21 h 2(f 45" cannot be the cor- 
rect time, by merely observing, that the enlightened part of the 
* Voyage de Humboldt, Partie Astronomique, (2 vol. 4to), vol. fi. p. 255. 
