407 



VII. 



TABLES 



FOR COMPUTING THE DIFFERENCE IN THE HEIGHTS OF TWO PLACES BY MEANS OF 



THE BAROMETER. BAILY. 



Baily, in his Astronomical Tables and Forviulce, page 111, gives tlie following 

 final formula : 



X =-- 60345.51 \l + .0011111 (/ + «' — 64°)^ 



X log of 11 X i^TToooTTx^^r,') } X 1 1 + .002695 cos 2 <t>i. 



Where <^ = the latitude of the place, 



/3 = the height of the barometer, 



T = the temperature, Fahrenheit, of the mercury, 



t =■ the temperature, Fahrenheit, of the air, 



/3' =z the height of the barometer. 



[_ at the lower 

 ( station. 



p =z the heignt oi the barometer, ^ 



r' =: the temperature, Fahrenheit, of the mercury, V*^ . "' 



t' z=z the temperature, Fahrenheit, of the air. ) 



The numerical values assumed are as follows : — 



The constant barometrical coefficient = 60158.53 English feet. 



The expansion of moist air for 1° Fahrenheit ^= .0022222. 



The expansion of mercury for 1° Fahrenheit = .0001001. 



The increase of gravitation from Equator to Poles = .00539. 



The radius of the Earth at (/> = 20898240 English feet. 



The height of lower station assumed r= 4000 English feet. 



Make A = the log of the first term, in English feet. 

 B = the log of 1 + .0001 (r — r'). 

 C =^ the log of the last term. 

 D = log^ — (log^' + B). 



Then, by the tables which follow, the logarithm of the difference of altitude in 



English feet 



= A + C + log D. 



Baily's Tables have been recomputed and extended by Downes, for Lee's Collection 

 of Tables and FormulcB (2d edit. pp. 84, 85). These new tables are given here as 

 revised by Mr. Downes for this volume. 



D 67 



