292 Reduction of the Observation of the 



vations to the time between the llrst and second. Therefor* 

 A E, B E^ and O E, are given. But O E is to (B + BE) 

 as (B O - B E) to (O F -^ F E),and B'F^'lfc '(B E -K F E) x 

 (B E - F E) ; whence A F, iB F, and the angle O A D he- 

 Softie known, and conse(|ucntly the nearest distance O D oF 

 lh6 centres,. as also A D the distance Merfciiry' his to move 

 from the tirst obsefvatioa to the middle of the transit, vvhicli 

 distunce divided by the horary motion will give the time. 

 The horary motion may be -either taken from the tables,- or 

 found from the observations, being = A B x 3600'^, and 

 divided by the time elapsed between the first and second 

 observations taken in seconds, and is the method here used 

 In determining the nearest approach of the centres, and ap- 

 parent middle of the transit. But they may with equal ease 

 be determined from the following algebraic formula which 

 the analysis gives us. t^et A, B, D, be the first, second, 

 and third distances, and x, y, z, the elapsed times between 

 the tirsi and second, second and third, and first and third 

 observations ; then .will the time between the first ohservatio!) 

 and the middle of the transit be 



_ y ^ '^~+~^' X A^ - z" B"- + .^' D 



Aud the nearest distance of the centres will be had from 

 this ibrmula : 



J/ A + z B -f xD^ y A - a ii- 4- .t D x y A -|> g 13 - x D x s- B - i, A 4- rl) 

 4X1/Z X 2/ A^ - 2 B' Vjc D^ 



Assuming the apparent horary motion of Mercury 

 = 355'^-37o, the nearest apparent approach of the centres 

 comes out = 6o'^'l37, at 21'' 14'" 4()'\d apparent time, as 

 deduced from the following set of observations. Several 

 others were calculated, which do not agree so well *, thouoh 

 their mean approximates to nearly the same quantity. Jf 

 the horary- motion be deduced from the observations, and 

 not taken from, the tables, the middle of the transit will 

 come out about six seconds sooner. 



* Owing to the defect arising' from the micrometer not being prdpef! v 

 VI. ;•. nag cable, as Ims been already itnted. '1'. F. ■■• -- 



Observations, 



