VII. 



TABLE S 



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



THE BAROMETER. BAILY. 



BAILY, in his Astronomical Tables and Formula, page 111, gives the following ' 

 final formula : 



x= 60345.51 Jl + .0011111 (< _|- *' 64 ) J 



X X - X SI + . 002695 cos 2 <*>;. 



at the lower 

 station. 



at the upper 

 station. 



Where $ = the latitude of the place, 



j8 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, 



T' the temperature, Fahrenheit, of the mercury, 



t 1 the temperature, Fahrenheit, of the air. 



The numerical values assumed are as follows : 

 The constant barometrical coefficient 

 The expansion of moist air for 1 Fahrenheit 

 The expansion of mercury for 1 Fahrenheit 

 The increase of gravitation from Equator to Poles 

 The radius of the Earth at <j> 

 The height of lower station assumed 



= 60158.53 English feet. 



= .0022222. 



= .0001001. 



= .00539. 



= 20898240 English feet. 



= 4000 English feet. 



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

 B = the log of 1 + .0001 (r r 1 ). 

 C = the log of the last term. 

 D = log/3 (log/3' + 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 Formula (2d edit. pp. 84, 85). These new tables are given here as 

 revised by Mr. Downes for this volume. 



D 67 



