190 MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



expressions, between the paper of 1823 and the calculations of Laplace, from which, 

 after all, no just inference can be drawn, it is not difficult to find between the same 

 paper and the view of the problem taken by the author of the Principia, in 1696, an 

 anology much more simple and striking, which deserves to be mentioned as it tends 

 to bring back the investigation to the right tract, which it seems to have left. Newton, 

 having solved the problem on the supposition that the density of the air is produced 

 solely by pressure, found that the refractions thus obtained greatly exceeded the 

 observed quantities near the horizon : and hence he inferred, in the true spirit of re- 

 search, that there must be some cause not taken into account, such as the agency of 

 heat, which should produce, in the lower part of the atmosphere, the proper degree 

 of rarefaction necessary to reconcile the theoretical with the observed refractions. 

 Now, in the paper of 1823, the sole intention of introducing the quantity/, not noticed 

 before by any geometer, is to cause the heat at the earth's surface to decrease in as- 

 cending at the same rate that actually prevails in nature ; which evidently has the 

 effect of supplying the desideratum of Newton. 



The remarks that have just been made are not called for by anything which 

 M. BioT has written in his dissertation on the refractions, inserted in the additions 

 to the C(mn. des Temps for 1839 ; because that author has fully explained the grounds 

 of what he advances, thereby enabling a candid inquirer to form his own opinion ; 

 but all the world are not of the same character as that distinguished philosopher. 



At every point on the earth's surface we are now acquainted with three things, not 

 hypothetical or precarious, that have an influence on the mean refractions. These 

 are, the refractive power of the air, the spherical figure of the atmosphere, and the 

 mean rate at which the density of the air decreases at the given place. These three 

 things are independent on one another, and on all other properties of the air: they 

 will therefore produce three independent parts of the quantity sought. The parts 

 thus determined may fall short of the whole refraction at any altitude, because there 

 may be causes not taken into account that co-operate in producing the result : but 

 each will unalterably maintain its proper share of the total amount, in whatever way 

 it is attempted to solve the problem, provided the solution is conducted on right 

 principles and not warped by arbitrary suppositions. It may therefore be said that, 

 in so far, an advance has been made in acquiring an exact notion of the nature of 

 this problem. 



The table in the paper of 1823 was compared with the best observations that could 

 be procured at the time of publication ; and the results were very satisfactory. After 

 the publication of the Tahulce Regiomontance, it was found that the table agreed with 

 Bessel's observed refractions to the distance of 88° from the zenith, which is as far 

 as his determinations can be depended on, with such small discrepancies as may be 

 supposed to exist in the observations themselves. So close an agreement between 

 the theoretical and observed mean refractions was very unexpected, and even con- 

 trary to the opinion very generally held on this subject. 



