An Extract of a Letter Written by Signor Cassini to the Author of the Journal des Scavans, Containing Some Advertisements to Astronomers about the Configurations, by Him Given of the Satellites of Jupiter, for the Years 1676, and 1677, for the Verification of Their Hypotheses

And thus the course of the water which issues by the Jet, is always entertained in the same state; because that proportionably, as the impulse is strong, the water entering faster, and consequently in greater quantity into the Pot, makes a greater compression of the Air, which the more strongly it is compressed and penned in, returns also with the greater force into its native state by means of its spring, and consequently throws out the water with greater force. An Extract of a Letter written by Signor Cassini to the Author of the Journal des Scavans, containing some Advertisements to Astronomers about the Configurations, by him given of the Satellites of Jupiter, for the years 1676, and 1677, for the verification of their Hypotheses. The Configurations of the Satellites of Jupiter, which are observed this year 1676, and which may be observed the next year, are of so great importance to the verifying of their Hypotheses, that Signor Cassini thought fit to advertise Astronomers, not to let this occasion slip (which doth not present itself but twice in 12 years) of observing them with a singular care and attention. For, by comparing the Observations of this year with those of the next, they will find an apparent Inversion of the whole System of the Satellites, which will come to pass towards the end of March next, according to his particular Hypotheses, which he proposes to verify by comparing these Observations with those of Galilaeus, Marius, and Hodierna, who undertook to dress Tables of their Motions. Since the Satellites have the center of Jupiter for the center of their particular motions, and that the circles by them described are not directly opposite to the Earth nor the Sun, there is always a part of each of those circles inferior to Jupiter, and another superior to him, and this, being compared to the center of the apparent disque of Jupiter, is sometimes turned to the South, sometimes to the North, by a perpetual change of inclination to our visual ray. Galileo believed formerly, to have found Rules of this Phænomenon, or perpetual change of inclination, by supposing the planes of those circles to be always parallel to the Ecliptique; for, by Galilei's supposition, the Satellites in the superior part of their circles should have their latitude, in respect of the center of Jupiter, ever contrary to the latitude of Jupiter in respect of the Ecliptique; which the Observations of this year contradict, forasmuch as the Satellites, being in the superior part of their circles, near to their conjunction. with Jupiter, have also the Meridional Latitude in respect of his center, as Jupiter hath, since the month of March, in respect of the Ecliptique. The contrariety of latitude between one Satellite, being in the superior part of his circle, and another being in the inferior part of his, is more sensible in the encounter of a Direct, which is always superior, with a Retrograde, which is always inferior, and particularly near to Jupiter. Signor Cassini foresees, 1. That, at the end of March next, the Satellites will no more have any latitude in respect of Jupiter's center, and that they will appear in a straight line in all their configurations between themselves and with Jupiter, and will eclipse one another; which, according to Galileo, should have come to pass ever since the first months of this present year, when Jupiter passed from the North-side to that of the South, and not the next year, when Jupiter will have a great Southern latitude. 2. That the straight line of the Satellites will be inclined to the Ecliptique, contrary to the Galilean Hypothesis. 3. That this disposition of the Satellites in a straight line in their encounter will last but a few days, though Galileo assure us that it lasts many months. 4. That the next Summer the situation of the circles of the Satellites will be found inverted, in respect of that which they have now; for, the superior Semi-circles, which at present are turned to the South, will then be turned to the North: which will overthrow the Hypotheses of Mairius and Hodierna, who suppose them always turned the same way. These Observations will serve to verify the Nodes of the Orbes of the Satellites with the Orb of Jupiter, and the Obliquity of the one to the others; which are the two Keys to the Theory of the Satellites. Signor Cassini settles these Nodes towards the thirteenth degree of Leo and Aquarius; but Galileo supposed them always to be with the Nodes of Jupiter, which are towards the beginning of Cancer and Capricorn. He finds the Obliquity of their circles to the orbite of Jupiter almost double to the obliquity of this orbite to the Ecliptique; whereas Galileo supposes it equal. Lastly, he (Cassini) retracts the motion, which he introduced to the Nodes of the Satellites (such as is described at the end of his first Tables) only to reconcile the Observations of Galileo with his, and he acknowledges, that the obliquity of their circles is permanent. The goodness of Signor Cassini's System, and the imperfection of the Hypotheses of Galileo are demonstrated by the Eclipses of the Satellites. Satellites that come to pass conformable to the calculus of Cassini, and differ days and hours from the calculus and predictions made upon the hypotheses of Galilei: Besides that there should happen a great many which do not happen according to the system of Cassini. E.g. according to the hypothesis of Galilei, the fourth of the Satellites should have more than 96 Eclipses in a year, of the duration of three or four hours; but according to the system of Cassini, the same Satellite will be three or four years without suffering any Eclipse. Which proceeds from nothing but the false situation of the Orbs supposed by Galilei; as the great difference of the time of the Eclipses that happen depends from this, that neither Galileo nor the other Astronomers do separate from the proper motion of the Satellites the appearances which do befall it by that of Jupiter about the Sun. And therefore 'tis, that they have taken for a simple and equal motion a motion compounded of an equal and unequal; whence they have slipped into an error about the Mean motions, which in progress of time hath so increased, that the Configurations drawn from their hypotheses for that time have almost no likeness at all with those that are observed. These old hypotheses were therefore far off from serving to find the Longitudes, as their Authors intended them; since it was impossible for them nor only to observe the Eclipses of the Satellites for some years to the nearness of an hour, but even to make us know and distinguish at this time one Satellite from another, whereas by the System of Signor Cassini one may predict for many years to come the Eclipses of the Satellites with as much preciseness, as those of the Sun and Moon by the Astronomical Tables. Methodus directa & Geometrica, cujus ope investigantur Aphelia, Eccentricitates, Proportionesque orbium Planetarum primariorum, absque supposita æqualitate anguli motûs, ad alterum Ellipses focum, ab Astronomis hactenus usurpatâ. Auth. Edmundo Hally Jun. è Collegio Reginae Oxon. Motus Terra annus per Eclipticam, opticam inaequalitatem inducit motibus cæterorum planetarum, Astronomis Copernicani nomine Parallaxeos orbis notissimam; quam quidem inaequalitatem, ex observationibus non multâ operâ datam, methodi sequentis basin firmissimam constituo; ubi præter observata nihil alius supponitur, quàm quod orbis Planetarum sint Ellipses, quodque Sol in foco omnium orbibus communis, sit constitutus, & denique, quod tempora periodica singulorum