of the Relative Intensities of Sounds. 9 



tirely reliable discussion of this relation, the problem will have 

 to be experimentally solved with the greatest care. If, however, 

 the relation between the intensities of pulses inside the tube and 

 those outside the mouth of the resonator shall be shown to be 

 different (and I think they will be) from what we, for illustration, 

 have here assumed, only the process of the numerical reduction of 

 the experiments will be modified, while the experimental method 

 remains secure. Indeed I cannot but consider that I have here, 

 by applying the principle of interference, so fertile in results in 

 optics, been the first to give an experimental method which will 

 determine with precision the relative intensities of two sonorous 

 vibrations producing the same note. 



Savart and many other experimenters have determined the 

 relative intensities of two sounds by placing sand or other light 

 particles on membranes and receding from the source of sound 

 until no motions of the particles were visible. Also Drs. Renz 

 and Wolf (Pogg. Ann. vol. xcviii. p. 595) give the results of 

 experiments on the determination with the ear of the intensity 

 of the sounds of a ticking watch. More recently Dr. Heller 

 (Pogg. Ann. vol. cxli. p. 566) has made an elaborate research 

 on the intensities of sounds, deducing mathematically his deter- 

 minations from the observed amplitudes of vibration of a mem- 

 brane; and Mr. Bosanquet (Phil. Mag. Nov. 1872) has just 

 published a paper in which he proposes, for the measure of the 

 intensities of sounds of pipes of different pitch, the determina- 

 tion of the quantity of air which each pipe consumes in sounding. 

 But all these experimenters acknowledge the want of precision 

 in their measures, and the difficulties in the actual practice of 

 their methods. 



When the resonators have such distances from their corre- 

 sponding sounding bodies that the phases of their impulses on 

 the membrane are opposed while their intensities are different, 

 a residual action is given ; and the intensity of this action on the 

 membrane will depend on the relative intensities of the sounding 

 bodies and the relative distances at which the resonators are 

 placed. It may here be interesting to consider the simplest 

 case, — that is, when the intensities of vibration at the two sources 

 of origin of the sounds are the same and the two resonators are 

 placed at various distances from these points of origin, but 

 always differ in their distances by one half wave-length. Let us 

 call A one of the resonators, B the other. Let A be successively 

 placed at distances from its sounding body equal to 1, 2, 3, &c. 

 wave-lengths, and B successively at distances equal to 1^, 2^, 

 3J, &c. wave-lengths. At each position of the resonators we 

 will suppose that the phases of vibration reaching the membrane 

 are opposed. The following Table gives the calculations made 



