OF FLUIDS ON VIBRATING ELASTIC SURFACES. 
331 
of the lines themselves, it was quite free from mark, and fully distended. 
All these are natural consequences, if the film be considered as a flexible but 
inelastic envelope formed over the whole surface whilst the heaps were rising 
and falling. 
103. The mode of action by which these heaps are formed is now very evi- 
dent, and is analogous in some points to that by which the currents and the 
involving heaps already described are produced. The plate in rising tends to 
lift the overlying fluid, and in falling to recede from it ; and the force which 
it is competent to communicate to the fluid can, in consequence of the physical 
qualities of the latter, be transferred from particle to particle in any direction. 
The heaps are at their maximum elevation just after the plate begins to recede 
from them ; before it has completed its motion downwards, the pressure of the 
atmosphere and that part of the force of the plate which through cohesion is 
communicated to them, has acted, and by the time the plate has begun to re- 
turn, it meets them endowed with momentum in the opposite direction, in con- 
sequence of which they do not rise as a heap, but expand laterally, all the 
forces in action combining to raise a similar set of heaps, at exactly interme- 
diate distances, which attain their maximum height just after the plate again 
begins to recede; these therefore undergo a similar process of demolition, being 
resolved into exact duplicates of the first heaps. Thus the two sets oscillate 
with each vibration of the plate, and the action is sustained so long as the 
plate moves with a certain degree of force ; much of that force being occupied 
in sustaining this oscillation of the fluid against the resistance offered by the 
cohesion of the fluid, the air, the friction on the plate, and other causes. 
104. A natural reason now appears for the quadrangular and right-angled 
arrangement which is assumed, when the crispation is most perfect. The hexa- 
gon, the square, and the equilateral triangle are the only regular 
figures that can fill an area perfectly. The square and triangle 
are the only figures that can allow of one half alternating symme- 
trically with the other, in conformity with what takes place be- 
tween the two reciprocating sets of heaps, fig. 26; and of these 
two the boundary lines between squares are of shorter extent 
than those between equilateral triangles of equal area. It is evi- 
dent therefore that one of these two will be finally assumed, and 
that that will be the square arrangement ; because then the fluid 
