produced by Vibrating Bodies. 33 



Vibrating strings present analogous pluenomena. 



Let us suppose that the string vibrated produces the funda- 

 mental tone with energy, and gives the harmonics only in a 

 slightly perceptible manner. Two very distinct images are then 

 seen in the extreme positions A^wB, p. 



A?«'B, fig. 3 ; these images are vi- ^' 



sible at the very places where the 

 velocity of the string is null or ex- 

 tremely small, in comparison with 



that by which it is affected when it traverses the intermediate 

 positions. 



If the bow is drawn so as only to give the octave of the 

 fundamental sound, two equal spindles are seen placed one 

 after the other, and each one giving two images of the string in 

 the positions where the velocity is annulled, as in AwM, Aw'M, 

 M;jB, M^B, fig. 4. These ap- 

 pearances are the immediate con- Fig. 4-. 

 sequence of the division of the 

 string into two distinct parts ^^ 

 which vibrate separately. ^ 



If the fundamental tone be drawn from the string and at the 

 same time its octave, so that these two sounds are ver}^ power- 

 ful in comparison with the other harmonics, which we will 

 suppose to be very weak, four images of the string are then 

 seen arranged as indicated in the figure. According to the 

 explanation commonly admitted of multiple sounds, whilst the 

 whole string vibrates, its two halves themselves vibrate, taking 

 contrary curves. Hence it follows, that when the string quits 

 the position AB, fig. 5, to take ^. 



the direction toward the curve '^' 



AaC6B,thefirsthalfofthestring " ^ 



AC will present its concavity, 

 for example, at AB, and the se- 

 cond half, CB, its convexity. Duringthis transfer, the velocities 

 of the different points of the string will tend to disappear 

 successively: the curve AaCiB is the spot which the different 

 points of the string attain when their velocity becomes null. 



After curving, as we have pointed out, the string will assume 

 opposite curves, and will then return in the direction of the 

 primitive curves, and so o!i. During these variations of form, 

 the points of the string will pass from the position AaCt'B to 

 the position AeC/B, where their velocity will be successively 

 annulled, then to the position AgH^B, where the velocities 

 are still null, then to the position AwHwB, where these velo- 

 cities become null for the fourth time; nnd lastly, they will 

 return to the position AaCfiB, where the velocities were first 



Phil. Man. S. 3. Vol. 36. No. 240. Jan. 1850. D 



