Prof. A. M. Mayer's Researches in Acoustics* 267 



ing cavity* and in the closed organ-pipe f, we find that each of 

 these vibrations follows the same law of reciprocating motion 

 as governs the vibrations of a freely swinging pendulum. But 

 other bodies, for instance the free reeds of organ-pipes and of 

 melodeonst, vibrate like the pendulum ; yet we can decompose 

 the vibrations they produce in the air into many separate pen- 

 dulum-vibrations, each of which produces in the air a simple 

 sound of a definite pitch. Thus we see that a pendulum-vi- 

 brating body, when placed in certain relations to the air on 

 which it acts, may give rise to highly composite sounds. It is 

 therefore evident that we cannot always decide as to the simple 

 or composite character of a vibration reaching the ear solely 

 from the determination of the motion of the body originating 

 the sound, but we are obliged to investigate the character of the 

 molecular motions of the air near the ear, or of the motion of a 

 point on the drum of the ear itself, in order to draw conclusions 

 as to the simple or composite character of the sensation which 

 may be produced by any given vibratory motion. Although we 

 cannot often detect in the ascertained form of an aerial vibration 

 all the elementary pendulum-vibrations, and thus predetermine 

 the composite sensation connected with it, yet if we find that 

 the aerial vibration is that of a simple pendulum, we may 

 surely decide that we shall receive from it only the sensation 

 of a simple sound. Thus, if we arm the prong of a tuning- 

 fork with a point, and draw this point on a lamp-blackened 

 surface with a uniform motion and in a direction parallel to 

 the axis of the fork, we shall obtain on the surface a sinusoidal 

 or harmonic curve § ; and this curve can only be produced 

 by the prongs of the fork vibrating with the same kind of 



gressively covered with the sand if the times of the two vibrations of the 

 pendulum are to each other as 4 to 5. 



* Helmholtz, Tonempfindungen, 1857, p. 75. Crelle's Journ. fur Math., 

 vol. lvii. 



t See Mach's Optisch-akustische Versuche, Prag, 1873, p. 91. Die 

 Stroboshopische Darstellung der Luftschwingungen. 



X The Rev. S. B. Dod, one of the trustees of the Stevens Institute, has 

 recently made an experiment which neatly shows this : — He silvered the 

 tips of two melodeon-reeds, and then vibrated them in planes at right angles 

 to each other, while a beam of light was reflected from them. The resul- 

 tant figure of their vibrations is the same as that obtained by two Lissajous's 

 forks placed in the same circumstances and having the same musical inter- 

 val between them as that existing between the reeds. 



-c—4" a ) • The length, on the 



axis, of one recurring period of the curve is X ; the constant a is the maxi- 

 mum ordinate or amplitude. The form of the curve is not affected by a ; 

 but any change in its value slides the whole curve along the axis of .r." It 

 is interesting to observe that this curve expresses the annual variation of 

 temperature in the temperate zones. 



