326 PHILOSOPHICAL TRANSACTIONS. [anNO I676. 



troduced to the nodes of the satelHtes, such as is described at the end of his 

 first tables, only to reconcile the observations of Galilaeo 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 hypo- 

 theses of Galilaeo are demonstrated by the eclipses of the satellites, which happen 

 conformable to the calculus of Cassini, and differ by days and hours from the 

 calculus and predictions made upon the hypotheses of Galilaeo : 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 Galilaeo, the fourth of the 

 satellites should have more than 90 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 Galilaeo ; as the great difference 

 of the time of the eclipses that happen depends on this, that neither Galilaeo 

 nor the other astronomers do separate from the proper motion of the satellites, 

 the appearances which befal it by that of Jupiter about the sun. And therefore 

 it is, that they have taken for a simple and equal motion, a motion compounded 

 of an equal and unequal ; whence they have fallen into an error about the mean 

 motions, which in progress of time has so increased, that the configurations 

 drawn from their hypotheses for that time, have hardly any likeness at all with 

 those that are observed. 



These old hypotheses were therefore far from serving to find out the longi- 

 tudes, as their authors intended them ; since it was impossible for them not 

 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, we 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. 



ji Direct and Geometrical Method of investigating the Ophelia, the Eccentricities, 

 and the Proportions of the Orbits of the primary Planets, without supposing the 

 Equality of the Angle of Motion at the other Focus of the Planets Ellipsis. By 

 Mr, Edmund Halley.* Translated from the Latin. N° 128, p. 683. 



The annual motion of the earth in the ecliptic, is the cause of an optical 

 inequality in the motions of the other planets, well known to the Copernican 



* Dr. Edmund Halley, a celebrated mathematician and astronomer, as well as one of the most 

 eminent and useful members of the Royal Society, was born in London, An, l656, and educated at 

 St. Paul's School there; from whence he was sent l673 to Queen's College, Oxford, where he 



