BAROMETER TO SEA LEVEL. 5 
of two stations, the temperature being ¢, the barometer reading at 
lower station 6, and at the upper station b-— 75. Hence, by (iii.), 
oY, = A, log 
ne S 
b- a 
Also & being the reduction, (iii.) may be written 
as B+ 
Z=A, log a: 
Combining these, we get 
R Z 108 
log (+ 3] —— log Tee 
1 Of 
2. Z 
ES RR, pate 
Sty Ne 12° eee, 106 
by the binomial theorem. 
J ee eS! 1 Z i, 1 ; “Ss 
td a a rae 
Formula (i.) is deduced from (iv.), by neglecting all terms beyond 
the first; and making 6 = 30 inches, if used with Table XVI.; but, 
if used with Table XIX.’, 6 may be any reading within the range of 
the table, and i, the corresponding number from the table. 
Although (i.) is sufficiently accurate for small heights, it is evident, 
on comparing it with the full formula (iv.), that it becomes more and 
more inaccurate as the height increases. 
If, in (i.), the reduced height B, were substituted for the observed 
height , the error would be relatively less; for Laplace’s formula 
may also be expanded in the form 
