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

 Consequently, making 



Mew 



= /, 



01 



W6haVe 7o X -l(2P -L )A.H* 



\=X +A\= Hi— , . . (B) 



7o __A.H« 



from which is immediately deduced equation 1 of the paper. 



2. Periodic Time of Revolution. 

 This quantity is well known to be expressed by 



t= \/{t Xcos *)' (C) 



consequently the number of revolutions in a given time <£) is 



n =^ = — 771-2 c« • • • ( D ) 



V(t Xcoe *) 



9 

 We have therefore 



(E) 



and consequently, when A\ is very small, 



A\ n An , 

 -— ~ — 2 — nearly, 



being equivalent to equation 2 of the paper. 



3. Condition of Equilibrium of the Mercury. 



♦ H' being the vertical height of a column of mercury whose 

 weight is equivalent to the atmospheric pressure, may be used to 

 express the action of the air on the open surface of the mercury. 

 The effect of gravity will be proportional to 



H cos a, 

 and that of centrifugal force to 



47r 2 sin r 



• 2 sin 2 «f" + T MI , „ 27r 2 sin 2 a /01? T . 

 7E*~~1- > -*=H.- 7 p-(2P -I^); 



consequently the condition of equilibrium of the mercury is ex- 

 pressed by the following equation, 



