86 



Let p = the pressure of a column of superincumbent air 

 of a given base, at the distance r from the centre. Then the. 

 pressure of a particle of air being measured by its magni- 

 tude, density and gravity, supposing tlie gravity at the sur- 

 face represented by unity 



f'ra* 



Ilence R = Q + (§8+^) l^-t Constant, 

 when /i = 0, Q and s = and p = I (§), 



Therefore constant = _*illi^® = — {m^-i) itan.s 

 Anereiore constant — ^^ ^^^ , ^ — ^ „ cos. ' e 



<Jonsequently the whole fluent from g- = (|) to ^ = is 

 R == Q — (m'— I) itan.i bccausc w is nearly = unity 



M ^ Q — ijUzilUJ^Hd. (7) 



a COS. * 9 



This expression as will be shewn farther on can be easily 

 reduced to that of Laplace (M6c. c61. torn. 4. p. 268.) But it 

 remains to shew how far from the zenith it can be used with- 

 out inducing an error greater than a small fraction of a 

 second. 



4. The principal part Q of this expression is, it is evident, 

 the deviation of a ray of light refracted at a given incidence 

 6 from air of the density (g) into a vacuum, and hence is en- 

 tirely independent of the variation of density in the atmos- 

 phere. When mis known Q is known. The method of find- 

 ing m will be considered hereafter. 



