VOL. LVIII.] PHILOSOPHICAL TRANSACTIONS. 521 



drawn to ever)' point of the sun's disk paA, which, without sensible error, may 

 be supposetl fixed during the whole transit; and that these right lines, on a plane 

 perpendicular to the line ts, joining the centres of the sun and earth, and pass- 

 ing through oB the apparent path of the planet seen from the earth's centre, 

 form the projection ike, whose centre is in c, cutting the path in the points i 

 and E. If now from c the line cd be drawn perpendicular to the ecliptic, a 

 spectator at t would see the planet in conjunction with the sun in respect to the 

 ecliptic, its centre being at d ; also half of the planet's disk will be seen immersed 

 or emerged when its centre is come to i or e. And if from any other point a, 

 of the earth's disk, at the bounds of the light, the sun be viewed, and hence in 

 like manner lines be drawn to every point of the sun's disk, the situation of the 

 sun's projection will be changed according to the magnitude and position of th, 

 or of its parallel and proportional cl ; so that the centre of the sun is not now 

 seen in c, but in l ; by which means also the said moments will be changed as 

 shown by the small letters, i being at i, n at d, e at e, by the effects of paral- 

 lax, which are thus to be determined when the observations of those moments 

 made at h are reduced to the earth's centre. Conceive further that by lines 

 drawn from the sun's centre s to every point of the earth's disk hrz, there is 

 made, on the same plane on which the sun is projected, the projection of that 

 disk NOL, which also is a circle whose radius cl is = the horizontal parallax of 

 the planet from the sun ; th remaining = the horizontal parallax of the planet : 

 for draw lm parallel to st, then, because of the very small and equal angles tsh, 

 MLH, will MH be =: the sun's horizontal parallax; and therefore tm = th — mh 

 = CL. If the point h should be not at the boundary of the light, but elsewhere 

 in the earth's disk turned towards the sun, then will cl be either exactly or very 

 nearly equal to the parallax of the planet from the sun, according as the altitude 

 of the planet and of the sun's centre is either nothing or very small. The effect 

 therefore of parallax depends on the divers situation of the centre of the sun's 

 disk in the circle lon, or, which is the same thing, on the divers place of the 

 observer in the hemisphere hrz; for the projection of that place and of the centre 

 of the sun's disk, seen from the same place, coincides in one and the same point 

 of the circle lon. Therefore the question, of estimating the effects of parallax, 

 is reduced to this, that, for any given time, to determine, in respect of cd, the 

 situation of any given place of the earth projected on the circle lon, which place 

 is reduced to l. For this end, there must be found cl, with the angle lcd, 

 intercepted by a projectal vertical circle and circle of latitude. And since that 

 angle depends on the paralactic angle, comprehended by the meridian and ver- 

 tical circle, this angle must be first found. 



§2. Therefore let the circle anb, fig. 8, represent the earth's hemisphere illumi- 

 nated and projected, as above, on the plane passing through the path of the 



VOL. xii. 3 X 



