420 M. Duhamel on the Multiple Sounds of Bodies. 



higher than a fifth, and the nodal Hnes were the two diagonals 

 of tlie plate. 



If now, after producing one of these sounds, which con- 

 tinues for a considerable time, the bow is employed in the 

 same manner as when it is used to produce the other sound 

 when the plate is at rest, the two sounds are heard at once : 

 the nodal lines disappear, as M. Savart had remarked, and 

 as Daniel Bernouilli had already observed in the case of 

 strings. There only remains to determine the relation of the 

 number of vibrations executed in the same time by two points 

 situated near each of the nodal lines, which only exist when 

 each sound takes place separately. This 1 have done by means 

 of the apparatus already mentioned; and I constantly found 

 the relation of 31 or 32 to 45, as I ought to find for the two 

 sounds, whose distance was a little less than a fifth. 



I should add that another verification, less susceptible of 

 accuracy, might be made. On bringing the ear close to one 

 of the corners, scarcely any but the low note was heard ; and, 

 on the contrary, on bringing it near to the middle of one side, 

 only the high note was heard ; whence it appeared to follow, 

 that the two sounds were produced by different parts of the 

 plate. 



I sought on the outline the point of separation of the parts 

 related to each number of vibrations; but this point varies 

 with the relation of the intensities of the two causes of vibra- 

 tion, and this inquiry is only of secondary interest. 



I communicated these results to M. Savart, and he wished 

 immediately to repeat the experiment with me, employing 

 resonant tubes, which he put in unison, first with one sound 

 and then with the other. On bringing one of the tubes in 

 succession close to the different parts of the plate, the sound 

 was considerably strengthened in some, and was not percep- 

 tibly in others : the first appeared therefore only to produce 

 the sound of this tube; the second produced a similar effect 

 with the second tube. These results perfectly agree with 

 mine. 



We finally considered the simultaneous sounds produced 

 by a large bell, and thought that we perceived in the case of 

 two, and even of three sounds, that each of them existed singly 

 in the same part of the surface. We did not perform this 

 experiment with the same degree of precision as the first, 

 because the result presented itself naturally as it was expected. 



Both the reasonings, therefore, and the experiments in 

 question, led to the admission of this general law of the co- 

 existence of sounds, that — 



Wheii ofie and the same vibratijig surface simidtaneously emits 



