266 Prof. A. M. Mayer's Researches in Acoustics. 



waves. If a second cord be attached to the other end of the 

 rod and waves be transmitted as before, the vibrations of the 

 rod set up waves in this cord which correspond in period and 

 length to those on the first cord, thus furnishing an illustration 

 of the reciprocity of radiation and absorption. 



The author has reason to think that, as nearly all the above- 

 described illustrations have been devised during- the last twelve 

 months, the method is capable of much further development and 

 greater perfection. 



XXXIX. Researches in Acoustics. — No. V.* 

 By Alfred M. Mayer f. 



1. An Experimental Confirmation of Fourier's Theorem as ap- 

 plied to the Decomposition of the Vibrations of a Composite 

 Sonorous Wave into its elementary Pendulum-vibrations. 



A SIMPLE sound is a sound which has only one pitch. Such 

 a sound is produced when, with a bow, we gently vibrate the 

 prongs of a tuning-fork and bring them near a cavity which re- 

 sounds to the fork's fundamental tone. An almost pure simple 

 sound can be obtained by softly blowing a closed organ-pipe. 

 On examining the nature of the vibratory motions of the 

 prongs of the forkj and of the molecules of air in the resound- 



* This paper is the fifth in the series of those on Acoustics already 

 published in the Philosophical Magazine. The preceding papers, however, 

 were not numbered. 



t Communicated by the Author, with corrections, from Silliman's Ame- 

 rican Journal for August 1874. 



Sections 1, 2, 3, 5, 6, and 7 of this paper were read before the National 

 Academy of Sciences during the Session of November 1873. Section 4 was 

 read before the Academy on April 21, 1874. 



\ In my course of lectures on Acoustics, I thus show to my students 

 that the prong of a tuning-fork vibrates like a pendulum : — I take two of 

 Lissajous's reflecting forks, giving, say, the major third interval, and with 

 them I obtain on a screen the curve of this interval in electric light. On 

 a glass plate I have photographed the above curve of the major third pas- 

 sing through a set of rectangular coordinates formed of the sines of two cir- 

 cles whose circumferences are respectively divided into 20 and 25 equal 

 parts. I now place this plate over the condensing-lens of a vertical lantern 

 and obtain on the screen the curve, the circles, and their net of coordinates. 

 Suspended over the lantern is a Blackburn's compound pendulum, which is 

 so constructed that its "bob " cannot rotate around its axis. The bob is 

 hollow, and a curved pipe leads from its bottom to one side of the pendulum. 

 The pendulum is now deflected into a plane at 45° with its two rectangu- 

 lar planes of vibration, so that the end of the curved pipe coincides with the 

 beginning of the curve over the lantern. The bob of the pendulum is fas- 

 tened with a fine cord in this position, and fine hour-glass sand is poured 

 into it ; the cord is now burned, and the sand is delivered from the pipe 

 as the swinging pendulum gives the resultant of its motions in the two 

 planes of vibration, while the photographed curve on the lantern is pro- 



