362 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
made for the purpose of determining 1 the mechanical value of heat *, give for J the value 
1390 ; and we therefore have JN = 234*1 with sufficient accuracy for use in calculating 
small terms. Calculating accordingly, with this for JN, and with the value 1*41 for k, 
<S> . 
the coefficient of — in (45), we find, 
<p, 
for *=2737 (temperature 0° Cent.), k=\{-{- '00126 x~ 
and for 
£=293*7 (temperature 20° Cent.), 
*=ft+-00076x® 
• • (46) 
Now according to Regnault we have, for dry air at the freezing-point, in the 
latitude of Paris, 
H=26215; 
and since the force of gravity at Paris, with reference to a foot as the unit of space 
and a second as the unit of time, is 32*1813, it follows that the velocity of sound in 
dry air at 0° Cent, would be, according to Newton’s unmodified theory, 
\/ 262 1 5 X 32* 1813 =918*49, 
or in reality, according to Laplace’s theory, 
Wf.\/ 26215X32*1813. 
But according to Bravais and Martins it is in reality 
1090*5, which requires that k= 1*4096, 
or according to Moll and Van Beck 
1090*1, which requires that &= 1*4086. 
The mean of these values of k is 1*4091. If this be the true value of k for 0° Cent, 
and the standard density ^ = 1^, the correction shown in (46) above would give 
fe = l*40784; 
or if it be the true value of k for air of the standard density, and the temperature 20° 
Cent., the correction will give 
k= 1*40834. 
Which of these hypotheses is most near the truth, might possibly be ascertained by 
reference to the original observations on the velocity of sound from which the pre- 
ceding results reduced to the. temperature 0° were obtained, but as the actual tempe 
ratures of the air must in all probability have been between 0° and 20° Cent., without 
going into the details of the calculations by which the reductions to 0° have been 
made, we may feel confident that It cannot differ much from either of the two pre- 
ceding estimates, and we may take their mean, 
k= 1*4081, (47) 
as probably a very close approximation to the truth. Now we have seen above that 
* Philosophical Transactions, 1849. 
