216 Lord Uayleigh on, our 



sphere at which the intensity is to be reckoned. F + iG 

 denotes the (complex) condensation, and F 2 -fG 2 the intensity. 

 In the present question of a sound situated say to the right 

 of the observer, the intensity at the right ear corresponds to 

 /a=+1, and at the left ear to /-<,= — 1. In the case of the 

 head the circumference (2itc) may be taken at about 2 feet 

 or a little less, so that 27rc/\ = J corresponds about to middle c, 

 or frequency 256. It will be seen that the difference of inten- 

 sities for fi= + l is only about 10 per cent, of the whole 

 intensity. 



For still smaller values of 27re/\, i. e. in the present appli- 

 cation for still graver notes, the difference of intensities may 

 be adequately expressed by a very simple formula. It appears 

 that 



(F^ + G^.^-tP + G^^^K 2 ^) 4 , 



while at the same time the total value of F 2 + G 2 approximates 

 to *25. A fall in pitch of an octave thus reduces the differ- 

 ence of intensities lb' times. At frequency 128 the difference 

 would be decidedly less than one per cent, of the whole; 

 and from this point onwards it is difficult to see how the 

 difference could play any important part. 



So far as I am aware no explanation of the above difficulty, 

 emphasised in 1876, has been arrived at. A few months 

 since I decided to repeat, and if possible to extend, the 

 observations, commencing with frequency 128. Two forks 

 of this pitch were mounted in the open air at a considerable 

 distance apart, and v\ere electrically maintained, one driving 

 the other. In connexion with each was a resonator which 

 could be put out of action by interposing (without contact) 

 the blade of a knife or a piece of card. An observer with 

 eyes closed, placed between the two forks and so turned as to 

 have them upon his right and his left, could tell with cer- 

 tainty which resonator was in action. The ears may be open 

 all the time; or, what is in some respects better, they may be 

 closed while the changes at the resonators are being made, 

 and afterwards opened simultaneously. If one ear be opened, 

 the sound will appear to be on that side ; but when the second 

 ear is also opened, the sound assumes its correct position, 

 whether or not this involves a reversal of the earlier judgement. 

 When the sounds were in front and behind, instead of to the 

 right and the left, several observers agreed that a discrimi- 

 nation between front and back could not be made. 



In another method of experimenting a single resonator and 

 fork (which need not be electrically maintained) suffice, but 



