[ 21 + ] 
fame diftance from the node of the fatellite’s orbit, at the com- 
mencement of both. For comparing eclipfes otherwife circum- 
ftanced, a more general formula may eafily be deduced from the 
fame principles. If A d be the inferable fegment in one cclipfe, 
AD in another (vide figure p. 189.), a the verfed fine - of the arc 
A d, b, of AD (the radius being unity), d the whole tluratioh 
of the fir ft eclipfe. 
o of the fecond, then ~ - V ' X 
d» 
o a 
r db is 
what the author would call the equation, between the two, 
ariftng from the different magnitudes of the infenfible fegment, 
or the time, by which the interval b. tween the obferved eclipfes, 
differs from the interval between the real paftage of the center 
in each eclipfe. This is a general formula, for aff eclipfes of the 
fame farellite. If the planet’s diftance from the node hath been 
the fame in both, then 0 — d, and this formula ch nges into the 
author’s. The more general one is here given, rather for the 
fuller explication of the theory, than for any neceffity that there 
is to have recourfe to it in practice. For, though the ul'e of it 
may fometimes be convenient, eclipfes of the fame Satellite may 
always be compared without it, when once the diameter of the 
fateilite*is known, and the magnitude of the infenfible fegment 
in each eclipfe determined, by reducing the obferveJ immerfion 
or emerffon to the true ingrefs or egrefs of the center. 
(b) The words printed in the Italic character are delignedly 
omitted in the tranffation, it being apprehended, that it is owing 
to fome inadvertency, that they appear in the author’s text. For 
unlefs they are expunged, the general defeription, here intended, 
of the author’s method of determining the diameters of the fa- 
tellites, will by no means agree with the examples of that me- 
thod immediately fubjoined. Thefe words imply, that the author 
takes the inftant of the difparition of the fatellite, in the con- 
tracled aperture of the diaphragm, for the moment of the con- 
tact of the fatellite’s limb with the edge of the fhadow, and 
makes that moment, fo determined, the bafis of his calculations : 
reafoning, as it ffiould feem, thus; “ When any part of the 
diameter of the fateilite, however fen all, hath entered the fha- 
dow, fome part of the light, which the obferver receives, ’hrough 
the aperture of the diaphragm, from the whole unfhaded dilc, 
will be intercepted. But that aperture is fo (mall, that the light 
tea remitted through it, from the whole unfhaded dife, is but juft 
fuflicient to be fcniible j and muff, therefore, ceafe to be fo, 
3 when 
