Mr. Ivory on the Theory of the Astronomical Refractions. 395 



- &c. : 

 or, in seconds, 



8 9 = 2072"-46-/'X62-4— /"x 10"*2— &c. 

 From this calculation it appears that the term multiplied by 

 f" and all the subsequent terms are too small to be sensible ; 

 and asy^ is much less than/J even the term multiplied hyf 

 can hardly exceed a few seconds at low altitudes. There is 

 great probability that the horizontal refraction is very near 

 34-' 30", and does not exceed this quantity. 



To prepare the foregoing expression of 8 fl for integration, 

 put 



^^ */ 2im A 



m = 10, ;— = tan <i>, e — tan -^; 



cos 9 ^' 2 ' 



then 



4 e 



cos* fl = i — ^^ ' X 2 «■ w. 



^ V me 



and we shall have 



8 e = sin fl X ; - X J / — r- . c-" 



P""^ e d X , 

 + X / — — . (2 c-^ — c-*) 



""•^/o — A— • (4'C-^''— 3c-*+a;c-*) '^ ^ '' 



o 



For the sake of abridging, the several integrals in succession 

 may be represented by Q^, Qj, Qg, Q3; so that the value of 

 8 will be thus written : 



89sin e X "^^f^ ' (Qo + ^» Qi-^ Q2+/', Q3). 

 [To be continued.] 



