170 Astroiioniicui and ytaiilical Collections. 



for every foot, on account of the diminution of temperature, or 

 as much more or less as this diminution is more or less rapid ; 



so that if the change were 1° in =r 55 feet, the refraction 



^ 494 



would be annihilated, and, if still more sudden, there would 



be a depression or looming, instead of an elevation. But in 

 ordinary circumstances, supposing Professor Leslie's estimate 

 of 1^ in 300 to be correct, we have -j-^q (o^t^oo — iriaoff) — 

 rToiiT70oo ^'°'^ the variation in a foot, and consequently, 

 1 16873000 feet for the radius of curvature of the ray ; which 

 is to the earth's radius, or 20900000 feet, as 5.6 to 1 ; conse- 

 quently, the elevation of a distant object must be -p^.^ of the 

 ano-le subtended at the earth's centre, since the angle contained 

 between an arc and its chord is always equal to half the angular 

 extent of the arc. 



F. The general temperature of the atmosphere will affect this 

 refraction in so slight a degree, that it may safely be neglected ; 

 but it would be always of importance to ascertain, if possible, 

 the comparative temperature at different heights ; and whenever 

 it is practicable to find the height h, corresponding to a depres- 

 sion of 1°. supposing it to be different from 300, we may em- 

 ploy as a divisor, instead of 11.2, the reciprocal of ^jto • 

 (__i___^PjL-^) divided by 10450000; or the reciprocal of 

 10450000 / 1 _ J_ \ - 10450000 /t— 54.7 



3540 \27000 AMh) ~ 3540 ' 27000 A ~ 



.1093(A-54.7 ) _ 1^0, _ 5.98 ^^^.^^ ^^.^^,^ ,^^3 

 h h 



becomes .1093 — .0199 = .0894 1= — — . as before. 



iii. Note respecting the Connaissance des Te?ns. 



It is right that the possessors of the Connaissance des Terns 

 should be informed, that a cancel and two pages of errata for 

 1822 were received in London after the delivery of the volume for 

 1 823, to which they belong. It ought also to be generally known 

 to practical astronomers, that the well-intended and well-con- 

 trived tables for the correction of the places of the stars, 



