On the Propagation of Sound. 205 
2754098 
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below 57°5 the station at the level of the sea; and to make the 
first correction for the expansion of the mercury, we have 
‘ 85° x 50°04. 
= 85° depression of the thermometer 
='266 of an inch: this quantity de- 
ducted from 30-04 leaves 29°774 inches, the correction for the 
barometer. 
Then the logarithm of 29°774 is 1-4738372 
Altitude of the air in fathoms .. *4590163 
Difference .. 10148209 
The correction for the expansion of the air, reduced to the 
standard temperature 31°, as is done in calculating heights by the 
barometer, we find thus: 
Temperature at the surface... 57:5 
27541 feet =a depression of .. 85°, or 27°°5 below zero. 
me hea ie +15° the mean heat; and 15°—31°=16°: 
hence we have this proportion : 
‘480: 16° :: 4590°163 : 153°005 the correction for 
the condensation of the air. 
BS Nig i aig. 9 1:0148209 
Correction... °01538005 
Inches 9°99 = :9995204 the logarithm of the height of 
the barometer at the elevation of 4590 fathoms. From hence it 
appears demonstrable, that in order to compress the whole cir- 
cumambient air within a circle whose semidiameter is 27541 feet 
greater than that of the earth, it would require an additional force 
equal to a pressure of 9°99 inches of the barometer, or nearly 
one-third of the whole weight of the atmosphere. Therefore, 
to resolve the proposed problem correctly, we must augment the 
velocity of sound, as deduced from the Newtonian theory, in the 
subduplicate ratio of the density of air, under a pressure of 30-04 
inches, and 20-05 respectively. The density of air made use of 
in the preceding part of this memoir is 0012353, the square 
root of which is *U3514. ‘The air under a pressure of 20-05 
inches requires a correction for temperature ; we shall take its 
_ variation from the two extremes at 42°.5. 
Then 0012858 * 2005 _ _ .900824493 x 42°°5 x-002078 = 
00007 2815,and -000824493 + -000072815 =-000897308 whose 
root is -02996. 
To find in what space of time a pendulum whose length is 
27541 feet will make one vibration ; we shall assume the measure 
of the one which oscillates seconds, in latitude 45°, as equal to 
29-117 inches, or 3°25975 fect ; and calculating from the esta- 
blished 
and 
