362' Astronomkal and Nautical Cullections. 



that the temperature varies the less rapidly as we ascend higher. 

 It is, however, perfectly justifiable, for the purposes of astronomy ; 

 to adopt the form of the equation which is shown by these ex- 

 amples to be converging, and to correct the coefficients by an 

 immediate comparison with observation ; and in this manner it 

 has been found that the formula employed in the Nautical 

 Almanac is abundantly sufficient for the purposes to which it 



is applied. This formula is .0002825==i;— + (2.47 + .5u'')'^, + 



s s 



3600 V ^^ +3600 (1.235 + .25 i>')^; its results are almost 



identical with those of the French tables, except in the imme- 

 diate neighbourhood of the horizon. But the effect of a 

 difference of temperature, at the place of observation, is not so 

 correctly represented by any of the tables commonly employed, 

 and requires to be separately examined.] 



9. The terrestrial refraction may be most easily determined 

 by an immediate comparison with the angle subtended at the 



earth's centre, the fluxion of which is , and — r- is ini- 

 tially the first part of the coefficient of the second term of the 

 series already obtained, and is equal to [about] 6 ; so that this 

 anole, while it remains small, is six times the refraction : com- 

 monly, however, the refraction in the neighbourhood of the 

 earth's surface is somewhat less than in this proportion. 



10. The effects of barometrical and thermometrical changes 

 may be deduced from the fluxion of the equation, if we make 

 m, p, and n, or rather t, vary : and for this purpose it will be 



convenient to employ the form ps — vr+ L _ /Y~s ~ "o" ^^' 



the value of the fraction, if we neglect the subsequent terms, 



becoming 3.41 ;and this expression is sufficiently accurate for 



calculating the whole refraction, except for altitudes of a few 



r I \ ss\ rr 



deerees. Now the fluxion of »= v V j-r-- -A — » 



° ' & \l (m — t] p 21 ss 



T ( \ SS\ TV . ( V 



which we may call /> tr: u 1- — — , is dw = 1- 



s \iu 2) ss \ s 



