BAEOMETEB, to sea LliTEL. 



'tif two stations, the temperature being t, tlie barometer reading at 

 lower station h, and at the upper station b -xts- Hence, by (iii.)> 



Also R being the reduction, (iii.) may be written 



j8 + i? 



CJombining these, we get 



^ 



106 



10& - 1 ' 



iience, 



1 + — = 



, Z 



10 6-1/ i i 



1 - i^) ' »^. 



Z 



1 1 



10 & "^ 1.2 



by the binomial theorem. 



5^. 



Z 



+ 1 



1 



10 6 



/ _Z_ ^_ _1_ _Z_ 

 .•.i2=/3 -^ '10 6 "^ 1.2 " ^ivr 

 \ 6 f o t 



6^. 



+ 1 



1 



106 



+ .. 



+ .... (ir.) 



Formula (i.) is deduced from (iv.), by neglecting all terms beyond 

 the fu'st; and making & = 30 inches, if used with Table XVI.; but, 

 if used with Table XIX. ', b may be any reading within the range of 

 the table, and W 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 



(V.) 



