MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 171 



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 atmosphere. When a ther- 

 mometer is elevated in the air, it is found that the mercury continues to be depressed 

 equably to great heights : in like manner the decrements of density will vary slowly 

 from being proportional to the spaces passed through ; so that a great share of that 

 part of the astronomical refraction which depends upon the constitution of the atmo- 

 sphere, must be ascribed to the initial rate at which the density decreases. This rate 

 is not hypothetical ; it is a real quantity independent of every other ; its mean value, 

 which alone we consider, is as determinate and as much the result of experiment as 

 is the refractive power of the air : and in a solution of the problem which is not 

 warped by arbitrary suppositions, and which deduces the effect only from causes 

 really existing in nature, the former quantity will produce a part of the refraction as 

 certain and unalterable, although perhaps not so considerable, as the Jatter. 



But although the initial rate of the decrease of density is an essential element of 

 the astronomical refractions, it may not alone be sufficient for a complete solution 

 of the problem. In ascending to great heights above the earth's surface, the decre- 

 ments of density will at length cease to be proportional to the spaces passed through, 

 or to the variations of temperature. The refraction of light by the atmosphere is a 

 complicated effect depending upon different considerations : but the influence of these 

 considerations on the mean refractions must be uniform and free from fluctuation, 

 and can arise only from quantities which are constant in their mean values at any 

 proposed observatory. In speaking of mean quantities we exclude whatever is hypo- 

 thetical, and confine our attention to such only as have a real existence in nature, 

 although it may not in all cases be possible to obtain exact measurements by direct 

 observation. As the refractions themselves are capable of being determined experi- 

 mentally, they may be made the means of ascertaining what is left unknown in the 

 formula for computing them ; and they may thus contribute indirectly to advance 

 our knowledge of the constitution of the atmosphere. 



In proceeding to treat of this problem according to the notions that have been 

 briefly explained, it remains to add that the mean effects of the atmosphere at the 

 same observatory (of which mean effects a table of refractions is one) are alone con- 

 sidered, without at all entering on the question whether such effects are different or 

 not, at different points of the earth's surface. It is very well known that the refrac- 

 tions, to a considerable distance from the zenith, depend only on the refractive power 

 of the air and the spherical figure of the atmosphere : so far there is no reason to 

 doubt that they are the same over a great part of the surface of the globe, according 

 to the opinion generally held by astronomers : but, at greater zenith distances, when 

 the manner in which the atmosphere is constituted comes into play, it is not so clear 

 that they may not be subject to vary in different climates, and at different localities 

 of the same climate. If a table of refractions at a given observatory contain a set of 

 fixed numbers, these must be deducible from quantities not liable to change, that is, 



z 2 



