and on Astronomical Refractions. 499 



+ [8-1894155] Ar> + [7-9925434] X"+ [7-7440827] X" 

 + [7-4492548] A + [7-1140008] X**+ [6-7436508] X 1 * 

 + [6-3433889] X 16 + [5-9048724] X* + &c. 



[4-9382822] X* + [5-7162512] X* + [6-1990788] X* 

 + [6-5124208] A + [6-7058125] X*+ [6-8073789] X 11 

 + [6-8341245] X I2 + [6-7797954] X+ [6-7124763] X 1 * 

 + [6-5779048] X 1 * + [6-3758464] A 1 " + [6-1424833] X" 

 + [5-909 1202] X 1 * + &c. 



= [2-441 1007] X 9 + [3-3458338] X 9 + [3-9500667] X 10 

 + [4-3853642] X" + [4-6996664] A" 12 + [4-9204991] X 13 

 + [5-0668412] X + [5-1470479] X*+ [5-1817987] JT" 

 + [5-1502344] A i? + [5-0587813] A' s + [4-9792296] X + &c. 



2 - 3 -J^5]4( F - x ' s )= [9-8470092] AT 10 + [0-1480392] X"+ [1-5496223] A" 12 

 + [2-0850470] X 13 + [2-4878504] AT 14 + [2-8026972] A* 15 

 + [3-0171128] A" 5 + [3-1689304] X" + [3-2999429] A 18 

 + [3-3830969] A 19 -f [3-4680509] A" 20 -f &c. 



The coefficients of the different powers of X in these series be- 

 come very small, but they acquire large multipliers from the suc- 

 cessive differentiations which are required to give the corresponding 

 terms in the expression for w. 



I find with this constitution of the atmosphere, A being the 



coefficient of X" in the expression for -. . 

 ^i = -6422 



AI = 1-9268 + -0245 = 1-9513 



A 3 = 2-6761 + -1635 + -0010 = 2-8406 



A 4 = 2-4085 + -5008 + -0109 -f -0001 - 2-9203 



^ 5 = 1-6110 + -9741 + -0531 + -0007 = 2-6389 



A 6 = -8617 + 1-3750 + -1640 + -0045 = 2-4052 



A 7 = -3854 + 1-5250 + -3657 + -0192 + -0003 = 2-2956 



A s = -I486 + 1-3920 + -6353 + -0595 + -0019 = 2-2373 



A 9 = -0504 + 1-0812 + -9009 + -1428 + -0074 = 2-1827 



A lo = -0153 + -7322 + 1-0335 + -2802 + -0229 + -0007 = 1-0848 



AH= -0042+ -4389 + 1-1265 + -4596 + -0561 + -0029 = 2-6882 



A K = -0010 + -2366 -f- 1-0329 + -6852 + -1094 + -0090 = 2-0741 



A J3 = -0002+ -1163+ -8410+ -8072 + -2051 + -0226 = 1-9924 



A u = -f -0529 + -5644 + '8410 + -3371 + -0492 = 1-8466. 



-^ = -6422 X + 1-9513 A" 2 + 2-8406 A" 3 + 2-9203 X* 

 + 2-6389 X t + 2-4052 A" 8 + &c. 



Hence by substituting these values of A lt A^ &c., in the ex- 

 pression for 6 given in p. 491, 1 find the first term in the refraction 



2K2 



