MATHEMATICAL PAPERS. 1 
the vifible difference of latitude between their centers, to find 
the fide OB, their vifible difference of longitude.* This may 
be obtained by Euclide, Book I, Prop. 47; or it may be 
found by common trigonometry thus ©» : Redius :: E» 
fine angle Eo? ; then Radius : op :: fine co-angle Eo p= 
angle E»o : OE. But OE may be obtained more expediti- 
‘oufly, thus ; find the logarithms for the fum and difference of 
©) and E» ; the half fum of thefe logarithms is the loga- 
rithm of oF. 
Having found, for the place from whence we defign to reck- | 
:on the difference of meridiars,- the parallaxes, and the vifible 
difference of longitude between the centers of the fun and 
moon, at the obíerved time of the beginning or ending of a` 
on of a duca x. or Sor both the 
ine the difference of uu ee? in time, between the firft 
_ place, 
from’ the limb of the fun, or from the fixed ftar 41'^ : Therefore, at the inftant 
when the begitining or end appears to us, it is obvious, that the centers cannot be 
fo far afunder by 43° 5 as the fum.of the femi-diameters ; _and by fo much muft 
this fum be Fora brief account of this infe&ion, fee Astroxomir 
par M. pe La LANDE, tome ii. art. 1992, 1993, edition feconde. 
* As the fan has. a vifible latitude, equal to bis parallax in latitude, the fide 
CE. is not a portion of the ecliptic, but is parallel toit : But as it’s utmoft diftance 
from it can never be more than between 8” and 9’, the difference between this fide 
and the vifible difference of longitude, is imperceptible. In an occultation, when 
the fiar’s latitude is large, this fide, parallel to the ecliptic, mult be enlarged, to 
give the vifible difference of longitude between the ftar and the moon’s center, in 
the ratio of the cofine of the moon’s vifible latitude, or of the ftar’s latitude to Ra- 
_ dius, according as the one or the other is neareft to the ecliptic. 
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