'Lord Rayleiglr's Acoustical Observations. 343 



concerned not with the relative, but with the absolute number 

 of beats executed in the given time. If we miscount the beats 

 in a minute by one, it makes just the same error in the result 

 whether the whole number of beats is 60 or 240. 



When the sounds are pure tones and are well maintained, 

 it is advisable to use beats much slower than four per second. 

 By choosing a suitable position we may make the intensities 

 at the ear equal ; and then the phase of silence, corresponding 

 to antagonism of equal and opposite vibrations, is extremely 

 well marked. Taking advantage of this, we may determine 

 slow beats with very great accuracy by observing the time 

 which elapses between recurrences of silence. In favourable 

 cases, the whole number of beats in the period of observation 

 may be fixed to within one tenth or one twentieth of a single 

 beat, a degree of accuracy which is of course out of the ques- 

 tion when the beats are quick. 



In some experiments conducted by Dr. Schuster and my- 

 self*, to determine the absolute pitch of a Konig standard 

 fork, I had occasion to observe some very slow beats. The 

 beating sounds were of pitch 128. One of them was steady, 

 proceeding from an electrically maintained fork; the other 

 (from the standard fork) gradually died away. In order to 

 be more independent of disturbing noises to which we were 

 exposed, a resonator was used connected with the ear by an 

 india-rubber tube. The standard fork was mounted at the 

 end of a wooden stick, so that it might not be heated by the 

 hand. As the vibrations became less powerful, the prongs of 

 the fork were caused slightly to approach the mouth of the 

 resonator, so as to maintain the equality of the two component 

 sounds. In this way it was possible to obtain very definite 

 silences, and to measure the interval of recurrence with accu- 

 racy. In one observation, extending over about two minutes, 

 the beat occupied as much as twenty-four seconds, and there 

 was no confusion. I have little doubt that even slower beats 

 might be observed satisfactorily if both components were 

 steadily maintained. 



Estimation of the Direction of Sounds with one ear. 

 In my former experiments (Phil. Mag. June 1877) I found 

 it difficult to obtain satisfactory observations with one ear 

 closed, although it was not doubtful that the power of estima- 

 ting directions was greatly curtailed. My desire to experi- 

 ment upon an observer deaf on one side has since been gratified 

 by the kind assistance of Mr. F. Galton. In January 1881 

 experiments were tried with him similar to those on normal 

 * Proc. Roy. Soc. May 5, 1881, p. 137. 

 2D2 



