1823.] for Barometrical Measurements. 359 



vapour succeed others which are at the maximum of humidity. 

 However, setting aside these extraordinary circumstances, every 

 thing leads us to beheve that we shall follow nature most closely 

 if we avoid these extreme cases ; and thus what seems most 

 simple is to take for the expression for F in the atmosphere the 

 half of the value which corresponds to the point of extreme 

 humidity ; that is to say, 



F = 0-002561 metre + t . 0-00043245 metre 

 {= 0-10082 inch + t . 0'01652) inch. 



In substituting this value in the expression for the coefficient 



C, it must be multiplied by the variable factor =--, but on account 



of the minuteness of this correction, and also on account of the 

 small difference in the values of h within the limits of ordinary 

 measurements, it will suffice to put for //, the constant value 

 0-76 m. = 29-921 in. which is the mean pressure at the level of 

 the sea. This substitution will possess also the advantage of 

 giving a less correction for the humidity in the higher strata of 

 the column, which agrees with nature ; for the humidity of 

 these strata generally diminishes in proportion as we ascend, and 

 sometimes the most elevated are extremely dry. Adopting this 

 simplification, we have 



1 -- ^ = 1 - y-Q^ [0-002561 m. + ^ . 0-00043245 in.] = " 



1 _ -0009628 - -0001626 . t. 

 Without sensible error this expression may be put under the 

 following form, [1 - -0009628] [1 - -0001627 . ^] which gives 



p _ A[l - -0009628] . g{\ - -0 001627. f] 

 \ + t . 00375 • 



The factor, depending on t, which is found in the numerator, 



'may be combined with that which arises from the temperature. 



On account of the smallness of the coefficient -0001627, we may 



without sensible error substitute — - in the place of 



1 --0001627 ,t. 



Thus we have in the denominator the product [1 + -0001627 . t'] 

 . [1 4- t . 0-00375]. In performing the multiplication we may 

 neglect the product of -€001627 x -00375 : and thus it becomes 

 [1 + -0039127 . f]. The coefficient of ^ in this result differs so 



little from -004, or — -, that we may, without fear of error, sub- 

 stitute for it this last value, which will simplify the calculation. 

 We have, therefore, 



C _ A [I - -0009628]. g 

 ~" [1 + ^.0004] * 



Thirdly, the variation of the force of gravity must affect both 

 the coefficient or ratio of densities of air and mercury, and also 

 the observed heights of the column of mercury at the two 



