On Atmospherical Refraction. 361 



766 t 



= rTT?; — ToT: = 1 .26, whence == 5.822. while the pheno- 



766—139 mp ' 



mena of refraction require this quantity to be about 6. Thus, 

 in Bradley's approximation, we first take r =r — , and then r 



3»=s 3oV , 3r= „ 



, and vr=rns 3r's, or, while s remains 



V vv ' s 



small, j9srr,Dr+3 — , which is sufficiently accurate near the 



f 

 zenith. If we make — ^ = 6, we shall have f = 1.3, and 

 mp 



t~176, which is equivalent to a depression of a degree 



of Fahrenheit in 227 feet : we shall then have, for f ', 



-1.3x.3xl.6— =24-.624 — , and ^ = (1.3 — .624) 

 ps ps dr* ^ 



= .676 — ^ = .676 X 16358, and ^ of this, or 1854, 



mp s mp's- 



is the coefficient of the third term. With the same value of ^, 

 taking w=, 15, this coefficient would become, upon a hypothesis 

 similar to Professor Leslie's, 2236. 



8. It is not possible, in the present state of our knowledge of 

 the subject, to determine, from observation, either the refraction 

 with sufficient accuracy to enable us to compute from it the law 

 of the variation of temperature, or the variation of temperature 

 with sufficient accuracy for computing the refraction. Con- 

 sidering, indeed, how improbable it is that the upper regions of 

 the atmosphere should be of the same temperature as the sur- 

 face of the hills on the same general level, we could scarcely 

 expect the agreement to be more complete than these computa- 

 tions make it ; and it is perfectly possible either that t may be 

 as great at 176, or that n may be .15 : but we cannot determine 

 from the observed refraction which of the laws of variation is 

 capable of representing it with the greatest accuracy : much 

 less should we be justified in believing, because Mr. Laplace's 

 formula happens to represent the refraction very accurately. 



