602 Lord Rayleigh on the Relation of the 



that for equal audibility at distances in the ratio of 2 : 1 the 

 radial amplitude of the larger can required to be 4*0 times 

 that of the smaller. Equal aerial condensations at the points 

 of observation require amplitudes in the ratio of 2 : \, from 

 which we infer that for equal audibilities the condensation 

 needed at pitch 128 is the double of that needed at pitch 256. 

 In like manner observations with another pair of cans showed 

 that the condensation needed at 256 was 1*6 of that needed at 

 512 vibrations per second. It did not appear feasible by 

 this method to go to higher pitch, but the range could be 

 extended at the other end. For this purpose the largest can 

 already spoken of was constructed, whose dimensions relatively 

 to the 128 can were as 3 : 2. In this case the interval was a 

 Fifth, and the comparison showed that the condensation 

 necessary for audibility at 85 per second was almost pre- 

 cisely the double of that needed at pitch 128. So far no 

 interval had been attempted exceeding the octave ; but sub- 

 sequently confirmation was obtained by a direct comparison 

 between the cans vibrating 256 and 85 per second. With 

 large intervals the difficulties are increased, as the amplitude 

 of the smaller can is too minute for satisfactory measurement 

 under the microscope. 



Since the numbers have merely a relative value, we may 

 call the condensation necessary for audibility at pitch 512 

 unity. The results are then summarized in the accompanying 

 statement. It was rather to my surprise that I found my 



N | 512 



s l'O 



256 

 1-6 



128 

 3-2 



85 

 6-4 



former conclusion as to the small variation of sensitiveness in 

 the octave 256 — 512 substantially confirmed. Below 256 and 

 especially below 128, it is evident that the sensitiveness of 

 the ear falls off more rapidly ; but even here the differences 

 appear much less than those calculated by Wien from his 

 own observations. I am much at a loss to explain the 

 discrepancy. Although doubtless criticisms may be made, 

 I should have supposed that both methods were good enough 

 to yield fairly approximate results. 



To give a general idea of the trend, a plot of the values of s 

 is given in fig. 2, the logarithm of the periodic time being 

 taken as abscissa. It would appear that the minimum s, 

 corresponding to maximum sensitiveness of the ear, would 

 not be reached under 1024 vibrations per second, and perhaps 



