^'^i-* PHILOSOPHICAL TRANSACTIONS. [anNO 176J, 



.: Therefore OB = O.OOOOOg 14398. 

 Therefore ao x o b = O.OOOOO9 1463 1458665466 16 

 Therefore V ao x ob = 0.0032024287 = o^. 

 But DB = 3ta = 1.500068593. 

 Hence db : oa; = 496.OO73 : 1. 

 These computations have been made with no small rigour. I was sensible 

 ; that, to obtain an accurate conclusion, it was necessary to determine ao with 

 extreme precision; and for that purpose I submitted to the laborious task of 

 computing the foregoing numbers to the 11 th or 12th decimal place, by the 

 common operations of arithmetic. In the result I differ from Dr. Stewart, by 

 much less than -^Vw part of the whole distance, that is, by less than 5 semi- 

 diameters of the earth ; a very contemptible difference in so nice a calculation. 

 That great mathematician indeed seems to have flattered himself, that he had 

 determined the sun's distance within tWo^t of the truth. I suspect that when 

 he affirmed this, he did not consider that to attain so great an accuracy in the 

 conclusion, the line E9 in his method (vide Stewart on the sun's distance, fig. 

 10), or AO in mine, should be determined strictly to the Ilth or I2th decimal 

 place. And after the utmost rigour of computation, I am afraid any pretensions 

 to such extreme nicety in the result will be but ill founded. For it is very likely 

 that these computations represent the sun's distance less than it really is: because 

 the whole progression of the moon's apogee (which is the basis of the calculation) 

 is ascribed to the sun's disturbance of the moon's gravitation to the earth. 

 Whereas part of it must be due to the disturbances of the planets. What part 

 is due to them we cannot tell, and therefore capnot allow for it. But in giving 

 the whole to the sun we certainly overrate his disturbing force, and by that 

 means must obtain too small a distance. It is most likely indeed, that the 

 motion of the apogee produced by the disturbing forces of the planets bears but 

 a very small, perhaps insensible, proportion to the whole. But those who are 

 masters of Dr. Stewart's theorems will easily perceive that an insensible error in 

 the proportion of the moon's gravity, and the sun's disturbance, may produce a 

 very sensible error in the proportion of the mean distances. And therefore the 

 real distance is probably greater by two or three semidiameters of the earth than 

 these computations make it. This however is much too nice a point for the 

 approaching transit, or perhaps for any method of observation to determine. 

 The highest expectations of astronomers will be answered, if they can come 

 within 50 or 60 semidiameters of the earth. 



It is to be hoped, that every civilized nation of the universe will give due at- 

 tention to that interesting phenomenon, which we, the present possessors of 

 these sublunary regions, shall behold no more ; and that proper persons will be 

 sent in due time, and duly equipped, to the most advantageous stations. If the 

 decisions of observation in so nice a point should be found to agree with the pre- 



