1823.] the Barometer io the Measurement of Heights. 105 



station ; and geometrical exactness requires that we should 

 augment the correction in proportion to the height of the sta- 

 tion ; but it must be allowed that cases where this is necessary 

 are very rare, and its effect on the exactness of measurements is 

 very inconsiderable. If the lower station be much elevated, we 

 shall rarely have a great height to measure above it : if but 

 little, we shall have only a very small correction to make ; so 

 that the small quantities which it introduces into the calculation 

 will generally be covered by the uncertainty from which no 

 observation is exempt. 



However, the learned coadjutor of M. de Humboldt has been 

 tmwiUing to neglect this correction ; and we find in the hypso- 

 metrical tables which he has just published, a small table of 

 quantities to be added to the measured heights according to the 

 absolute elevation at which the lower barometer is placed ; an 

 elevation sufficiently indicated by that of the column of mercury. 

 I have borrowed from him this table, merely transforming it into 

 logarithms to agree with the system of calculation which I have 

 adopted (Table 6). The divisions of the barometer in the first 

 column are sufficiently near for the degree of accuracy required : 

 if greater exactness be desired, it may be sufficiently attained 

 by means of the column of differences. 



It only remains to take into account the mean temperature of 

 the column of air. The mode of effecting this correction 

 according to the formula is extremely simple. The double sum 

 of the thermometers will be positive or negative as it is above or 

 below zero : the operation is obvious from the following 

 example ; 



Let 2 (? + O = + 40; we have J-^ « 1-040 



If it be = - 40, it becomes ^^ = 0-960 



For the logarithms of these numbers, the observer will at once 

 refer to the common tables. To have given a table of them 

 would have been merely a superfluous transcription. 



The sum of the five logarithms thus obtained, and which it is 

 convenient to write in a column for addition, is the logarithm of 

 the elevation required, expressed in measures of the same kind 

 as those to which the constant coefficient has been reduced. 



It is obvious then that this shght operation is much easier to 

 perform than to explain : it is reduced to transcribing numbers 

 previously prepared. No auxiliary calculations — no taking of 

 proportional parts — no interpolations are requisite. My tables 

 are constructed in such a form as to furnish at once all the frac- 

 tions which are worth taking into account. They cannot possess 

 this advantage without some want of brevity ; but it is a matter 

 of great indifference for the tables to be somewhat long, while it 

 is by no means so that the calculation should be short, clear, and 

 easy to verify in all its parts. In the method which I recommend, 



