434 Mr. W. J. M. Rankine on a proposed Barometric Pendulum, 



then the mean deviation of the length of the equivalent simple 

 pendulum is given approximately by the formula 



A\= -2 h An nearly; .... (2)* 



which value being substituted in equation 1, transforms it to the 

 following, 



and gives the mean deviation of the square of the actual oblique 

 barometric height from the square of the normal oblique baro- 

 metric height. 



We thus obtain the mean of the squares of the oblique height 

 during the period of registration, which may be represented thus : 



m.H 2 =iy+A.H 2 (4) 



The square root of this may be taken as a first approximation 

 to the mean value of the oblique height. 



To obtain a nearer approximation, let JM.h be the isotropic 

 mean of the maximum deviations upwards and downwards, from 

 the first approximate value of the mean height, which deviations 

 may be ascertained by other instruments ; then a second ap- 

 proximation to the mean oblique height is 



ttt.H = /V /(m.H'-i(w.A) 2 ). . . . (5) 



The several quantities denoting lengths in these formulae are 

 supposed to have been corrected for expansion ; the mean devia- 

 tion from the normal temperature having been ascertained by a 

 thermometric pendulum, or otherwise. 



The quantity Itt . H, thus ascertained and corrected for tem- 

 perature, has finally to be corrected for the obliquity of the 

 position of the barometer, and for centrifugal force, by the fol- 

 lowing formula : — 



Let a denote the angle made by the pendulum with the vertical; 



T, the mean time of one revolution ; 



tit . H', the corrected mean height of the barometric column ; 

 then 



tti tt f 27r 2 sin s a /4 .,, TX 1 

 ttt.H' = m.HJ cosa+ jp — (p¥—L)>. 



(6)t 



The first term between the brackets represents the effect of 

 obliquity ; the second, that of centrifugal force. 



* See Appendix 2. 

 t See Appendix 3. 



