K'OTES. 



461 



NOTE 182, p. 143. Fig. 45 represents sections of an open and of a 

 shut pipe, and of a pipe open at one end. When sounded, the air spon- 

 taneously divides itself into 



segments. It remains at rest Fuj. 45. 



in the divisions or nodes n n', 

 &c,, but vibrates between 

 them in the direction of the 

 arrow-heads. The undula- 

 tions of the whole column of 

 air give the fundamental note, 

 while the vibrations of the 

 divisions give the harmonics. 



NOTE 183, p. 144. Fig. 1, 

 plate 1, shows the vibrating 

 surface when the sand divides 

 it into squares, and fig. 2 

 represents the same when the 

 nodal lines divide it into triangles. The portions marked a a are in dif- 

 ferent states of vibration from those marked b b, 



NOTE 184, p. 145. Plates 1 and 2 contain a few of Chladni's figures. 

 The white lines are the forms assumed by the sand, from different modes 

 of vibration, corresponding to musical notes of different degrees of pitch. 

 Plate 3 contains six of Chladai's circular figures. 



NOTE 185, p. 145. Mr. Wheatstone's principle is, that when vibra- 

 tions producing the forms of figs. 1 and 2, plate 3, are united in the same 

 surface, they make the sand assume the form of fig. 3. In the same 

 manner, the vibrations which would separately cause the sand to take the 

 forms of figs. 4 and 5, would make it assume the form in fig. 6 when 

 united. The figure 9 results from the modes of vibration of 7 and 8 com- 

 bined. The parts marked a a are in different states of vibration from 

 those marked b b. Figs. 1, 2, and 3, plate 4, represent forms which the 

 sand takes in consequence of simple modes of vibration ; 4 and 5 are those 

 arising from two combined modes of vibration ; and the last six figures 

 arise from four superimposed simple modes of vibration. These compli- 

 cated figures are determined by computation independent of experiment. 



NOTE 186, p. 146. The long cross-lines of fig. 46 show the two 

 systems of nodal lines given 

 by M. Savart's laminse. 



NOTE 187, p. 146. The 

 short lines on fig. 46 show 

 the positions of the nodal 

 lines on the other sides of 

 the same Iamina3. 



46 - 



NOTE 188, p. 146. 



Fig. 47 gives the nodal lines on a cylinder, with the paper rings that mark 

 the quiescent points. 



Fig. 47. 



