VOL. LXIII.] PHILOSOPHICAL TRANSACTIONS. 431 



botl). For comparing eclipses otlierwise circumstanced, a more general formula may easily be deduced 

 from the same principles. If Atl be the insensible segment in one eclipse, a d in anotlier (vide tlie 

 first figure), a the versed sine of the arc Ad, b, of a d, the radius being unity, d the whole duration of 



the first eclipse, /'of the 2d, then -rr- x (^a — db) is what the author would call the equation, be- 

 tween tlje two, arising from the different magnitudes of the insensible segment, or the time by which 

 the interval between the obser\ed eclipses, differs from die interval between the real passage of the 

 centre in each eclipse. This is a general formula, for all eclip)ses of the same satellite. If the planet's 

 distance from the node has been the same in botli, then ^ =. d, and tliis formula changes into tlie 

 author's. The more general one is here given, ratlier for tlie fuller explication of the tlieory, than 

 for any necessity that there is to have recourse to it in practice. For, though the use of it may soVne- 

 times be convenient, eclipses of the same satellite may always be compared without it, when once the 

 diameter of die satellite is known, and the magnitude of the insensible segment in each eclipse de- 

 termined, by reducing die observed immersion or emersion to the true ingress or egress of the centre. 



(*) The words printed in the Italic characters are designedly omitted in the translation, it being ap- 

 prehended, that it is owing to some inadvertency, that they appear in the author's text. -For unless 

 they are expunged, the general description, here intended, of the author's method of determining the 

 diameters of the satellites, will by no means agree with die examples of that method immediately sub- 

 joined. These words imply, that die author takes die instant of the disparition of the satellite, in the 

 contracted aperture of the diaphragm, for the moment of the contact of die satellite's limb with the 

 edge of the shadow, and makes that moment so determined, die basis of his calculations : reasoning 

 as it should seem thus. ' When any part of the diameter of the satellite, however small, has entered 

 the shadow, some p>art of the light, which the observer receives, through die aperture of the diaphragm, 

 from die whole unshaded disc, will be intercepted. But that aperture is so small, that die light trans- 

 mitted through it, from the whole unshaded disc, is but just sufficient to be sensible; and must there- 

 fore cease to be so, when it is in the smallest degree diminished, i. e. when the very smallest part 

 imaginable of the disc is shaded. Therefore the moment of the disparition, in the aperture of the 

 diaphragm, is the true commencement of the eclipse, or difi'ers from it by less than any assignable 

 difference.' 



But it appears, from the examples given afterwards, that the author's calcijlations proceed on much 

 safer principles. Having determined the portion of the disc, that is insensible on die whole given 

 aperture of his telescope, he computes what larger portion will be insensible, on die smaller given 

 aperture of his diaphragm. And then, by observing the two disparitions, the earlier one in the dia- 

 phragm, the other in the telescope with the object-glass uncovered, the last of which he calls die true 

 immersion, he knows the dme in which a given portion of the diameter enters the shadow, and con- 

 sequently the time in which the whole enters; which determines the magnitude of the whole, in parts 

 of the satellite's orbit, or its apparent magnitude to an observer of Jupiter's centre. 



C) The disadvantage of using too great an aperture is, that the part of die diameter obtained by ob- 

 servation, from which the whole is to be concluded, will be less than the same mediod of observation 

 would give, with a more contracted aperture. For the larger the aperture of the diapliragm is which 

 is applied to the object-glass, the less is the difference between that aperture and the whole aperture of 

 the telescope ; consequendy the less is the difference between the segments, which are insensible in 

 these apertures severally, and the less the portion of the diameter, which passes over die shadow's 

 edge, between the two disparitions. 



(<') In eclipses, when once the satellite has disappeared, or is become visible, die author says, we 

 are not to expect those fits of glimmering and extinction, whicli he has described as taking place, when 

 we observe the uneclipsed satellite with very contracted apertures. The reason is plainly this : in im- 

 mersions, a part of the disc is still indeed enlightened, when the satellite disappears ; and die quantity 

 of light, transmitted from this part to the observer's eye, must be very different, in different states of 



