278 Mr. Ivory o?i the Theory of the Astronomical liefjactiuns. 



mosphere were so well known as to enable us to deduce the 

 temperature, the density, and the pressure at any given alti- 

 tude, from the observed condition of the air at the earth's sur- 

 face, it might be possible to pitch upon an atmosphere inter- 

 mediate between the extreme cases, in which the irregularities 

 would compensate one another. From such an atmosphere 

 the mean i-efractions used in astronomy might be correctly 

 computed. But in reality we have no exact knowledge of the 

 variations to which the air is sulyect in ascending above the 

 surface of the earth. The diffusion of heat and aqueous va- 

 pour, the laws which regulate the density and pressure, are 

 but slightly and hypothetically known. Many laborious re- 

 searches in the lower part of the atmosphere, to which access 

 can be had with instruments, have not been attended with 

 complete success; and they have thrown no light upon what 

 takes place in the upper parts. The limit of the atmosphere, 

 or the height at which the air ceases to have power to lefract 

 light, is uncertain, and is, no doubt, as well as the figure of 

 the limiting surface, subject to continual fluctuation. Re- 

 flecting on what is said, it must be evident that the mean re- 

 fraction of a star, which is a fixed quantity, cannot possibly 

 be deduced from an atmosphere daily and hourly varying in 

 its essential pi'operties. 



A table of refractions, such as is used in astronomy, con- 

 tains only mean effects of the atmosphere, that take place at 

 a given point of the earth's surface; and they should properly 

 be compared with other mean effects at the same place. Of 

 these mean eiiects a principal one is the height that must 

 be ascended in the air for depresrdng the thermometer one 

 degree, from which another mean effect is easily deduced, 

 namely, the rate at which the density of the air decreases as 

 the height increases. The values of these quantities, as oc- 

 casionally determined at any particular place, will vary ac- 

 cording to the actual state ol" the air; but a multitude of par- 

 ticular determinations embracing every vicissitude of the at- 

 mosphere, will at length lead to mean quantities which are 

 constant, and such as would be observed in the same at- 

 mosphere that produces the mean refracuons. 



It is found that the refractive power of air depends on the 

 density to which it is proportional ; and hence the rate at 

 which the density varies at the earth's surface, must have a 

 great influence on the quantity of the astronomical refractions. 

 It furnishes a key to the scale of the real densities in the at- 

 mosphere. When a thermometer is elevated in the air, it is 

 found that the mercury continues to be depressed equally to 

 great heights; in like manner the decrements of density will 



