and Levelling, fyc. 333 



give an elevation of 240 feet to depress Fahrenheit's thermo- 

 meter 1°, or 430 feet for 1° centigrade. From these conside- 

 rations the last term of formula (12) becomes ^-r--. — — . , and 



fl (^ 1 + p*) 



since S t — — ■ , the preceding becomes by substitution 



}h 



0.004112 — 



430 0.0000096 



2h(l + fit) I + fit 



Combining the two last terms of formula (12) by means of the 

 last expression, and they become in a common denominator 



86 O.OOOOOOC I 

 1(1 + fit)~ 1(1 + fit) 



Now since / = 26100 feet by (4) 



1 — ^-0.0000096 Z 1 — "j/— 0-.25 0.75 — |/ 

 86 8 6 8 6 



T(l + fit) ~~ 1(1 + fit) ~ 1(1 + fit) 



Replacing the factor consisting of the two last terms in for- 

 mula (12) by this equivalent expression, it becomes 



3 3 f 



n = ^-n • 6 



2 B 1 + fit 



1 / J_ \ 4 86 _ 

 1 + fi' tV + 126/ 1(1 + fit)~ 



ar 



b \l +fi t) • 1 +/3'tV + 12&Jv4 86/ 



If the two last factors be multiplied together, the product is 

 -— rTh — dm- Because ^-75 must always be a very small 



4 10 6 32 6'' 32 6 4 ^ - 1 



quantity, it may without sensible error be neglected, and the 



3 / 

 preceding expression becomes - — ^j very nearly. By means 



of these simplifications equation (12) finally becomes 



» - & ■ b ■ (irrJ • rrV. 7S - Q ■ • • (13 > 



Adapting this formula to 30 inches of the English barometer, 

 and 50° of Fahrenheit's thermometer, it becomes 



: n = SSJ ■ h ■ ( i + k«-50°j ) 8 ' 1+^-50°) (°- 75 - i&) • (14) 



Taking the values of a, B, I as formerly stated, and! 

 r = 20922G42 feet = a, the radius of the equator equal to 

 half the sum of the radius of curvature of the meridian, and 



VOL. XXX. NO. LX. APRIL 1841. X 



