for the Registration of the Mean Atmospheric Pressure. 435 



In Appendix 4, it is shown how the foregoing formula? may 

 be simplified under certain special circumstances. 



I shall not at present attempt to assign the best proportions 

 for the barometric pendulum, nor the best manner of construct- 

 ing it, for those particulars will be most readily fixed by practical 

 trials. When this has been accomplished, it appears to me pro- 

 bable that the method here proposed of ascertaining the mean 

 barometric pressure during long periods of time may probably 

 be found more accurate than any other, as well as less laborious. 



Glasgow, July 9, 1853. 



APPENDIX. 

 Investigation op the Formulae. 



1. Relation between the deviations of the oblique height of the 

 mercurial column and those of the centre of oscillation. 



The point of suspension being taken as the origin of x, mea- 

 sured along the pendulum, let x x denote the position of the sur- 

 face of the mercury in the closed leg of the siphon, and x% its 

 position in the open leg, in the normal condition as to pressure 

 and temperature. Then 



W,2-{-Xl=: ZKo — AJq', X% X^~ I1q' } 



If dfjb denote an element of the mass of the pendulum, and fi 

 its entire mass, the length of the equivalent simple pendulum 

 revolving at the same angle with the vertical is known to be 



Jxdfju 7 ft + Afxd/ju 



Now, M being the mass of unity of volume of mercury, and co 

 the sectional area of the siphon, 



A/xdfju=M(o< I -| 2 2 \{xdx) 



= -M«{^-*OAH+i(AH)»}=-^A.H« 

 Afx*dp=Mco< I -4 2 Ua»dx) 



LJ*,-.-AH J# 2 J 



= -^(2F -L )A.IP. 



