Mr. Ivory on the Theort^ of the Astronomical Refractions. 279 



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 den- 

 sity 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 sup- 

 positions, 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 latter. 



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 ascendinff to great heights above the earth's surface, the 

 decrements of density will at length cease to be proportional 

 to the spaces passed through, or to the variations of tempera- 

 ture. The refraction of light by the atmosphere is a com- 

 plicated 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 hypothetical, and confine our atten- 

 tion to such only as have a real existence in nature, although 

 it may not in all cases be possible to obtain exact measure- 

 ments by direct observation. As the refractions themr.elves 

 are capal^le of being determined experimentally, 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 

 atmos})here. 



In proceeding to ti'eat of this problem according to the no- 

 tions 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 

 considered, 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 refractions, to 

 a considerable distance from the zenith, depend only on the 

 refractive power of the air and the spherical figure of the at- 

 mosphere; so far there is no reason to doubt that they are 

 the same over a great part of the surface of the globe, ac- 

 cording to the opinion generally held by astronomers ; but, 



