170 MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



observations at every altitude. The Table, in the same work, extending to 85° of 

 distance from the zenith, which the supplementaiy one is intended to complete, may 

 likewise be considered as having the authority of actual observation ; for although a 

 theoretical formula was used in the calculations, yet the results have been carefully 

 corrected by a comparison both with the observations of Bradley and with those 

 made with very perfect instruments in the observatory over which Bessel presides. 

 These two make together a table of mean refractions of the highest authority ; and 

 being free from hypothetical admissions, to speak with precision, they form the only 

 table of the kind of which astronomy in its actual state can boast. 



The mean refractions, being a fixed set of numbers at any proposed observatory, 

 are independent of temporary changes in the state of the air. If the general consti- 

 tution of the atmosphere were so well known as to enable us to deduce the tempera- 

 ture, the density, and the pressure at any given altitude, from the observed condition 

 of the air at the earth's surface, it might be possible to pitch upon an atmosphere in- 

 termediate between the extreme cases, in which the irregularities would compensate 

 one another. From such an atmosphere the mean refractions used in astronomy 

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

 variations to which the air is subject in ascending above the surface of the earth. 

 The diffusion of heat and aqueous vapour, the laws which regulate the density and 

 pressure, are but slightly and hypothetically known. Many laborious researches 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 refract light, is uncertain, and is no doubt, as well 

 as the figure of the limiting surface, subject to continual fluctuation. Reflecting on 

 what is said, it must be evident that the mean refraction of a star, which is a fixed 

 quantity, cannot possibly be ded uced from an atmosphere daily and hourly varying 

 in its essential properties. 



A table of refractions, such as is used in astronomy, contains 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 eff*ects a principal one is the height that must be ascended in the air for de- 

 pressing the thermometer one degree, from which another mean effect is easily de- 

 duced, namely, the rate at which the density of the air decreases as the height in- 

 creases. The values of these quantities, as occasionally determined at any particular 

 place, will vary according to the actual state of the air ; but a multitude of particular 

 determinations embracing every vicissitude of the atmosphere, 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 refractions. 



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 



