On the almosp/ierical Refraction. 323 



posed, if the heat decrease in the same proportion with the 

 pressure, the depression of 1° of the centigrade tlierniometer 

 will correspond to an elevation of nearly Wo^j "'■ about 17 f 

 fathoms. 



If we still neglect the effect of temperature, or, which is the 

 same thing, suppose the heat to be invariably the same in every 

 part of the atmosphere ; but take into account the changes of 

 density arising from inequality of pressure according to the law 

 of Mariotte, we shall have another hypothesis very difierent from 

 that of Cassini ; the air now expanding above the earth to an 

 inilimited extent. In this case the thermometer, at whatever 

 elevation, would mark the same temperature ; or, in mathe- 

 matical language, the elevation necessary for one degree of de- 

 pression would be infinitely great. 



Between the two extreme cases just described we may con- 

 ceive that an infinite number of intermediate ones are interposed, 

 while the total height of the atmosphere increases from its least 

 limit of 4343 fathoms to be infinitely great; the heat in each 

 particular atmosphere decreasing uniformly as the elevation in- 

 creases, which is the law most conformable to experience. We 

 have thus an infinite number of different hypotheses, in all of 

 which the refractions will be the same to the extent of 74° from 

 the zenith; coinciding in every case with the formula of Laplace, 

 tire exactness of which is indisputably established by observa- 

 tion. But beyond the limit mentioned, the refractions will di- 

 verge from one another, and each particular case will have a 

 horizontal refraction peculiar to itself. We may thus account 

 for the inaccuracies that occur when a formula, naturally fitted 

 to represent the refractions near the zenith, is extended, in an 

 empirical manner, to the whole quadrant ; and likewise for the 

 shifting which such afornuila requires to be made in its elements, 

 wl'.en it is compared with exact observations made near the ho- 

 rizon. If indeed we consider the problem of refractions as one 

 to be solved by observation alone, we may conclude that it is in- 

 determinate, or admits of an indefinite number of solutions: and 

 this is no more than an opinion, expressed in several parts of his 

 writings, bv Delambre, the astronomer of the present day, whose 

 authority on every point of astronomical science will be allowed 

 to be the highest. 



In the hypothesis of Cassini the horizontal refraction is 1289"; 

 and it amounts to 2394" in the other extreme case of an atmo- 

 5|)here of an unlimited height. The hypothesis advanced by 

 Thomas Simson, of a density decreasing nniforudy with the ele- 

 vation, is also contained in the series of atmospheres above n»f n- 

 tioned, coinciding with the one that has its heigivt equal to aiiSO 

 fathoms, or double that of Cassini ; and in this case the hori- 

 S s 2 zontal 



