544 BESSEL ON BAROMETRICAL 



agreement of the partial results in the earlier as well as in the 

 later series, it indicates a constant error, and there can be there- 

 fore no propriety in taking the arithmetical mean of the two de- 

 terminations. I see no other course at present than to employ 

 both, and to await a future decision on the differences which 

 may result therefrom. 



10. 



Having gone through the different assumptions involved in 

 formula (11.), I return to this formula, and will now show its 

 application to barometrical measurements of height. 



The pressures P and P' at the elevations h and h', are de- 

 ducible from the barometrical observations there made. If we 

 denote one of the heights of the barometer by b, the temperature 

 of the mercury and of the scale by which the height is measured 

 by t, and assume that the scale is of brass as is usual, we obtain 

 the mass of mercury supported by each unit of surface 



_ A 53242 + t 5550 



~ '' ■ 53242 + {t) ' 5550 + t" 



where [t) signifies the normal temperature of the unit of measure 

 of the barometer-scale, and Avhere the unit of volume of mercury 

 at the temperature of melting ice is taken as the unit of the mass. 

 This mass presses in proportion to the force of gravity to which 

 it is exposed ; or with the force 



^3) (^)'' 



and the pressure which it exerts is the product of both divided 

 by the assumed unit of pressure ( = 336^"905). Thus we obtain 



p_ {9)b ( « y . 53242 -|- t _ 5550 

 " 336-905 \a -\- h) ' 53242 \- {t) ' 5550 + t ' 



and its Briggs's logarithm in formula 1 1, with sufficient approxi- 

 mation, 



, , , 336-905 (53242 + (/) ) 

 = log 6 - log ^3242 



'* \5550 53242J a 



If we put for a the geometrical mean of the two semi-diame- 

 ters of the earth (log 6-5140838, Ast. Nach., 333), and for {t) 

 the normal temperature of the French standard foot = 16°-25, 

 then 



