ON THE AUGMENTATION OF SOUNDS. 67 



a given diftance; confequently the increafed force thus im- 

 parted to a found, muft be afcribed to the co-operation of the 

 vibrations communicated in the firfl experiment to the plate 

 of iron ; for by uniting with thole of the watch, they evidently 

 augmented the power of the latter inftrument. 



A rational theory of the forces of founds may be formed, Theory of the 

 by help of the preceding observations, in the following manner : augmente( j by 

 Firfiy Suppofe the plane ABC (Plate IV.) to be one of the fur- the vibrations of 

 faces of an elaftic body, and let it receive an impulfe at the ? n g the"^"^^ 

 point O; then O will recede from the ftroke in a right line body, 

 perpendicular to ABC, drawing after it all the contiguous 

 particles, which, in their turn, will change the place of the 

 next circle of particles. In this manner a circular dent 

 OMEQTF will be formed ; the center of which O will be 

 below the plane ABC; M, the higheft part of the margin, 

 will be above it ; and the extreme circle EQTF, bounding 

 the whole, will lie in the plane. Second, Thus will a circu- 

 lar fwell be formed on the plane, refembling the circular wave 

 produced by a ftone dropped into water. A feries of thefe 

 fwells will follow the firfl, each of which, in fucceffion, will 

 lie more remote from the center O than its predeceffor. Third, 

 The collective force of each fwell is equal to that of the firfl: 

 impulfe ; and it is diftributed over the furface of a ring, having 

 O for its center and O E for. its breadth ; i. e. all the rings are 

 of equal breadths, but unequal diameter. Fourth, The effect 

 of the ftroke is thus progreffively propagated from O to the 

 more diftant parts of the plane ABC, with an uniform velo- 

 city. Fifth, Let P be the place of the ear in the right line 

 O P, perpendicular to A B C ; alfo let GHIJK be any fwell 

 in the fame plane ; then will the effe6i of that fwell be carried 

 to the ear, in the conical fhell O G I J K P ; and the impulfe 

 imparted to the auditory organs, through the medium of this 

 fhell, will be greateft when the diameter of the ring O I is 

 leaf!, and the contrary. Sixth, If A B C be a concave fphe- 

 rical furface, having P for its center, all the fwells will fuc- 

 ceffively exert equal forces on the ear at P. Seventh, If O P 

 be put equal to a, and / meafure the force of a ftroke at the 

 diftance I ; then let v equal the velocity with which this force 

 is propagated from O over the fpherical furface, and I the 

 breadth of the rings covered by the fwells, the force im- 

 preffed on the ear at P in a given interval of time, is equal 

 F 2 to 



