Mr. Ivory o)i the Theory of the Astronomical 'Refractions. 99 



which may be shortly denoted by y x % (0), has been com- 

 puted by means of the equivalent series, for every half de- 

 gree between 85° and 88°, the results being as follows : 



6 



/'X;i(f) 





</ 



85° 



/' X 1-5 



85i 



/' X 2-0 



86 



/' X 3-3 



86^ 



/' X 4-9 



87 



/' X 7-4 



87* 



/' X 11-2 



88 



/' X 17-0 



From this view it appears that^'', although considerably less 



2 

 thany or-— may still have some influence on the refractions 



at ver}- low altitudes. The mean refraction in Bessel's table, 

 and in the new table, can hardly be supposed to differ 2" 

 from the true quantity, which would limit /' to be less than 



— . It is a matter of some importance to obtain a near 



value of y : and it is probable that this can be accomplished 

 in no other way but by searching out such values ofy andy' 

 as will best represent many good observed refractions at alti- 

 tudes less than 5°. If such values were found, our knowledge 

 of the decrease of heat in ascending in the atmosphere would 

 be improved, and the measurement of heights l3y the baro- 

 meter would be made more perfect. 

 April 25, 1838. 



Table I. 



Mean Refractions for the Temperature 50° Fahrenheit, and 

 the barometric Pressure 30 inches. 





S L Log 1 L 



Diff. 



T. 



c. 



.a 

 1^ 



S^. 



Log I 6. 



DifF. 



T. 



C. 



o 

 1 



2 

 3 

 4 

 5 



6 



7 



O' 1-02 0-0085 

 2-04 0-3097 

 3-060-4860 

 4-080-6112 

 5-110-7086 

 6-14'0-7882 

 7-i7|o-8557 



3012 



1763 



1252 



974 



796 



675 











7 



8 



9 



10 



11 



12 



13 



7-17 

 8-21 

 9-25 

 10-30 

 11-35 

 12-42 

 13-49 



0-8557 

 0-9144 

 0-9663 

 1-0129 

 1-0553 

 1-0941 

 1-1300 



587 

 519 

 466 

 424 

 388 

 359 













H2 















