46 REPORT — 1876. 



attaching a vibrating portion of it to tuning-forks, was discussed. It was shown 

 that the mode of transmission is such as to lead to transformation, whereby the 

 analysis is vitiated. 



Mr. J. B.iillie Hamilton's experiment, in which an harmouium-reed is made to 

 support the vibrations of a wire sounding its harmonics without actual attachment, 

 was shown to be a case of transformation. 



The production of harmonics by resonance from the Jew's harp or harmonium- 

 reeds without wind was discussed ; and it was shown that they may be regarded 

 as giving rise to discontinuous impulses at the moment when they close the open- 

 ings in which they fit. 



It was then shown how a series of discontinuous impulses may be expressed 

 mathematically ; and from the fact that the expressions involve pendulum-vibrations 

 corresponding to the harmonics, it was shown to follow that harmonic vibrations 

 may be excited by such a series of impulses. 



The nature of the modification the expressions require for application to the siren 

 was pointed out, and it was thus explained how the siren tone comes to involve 

 harmonics of considerable intensity. 



We now come to the problem of transformation of simple-sound vibrations by 

 transmission through air. 



An experiment was described in which a large tuning-fork was presented to a 

 series of resonators (organ-pipes) tuned to its harmonics ; the result was that, ^vitll 

 the fork aj^ue, they were audible up to the tierce inclusive (harmonic of lifth order), 

 and with a disk of wood fastened on to the prong they were audible up to the 

 harnionic seventh inclusive. 



A mathematical investigation of the transformation of simple vibrations in air 

 was then cai'ried out, and applied to the above experiment. It results that for the 

 fiftli harmonic of the fork, which was clearly heard, the flow of energy should be 

 approximately 



;- — — -— foot pounds per second, 

 2x10'" ^ ^ 



This seeming extraordinarily minute, an experiment was made with a small tuning- 

 fork of about the same pitch as the fifth harmonic above mentioned. The time of 

 diminution of the amplitude to -^-^ was observed and the initial amplitude. From 

 this the amplitude was calculated at the subsequent time when the sound just 

 ceased to be audible. The flow of energy per second at this point was estimated 

 approximately at 



4^^ foot pounds, 



which agrees pretty well with the above number deduced from theory. 



It was then pointed out tliat the intensity due to a given flow of energy is diffe- 

 rent in different parts of the scale. Helmholtz has remarked this (p. 264 of Ellis's 

 Helraholtz) ; and, in a paper in the 'Philosophical Magazine' (Nov. 1872), the writer 

 showed that, if we admit that in similar organ-pipes similar proportions of the 

 energy of the wind supplied are converted into sound, the mechanical energy of 

 notes of given intensity varies inversely as the vibration number, a law in accordance 

 with the indications given by Helmholtz. 



The theory was then applied to ascertain the extent of the development of har- 

 monics in a tubular resonator tuned to the fundamental. Such development turns 

 out to be very considerable. In consequence of this we cannot generally assume 

 that the notes produced by resonators are simple tones. The bearing of this on a 

 recent important paper of KcEuig's was alluded to. 



True Intonation, illustrated by the Voice-Barmonium with, Natural Finger^ 



board. By Colin Brown. 



A series of harmonics forms an arithmetical progi-ession, the number of the 

 vibrations between any consecutive members of the series being equal. The vibra- 

 tions rapidly increase in velocity in the higher harmonics, while the musical inter- 



