105 



But both these formulae must be considered empirical. W<i 

 are entirely unacquainted with the law of variation of den- 

 sity at different heights, and therefore as has been shewn we 

 cannot deduce from theory a formula of refraction that will 

 serve much below 80°. It has been shewn indeed, art. 6. that 

 if the density decrease uniformly, the refraction may be 

 expressed by a similar formula, and that above 80° the re- 

 fraction will not be sensibly changed by any law of variation 

 of density ; but then if 56",9 be the constant quantity, the 

 co-efficient of refraction must be 4,l4,* that is the mean ref. 

 = 56",9 tan. (^ — 4,14 ref.) Therefore the two formula used 

 in columns A and B are certainly inexact for all zenith dis- 

 tances less than about 80°. For greater zenith distances, 

 the first formula will perhaps be found as exact as any other 

 now known, at least as far as 87° 40'. But I do not attach 

 much importance to it. I had deduced it before I was so 

 well convinced as I am at present of the little value of ob- 

 servations near the horizon, and I may add of the impossi- 

 bility of investigating an exact formula. 



The mean of column C gives 36'. 36'. 46",54 for the co- 

 latitude of the observatory or 53 23 13,46 for the lati- 

 tude, which I conceive cannot possibly err | of a second 

 from the truth. 



* For if -^—jn ss 56",9 m— 1 -: ,0002758, and therefore ^(m-i) T =^ *'** 



vid. art. 6. equat. (5)' 



VOL. XII. t Q 



