the Barometric Formulce, Sfc. 629 



even an extremely great number of observations, hygrometric as well as baro- 

 metric, because of the error arising from assuming the arithmetic mean of 

 temperatures as given by the detached thermometer to be the real mean tem- 

 perature of the atmospheric column between the stations of observation. 



For it is to be borne in mind, that this last eri'or in no way resembles the 

 unavoidable small errors of observation, which are sometimes above, sometimes 

 below the mark, and which errors may be rendered (for practical purposes) 

 nearly insensible by using a sufficiently great number of observations. In fact, 

 the error connected with the mean temperature of atmosphere, — when observa- 

 tions by night as well as by day are made, — have the same sign, being minus 

 (-), which has been established as fact by the result of ten years' observations 

 made at the Convent of the Great Saint Bernard and the Observatory of Geneva, 

 when compared with the height of the Convent above the Observatory, 

 obtained by extremely accurate spirit-levelling. This fact will be pointed out 

 to the Academy in a satisfactory manner, before this paper is brought to a 

 conclusion. 



I have now to call the attention of the Academy to a small Table, showing 

 the heights of the Convent of the Great Saint Bernard above the Observatory 

 of Geneva, as calculated by the formula of M. E. Plantamour (which is only 

 a variety of Bessel's formula), as calculated by formula of Bessel, as calcu- 

 lated by my own formula, as calculated by that of Laplace, as calculated by 

 that of Batley, the same with that of Poisson (this latter being but a modifi- 

 cation of Laplace's). The same Table shows the error of each formula ; also 

 the influence of the vapour of water of the atmosphere in adding to the height, 

 as calculated from a formula suitable to an hypothetic atmosphere of simple 

 dry air. The errors shown in this Table have been obtained by comparing the 

 heights, as calculated by the five formula, with the true height, ascertained by 

 extremely accurate spirit-levelling. — (Vide tract, entitled "Nivellement du 

 Grand-Saint-Bernard, par Messrs. F. Burnier et E. Plantamour," being one 

 of the tracts which I have presented to the Academy. ) 



Let i? represent the height of the Convent of the Great Saint Bernard above 

 the Observatory of Geneva, as obtained by calculation from the mean of ten 

 years' observations, hygrometric an I barometric, made by night as well as by 

 day, at the Convent and at the Observatory, from the year 1841 to 1850, both 



