i}4 PHILOSOPHICAL, TRANSACTIONS. [anNO IjGS. 



more certainty ; because the determination of the apparent least distances of the 

 centres, from the observed total durations, may be depended on to a very great 

 precision : but the same cannot be said with regard to the apparent least distance 

 of the centres measured at Rodrigues. For M. Pingre tells us that he used a 

 very good micrometer, fitted to a refracting telescope of Q feet focys, the object- 

 glass of which was but an indifferent one ; and we are very certain that in 

 measuring with a micrometer of this sort, dark objects on a white field or ground, 

 if the image is any way indistinct, the angle measured will be less than the true 

 angle, and vice versa when a bright object is measured on a dark, ground. As a 

 proof of this remark, we find that M. Pingre measured and found the diameter of 

 Venus when on the sun, = 54".7, whereas we are certain that it was above 58" ; 

 and therefore we may presume that the measurements of the greatest distance of 

 the limbs might be greater than the true distance ; and, as a further proof of the 

 uncertainty of the measurements made with this instrument, we find that M. 

 Pingre makes the distance of the limbs greatest, several minutes after it was past 

 the greatest. 



Mr. S. now produces at one view the means of the several determinations of the 

 sun's parallax, by the before-mentioned 3 several methods, which contain the sub- 

 stance of this whole paper, 

 l"" The mean of U6" comparisons of the internal contacts observed at places to the north 



of the line only, gives the sun's parallax = 8.555 



S*"" The mean of 21 comparisons of the internal contacts, with that at the Cape, givts the 



sun's parallax .-. = 8.56' 



3"° The mean of '2 1 comparisons of the internal contacts with that at Rodrigues, gives the 



sun's parallax = 8.57 



4'° The mean of the comparisons of the total durations gives the sun's parallax = g.Sl 



5'° The mean of the apparent least distances of the centres compared with that measured at 



Bodrigues, gives the sun's parallax = 3.56 



6'° The mean of the apparent least distances of the centres by computation from the total ^^ 



durations compared together, gives the sun's parallax. = 8.53 



The mean of these 6 means gives the sun's parallax = s.566 



And if we reject the mean arising from the comparisons of the total durations, which is the 



least certain, the mean of the other 5 means gives the snns parallax = 8.557 



Thus is the sun's parallax on the day of the transit concluded to be = 8". 56, 

 and that from 3 different modes of comparing together a great number of ob- 

 servations variously combined, the several results so nearly coinciding, that it 

 seems impossible that the mean of them all can err -j-v of a second, and that 

 probably the error does not exceed -^-^ part of the whole quantity, as Dr. Halley 

 had many years since confidently presaged. 



P. S. M. Pingre, in his aforesaid memoir, seems to think that there must be 

 some mistake in Mr. Mason's observation at the Cape, because by comparing 

 the observations of Jupiter's satellites made by Mr. Mason at the Cape, with those 



