VOL. LIII.] PHILOSOPHICAL TRANSACTIONS. 51 



We may also proceed to find the sun's parallax by means of the least distance 

 of the centres, as observed in two or more places where the effect of parallax was 

 contrary ; or if the least distance of the centres was only determined at one place, 

 it may be found by calculation at any other place, where the total duration was 

 observed. But in this and the last case the elements of calculation are required 

 with so rigorous an exactness, that perhaps these methods are only to be called 

 in to illustrate and confirm the others. 



Mr. Pingre confined himself principally to the determination of the least dis- 

 tance of the centres. At '21'' 43"^ 11' he found the distance between the nearest 

 limbs of Venus and the sun to be the greatest = 5' 5T'.2, or 5' bT'A when cor- 

 rected by refraction. This distance being subtracted from 15' 19'''.5, the dif- 

 ference of the semidiameters, leaves Q' 22*. 1 for the least apparent distance of the 

 centres. But as that observation was made rather too late, when the distance 

 of the centres was greater than it ought to be, he found by calculation that it 

 should be diminished by O''.^"!. The true apparent least distance of the centres 

 by actual observation was therefore of 21 ".88. In order to be more secure of 

 this result, Mr. Pingre compared a large number of observed distances, both at 

 the beginning and towards the middle of the transit, with the distance deter- 

 mined by internal contact, and after excluding every doubtful observation, he 

 found the least apparent distance of the centres to be q' 21 ".69. By comparing 

 this distance with the distance deduced from the total duration, as observed at 

 any place (the method of finding which he has given at large in his memoir in- 

 serted in the Memoirs of the Academy of Sciences for 1761) and by knowing 

 from calculation what influence a parallax of 10" for instance would have on 

 those distances, he found the sun's parallax as in the following table : 



PI Observed du- L. distance of centres L. dist. deduced Sun's p«. 



rations. from the durations. from calculation. rallax. 



Tobolsk! 5" 48"" 53'.25 9' 5r'.53 9' 52".24 10".125 



Stockholm 5 50 43.5 y 54.85 9 55.83 10.03 



Upsal 5 50 26 9 55.62 9 5595 10.23 



Cajaneburg 5 49 54 9 55.6l 9 55.6l 10.00 



Tornea" 5 50 09 9 55.28 9 56.08 IO.O9 



By taking a mean of these determinations, we find the sun's parallax to be 

 10". I. In the above calculations the sun's semidiameter was supposed = 15' 

 48".5, and that of Venus 29'. Observers, says Mr. Pingre, have found, the 

 former to be about 2" less, and the latter on the contrary half a second 

 larger. By calculating on the supposition of a difference of 2" in the dif- 

 ference of the semidiameters of the sun and Venus, the least distance of 

 the centres at Tobolski, Stockholm, Upsal, Tornea°, and Cajaneburg, ought to 

 be 3". 12 less, and at Rodrigues 2".56 or 2".6o, and the sun's horizontal paral- 



H 2 



