the Barometric Formulce, ^c. 625 



able to determine the desired new constant as accurately as it was my wish to 

 determine it ; when, in examining with care the formula already submitted to 

 the Academy, I perceived that as it takes account of every quantity, however 

 small, of aqueous vapour which may be formed in the atmosphere, it necessa- 

 rily answers for a state of atmosphere in which the vapour of water becomes 

 nothing; consequently, the desired new constant must be such as belongs 

 to a formula suited to a hypothetic atmosphere consisting of absolutely dry 

 air. Now the constant for such a fornuila is obtainable from the well-known 

 equation 



C= j7 — „ metres; 



in which C represents the desired new constant ; M^ the modulus of common 

 logarithms ; and D the ratio of the specific gravities of dry air and quicksilver, 

 under a pressure of 0'76 metres of quicksilver. For proof of this equation, and 

 the mode of obtaining the required new constant, vide Appendix, pp. 658, 

 659, and 660. 



The constant obtained in this manner for latitude 45°, at the level of the 

 sea, at freezing-point = 18404-9 metres = 60384-6 English feet {vide Appendix, 

 page 659). 



It is worthy of notice, that the constant thus determined from the considera- 

 tion of the ratio of the specific gravities of dry air and quicksilver, is more cor- 

 rect than a constant obtained from any number, however great, of observations 

 hygrometric and barometric, because, although by a very great number of obser- 

 vations, their unavoidable errors, sometimes over and sometimes under the truth, 

 may be neutralized, or rendered for practical purposes insensible ; yet the errors 

 which arise from assuming the arithmetic mean of temperatures, given by the 

 detached thermometers, to be the real mean temperature of the atmospheric 

 column between the stations of observation, cannot be in the least degree dimi- 

 nished by any number of observations, however great. It is, moreover, worthy 

 of special attention, that without a formula, which makes correct allowance for 

 the hygrometric state of the atmosphere, the new constant obtained by means 

 of the equation 



C= T7 — 7^ metres, 

 4n 2 



