Mr. Ivory on the Theory of the Astronomical Refractions. 7 



the true spirit of research, 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 de- 

 gree of rarefaction necessary to reconcile the theoretical with 

 the observed refractions. Now, in the paper of 1823, the sole 

 intention of introducing the quantity f not noticed before by 

 any geometer, is to cause the heat at the earth's surface to de- 

 crease in ascending at the same rate that actually prevails in 

 nature; which evidently has the effect of supplying the desi- 

 deratum 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 Conn, des 

 Temps for 1839; because that author has fully explained the 

 grounds of what he advances, thereby enabling a candid in- 

 quirer 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 refrac- 

 tive 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, l^he 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 re- 

 sult: but each will unalterably maintain its proper share of 

 the total amount, in whatever w-ay it is attempted to solve the 

 problem, provided the solution is conducted on right prin- 

 ciples 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 publi- 

 cation ; and the results were very satisfactory. After the 

 publication of the Tabulce llegiomontanfc, it was found that 

 the table agreed with Bessel's observed refractions to the di- 

 stance of 88° from the zenith, which is as far as his determi- 

 nations 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 contrary to 

 the opinion very generally held on this subject. 



Astronomers are in the habit of using different tables or 



