1831.] on Vibrating Elastic Surfaces. 349 



between squares are of shorter extent than those between 

 equilateral triangles of equal area. Tt is evident therefore that 

 one of these two will be finally assumed, and that that will be 

 the square arrangement ; because then the fluid 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 con- 

 sidered as a pendulum vibrating to and fro under a given im- 

 pulse ; the various circumstances of specific gravity, 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 interval. 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 ex- 

 tent 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 nor- 

 mally, are all evident consequences. The permanency of the 

 lateral extension of the heaps, when the velocity of the vibra- 

 ting plate varies, is a very marked effect ; and it is probable 

 that the investigation of these phenomena may hereafter im- 

 portantly 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 vi- 

 brating, cause an elevation or depression in the fluid there; the 

 smallest atom of dust falling on the surface, or the smallest eleva- 

 tion 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 extended 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. 



