332 
MR. FARADAY ON THE FORMS AND STATES 
will offer the least resistance in its undulations to the motions of the plate, or 
will pass most readily to those positions into which the forces it receives from 
the plate conspire to impel it. 
105. All the phenomena observed and described may, as it appears to me, 
be now comprehended. The fluid may be considered as a pendulum vibrating' 
to and fro under a given impulse ; the various circumstances of specific gra- 
vity, cohesion, friction, intensity of vibrating force, &c. determining the extent 
of oscillation, or, what is the same thing, the number of heaps in a given inter- 
val. When the number of vibrations in a given time is increased, these heaps 
are more numerous, because the oscillation, to be more rapid, must occur in a 
shorter space. The necessity of a certain depth of fluid (73) is evident, and 
also the reason why, by varying the depth (82), the lateral extent of the heaps 
is changed. The arrangement of the sand and lycopodium, by the crispations, 
and the occurrence of the latter at centres of vibration, and only upon surfaces 
vibrating normally, are all evident consequences. The permanency of the 
lateral extension of the heaps, when the velocity of the vibrating plate varies, is 
a very marked effect, and it is probable that the investigation of these phe- 
nomena may hereafter importantly facilitate inquiries into the undulations of 
fluids, their physical qualities, and the transmission of forces through them. 
106. As to the origin or determination of crispations, no difficulty can arise ; 
the smallest possible difference in almost any circumstance, at any one part, 
would, whilst the plate is vibrating, cause an elevation or depression in the 
fluid there ; the smallest atom of dust falling on the surface, or the smallest 
elevation in the plate, or the smallest particle in the fluid of different specific 
gravity to the liquid itself, might produce this first effect ; this would, by each 
vibration of the plate, be increased in amount, and also by each vibration ex- 
tended the breadth of a heap, in at least four directions: so that in less than a 
second a large surface would be affected, even under the improbable supposition 
that only one point should at first be disturbed. 
10/. I have thought it unnecessary to dwell upon the explanation of the cir- 
cular linear heaps (83.93. 110) produced on long or circular plates by feeble 
vibration. They are explicable upon the same principles, account being at the 
same time taken of the arrangement and proportion of vibrating force in the 
various parts of the plates. 
108. The heaps which constitute crispation (as the word has been used in 
