658 Lieutenant Rennt on the Constants of 



APPENDIX. 



On the Constants of the Barometric Formul.i:. 



0*7fi 

 The expression C = -r-. j-. metres, by which is calculated the constant of a baroraetric 



formula for a suppositious atmosphere of simple dry air, perfectly free from vapour of water, 

 in which expression C represents the constant of the formula, M the modulus of com- 

 mon logarithms, and D the ratio of the specific gravity of dry air to that of quick- 

 silver, under a pressure of 0-76 metres of quicksilver, may be obtained in the following 

 manner : — 



It is obvious that the height of a column of dry air of uniform density = —jj metres. 



Let us now suppose a column of dry air to be divided into an extremely great number of strata 

 of equal thickness. Let n be a number extremely great : consequently the thickness of the 

 lowest stratum (as also that of every other stratum), or the distance between the lower and 



upper surfaces of such lowest stratum, may be represented by the quantity - metre. It is 



also obvious that the density of such stratum (though not mathematically uniform) has 

 uniformity for its limit of variableness. If we now assume as measure of the pressure at 

 the lower surface of the lowest stratum, the height of a column of dry air of uniform density 



= -jr- metres, we have for measure of pressure at the upper surface, distant from the lower 



surface, by a quantity = - metre, the expression —j=r metres. But n being a number 



extremely or indefinitely great, in place of these expressions we may employ the expressions 



-K- + - and -?r-; making use of the well-known barometric formula (A =Cx com. log. -, 

 D n D ° ° p 



in which h is the height of one station above the other, C is a constant quantity, sxidi p,p 



ro-76 



are the pressures at the lower and upper stations, we have - = C x com. log. 



0-76 1 1 



0-76 [ ' 



or, 



^c..,,«„„.io,.]i.l„^j = c.*|l„^-l(i„4,)M.c.j, 



