332 PHILOSOPHICAL TRANSACTIONS. [aNNO J 686. 



that it did not happen just at the full moon, but about a day after it : and, 

 which is very extraordinary, being a coincidence that hardly ever happens, it 

 occurred at the same point of time, and with the same appearance, as in the 

 first occultation above-mentioned, of 1646 ; when the moon had decreased for 

 2 days, and doubtless exhibited the same libration also ; for the section of light 

 and shadow was just the same, and passed through the same spots, which I 

 cannot sufficiently admire ; that is, at the greater and less hyperborean lake, 

 also at the Riphean mountains, through Palus Maeotis, by the great Caspian 

 lake, and its lower bay to mount Nerosus. On the other hand, the second 

 occultation, of 1679, was under different circumstances, as it happened not at 

 the full, but near the new moon, being about 3 days before the conjunction. 

 Of the present occultation, of 1686, the principal phaenomina are the fol- 

 lowing : viz. At 



1 1** 7"" 9' the beginning, or external contact. 



11 7 54 the central immersion. 



11 8 39 internal contact, or complete immersion. 



11 49 15 beginning of the emersion. 



1 1 50 O the central or half emersion. 



11 50 45 the complete emersion. . 



In this occultation, it appears that Jupiter's path line behind the moon, was 

 a chord of near 104°, in the north part of the moon, the diameter of which, 

 measured by a micrometer, was 3l' just. From the observations, M. H. derived 

 the diameter of Jupiter, viz. 51" 42'", and which then measured about 50" by 

 means of the lunar spots; whereas in the year 1679, when he observed a similar 

 occultation, the diameter of Jupiter was only 30" 53'", which he prefers to the 

 former measure, as, being made in the day time, the adventitious rays of the 

 stars and planets were much dispelled by the sun's light. 



Methodus Figurarum lineis rectis et curvis comprehensarum quadraturas determi' 

 nandi. Autfwre J. Craige, Ato, Lond. l685. N° 183, p. 185. 

 The great use of drawing the tangents of curve lines, has induced the mo- 

 dern mathematicians to endeavour to discover general methods of finding the 

 tangents of curve lines ; as may be seen from the several ways invented by 

 Descartes, M. Fermat, Dr. Barrow, Dr. Wallis, Tschurnehuys, and Leibnitz. 

 But no one has attempted to invert this problem generally, that is, having the 

 tangent, to find the curve line whose tangent it is. Therefore the author of 

 this treatise, perceiving that this would give a general method of determining 

 the quadrature of any curvilinear space, has laid down a rule for inverting 

 Slusius's method mentioned in the Philosophical Transactions, N° 90. He has 



