1823.] the Barometer to the Measurement of Heights, 103 



other terms, it will be reduced to log. (^jj, 10000 toises very 

 nearly, and the last factor of the formula will be : 



(log. :?^ +-868589) i (log. (4W •86«589) 



1 J- i 5 LL = 1 4- liiZ 



^- (-h) ^- (-h) 



Aog. (I) I0000\ ^ ^ _^ (log- (^) ^ -863589) 



Under this form the last factor has only a single variable 

 element; namely, log. L^. It becomes then very easy to cal- 

 culate, and to reduce into an auxiliary table. This M. Oltmann's 

 has done in the barometrical measurements of M. Humboldt, 

 p. 71. 



But it was possible to go still further, and I have attempted in 

 my turn to improve upon the method of M. Oltmann's by the 

 same means of which he has taught us the use. 



In examining his supposition, I observe that it is only rigo- 

 rously exact for the mean temperature of 15° at the equator, and 

 15*7° at lat. 45°. Elevations are often to be measured at a tem- 

 perature very different from this, and I have thought it necessary 



^ it + t'\ 

 to take into account in this factor the variations of — -foQQ — • It 



will suffice for this purpose to suppose the coefficient 60158 suc- 

 cessively diminished and increased by quantities corresponding 

 to different temperatures, and to transform the table of M. Olt- 

 mann's to one of double entry, having for its arguments 



{4r\f ai^d 2 (/ + t')\ that is to say, the difference of the loga- 

 rithms, and the double sum of the thermometers. 



In this way there is nothing neglected in the correction for 

 the diminution of gravity, except the part belonging to the lati- 

 tude, or 1 + -0028371 . cos. 2 ^. But taking it from the mean 

 latitude to the equator, it only affects the factor as if there were 

 a variation of 0*7° in the temperature, which is altogether insen- 

 sible, since a variation of 2*5° only affects it by a unit in the 

 fifth decimal place of the logarithm of the correction. 



Use of the Tables. 



The whole operation of using the tables will be sufficiently 

 obvious to those who have had the least practice in matters of 

 this kind ; but some explanation is necessary for the sake of 

 those who are less versed in such operations. 



The operation is simply this : we suppose the barometers to 

 have been well compared together, and the thermometers divided 



