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more powerful in the case of a comet, on which the sun’s influ-ence is diminished by greater distance, and whose velocity is suchthat if it was only increased by one part in 120, the elliptic wouldbe converted into a parabolic course. He shews likewise that thecomet in the summer of 1081 was for several months closelyunder the influence of Jupiter , the effect of whose attraction fromthis proximity became then about T V of that of the sun ; so thatthe nature of the comet’s curve must have assumed a figure“ flexu hyperboliformi Jovem respiciente, . . speciem curvaa ad-modum composite atque hactenus geometricis intractabilis.” Ju-piter likewise lay almost directly over the comet’s path, and tothe north, so as to have drawn it up from the ecliptic, and in-creased the inclination of the plane, in which it was moving m .Lastly, the comet, while it was beyond Jupiter , was drawn for-ward by the combined attraction of the sun and planet; butwhen it had passed that point, the action of Jupiter tended toretard it. Now r , under all the circumstances of the case, theformer state must have been of longer duration than the latter,and the velocity of the comet must therefore upon the whole havebeen increased. He clearly saw the consequence, although hedid not, and possibly at the time was not able to estimate theexact amount of it. He says, “ haec levi tantum calamo a nobistacta;” but the description is relative, and the strength of Hal-ley’s pen must be kept in mind when the sentence is applied tothese remarks. The increase of velocity would of course carrythe comet further off in its aphelion, and add to the length oftime which must elapse before its return :—but his own remark-able conclusion ought to be expressed in his own words—“Pro-inde aucta hoc excessu velocitate propria comeUe, probabile fitreditum ejus non nisi post periodum longiorem 76 et ampliusannorum, circa finem anni 1758 vei initium proximi, fulurum.”And the comet came to its perihelion in March 1759".

The remark which Halley made with reference to the comets

m By referring to the table in the Phil, generalized too rapidly in thinking thatTrans., it may be seen that the comet’s because this comet returned, all the restperihelion lay to the north. The column must do so likewise : in accordance withof “ Latitudo Perihelii” having been this idea he says, “Hie est cometarumomitted in the second edition, it might quasi Mercurius, aretiore orbe et breviorehave been well to have introduced some periodo solem ambiens, dum caeteri omnesnotice to mark in each case the side of latius expatiantur.” What would he havethe ecliptic on which it was situated. thought of Enke and Biela’s comets ?

n It has been mentioned that Halley