and on Astronomical Refractions. 507 



sions. It is also indispensable that the relation implied or ex- 

 pressed between z and w should be in exact conformity with the 

 conditions attributed to the atmosphere, and in this respect the 

 table of mean refractions of the late Mr. Atkinson in the Memoirs 

 of the Astronomical Society appears to me not to rest upon a solid 

 foundation. 



Mr. Ivory connects the pressure and the density by the relation 



2 



P - -77777 JL + -22222 -%. 



P S 5 



M. Biot finds 



^= -761909002718 4 + -238167190564 -S- 



-000076193282, 



when the coefficients are so taken as to apply as nearly as the ques- 

 tion will admit of throughout the whole extent of the atmosphere. 

 But, by a careful examination of the data, M. Biot finds that at 

 the earth's surface the following relation is more accurate. 



7) e P 2 



* = -956643870584 -*r + '120146052460 Sg 



p r F 



-076789923044 (p. 69.) 

 and at the upper limit of the atmosphere 



v P ? 



-. - -6604978157646 4" + '4159581823536 -^ 

 P P P 



-00006605394115. 



According to my view this equation does not contain the true 

 mathematical law which connects the density and pressure, but of 

 course a parabola of this kind may always be found which will 

 osculate the true curve at any given point. 



In the Comptes Rendus des Stances de V Academic des Sciences, torn, 

 viii. p. 95, M. Biot verified and adopted a calculation of Lambert, 

 who found from the phenomena of twilight the altitude of the at- 

 mosphere (hauteur des dernieres particules d'air reflechissantes) to 

 be 29,115 metres. 



It is unnecessary to dwell any further at present upon this sub- 

 ject, because if my theory of the Heat of Vapours be correct, the 

 calculation of Astronomical Refractions, founded upon conditions 

 which are not in conformity with that theory, becomes a problem of 

 mere curiosity. 



