454 On Refraction. 



thermometer 45° of Fahrenheit without, or 4 9° within, which 

 he considers as the mean state of the atmosphere*. With 

 respect to the latter, he finds the multiplier for all degrees 

 below 49° within, to be -0024 ; and above! 40° within, 

 •0023 f: but for those above or below 45° without, he finds 

 it -0021. Instead, however, of the number 3, which Dr. 

 Bradley had adopted for his coefficient of r, Mr. Groom- 

 bridge finds that 3*3625 agrees better with observations ; 

 consequently his numbers and coefficients will give us the 

 following four equations. 



1st. For the thermometer within, and below 49°, putting 

 d = 49 — A. 



Refr". = 58"-lI9'iX/,(Z — 3«3625r) x — —. x (1 -}- -002k/). 



2dly. For the thermometer within and above 49", put 

 d = /i — 49. 



Refr". = 5S"-1192x£,(Z — 3'3625r)x— -g X (1— 0023J), 



3dly. For the thermometer without and below 45°, put 

 d = 45 —h. 



Refr". = 58"'1192 X/,(Z — 3-3625r) x -■ X (1 -f-'002ld), 



4thly. For the thermometer without and above 45°, put 



d = h —45. 



Refr". = 5S"-1192X£,(Z — 3*3625r)x— -^ X (1 -•0'021 d). 

 Or, in logarithms : 



1st. Thermometer within and below 49°, put d = 49° —h° f 

 then : 



L. tan. ( Z r ) + L.&-f L.(10000 + 24^) -f 



6*29303 == L. Ref." 



* Mr. Kirwan states that the mean temperature of any place is equal to 

 84 — Sis' 2 , latitude. According to (his the mean temperature of Blackheath 

 would be 5^°8, but its exposed situation may possibly be the cause of this 

 •mall difference — Estimate of the Temperature of different Climates, or Dal- 

 ton's Meteorological. Observations, pa;-;e 160. 



f Mr. Palton found likewise that the expansion of air from 55° to 1S3§, 

 or for the first 78.;", was 167 parts, whilst th6 expansion irom ISS^* to 212°, 

 or for the next 78£°, was only 1 58 parts, or nine less i hjU> 1 lie former. So that 

 it appears there is a difference between the expansion of air for the high de-. 

 grees and that for the low ones. — Manchester Memoirs, vol. v.; or Thom- 

 son's Chemistry, vol. i. p. 490, edit, of 1810. 



2d. Ther- 



