VOL. Tin.] PHILOSOPHICAL TRANSACTIONS. 65 



abcdefz is equal to double the last right line, 2zw; and that aw is equal to 

 half the circumference of the circle, whose diameter is zw; also universally, that 

 the triangle T b n represents the right line zw ; and the square T b 1125, tiie 

 curve abcdefz; and the quadrant y" y 25 represents the right line aw; and 

 the parts of one respectively the parts of the other. As, if T— ^ represents 

 £^y then ^£^^25 will represent a^, and T— ^25 will represent af. — I say 

 lastly, that a ball suspended by a string of a proper length, and vibrating between 

 two cycloids, describes or moves in a cycloid. Consequently these vibrations 

 are synchronous. Q. E. D. 



Observations of Jupiter s Transits near some Fixed Stars; useful for determining 

 the Inclination of that Planet to the Ecliptic. By Mr. Flamsteed. N° 94, 

 p. 6033. 



The inclosed paper contains some observations of Jupiter, which being made 

 from a more convenient station than I commonly have used, are more accurate 

 than my former ones: and the planet being in a fit place of his orbit, they are 

 the most useful for determining his inclination to the ecliptic, that we can 

 again expect these six years, or perhaps before he returns again to this place. 

 Had the latitudes of the fixed stars of Tycho's constitution been exact and co- 

 herent, we should easily have determined the precise quantity of this inclination, 

 and those regular inequalities we find in this and in all the other planets, which 

 are irrepresentable by numbers, only by reason of some latent errors in the places 

 and latitudes of the fixed. 



It would be a task deserving the pains and accuracy of the learned Cassini, and 

 of all others that have good observatories and instruments, to endeavour the 

 restoring of the fixed stars, especially of those that are near the ecliptic. Had 

 I only a convenient place for observing, a ready assistant, and other necessary 

 accommodations, I should not doubt in a few nights to rectify many of Tycho's 

 errors ; and to add some stars to his catalogue, as well visible to the bare eye, 

 yet omitted, as telescopical ones. 



I have made lately some observations of the utmost elongations of the three 

 innermost satellites ; which I find greater than Signor Cassini states them, but 

 almost the very same with Mr. Townley's. But I have just cause to suspect 

 some eccentricity in the third ; fori find its elongation greater on the one hand 

 of Jupiter, than on the other.. I intend, at another opportunity, to make more 

 trials as carefully as I can, either to confirm or destroy this observation. 



The observations are omitted, as not now of any use. 



VOL. II. K 



