VOL. LVII.] PHILOSOPHICAL TRANSACTIONS. ^Lflt- 



vious conclusions of theory, the disciples of Newton will have no small reason to 

 exult in a new attestation of nature to the truth of their great master's doctrine. 

 But it is much to be wished, that they who shall be deputed to prosecute this 

 curious search, in distant and sequestered parts, may divest themselves of all pre- 

 judice; that they may have nothing at heart, but that which the world will ex- 

 pect from them, the advancement of real science; that they may be diligent in 

 their observations, and faithful in their reports ; and not sacrifice the repose of 

 their own minds, or the interests of philosophy, to the credit of an admired hy- 

 pothesis, the memory of a friend, or the jealousies of rival nations. If the 

 moon's mean distance from the earth be 60-I- semidiameters of the earth, the 

 sun's mean distance is 30008.4416 semidiameters of the earth. The sun's semi- 

 diameter is to the semidiameter of the earth, as 139.876 to 1. The globe of the 

 sun is to the globe of the earth, as 27367I8.8 to 1 ; and the sun's horizontal 

 parallax is 6" 52"'.415. 



To satisfy myself more fully of the accuracy of my work, I have recomputed 

 the whole, from the determination of ea, in Dr. Stewart's approximating method. 

 I found the proportion of db to u* (see Dr. Stewart on the distance of the sun, 

 fig. 10) that of 496.00579 to 1; and the proportion of db to t\y, that of 

 496.OO8O5 to 1 . The mean of these two gives the proportion of db to oar, nearly 

 that of 496.0069 to 1. Which differs from the result of my former computation by 

 less than xttwo-o of the whole ; and the method of the former computation is 

 undoubtedly the most accurate. 



Supplement to the Foregoing Paper. 



In deducing the distance of the sun in semidiameters of the earth, and his 

 horizontal parallax, from the proportion above concluded between the sun's mean 

 distance and that of the moon ; I have supposed the latter to be 604. semidiame- 

 ters of the earth, as it is reckoned by Sir Isaac Newton. According to the 

 hypothesis which seems to be now generally received, that the density of the 

 moon is very nearly equal to that of the earth, (the French reckon it rather less) 

 the moon's mean distance should be little more than 60.23207, that is, not 

 quite 60^ semidiameters of the earth. But from some computations that I have 

 formed with great care ; I have reason to think, that Sir Isaac Newton's deter- 

 mination is much nearer to the truth ; that the density of the moon is actually 

 greater than that of the earth, in the proportion of 6 to 5 nearly ; and that the 

 moon's mean distance amounts to 6o.44 1 semidiameters of the earth ; which 

 differs from the distance assigned by Sir I. Newton, by less than -nsVr of the whole.* 



* Notwithstanding the seeming confidence of this excellent mathematician, in the calculations of 

 I he earth's distance from the sun, as given by Dr. Stewart and here repeated by himself, it appears 

 that the result is far from being accurate, being about a 4th pait too great; owing partly to inaccu- 

 racies in the data assumed and employed in the calculation, and partly to the rejection of certain terms 



