36 PHILOSOPHICAL TRANSACTIONS. [anNO 1763. 



paper on this subject, except that in reducing time to space, he has made use of 

 4' 0''.03 for the horary motion of Venus in her path. 



Mr. S. adds the following method of determining the apparent least distance of 

 the centres of the sun and Venus from the observation of the total duration of 

 the transit observed at any one place, and also the geocentric least distance of the 

 centres. 



Let BCPL, (fig. 3, pi. 1,) represent the sun's disk ; lsp the ecliptic; or the 

 geocentric path of Venus over the sun ; ad the apparent path at any place, to 

 the north of the plane of Venus's orbit ; sm the geocentric least distance of the 

 centres ; ak the parallax of latitude at the internal contact at the ingress ; 

 ND the parallax of latitude at the internal contact at the egress ; A.b the 

 parallax of longitude at the ingress ; and en the parallax of longitude at the 

 egress. It is required to find sf, a perpendicular let fall from the centre of the 

 sun on the apparent path, and thence to find sm the geocentric least distance of 

 the centres of the sun and Venus. 



If the parallax of longitude at the ingress retard, and the parallax of longitude 

 at the egress accelerate, the total duration will be shortened by the sum of these 2 

 parallaxes of longitude, viz. by J^b and cd ; and if we make no allowance for 

 these parallaxes, the apparent path will appear to have been bc, consequently a 

 perpendicular from the sun's centre on bc will be se, longer than the perpendicular 

 on the true apparent path, by fe. Now since it is certain that the parallaxes of 

 longitude do not depress or elevate the planet, but only alter the position of the 

 planet in a direction perpendicular to the axis of its orbit, therefore the parallaxes 

 of longitude, in time, are in this case to be added to the observed time of the 

 total duration : in consequence of which, the obser\'ed time of total duration, bc 

 -\- Kb -\- CD are = to the chord described by the planet in its passage over the 

 sun ; and if the semidiameters of the sun and Venus are known, their difference 

 is known, which is = to the line as : af, from what has been said, is also known, 

 therefore sf may be found. But this sf is not the apparent least distance of the 

 centres ; for if we compute the parallax of latitude for the apparent middle of the 

 transit, we shall find it greater than mf, which mf is only a mean between the 

 parallaxes of latitude at the ingress and egress. Let therefore the difference be- 

 tween MF and the parallax of latitude, computed for the middle of the transit, be 

 added to sf, and the sum will be = to the apparent least distance of the centres 

 nearly ; and if from this sum we subtract the parallax of latitude, computed for 

 the middle of the transit, the remainder will be the geocentric least distance of 

 the centres nearly. 



A true, and more ready method, to find the geocentric least distance of the 

 centres, consequently the apparent least distance of the centres, at any place 

 where the total duration has been observed, is thus : — 



Reduce the total duration observed to the centre ; reduce the central seini-du> 



