250 Mr. Riddle on Mr. Burns's Nautical Problem. 



In the equations (d), if the pressure be expressed by means 

 of the density (1— «), we shall get, 



jD = /3(1 -w) + (l-^)(l-a))^ (e) 



In the Philosophical Transactions for 1823, the refractions 

 are computed by means of this equation, viz. 



J" being equal to \. Now if we determine /3 so as to make 

 the initial gradation of heat the same in the two atmospheres, 

 the refractions in both will very nearly coincide, the difference 

 amounting only to a few seconds at the horizon. And al- 

 though the matter is not of much importance, yet it seems 

 reasonable to give the preference to the formula (e), which is 

 a mean between two extreme cases pointed out by the laws to 

 which air is subject in its dilatations. 



Instead of determinating |3 by means of the gradation of 

 heat at the earth's surface, in which there is considerable cer- 

 tainty, it will be better to employ for the same puipo.'se some 

 good observed refractions. About eight or ten good observa- 

 tions will be required between the altitudes 0° and 10"; for 

 at greater altitudes the refractions are nearly the same in every 

 constitution of the atmosphere. We must then compute the 

 same refi'actions in the two atmospheres of the formula ; and j3 

 will be found by making each observation the same mean be- 

 tween the quantities computed in the two extreme cases. If we 

 make /3 = |, the horizontal refraction will be about S-t', and the 

 height for depressing the centesimal thermometer one degree 

 equal to 84 fathoms, supposing the standard barometer 30 in. 

 and the mean temperature 50° Fahrenheit ; and if /S = i, the 

 horizontal refraction will be about 35', and the gradation of 

 heat 120 fathoms for one centesimal degree. The true atmo- 

 sphere is undoubtedly contained between these limits. 

 Oct. 6, 18:35. ■ James Ivory. 



XXXIV. Remarks* o7i the Method proposed by Mr.BuRNsybr 

 gilding the Latitude bij Double Altitudes. By E. Riddle, Esq. 



To the Editor of the Philosophical Magazi?ie and Jomnal. 

 Sir, 

 IV/TY attention has been drawn to a communication in your 

 -^~-*- last Number, from James Burns, B. A. ; and I trouble 

 you \vith a few lines, to point out that Mr. Burns has 7iot done 

 what he imagines he has done ; viz. given an improxied solution 

 to the double altitude problem. 



[* Sec also a letter from Thomas Henderson, Esq. infra p. 283. — Edit.] 



Indeed, 



