1830.] 
Velocity of Sound. 
311 
Now Laplace’s formula affording us no assistance in determining the value of C, 
we have no resource but to compute it troiu that theorem which we have shewn 
P 28 14 
to agree so well with observation. Assuming therefore, — = — = our formula 
V 30 15 
gives a? = 298.29 fathoms, from which C = 3°, and consequently by Laplace xzz. 2993. 
P 25 5 
or 1 fathom above ours. Putting — = — = ours gives 78.83, and C = 8°, and 
P 30 6 
p 20 2 
hence, Laplace’s 782.47, or 1.59 above ours. Again, when = — = — , we have 
P 30 3 
from our theorem 1704.8 fathoms, and C= 17°, 42, and from Laplace’s 1708, 1, or 
only 3, 3 more, in an altitude of nearly two miles. In Gay Lussac’s great ascent, 
the temp, sunk from 30°,8 Cent, to — 9°,5 ; the barometer from 1000 to 432 ; 
the density of the air from 1 to 4 ; and we are informed the height ascended, 
doubtless determined from these data by Laplace's formula, was 7030 yards, or 
3815 fathoms from the barometric condition: our formula gives 76'00 yards, or 
3800 fathoms, that is, 15 fathoms less in a height of miles. The depression of 
temp, as we have seen in the table, differs likewise only about 1$°. 
It should here be observed, that if Laplace's formula coincided perfectly with 
observations ; and the greater the height the more it must diverge from nature ; 
for by that formula, the atmosphere must be infinite in extent, a palpable absur- 
dity, which Laplace himself acknowledges. However, the differences which we 
have shewn to exist between the two formula, are much within the limits of error, 
to which probably the best observations could pretend in such heights. 
Tiiere is a source of error in barometric admeasurements, which it will he difficult 
for any theory to esiimate or avoid, namely, the unequal distribution of vapour 
in the atmosphere. This will, in general, tend to depress the lower barometer too 
much, and consequently to give the altitudes too little. It is probable this may 
never occasion an error of serious moment, but it will undoubtedly always have 
some influence. 
If we suppose D d to denote the densities of the air corresponding to P p t the 
combination of our two theorems gives 
d 1 
or in Lussac’s — = (,432) § = - differing from his § by only 3 | 5 th part. 
D 2,0126 
From these instances some idea may be formed of the perfect fidelity with 
which the theorems I have given represent phenomena ; probably it will not be ha- 
zarding too much to affirm, that the success of them is greater than could have 
been anticipated ; and that there is scarcely a parallel instance in science, in 
which investigations begun, and conducted so absolutely independent of experi- 
mental aid, have been so thoroughly confirmed by phenomena. Their mathematical 
analysis will appear in the work already alluded to. 
Several important consequences flow from these theorems, besides those we 
have mentioned ; some of which we shall here notice. 
1st. The velocities of sound, and the transmission of heat by the air, are the 
same. 
2d. The total altitude of the air is equal to 
rh (F+448) 
80 
or, at a medium, better than 30 miles; and at other times varies directly ns the 
Fahr. temp. - 4 - 448. 
3rd. Since r and h are estimated at a common temperature, when air is con- 
stant, the other must be constant too in the same air ; and therefore the quantity 
of air has nothing to do with its total altitude. This would be the same, whether 
there was a half, a third, or a 100 times the quantity. . . „ 
4th. Other things being alike, the altitude of an atmosphere is reciprocally 
proportional to the attraction of the body it surrounds at its surface, and the specitic 
gravity of the air under a given pressure and temperature conjointly. Ir, there- 
