[ 166 ] 
That the before-mention’d folar Eclipfes might be 
applied to the Examination of the Lunar Motions, 
I contrived the following Method ; which I think ren- 
ders Eclipfes of the Sun as ufeful at leaft as thofe of 
the Moon are in that Bufinefs. 
£ I 
Let ABC in the annexed Figure reprefent half the 
Earth’s enlightened Disk, AEC a Portion of the Eclip- 
tic projected thereon FGH the Path of the Moon’s 
Shadow over the Disk, El, the univcrlal Meridian, a 
the Situation of the Place at the Beginning of the 
Eelipfe, /3 its Situation at the End thereof, S the Cen- 
tre of the Shade at the Beginning, and g its Centre 
at the End of the Eelipfe. Draw EG, a£, and 
/3>j, perpendicular to the Path of the Shadow, 
parallel thereto ; join aS and /3e, and through 
draw Gat perpendicular to A C. 
Then (computing the true Places of the Sun and 
Moon at the obferved Times of the Beginning and 
End of the Eelipfe) wc fhall have given Se the Mo- 
tion of the Moon from the Sun in her Orbit during 
the Time of the Eelipfe, and a. S' = /3 e the Semidia- 
meter of the ‘Penumbra which are to be reduced 
into fuch Parts as the Semidiameter of the Disk con- 
tains 
