Determination of the Velocity of Sound. 451 
wave remained the same as before. This caused me to examine 
the question of the propagation of waves in an elastic medium 
ab initio; and the result is that I have, I believe, detected a 
flaw in the problem as previously treated, which being remedied, 
there results from theory a value of the velocity of sound which 
agrees accurately with the experimental value found by Pictet, 
and with the following remark of Young:—“ From a com- 
parison of the accurate experiments of Derham, made in the 
daytime, with those of the French Academicians, made chiefly at 
night, it appears that the ¢rue velocity of sound is about 1130 
feet in a second;” and this agrees exactly with the value which 
I obtain by the theory, which I will now proceed to lay before 
your readers. 
1. There is a fundamental difference in the mechanical actions 
of two elastic media, one of which is supposed to be continuous, 
and the other to consist of particles separated by finite intervals. 
Let AZ be an elastic medium; divide it 
by imaginary planes into extremely thin 
slices D, E, F,..., so thin that each con- 
tains only one layer of particles; in other 
words, the thickness of the slices will be 4....|D|E|F|/G)H]....2 
equal to the distance between the particles 
of the medium. Now according to the 
common solution of the problem of sound, 
the medium is supposed to be continuous ; 
that is, any slice (as F) is pressed upon only by the two slices 
(E, G) with which it isin immediate contact. And, correspond- 
ing to this, any slice (F) is supposed to exert no direct pressure 
on any slices beyond the two (K, G) with which it is in contact. 
Hence all the motion which any one slice (F) has, it received 
from one of its immediate neighbours (E), and transmits it 
wholly to the other (G). This is the system of medial action 
supposed in the investigation of the differential equation of sound 
as commonly given. 
But this supposes molecular action to extend from any one par- 
ticle to those only which are nearest to it, —a supposition for which 
there is no foundation whatever in nature. It is certain, how- 
ever, that molecular action extends to avery small finite distance, 
and therefore enables molecules which are separated by any 
distance not exceeding that, to act on each other. Hence any 
slice (F) is pressed upon by H, I,... as well as by G, on one 
side; and by D, C,... as well as B, on the other; and not all, 
but only some portion of, the motion which (F) receives does it 
receive from 3; the rest comes from D, C,...; and the motion 
which F has received it does not wholly transmit to G, but it 
distributes it among G, H, I,.,. the slices within reach of its 
