530 BESSEL ON BAROMETRlCAt. 



except in the case when the two points, of which the difference 

 of elevation is to be measured, are in the same perpendicular. 

 It follows, from the knowledge we have obtained of these diver- 

 sities, that barometrical determinations of the difference of ele- 

 vation of two points, even if resting on observations repeated 

 for years, remain the more doubtful the more distant the points 

 are from each other. If we imagine surfaces surrounding the 

 earth in which the mean pressure of the atmosphere is equal, 

 then all we obtain by the barometer is the determination of dif- 

 ferences of elevation relatively to these surfaces ; but whether 

 the surfaces at which the two points are situated differ more or 

 less from parallelism with the surface of the earth, remains 

 wholly unknown to us, whilst Ave are ignorant of the function 

 of longitude and latitude which determines their relative posi- 

 tion. This opens a new view in regard to observations on the 

 pressure of the atmosphere ; we have to examine for all points 

 of the earth the height of the [atmospheric] surface at which a 

 determinate [mean] pressure is found ; but we cannot as yet 

 determine more nearly, the amount of imcertainty arising from 

 the assumption of this height being everywhere the same. 

 Also the uncertainty, arising from the oscillations considered as 

 accidental, cannot be given more nearly ; and even if, for the 

 purpose of learning them more correctly, we were to make long- 

 continued observations at points at different elevations, the dif- 

 ferences which might appear could still only be regarded as 

 caused by the combination of these causes with other as un- 

 avoidably erroneous assumptions. 



The constitution of dry air has been assumed such as it was 

 supposed to be at the time that Biot and Arago obtained for its 

 density the determination given in the first section. If the pro- 

 portion of oxygen were to be altered by n hundredths, its den- 

 sity would be changed by n . 0'001337, and a difference of ele- 

 vation computed under the assumption of D = r.ynn.Q ^^ould 



require to be altered in the ratio of 1 : 1 + « . 0-001337. Hum- 

 boldt and Gay Lussac, in nineteen days, between the l7th 

 Nov. and 23rd Dec. 1804, found no sensible alteration in the 

 proportion of oxj-gen, which seems to justify the assumption of 

 a constant proportion in the two principal constituents of the 

 atmosphere. 



In the meatime, however, it is known that Dalton has con- 



