358 Proceedings of Societies. 



fluidity of the glacier in cold weather, which retards (as we know) the 

 motion of all its parts, but especially of those parts which move most 

 rapidly in summer. The dis -proportion of velocity throughout the length 

 and breadth of the glacier is therefore less, the ice more pressed together, 

 and less drawn asunder ; the crevases are consolidated, while the increased 

 friction and viscosity causes the whole to swell, and especially the inferior 

 parts, which are the most wasted." — (See also Seventh Letter on Glaciers, 

 p. 4"") of Appendix to the same work.) 



Monday, 19th February 1855. James Tod, Esq., in the Chair. 



The following Communications were read : — 



1. On the Mechanical Action of Heat: — Supplement to the first Six 

 Sections, and Section Seventh. By W. J. Macquohn Rankine, Esq., 

 C.E. 



2. On an Inaccuracy {having its greatest value about 1") in the usual 

 method of computing the Moon's Parallax. By Edward Sang, Esq. 



When, as in the usual operation, the moon's obscured zenith distance 

 is corrected for the effects of atmospheric refraction, the zenith distance so 

 obtained is that of the rectilineal part of the ray of light between the planet 

 and the upper surface of the air ; and on applying that correction as at 

 the observatory, we do not obtain the direction of the moon as it would 

 have been seen if there had been no atmosphere, but that of a line drawn 

 parallel to the first part of the ray, and therefore passing below the moon. 

 The true direction of a straight line drawn from the observer to the planet, 

 must differ from this direction by the angle which the curved part of the 

 ray 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 index 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 uncor- 

 rected zenith distance, multiplied by the index of refraction 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 30°, 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 

 .j4!J4, — this ratio being the index of refraction bf 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. 



