On a proposed Barometric Pendulum. 433 



cation of the variations of the rate of a clock, viz. to determine 

 the mean barometric pressure during long periods. 



For this purpose the clock should be regulated by a centri- 

 fugal or revolving pendulum, part of which should consist of a 

 siphon barometer. The rising and falling of the mercury would 

 evidently affect the rate of the clock ; so that from the number 

 of revolutions of the pendulum in a given time might be deduced 

 approximately the mean height of the mercurial column during 

 that period. 



The formulae applicable to this calculation are the following, 

 the demonstrations of which are given in an Appendix. 



The suffix being used to designate a certain normal con- 

 dition of the barometric pendulum as to temperature and pres- 

 sure, to be employed as a standard of comparison, let 



y represent the distance, in this condition, of the centre of 

 gravity of the pendulum from the centre of suspension ; 



X , the distance of the centre of oscillation from the centre of 

 suspension, or the length of the equivalent simple pendulum ; 



F , the distance from the centre of suspension to the lowest 

 part of the central line of the siphon ; 



L , the sum of the lengths of the mercurial columns in the 

 two legs of the siphon, measured from the same point ; 



H , the difference of those lengths, which may be called the 

 oblique height of the barometric column ; 



l , the length of a column of mercury, of sectional area equal 

 to that of the column in the siphon, whose weight would be equal 

 to the whole weight of the pendulum. 



Let A be used to designate deviations from this normal con- 

 dition. 



Then the deviation of the square of the oblique height is con- 

 nected by the following equation with the deviation of the length 

 of the equivalent simple pendulum 



A.H*= 4^yoA\_ 



\ p + A\-2F +L w 



If the weight and dimensions of the barometric pendulum be 

 so adjusted that the deviations of the length of the equivalent 

 simple pendulum are always very small compared with the 

 normal length, then the above formula may be used to calculate 

 the mean deviation of the square of the oblique height H by 

 means of the mean deviation of the length of the equivalent 

 simple pendulum. 



The latter deviation is to be determined as follows : — 



Let n be the number of revolutions of the pendulum during 

 a given period in the normal condition ; 



n + An the actual number of revolutions ; 

 * See Appendix 1. 



