636 



Lieutenant Eennt on the Constants of 



of observation above the other ; B and B' indicate the barometric pressures, 

 fully and completely corrected ; and N indicates the product of various factors 

 relating to latitude, to mean temperature, &c., &c. 



Now, if reference be made to my former paper, it will appear that my own 

 formula, in making correct provision for the hygrometric state of the atmo- 

 sphere, differs only from formula in previous use by replacing in such formula 



the expression log ^^ by the expression log ^ /ifpy N°^^' ^"^ reference 



J) 



to the formula of Bessel, we find he replaces the expression log -p, by the 



expression ^—r-r^x'iog 7^; so that if both these new formulse be sound, 



1 3V (// ) B 



VBB' 



we ought to have equality between the expressions, 



log 



B'-W(ff) 



, and 



1 



, B 



—%VUl)''°B'- 

 V'BB' 



Now, let any one employ even extreme values of BB', and |\/(^') in these 

 expressions, and he will find the difference practically insensible ; for instance, 

 in making use of the mean of the ten years' observations, hygrometric and baro- 

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

 heights calculated, according to Bessel's formula and my own, differ only by 

 the hundreth part of a metre ; the heights by Bessel being 2066'36 metres, and 

 by my own formula being 2066'35 metres ; as to correctness, therefore, the one 

 formula is as good as the other, but as to facility of calculation, mere inspection 

 points out the superiority of the one over the other. There is, moreover, this 

 peculiar difference between the two formulis, that the differential equation, the 

 integration of which has produced my formula (vide former paper) is mathe- 

 matically correct, so that whenever the laws of the variation of atmospheric 

 temperature and of the elastic forces of the vapour of water shall be ascer- 

 tained exactly by experiment, we shall have, by a simple employment of the 

 well-known rules of the integral calculus, a formula for barometric observations 

 mathematically correct also. "With respect to the formula of Bessel, it is only a 

 close approximation to truth, without being mathematically and strictly cor- 



