Astronomical and Nautical Collections. 375 



it is indeed possible that, though the atmosphere is certainly of 

 the same mean temperature as the earth at the base of the moun- 

 tain, and probably at its summit, it may be a little colder at the 

 middle of its height ; but this diversity is by no means shown by 

 any actual observations that have been recorded; and even if 

 Mr. Ivory's hypothesis for the densities be allowed to be most pro- 

 bable, it will not follow that the temperatures must not decrease 

 more rapidly at moderate heights than he supposes, in order that 

 the contraction of bulk may keep pace with his formula. 



For the atmosphere of infinite height, in which jf =: — , Mr. 



Ivory finds the horizontal refraction 34' 18". 5, or 17".2 more than 

 for an atmosphere 25 miles in height, and 27" more than the quan- 

 tity generally admitted by^astronomers. It seems, therefore, to 

 follow that for an optical hypothesis, an atmosphere less than 25 

 miles high might have the advantage ; even if it did not afford the 

 greater facility of direct computation which has since been pointed 

 dut. 



Having examined the comparative effect of different hypotheses 

 respecting the height of the atmosphere on the refraction, Mr. Ivory 

 proceeds to accommodate his formulas to the more ready com-pu- 

 tation of the mean refraction, and of the barometrical and thermo- 

 metrical corrections in the case of the constitution, which appears 

 on the whole to come the nearest to the truth. It seems, however, 

 questionable, whether the value of the exponent of the density 



— is not a little too great, since it is derived from observations 



on mountains at small heights ; for it is probable that the very 

 summits of the highest mountains that we can ascend oj^ght to be 

 chosen for determining the rate of variation of temperature, if it is 



to be'supposed uniform, and that if we take the exponent _£== — 



dy 4 



only, there will be a deficiency which requires to be compensated, 

 by assuming the rate of variation to become more rapid in ascend- 

 ing ; and this seems to be the case in the atmosphere of 18 miles, 



