516 [March 26, 



Now putting B5=yB, we have 



logB-log ^logj-- =j*.y+ y 2 + y 3 + y 4 + . 

 where /* is the modulus of the tabular logarithms, and 



always a convergent series as y is always a proper fraction, and small 

 when y is small, as it is for moderate heights. 

 Hence 



60309-19. (logB-log 5) = 



The constant 52384 has been changed to 52400 to facilitate calcula- 

 tion and to divide the correction for the first two thousand feet, and 

 c f has consequently been altered to c, the tabular values of which 

 were calculated as follows. 



Put *= 52400 5n^ = 52400 . -2L, 



B+ 2 y 



whence 



y ~~ 



52400 + x 

 Then (e) becomes 



x + c= 60309- 19. (log B- log b) = -60309' 19 log (1-y) . (g) 



Make x successively =1000, 2000, &c. up to 30,000, and find the 

 corresponding values of -y from (f) and c from (g). 



As the differences in the values of c are not uniform, slight errors 

 may arise from neglecting second differences in interpolation, but 

 they can scarcely even affect the result by a single unit, and may 

 therefore be safely disregarded. Laplace's formula itself cannot be 

 depended on within much larger limits. 



The Table of corrections and transformation of Laplace's formula 

 here given allow of the following simplification in the logarithmic 

 calculation of AH. 



