624 ' PHILOSOPHICAL TRANSACTIONS. [aNNO I768. 



the retrograde motion of the planet, will the eastern point i be the place of the 

 planet's centre, when the spectator in l sees the beginning or end of the im- 

 inerging; but the western point e for the place of the planet's centre about the 

 contact of the emersion. And for the calculations of these contacts, there will 

 be determined the side ni or ne in the triangle, now given, dlz or DLe. Put 

 then e If ?/ = M ; where the sign — takes place in observations after noon, except 

 when a >» QO" + b ; but the sign + in the forenoon observations, unless a < 

 90° — b ; that is, the planet's path being at ^ more south, or at Q, more north 

 than the sun's centre. But when the planet's path at those nodes have the op- 

 posite situation, the order of the signs is reversed; viz. + in the afternoon, and 

 — in the forenoon observations; unless when q >- 90° + ^ and a < 90° — b. 



Tj . rsin. rsin. »/ . n • "* • / i \ /■ \ j "» 



rut now : = sm. z; then will 01 = -. — .sm.(M + z),(a); andDE = ^ — • 



OTsin.j^ sin. a ^ — i'\ > sin.u 



sin. {xL 4I z') , (b); where (a) serves for the computations of the contacts of the 

 immersion, and (b) for those of the emersion. 



Carol. 1. If with the centre c and radius = m the path be cut in i and b; 

 and if there be put p = O ; the points l, i, e coinciding with c, i, e respectively ; 



we shall haveni = -. — . sin. (e + c), (c); and de = -: — . sin. (e X c), (d) ; 

 sin.e ^ — /' V /' sm. c ^ ' /' \ / 



sin. c being = — — '—. To the tenor of these formulas the contacts, as seen 

 from the centre of the earth, are computed. And the upper signs of the equa- 

 tions (a), (b), (c), (d), are to be observed, if the planet transit the sun, at ^ 

 with south, or at Q, with north latitude; but in the opposite nodes, the lower 

 signs take place. 



Corol. 1. Therefore the effect of parallax about the immersion becomes 



--— ,. sin. (e + z) ^— . sin. (e + c), which converted into time, is to be sub- 



sin. M ^ — ' sin. e ^ — -" 



traded if negative; but if positive, it will be added to the moment of observa- 

 tion, which will give the moment of time reduced to the earth's centre. But at 



the emersion the effect of parallax will be = /" , . sin. iii + z') '■ — "^ , 



•^ sin. u \ I / sin. e 



which changed into time, if negative, it is to be added to the moment of obser- 

 vation; but if it come out positive, it must be subtracted from the same, to 

 give the moment of observed time reduced to the earth's centre. 



Coral. 3. If n = 0, that is, if the planet's path pass through the sun's centre; 

 then the point d coinciding with c, fig. 12, it will be 



ci = -~. sin. (v + s) for the immersion, and ce = -; — ,. sin. (v + s\ for the 

 sin.t) ^ — ■' sin. V \ I / 



emersion. But in the equations (c) and (d), cor. 1, it becomes now c; there- 

 fore for the earth's centre there remains ci = ce = w. And hence, for this 

 case, the effect of parallax will be, at the emersion 



-7^ sin. (v + s) — m, and at the emersion -7^. sin. (v' + /) — m. As to 

 sin. XI ^ — ' sin. V \ 1 / 



