232 SIXTH REPORT 183fi. 



nitely slow, or the temperature is uniform. If m = 1*375, 

 which is the ratio of the specific heats in Gay-Lussac's experi- 

 ment, and consequently the value of m on Dalton's hypothesis, 

 because the air on this supposition possesses the greatest possible 

 degree of co'd that can be produced by rarefaction, the calcu- 

 lated amount of decrement of temperature is 1° centesimal for 

 an altitude of 67| fathoms, and the total height of the atmosphere 

 is 20 miles. But according to Mr. xVtkinson's memoir, 1° is the 

 real amount of depression in the first 80 fathoms of ascent. 

 Mr. Ivory adopts 90 fathoms from the temperature observed in 

 Gay-Lussac's balloon ascent, and derives | for the cori'esponding 

 value of m. From all this it appears that the theory we are ex- 

 amining, being pursued by mathematical reasoning to its con- 

 sequences, is shown to be an approximation to fact, but not 

 accurately true, because it assigns too large a rate of decrement 

 of temperature to the lower strata of the atmosphere ; and, if 

 Atkinson's formula be correct, it errs also in giving a uniform 

 instead of a decreasing rate of decrement in ascending to the 

 higher regions. 



Mr. Ivory, in his celebrated paper* on astronomical refrac- 

 tions, has pursued a different train of reasoning with reference 

 to this subject. He there sets out with supposing the decre- 

 ments of temperature to be equal for equal increments of height, 

 and is readily conducted (p. 4.J7) to an equation equivalent to 

 p = p"'. When the value |, derived from Gay-Lussac's ascent, 

 is substituted for ?h, this equation answers very well the purpose 

 of calculating a table of refractions, and gives them with great 

 accuracy for altitudes very little above the horizon. It does not 

 come within the province of this Report to speak of the problem 

 of astronomical refraction, excepting so far as it bears upon 

 the constitution of the atmosphere ; I shall therefore only remark 

 that a comparison of refractions, determined by astronomical 

 observations with refractions calculated on any theory of the 

 constitution of the atmosphere, does not serve as a good test of 

 the truth of the theory. It results from the reasoning in the 

 M^canique C^lesfef, that as far as 74° of zenith distance the 

 calculated amount of refraction agrees very nearly with the ob- 

 served, independently of any assumed law of decrease of density. 

 Dr. Brinkley showed the same thing in a more direct manner J, 

 and obtained a formula, the error of which at 80° 45' of zenith 

 distance does not amount to half a second, whatever be the va- 

 riation of density in the atmosphere. When the comparison is 



• Phil. Trans., 1823, p. 409. f 'iv- x. c. i. 



I Transactions of the Royal Irish Academy, 1815, vol. xii. p. 7?. 



