, 79 



consists of two parts, one the refraction that would take 

 place were the earth a plane, the other the effect due to 

 the spherical form. The latter at 80° zenith distance 

 amounts only to about 12", and at 40° zenith distance is in- 

 sensible. 



It is shewn that at 80' 4o' the error of the formula deduced 

 cannot amount to half a second, whatever be the variation of 

 density in the atmosphere. 



;As the approximate formula for refraction as far as about 

 74° from ,the zenith is independent of the law of variation of 

 dejnsily, it follows that, whatever law be assumed, the same 

 conclusion ought to be deduced as far as about 74°. This is 

 shewu from direct investigation by assuming different laws of 

 variation of density ; which beside affording some conclu- 

 sions useful in our euauAfipS P», this subject, may be consi- 



,^^pi;ed..api.u.terestiug., ^ ., 



,,i.,Xl^(^ rpsult? Qf th^ .ex4>eriment8 of M. M. Biot & Arago 

 ,pr; the r<Efi;£^cUy.e.fprce. of ,^ir, and, of Mr. Da,ltou and M. 

 Gai-Lussac on it,lieteflects of the change of temperature on the 

 density of air^re applied, aqd a general expression for refrac- 

 tion .at ,a,ny. zenith distance Jess than about 80° obtained, 



J which is entirely independent of astronomical observations..- 



From this general ex pressioii , I have .formed two tables, 

 by help of which th.Q refijaction at any zenith distance less 

 than 80° may be calculated with much convenience. 



From a, comparison of the co-latitude determined by stars 



■ftf'M;.'^teiPyi^» iPifi^:^,^,;^'^^ s^ni,^^ ^determined by star^im(^re re- 

 ihno'i ' /d fl^vi.^ ahtikoijiibiitii atli wiai 'lo 



