NOTES. 



419 



or water, diverge in all directions from their origin I, fig. 43, as from a 

 center. When they meet with an obstacle 8 S, they strike ngainst it, 

 and are reflected or turned back by it in the same form, as if they had 

 proceeded from the center C, at an equal distance on the other side of 

 the surface SS. 



NOTE 175, p. 132. Elliptical shell. If fig. 6 be a section of an ellip- 

 tical shell, then all sounds coming from the focus S to different points 

 on the surface, as TO, are reflected back to F, because the angle T m 8 

 is equal to imF. In a spherical hollow shell, a sound diverging from 

 the center is reflected back to the center again. 



NOTE 176, p. 136. Fig. 44 represents musical strings in vibration ; the 

 Fig. 44. 



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 of rest; the 

 fourth figure shows the real motion when compounded of all three. 



NOTE 177, p. 137. Fig. 45 represents sections of an open and of a shut 

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

 sly divides itself into segments. . It remains at rest in the divisions 



or nodes nn'.&c., but 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 har- 

 monics. 



NOTE 178, p. 139. 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. 



