in whicli « =: -l^M- = i^^^'> 



But '^''^'^ = "''~^ 



Therefore expanding "^^^ by the powers of m — 1 



« = (w— 1) — i (m— 1) ' &c. 

 substituting this value for ctin Laplace's formula. „o,r^, 



-n_/? (»i — 1 ) tan, fl (w — 1) I toM. & (m — I) « < flK. 3 9 , 



* "~ wi. 1' a COS.* 9 sin. t" ' 2 «». 1" ' ■■* ^ 



same as equation (i) article 9, excepting the term there in- 

 troduced to make the formula applicable as far as ^ = 

 80 ".45/ 



Value of ^li, and of — -Tables of Refraction. 



11. The refractive force of air being assumed proportional 

 to its density, the value of tn is variable, and its changes are 

 known by the variations of the barometer and thermometer. 



Let m be the value of m when the height of the baro- 

 meter = 2^,60 inches, and the height of Farenheit's thermo- 

 meter =?= 50°. Let also b represent the height of the baro- 

 raeter, and t the height of the thermometer corresponding 



t^P ^"" .ftw bauo] XI r .iifi i! ao-fo't'o7ijo 



j^. It appears by the results of the experiments of Dal ton 

 and Gay Lussac, tliat a column of air denoted by unity at 

 the temperature of 32' of Farenheit becomes l,37Ji at the 

 voi. XII. r 



