a On the Propagation of Sound. 203 
as he procéeded upon the true principles of philosophy: his 
subsequent surmises are not worthy of notice, except as coming 
from such an exalted character, 
This great man has demonstrated in ‘the fore-mentioned pro- 
position, that the number of pulses propagated is the same with 
the number of vibrations of the tremulous body; that they are not 
multiplied in their progress ; and that as soon as the pulses cease 
to be propagated from the tremulous body, it will return to a 
state of rest. Again, in the 48th proposition of the same book, 
Newton has. clearly solved an important question, in favour of 
the theory we have ‘advanced ; viz. that the velocities of the pulses 
are in a ratio compounded of the subduplicate ratio of the den- 
sity of the medium inversely, and the subduplicate ratio of the 
elastic force directly. 
If the atmosphere were of a uniform density at different di- 
stances from the earth’s surface, the velocity of sound as deduced 
from the law of pendulous bodies would be exact ; but, as the 
air is a medium that decreases in density as the distance from 
the earth increases, it Sheree to me to require a different view 
of the subject. 
When the height of the mercury in the barometer and the 
temperature of the atmosphere are obtained, we can easily find 
the altitude of a column of air that would reach to the top of 
the atmosphere ; and if it were of an equal density and elasti- 
city in all its parts, the velocity of sound as recorded by Newton 
would be rightly stated. But it is otherwise; the atmosphere is 
not equally dense at every elevation, which the proposition of 
Newton requires.. The question is then, What force is necessary 
to overcome the elastic power of that portion of the air which 
exists above the assumed height of the atmosphere, in order to 
compress the whole mass of the air within that limit? 
Before we proceed in the investigation of the proposed subject, 
several preliminary inquiries are requisite. It appears from ex- 
periments carefully made by Mr. Tralles*, that the density of 
dry air at 32° of Fahrenheit’s thermometer, and under a pressure 
of 29-92 inches, is equa! to -00129918, the specifie gravity of 
water being taken as unity, and under the same circumstances 5 
and to ‘0012770 when the same thermometer is at 39°83, which 
point Mr. Tralles has ascertained to be the maximum density of 
water, the barometer remaining as before. The specific gravity 
of mercury is 13°59925 at the former standard, and 13°59655 at 
‘the latter. Now by ‘taking a mean between the experiments 
made by Gay-Lussae and those of Dalton on the expansion of 
dry air, it appears that for every additional degree of Fahrenheit’s 
* Nicholson’s Journal, vol, xxv. p. 79. 
thermometer ~* 
