MATHEMATICAL PAPER S. 19 
The difference between the fun’s or ftar's longitude and the 
moon's thus found will, it is obvious, be the true difference of 
longitude between them. But this may be found more readily 
thus—In eclipfes, if the vifible difference of longitude and the 
moon's parallax in longitude from the fun, and in occultations, 
the moon's fimple parallax, be both additive or both fubtrac- 
. tive, their fum is the true difference of longitude, between the 
moon and fun or ftar. If theone is additive, and the other fub- 
tractive, their difference is the difference of longitude. 
It fometimes, though rarely, happens, that the moon, at 
the beginning of an eclipfe or occultation, has paft the true 
conjunétion,* although her vifible longitude is lefs ; this is the 
cafe when the parallax, being additive, is greater than the dif- 
ference is d between the moon and fun or ftar. . We 
true — at t the end. 
'The true difference of longitude between the moon and fun, 
or moon and ftar being found, both for the beginning and end- 
ing « ofa folar. eclipfe, or. of an: occultation, where both have 
"min ! , the fum of thefe, when the 
moon was on dilea ide of the point of the true ecliptic 
conjunction, at the beginning and ending or the difference, 
when fhe was upon the fame fide in both, will be her. whole 
motion in longitude from the fun or ftar during the time of the 
capella ae eclipfe 
# 
* We fhall find an inftance of this at the beginning of the folar eclipfe at Green- 
wich, June 24, 1778. 
