a 
52 REPORT—1840. 
to express different motions. Thus the ondes dentelées, and the waves 
of constant transmission, are alike expressed, and their length is deter- 
mined in a function of the disturbance, &c. Now it appears to the 
author, that the same expansion which leads to the waves of constant 
transmission, ought, when the circumstances of the motion are assumed 
to be such as to admit of it, to lead also to the wave of solitary trans- 
lation. If it do not, then it would appear that the theorems of Fourier 
and Cauchy cannot give in terms of x a discontinuous function of the 
nature required, or such that its differentials with respect to # and y 
shall vanish at the same time. If, on the other hand, the theorems 
do suffice to express the requisite function, then shall we expect to find 
not the velocity only, but the complete form of the wave, which results 
from a given disturbance. We shall, in fact, be furnished with the 
length of the wave. It ought to be stated, that the author has sought 
in vain to deduce it from the equation which gives the velocity of 
transmission, and with as little success from the value of the discon- 
tinuous function which he used in his first memoir; but with the gene- 
ral formula itself, although he has not positively discovered the impos- 
sibility of discovering the thing sought for, he has yet found consider- 
able difficulties. The principal of these is the multitude of series 
which must be accurately summed before the equations can be formed. 
He was in consequence led to point out such difficulties to the Asso- 
ciation, with the hope that some member might take up the subject, 
and, by removing them, render the subject susceptible of application 
to the theory of the tides*. 
On the Agency of Sound. By Mr. Suanv. 
The author commenced his paper by remarks on the neglect mani- 
fested toward preserving or assisting cur hearing; and having laid 
down, in a series of propositions, his views regarding the origin 
and conduction of sound, observes, that it is difficult to reason on the 
operations of nature and the motions and influence of matter not per- 
ceptible to the eye. In the present case, however, we are enabled to 
judge partly by our ocular faculty and in part from our sense of hear- 
ing. ‘That the vibratory and undulatory or oscillatory motions are not 
only prevalent in the musical string, but in all matter in a state of 
agitation, is indicated by the following facts :—1st. In a musical string 
of a given diameter and tension, when set in motion, the extent of the 
undulations is in the ratio of the length of the string—each undulation 
gives out a distinct sound, conformable in duration to the extent of 
the undulation. @2nd. In the walls and ceiling of an apartment these 
principles of action are also equally apparent ; wherever there is an 
extended surface in any one place, the undulations are also extended, 
and these produce distinct sounds in the ratio of their extent. If the 
* At the request of the General Committee, Professor Kelland has under- 
‘taken to draw up a report on this subject, to be presented to the Association. 
