VOL. XXXIII.] i'HILOSOPHICAL TRANSACTIONS. 7,i 



this last transit, with a surprising exactness, even beyond his hopes, making 

 the time of the mitldle, or nearest approach of the centres of the sun and 

 Mercury, Anno 1723, Oct. •ig'^ 5^ JQ"" app. time, which was found by obser- 

 vation at 5*^ 14-1-™, only 4-l'" sooner ; and, m latitude, Mercury was but 6 seconds 

 more southerly than he had computed it; the error in longitude being little 

 more than 2 diameters of this exceedingly small planet; and in latitude only a 

 single semidiameter. So that for the future astronomers may trust his table of 

 these transits, in Trans. N° 193, to a few minutes of time, and not wait with 

 the uncertainty of hours, nay days, as has lately been done. 



But, in order to obtain a yet further degree of exactness by help of this ob- 

 servation, it may be most expedient to compare with it the ingress observed at 

 St. Helena; because in that, as well as in this, the latitudes of the planet being 

 very small, a little error in them will not so much affect the longitudes. Sup- 

 posing therefore, that Anno l677, Oct. 27'^ 2i^ 26"" 15' at St. Helena, or 

 21*^ 50"^ 15* app. time, at Greenwich, the centre of Mercury entered on the 

 sun, and that at that time he was 8J- degrees on the sun's limb, to the north 

 of the ecliptic, according to what is above concluded, it follows, that he had 

 then 2' 20' north latitude, and l6' 5" greater longitude than the sun's centre; 

 as in this present transit, Oct. 29'' 2^ 41"" 30' app. time, at Greenwich, he had 

 3' 40" north latitude, and 15' 50' more longitude. 



Now the apparent geocentric differences of longitude, are to the real helio- 

 centric differences, as the planet's true distance from the sun, to his distance 

 from the earth; that is, in both cases, as 313 to 676; therefore, in 1677, 

 Mercury wanted 34' 45" of the conjunction with the sun; and, in 1723, but 

 34" 13'", at the times of his apparent ingress on the disk. And, equating the 

 times, he finds that the sun, Anno 1677, Oct. 27^ 2l'' 34'" 20' aeq. time, was 

 in n\, 15° 36' 55", and consequently Mercury's heliocentric place y 13° 2' 10': 

 and. Anno 1723, Oct. 29^ 2*" 25"' 30' aeq. time, the sun was in n^ l6° 39' 43", 

 and therefore Mercury at that time in y l6° 5' 30'. 



Mercury therefore, in 46 years, with 11 intercalations, and besides l"* 4'' 

 51'" 10% has made 19I revolutions to the equinoctial points, and over and 

 above 1° 3' 20". But, by the Scholion to Prop. XIV. Lib. 3. Nat. Philos. 

 Principia Math, the motion of the Aphelion of Mercury, from the equinox in 

 that time, is 40' 18"; so that there remains 23' 2* of true anomaly to be re- 

 duced to the mean : now the mean anomaly of Mercury, in both cases, being 

 5 sig. 12° 23' 2" of true anomaly, gives 15' 24" mean anomaly; which added 

 to 40' 18", becomes 55' 42", for the mean motion above so many revolutions: 

 and this is to be increased by 8', to reduce it to the plane of Mercury's orb, in 

 all 35' 50". 



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