586 PHILOSOPHICAL TRANSACTIONS. [aNNO 1682-3. 



but the earth reduced, and consequently the satellite, in 11* 28° 18' from the 

 first of Aries. The interval of time is 8655 days gh. 20m.; in which the 

 satellite had made a certain number of revolutions to the fixed stars, and besides 

 9' 25" 28', or 205° 28', whose complement to a circle 64° 32', is 2 days, 20h. 

 36m. motion of the satellite, according to Huygens. So that 8658 days 5h. 

 56m. or 12467876 minutes of time, is the time of some number of entire re- 

 volutions ; and dividing that interval by 15 days 22h. 39m. or 22959m. (the 

 period of Huygens) the quotient 543 shows the number of revolutions; and 

 again dividing 12467876m. by 543, the quotient 22961-^1^^1- or 15 days 22h. 

 41 m. 6s. appears to be the true time of this satellite's period. Hence the diurnal 

 motion will be 22° 34' 38'^ 18'", and the annual besides 22 revolutions 10* 

 20° 43'. Having made tables to this period, I found that in the apogaeon ob- 

 serv^ation of Huygens the satellite was above 3° faster than by my calculus, and 

 that in the three other observations of my own, being likewise in the superior part, 

 it was 24- degrees slower than by the same calculation. Now it is evident that 

 these differences must arise from some eccentricity in the orbit of this satellite, 

 and that in March 1659, the apocronion, as I may call it, was somewhere in 

 the oriental semicircle, and that in November l682 it was in the western semi- 

 circle, and supposing the apocronion fixed, it must necessarily be between 9' 

 23° 46' and 11* 28° 18' from the first star of Aries, that being the common 

 part between those two semicircles : and because the difference was greater in 

 Huygens's observation than in mine, it will follow that the linea apsidum, or 

 apocronion, should be nearer to 9* 23° 46' than to 11* 28° 18.' I will sup- 

 pose 10* 22° 00' from the first star of Aries, which also happens to be the place 

 of Saturn's equinox, and the greatest equation about 2 4- degrees. On account of 

 this inequality, the mean motion of the satellite will be found about 2° 45' 

 slower in 23-i- years, or 7 m. in a year; whence I state the annual motion at 10* 

 20° 36' above 22 revolutions, and the correct epocha for the last day of Decem- 

 ber 1682, at noon, in the meridian of London, 9* 10° 15' from the first star 

 of Aries ; from which elements I compose the following table.* 



The other two satellites of Saturn discovered by Signer Cassini at Paris, 

 Anno 1672 and 1673, I must confess I could never yet see. I have been told 

 that they disappear for about f of Saturn's revolution, and were only to be seen 

 when the ansae were very small, it being supposed that the light which proceeds 

 from the ansae, when considerably opened, might hide these satellites. In the 

 year l685, when the ansae will be quite vanished, will be a proper time to look 

 for them, that so we may bring their motion to rule, and know where to find 



* These are omitted^ as of no use now. 



