490 



NOTES. 



straight lines are the strings when at rest. The first figure of the four would 

 give the fundamental note, as, for example, the low C. The second and third 

 figures would give the first and second harmonics ; that is, the octave and the 

 12th above C,nnn being the points at rest; the fourth figure shows the real 

 motion when compounded of all three. 



NOTE 177, p. 159. Fig. 45 represents sections of an open and of a shut pipe, 

 and of a pipe open at one end. When sounded, the air spontaneously divides 

 itself into segments. It remains at rest in the divisions or nodes n ri, &c., but 



Fig. 45. 



vibrates between them in the direction of the arrow-heads. The undulations 

 of the whole column of air give the fundamental note, while the vibrations of 

 the divisions give the harmonics. 



NOTE 178, p. 161. 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 different states of 

 vibration from those marked b b. 



NOTE 179, p. 162. 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 vibra- 

 tion, corresponding to musical notes of different degrees of pitch. Plate 3 

 contains six of Chladni's circular figures. 



NOTE 180, p. 163. Mr. Wheatstone's principle is, that when vibrations pro- 

 ducing 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 combined. The parts marked a a are in different 

 states of vibration from those marked b 6. 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 complicated figures are determined by computation independent of ex- 

 periment. 



