Mr. Ivory on the Astronomical lie/hut ions. 421 



metrical measurements as well as in that of the astronomical 

 refractions. It is confirmed by experience to the greatest 

 heights to which we have been able to ascend. Adopting this 

 law, I next inquire into all the constitutions of the atmosphere 

 in which it is fulfilled. I find that they are all comprehended 

 in these very simple equations, viz. 



m+l 

 JL _ (Jj) m 

 P' \ 4 / 





-(■tt 



The letters p', §', t, denote the barometric pressure, the 

 density, and temperature at the surface of the earth ; and the 

 same letters without the accent, stand for the same things at 

 any height in the atmosphere ; m is an arbitrary number, and 

 (3 the expansion of air for one degree of the thermometer. 

 Now we know that every hypothesis respecting the atmo- 

 sphere will give the refractions actually observed as far as 70° 

 from the zenith ; therefore if we determine the value of m 

 that will bring out the true horizontal refraction, we shall ob- 

 tain a constitution of the atmosphere, and a formula for the 

 refractions, that must nearly coincide with Nature. But there 

 is another way of finding ?n, which is preferable because it 

 depends upon a quantity less complicated than the refractions. 

 If we put .r for the height above the earth's surface, we have 

 this general equation, viz. 



p=f-gdx, 

 p being equal top' when x=0. By combining this equation 

 with the two former ones, it will be easy to prove this for- 

 mula, viz. 



m __££. 



m+l p. ' 



I being the homogeneous atmosphere, and [x. the height that 

 must be ascended at the earth's surface in order to depress 

 the thermometer one degree. If we substitute the value of 

 I, and take the most probable determination of ft, we shall 

 obtain ra = 4; 



and thus, in the atmosphere of the earth the foregoing equa- 

 tions become 



;/ \ e' / 



l+Hr' \ J ) 



The refractions are next computed, supposing that the re- 

 lation between the pressure and density i^ represented by these 



equation*;. 



