128 HEIGHTS DETERMINED BY THE BAROMETER. 



Substituting this in (11), and reducing Naperian to com- 

 mon logarithms by multiplying by m, the modulus of the 

 common system, we have 



_ w 0(r'-T), (12) 



from which the value of z can be determined when z' is 

 known. 



COR. 1. If the lower station be nearly at the level of the 

 sea, z' = 0, and (12) becomes 



(13) 



COR. 2. In the above investigation no account has been 

 taken of the variation of gravity at different parts of the 

 earth's surface. From a comparison of the results obtained 

 by causing pendulums to oscillate in different latitudes, if g 

 be the measure of gravity at a place of latitude A, and g' at 

 a place of latitude A', it has been found (Poisson, Art. 628) 

 that 



g 1 .002588 cos 2A t 



'g' ~ I .002588 cos 2A' ; 



k k 1 .002588 cos 2A' 



therefore, - = - t , - pr nt . CQC -JTT-* (14) 



mg mg 1 .002588 cos 2A 



If A' be the latitude of Paris, the value of the quantity 



, (1 - .002588 cos 2A') (15) 



mg v 



is nearly 18336 French metres,* or about 60158.56 English 



* A French metre is 89.37079 inches. 



