OF TiiE MOTIONS OF FLUIDS. 3 \7 



sia COS 9~)::z^r-ghy—Q^y; and 1/= -I f ^ + ^ 



u cos 5 \ 

 sin 6^ } 



Scholium 1. These oscillations of the atmosphere mast 

 produce analogous oscillations in the heights of the baro- 

 meter. In order to determine these from those of the 

 atmosphere, we may consider a barometer fixed at any 

 given height above the surface of the sea. The height of 

 the mercury is proportional to the pressure, to which the 

 surface exposed to the air is subjected ; it may therefore be 

 represented by Icj^ : but this surface is successively exposed 

 to the pressure of different level strata, which rise and fall 

 like the surface of the sea: consequently the value of (> at 

 the surface of the mercury varies, first so far as it belongs 

 to a level stratum, which in the state of equilibrium was less 

 elevated by a quantity ay, and secondly because, in the state 

 of motion, the density of a given stratum is increased by the 



quantity a^ or — y^. In virtue of the first cause the va- 

 riation off is — ay -T-^, or ^ • ; [since this variation must 

 dr I 



be to (f) the whole density, as the elementary column ay to 

 the height /] ; consequently the total variation of the density f, 



at the surface of the mercury, is a(f ) ilL_X-. Hence, if we 



call the height of the mercury A: in the state of equilibrium, 

 its oscillations in the state of motion will be expressed by 



the quantity — — — — ; consequently these oscillations are 



similar at all heights above the sea, and proportional in 

 their extent to the heights of the barometer. 



Scholium 2. It now only remains, for the determina- 



