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the Calculation of the Eclipses of the First Satellite of Jupiter, which is other-wise Operose even to tVie Skillful. The Tables have for Principies, that thisSatellite Revolves to the Sun in i d 18tr x8' 36", so precifely, that in iooYears the Difference is not sensible; That in the Time of the Revolution ofJupiter to his Aphclion , which he supposcs in 433xd 14h 51' 48", this Sa-tellite makes exactly X448 Mönchs or Revolutiuns to the Sun ; and dividingthe Orbite of Jupiter into 2448 parts, he has in a Large Table of Equationfhewn what is the lnequality ot the Motion of Jupiter in each Revolution rc-duced to timc, affuming, Lbirdly, the greatest Equation of Jupiter y° ^i /4c/ 7 . whcnce the hourly Motion of the Satellite fronn Jupiter being 8° xBL,it follows that the greatest lnequality ( Jupiter pafling the Signs of Cancerand Capricorn, ) amounts to 39' 8* of Time, to be added in Cancer , sub -stracted in Capricorn. Lastly , As to the Epocha, or beginning of this Scricsof Revolutions, he has determined the Aphclion of Jupiter about 1 1 , Degreeforwarder than Astronomia Carotina, and above two Degrees morethan the Rji-dolphine Tables, •vi\. precisely in 9 0 of Libra, in the beginning of this Cen-tury, which perhaps he finds the proper Motion of Jupiter about the Sun atthis time to require ; and the Number of Revolutions lince Jupiter was last inPcrihelio , is here stiled Kutn. I.

A Sccoud lnequality is that which depends on the Distance of the Sunsirom Jupiter, which he says Mr. Rpmer did niest ingenioufly explain by theHypothesis of the Motion of Light; to which yet C affui i by his mannet ofCalculus seems not to affent, though it be hard to imagine how the Eartlh Po-sition in refpect of Jupiter (hould any way affect the Motion of the Satellites.This lnequality he makes to amount to two Degrees in the Satellite' s Motion,or 14' lo" of Time, wherein he supposes the Eclipses to happen so muchsooner when Jupiter Opposes the Sun, than when be is in Conjunction withhim. The Distribution of this lnequality he makes wholly to depend onthe Angle at the Sun, between the Earth and Jupiter, without any Regardto the Excentricity of Jupiter, ( who is sometimes b a Semidiameter of theEarth's Orb, farther from the Sun than at other times ) which would occa-sion a much greater Difference, than the lnequality of Jupiter and the Earth'sMotion, both of which are accounted for in thele Tables with great Skilland Addrcss. But what is most stränge, he Afsirms that the ftme Inequaibty of two Degrees in the Motion, is likewise found in the other Satellites,requiring a much greater Time ; as above two Hours in the 4^ Satellitewhich if it appeared by Observation would overthrow M. Rjimcfs Hypo-thesis entirely. Yet I doubt not herein to make it Demonstratively plain,that the Hypothesis of the Progressive Motion of Light is found in all theother Satellites of Jupiter to be neccstary, and that it is the same in all; therebeing notbing near so great an Annual lnequality as M. Cajstni supposes intheir Motions, by his Table, p. 9. and his Praccpta Calculi . T. he Methodhowever used to compute this is very Curious; for having found that whilstthe Sun Revolves to Jupiter, there pass 398«* xi* 1 13k wherein are madeRevolutions of. the Satellite to Jupiter , the Number of Revolutions

since.