xlii 



INTRODUCTION. 



in which K (log B — log B) is an approximate value of Z and the factors 

 in the brackets are correction factors depending respectively on the air 

 temperature, the humidity, the variation of gravity with latitude, the 

 variation of gravity with altitude in its effect on the weight of mercury in 

 the barometer, and the variation of gravity with altitude in its effect on the 

 weight of the air. With the constants already given, the formula becomes 

 in English measures: 



Z (feet) = 60368 l (log B - log B) |~[i + 0.002039 (0 - 32 )] 



(i+0 



(i + O.OO264O COS 2 — O.OOOOO7 COS 2 2 </> 

 + O.OOOO45) (I + O.OO239) 



In order to make the temperature correction as small as possible for 

 average air temperatures, 50 F. will be taken as the temperature at which 

 the correction factor is zero. This is accomplished by the following trans- 

 formation : 



1 + 0.002039 (0 - 32 ) = [1 + 0.002039 (0 - 50 )] [1 + 0.0010195 X 36 ]. 



The second factor of this expression combines with the constant, and 

 gives 60368 (1 + 0.00 10 1 95 X 36 ) = 62583.6. 

 The first approximate value of Z is therefore 



62583.6 (log B Q -log B). 



In order further to increase the utility of the tables, we shall make a 

 further substitution for log B Q — log B, and write 



62583.6 (log B - log B) - 62583.6 (log 

 Table 51 contains values of the expression 



29-9 

 B 



log 



29.9 

 B c 



62583.6 log ^ 



for values of B varying by intervals of 0.01 inch from 12.00 inches to 30.90 

 inches. 



The first approximate value of Z is then obtained by subtracting the 

 tabular value corresponding to B Q from the tabular value corresponding to 

 B (B and B being the barometric readings observed and corrected for 

 temperature at the upper and lower stations respectively). 



Table 52 gives the temperature correction 



Z X 0.002039 ( 0- 50 ). 



1 In accordance with the relation between the meter and the foot given on p. xix, this 

 constantshould be 60367. (See Table 14.) 



