Mr. Ivorv on the 'iheori) of the Astronumkal Refractions. 'M5 



Philosophical Transactions for 1721. Two elements only are 

 sufficient for computing all the numbers in a table of refiac- 

 tions constructed by assuming that the density is proportional 

 to the pressure, namely, the refraction at ^■5" of altitude, and 

 the height of the homogeneous atmosphere, which is deducible 

 from the horizontal refraction. The table of Halley, there- 

 fore, contains in itself all that is required for ascertaining 

 whether it was calculated or not by the principle alluded to 

 in the letters of Newton to Flamsteed. Kramp seems to be 

 the first who sought in the table for the manner of its construc- 

 tion; and his discoveries in this branch of science enabled 

 him to assign the height of the homogeneous atmosphere, 

 which is one essential element. The refraction at 45° of 

 altitude, which is the other element, is found in the table equal 

 to 51- ', or, in parts of the radius, to -0002618: and Kramp 

 found 4377* toises for /, the height of the homogeneous at- 

 mosphere ; so that, if a be the radius of the earth in toises, 



we have 



« = -0002618, 



= — = -0013356; 

 a 



and the two elements, a and i, are sufficient for computing the 

 whole table, if it be such as is mentioned in the correspond- 

 ence between Newton and Flamsteed. The formula for the 

 refraction in the supposed constitution of the atmosphere has 

 been given both by Kramp and Laplace ; and it may be taken 

 from "he paper in the Philosophical Transactions for 1823, 

 p. 411, 



X = 4- = -19601, A = \/ cos-fl + 2 is, 

 I 



,, p2dst-^' 

 8X^ /^4- dsc *\ 



2, J A 



the integrations extending from 5 = to s = c/3 . The co- 

 efficients of this fornmla are as follows: 



* Anal, dcslicj'radions Aslronnnwiuca, p. 11>. 



