(152 PHILOSOPHICAL TRANSACTIONS. [ANNO 1785. 



tautias curtatas.) This supposition is changed and altered till the calculation 

 will agree with the 3 observations, then the difference between 2 longitudes is 

 the angle comprehended between the 2 shortened distances in the plane of the 

 ecliptic ; the whole reduced to the plane of the comet's orbit by means of the 

 heliocentric latitude, gives the difference between the anomalies comprehended 

 by 2 radius vectors, the problem then is reduced to 2 radius vectors being given, 

 with the angle comprehended, to find the 2 true anomalies, the perihelial dis- 

 tance, and the time the comet takes in running its anomalies. Mr. Z. then 

 gives the algebraical solution at full length, which is to be found in the authors 

 on astrouomy. 



With regard to the transit of Mercury, which happened Nov. 12, 1782, it is 

 remarked that the sky not being very favourable, only the two internal contacts 

 were observed ; the first internal contact was observed by M. St. Jacques de Syl- 

 vabelle, at 3 h 18 m 30 s apparent time; the last internal contact by the same, 

 at 4 h 30 ni 16 s ; by M. Bernard, his assistant, at 3" 33™ 14 s 31 



4 h 2g m 13 s . The nearest distances of Mercury's \ *% f/ jp 



limb to that of the sun in the northern part of Parts of the micrometer 



its disc were, at 



The apparent diameter of the sun was 2174 parts of this micrometer: I sup- 

 pose the before-mentioned 2174 parts = 32' 26". Q. I conclude further, by the 

 observations, the middle of the transit at 3 h 54 m 7 s . 25, whereas I fix, by inter- 

 polation, the distances of the limbs at 3 h 54 m 7 s . 25 = 35 .6 ; I have therefore 

 semi-diameter of the sun = 16' 13 // .4 — 35".() = 15' 37 // .8 4- semi-diameter of 

 Mercury 6" = 15' 43".8 = to the least distance of centres of the sun and Mer- 

 cury. By M. De La Lande's tables it is 15' 42", only a difference of 1".8. 



M. Wallot at Paris has observed this transit 



at the Royal Observatory. First external contact. . 2 h 56'™ 28 s 



Mr. Z. then adds a remark on the diameter f Tst i " ternal contact - -323 



Second 4 \< 18 



of Mercury, which the astronomers supposed in Second external 4 22 53 



this transit = 12". Let abc, fig. Q, pi. 8, represent the sun's disc ; in p an ex- 

 ternal, in a an internal contact ; anc the apparent path of Mercury over the 

 sun. The semi-diameter of the sun = 972", this of Mercury in our supposi- 

 tion = 6", mn = 942" the least distances of the centres. In the right-angled 

 triangle mnp it is mp = 972" + 6" = 978", m« = 972" — 6" = 966"; there- 

 fore np will be found = 260", and nq= 210": now np — nq = pq = 50", 

 which converted into time gives 8 ra 14 s for the time the diameter of Mercury em- 

 ployed to run over the sun's limb ; but by the observations of M. Wallot I find 

 this time constantly in both contacts 5 m 35 s ; therefore 8 m 14 s : 12" :: 5 m 35 s : 

 8".137, which should be the diameter of Mercury; and indeed M. Wallot, by an 

 immediate measure, taken with an excellent wire-micrometer, finds this apparent 



