VOL. LIII.J VHILOSOPHICAL TRANSACTIONS. 3l 



Mr. S. now proceeds to the determination of the sun's parallax by the least 

 distance of the centres. There came to his hands only two measurements of the 

 greatest distance of the limbs of the Sun and Venus, one at Tobolsk and the 

 other at Rodrigues. He only considers the measurement at Rodrigues, because 

 there seems to be some mistake in the measurement at Tobolsk. If we suppose 

 the sun's parallax = 8*.5, then the apparent middle of the transit happened at 

 Rodrigues at Q^ 37"' 30*. There is a measurement by M. Pingre of the greatest 

 distance of the limbs at Q*' SS" 13% which is so near the middle of the transit that 

 we may safely take this quantity, viz. 5' 54". 6,* for the greatest distance of the 

 limbs of the Sun and Venus, and especially as it is marked an exact observation. 

 This measurement therefore gives the apparent least distance of the centre of the 

 Sun and Venus at Rodrigues = g' 1\"A. Supposing then this measurement to 

 be exact, here follows an irrefragable argument, independent of all other methods, 

 to prove that the parallax of the sun is very nearly = 8 '.5. Let us suppose the 

 sun's parallax = 10' ; and let us compute by the following method the apparent 

 least distance of the centres at Tobolsk ; thence we shall find that the geocentric 

 least distance of the centres at Tobolsk is 567'''.4l6, and by the observation at Rod- 

 rigues the geocentric least distance of the centres is = 572 ".6l2 ; so that on this 

 supposition we have two different geocentric least distances of the centres, which 

 being absurd, it follows that the sun's parallax is not 10". Again let us suppose 

 that the sun's parallax is = 7" ; we shall find that the geocentric least distance of 

 the centres by the observation at Tobolsk is = 575".356, and by the observation 

 at Rodrigues it is = 5()9".248. Thus then again we have two different geocentric 

 least distances of the centres, which being absurd, it follows that the parallax of 

 the sun is not 7". Again if we suppose the sun's parallax = 8" or 9", we shall 

 find that the same absurdity will follow, but in these last two suppositions 

 we shall find that the differences of the geocentric least distances of the centres 

 are not so great as on the suppositions of 10' and 7 ', it therefore follows that 

 the parallax of the sun is less than 9" and more than 8". And if we continue 

 to reason in the same manner, we shall find, that on the supposition that the sun's 

 parallax is = 8 .5, the geocentric least distances of the centres, severally found by 

 the observation at Tobolsk and at Rodrigues, is very nearJy the same, consequently 

 that the sun's parallax is very nearly = 8". 5. If we pursue this subject to a greater 

 precision^ and suppose that the measurement of the greatest distance of the 

 limbs of the sun and Venus, taken by M. Pingre, to be perfectly exact, and com- 

 pute on true -f- principles the apparent least distances of the centres, from the 



* Mr- S. all along considers the observation of M. Pingre at Rodrigues as it is printed, from his 

 own letter, in the Phil. Trans. — Orig. 



+ He says on true principles, because he had reason to think that there is a mistake in the method 

 given by M. Pingre in the aforesaid memoir. — Orig. 



