293 



from this direction by the angle which the curved part of the raj 

 subtends at the moon's centre ; and the neglect of this angle may- 

 cause a sensible error in estimating the parallax. 



It is a well-known property of refraction by concentric strata, 

 that the perpendiculars let fall from the centre of curvature upon 

 the tangent to the path of light are inversely proportional to the 

 indices of refraction of the medium at the two points of contact. 



From this property it very easily follows that the sine of the 

 true parallax is obtained by multiplying the sine of the horizontal 

 parallax by the sine of the observed zenith distance, and by the in- 

 dex of refraction of the air at the Observatory. 



And if the horizontal parallax given in the almanac, instead of 

 being the half angle under which the earth would have been seen 

 from the moon if there had been no atmosphere, had been the true 

 horizontal parallax, or half the angle which, in the actual state of 

 things, the earth does subtend at the moon, — the true method of 

 computing the parallax would only differ from the common one in 

 the use of the uncorrected instead of the corrected zenith distance. 



In the common formula, the multiplier is the sine of the zenith 

 distance corrected for refraction ; in the true formula, it is the sine 

 of the uncorrected zenith distance, multiplied by the index of re- 

 fraction of the air. 



For the purpose of obtaining the maximum error of the common 

 formula, it is observed that when the moon is in the horizon, the 

 zenith distances being nearly 90°, have their sines sensibly equal to 

 each other, and that then the true multiplier must exceed the usual 

 one in the ratio of 3405 to 3404, — this ratio being the index of 

 refraction of air in its mean state ; wherefore, at the horizon, the 

 parallax, as usually computed, must fall short of the true parallax 

 by one 3404th part of itself. 



This ratio holds good for all planets ; and it is only in the case 

 of the moon that the error becomes sensible, being then almost ex- 

 actly one second of an arc. 



The following Gentlemen were elected as Ordinary Fel- 

 lows : — 



1. Robert Etheridge, Esq., Clifton, Bristol. 



2. John Inglis, Esq., Dean of Faculty. 



3. Rev. James S. Hodson, Rector of the Edinburgh Academty. 

 VOL. II. 2 A 



