,2 



and on Astronomical Refractions, 499 



4- [8-1894155] A 10 4- [7-9925434] X"+ [7*7440827] A" 12 

 + [7-4492548] A" 13 + [7-1140008] A ,4 4- [6-7436508] X 15 

 + [6-3433889] A 16 + [5-9048724] A 1 ? + &c. 



g-^ (FA 3 ) = [4-9382822] X* + [5-7162512] X* 4- [6-1990788] A 8 

 + [6-5124208] X* 4- [6-7058125] A»°-f [6-8073789] X 11 

 + [6-8341245] A 12 + [6-7797954] A" 13 4- [6-7124763] A" 14 

 + [6-5779048] X 15 4- [6-3758464] jw.f [6-1424833] A 1 ? 

 4-[5-9091202]A 18 4-&c 



2 ^ . S (F X*) = [2-4411007] A" 8 4- [3-3458338] X s * 4- [3-9500667] A 10 

 + [4-3853642] A" 11 4- [4-6996664] A ,2 4- [4-9204991] A" 13 

 -f [5-0668412] A" 14 4- [5-1470479] Xi 5 4- [5-1817987] X™ 

 4- [5-1502344] X^-f [5-0587813] A ls 4- [4-9792296] A 19 4- &c. 



2 3 4 5i4( Fl5 ) = [9-8470092] A™ 4- [0-1480392] A 11 4- [1-5496223] A" 12 

 + [2-0850470] X 13 4- [2-4878504] A" 14 4- [2-8026972] A 15 

 4- [3-0171128] A 16 ^4- [3-1689304] A 1 ? + [3-2999429] A 18 

 4- [3-3830969] X* + [3-4680509] X 2 ° + &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 ca. 



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



coefficient of JC 1 in the expression for - — . 



A x = -6422 



A 2 = 1-9268 4- -0245 = 1-9513 



^3 = 2-67614- -1635 4- -0010 = 2-8406 



A 4 = 2-4085 4- -5008 4- "0109 4- -0001 - 2-9203 



A- = 1-6110 4- -9741 + -0531 4- -0007 = 2-6389 



A 6 = -8617 4-1-3750 4- -1640 4- -0045 = 2-4052 



A 7 = -3854 4- 1 -5250 4- -3657 4- 0192 4- -0003 = 2-2956 



A 3 = -I486 4- 1-3920 4- -6353 4- -0595 4- -0019 = 2-2373 



A 9 = -0504 4- 1-0812 4- -9009 4- -1428 4- -0074 = 2-1827 



A l0 = -0153 4- -7322 4- 1-0335 + -2802 4- -0229 4- -0007 = 1-0848 



A n = -0042 4- -4389 4- 1-1265 4- -4596 4- '0561 4- -0029 = 2-6882 



A u = -00104- -2366 f 1-0329 4- -6852 4- -1094 4- -0090 = 2-0741 



A n = -0002 4- '1163 4- -8410 4- -8072 4- -2051 4- -0226 = 1-9924 



A 14 = + -0529 4- -5644 4- -8410 4- -3371 4- -0492 = 1-8466. 



-j-^ = -6422 X 4- 1 "95 1 3 A 2 4- 2-8406 A 3 4- 2-9203 A" 4 

 4- 2-6389 A 5 4- 2-4052 A 6 4- &c. 



Hence by substituting these values of A l9 A 2 , &c, in the ex- 

 pression for 5 6 given in p. 491, I find the first term in the refraction 



2K2 



