Motions of mediately agitated Membranes. 337 



that the transitions of the different phenomena do not show 

 themselves when these phaenomena appear most regularly and 

 forcibly, but only when they become indistinct and indefinite. 

 Now the sounding vibrations (which Chladni always considers 

 by themselves) are constantly the most uniform and the most vio- 

 lent vibrations. There is, therefore, probably, a transition from 

 a sounding vibration, through a series which do not produce 

 sound (such as are less distinct and precise) standing vibra- 

 tions, to a very different sounding vibration ; but there is no 

 transition from a sounding vibration through nothing but 

 sounding vibrations to a quite different sounding vibration (pro- 

 ducing a much higher or much deeper tone). However, Savart 

 is perfectly right in affirming that many of the distortions of 

 the figures of sound observed by Chladni are the beginnings 

 of the transition of one kind of vibration to another, and that 

 in these distortions, even the number of vibrations, whilst the 

 tone is becoming weaker and beginning to cease, is a little al- 

 tered. But if a vibrating body gives a distinct tone, it is in a 

 very uniform and violent vibration, which is only possible when 

 the number of its vibrating divisions is strictly fixed, and the 

 sum of the motions is in all as equal as possible, in which case the 

 height of the tone {the velocity of the vibrations) is unchangeable, 

 as it depends as much on the elasticity and form of the membrane, 

 as the velocity of the vibrations of a pendulum of a given length 

 on gravitation. This rule, laid down by Chladni, has thrown 

 an extraordinary light and intelligibility on all acoustic phae- 

 nomena. 



In order, therefore, to render what has been said still more 

 intelligible ; and in consequence of there being several simi- 

 larities in the motions of membranes observed by Savart, with 

 the vibrations of sounding elastic plates; and finally, as it is 

 now generally necessary to find out by experiment as closely as 

 possible the extension of small vibrations on visible bodies ; — I 

 shall here communicate from the 32nd volume of the Ann. de 

 Chimie et de Physique, the phaenomena discovered by Savart. 



Savart examined the lines upon which the sand remains in 

 its place on mediately agitated bodies. 



If an equally-stretched square rectangular or triangular 

 membrane is mediately and regularly agitated, grains of sand 

 scattered over it are thrown off from equally large and regu- 

 larly-bounded divisions of those membranes, but are collected 

 on the limits of these divisions nearly in the same manner as 

 they are on the sounding plates. 



Savart wished to cause the stretched membranes to vibrate 

 mediately and with the utmost uniformity, and thereby to de- 

 termine at his pleasure, the quicker or slower result of the 



New Series. Vol. 3. No. 17. May 1828. 2 X agitations, 



