302 Observations on the 



rare ; ou ce qui revient au meme les rayons du soleil qui rasent 

 la lune, soufFrent une refraction d'autrant plus grand qu'ils 

 s'approchent a ce corps, et par consequent, s'inclinent vers 

 I'axe du cone d'ombre au lieu de parvenir en ligne droite du 

 soleil jusqu'a notre ogil*." 



It is not intended to enter into any discussion of the various 

 details connected with this part of the subject, as being foreign 

 to the present design ; no opportunity having occurred of com- 

 paring former opinions with the results of actual observation. 

 It may be necessary, however, briefly to shew, how far the 

 conclusions legitimately derived from the two principal theories 

 are decisive of the general question. In one respect their prin- 

 ciples are identical ; both assuming that these luminous rings 

 arise from the rays of light being inclined towards the axis of 

 the conical shadow ; they differ only as to the primary cause in 

 which this defection originates. In the one it is maintained, 

 that the moon being surrounded by an atmosphere of the same 

 nature as ours, its effects in refracting the solar rays must also 

 be similar, and that these illumined circular areas seen round 

 the margin, to the extent of ^^j, or in some instances ^'^, of the 

 moon's diameter, are thus produced. Now, as the refractive 

 properties of homogenous media depend on their densities ; 

 and, since, from the diminution of gravity, the density of the 

 earth's atmosphere is to that of the moon's nearly as 408 : 139t, 

 their refraction must be in the same proportion. The mean 

 elevation, also, at which the atmosphere of the former is capable 

 of reflecting the twilight, is about -^'^ of a diameter of the latter, 



char. diiir. 



therefore, as 408 : 1 39 : : ^'^ : — the altitude of lunar refrac- 

 tion on the highest estimate, which, however, is not equal to one- 

 tenth of the extent of the appearances in question. But as 



• 3Iem. de V Acad, des Sciences, a}i. 1765. See also 3Iem. de Berlin, 

 1748, p. 103. Where Euler adopts tlie theory of a hinar atmosphere, 

 and Mem. pour seiiir a I' Hist, del Astron. 1733, p. 243 — 30, &c. in which 

 De I'sle supports the hypothesis of inflection. 



f Newt. Princip. Mathem. From an erratum in page 34 of last Number, 

 gravity at the surface of the moon is said to be diminished " one- third" 

 instead of to " one-third'' " nearly-" 



