418 Lord Bayleigh on the Limits of Audition. [April 9, 



In sucli experiments the whole energy emitted is very small, and 

 contrasts strangely with the 60 horse-power thrown into the fog- 

 signals of the Trinity House. If we calculate according to the law of 

 inverse squares how far a sound absorbing 60 horse-power should be 

 audible, the answer is 2700 kilometres ! The conclusion plainly 

 follows that there is some important source of loss beyond the mere 

 diffusion over a larger surface. Many years ago Sir George Stokes 

 calculated the effect of radiation upon the propagation of sound. His 

 conclusion may be thus stated. The amplitude of sound propagated 

 in plane waves would fall to half its value in six times the interval 

 of time occupied by a mass of air heated above its surroundings in 

 cooling through half the excess of temperature. There appear to be 

 no data by which the latter interval can be fixed with any approach 

 to precision ; but if we take it at one minute, the conclusion is that 

 sound would be propagated for six minutes, or travel over about 

 seventy miles, without very serious loss from this cause. 



The real reason for the falling off at great distances is doubtless 

 to be found principally in atmospheric refraction due to variation of 

 temperature, and of wind, with height. In a normal state of things 

 the air is cooler overhead, sound is propagated more slowly, and a 

 wave is tilted up so as to pass over the head of an observer at a 

 distance. [Illustrated by a model.] The theory of these effects has 

 been given by Stokes and Reynolds, and their application to the 

 explanation of the vagaries of fog signals by Henry. Progress would 

 be promoted by a better knowledge of what is passing in the atmo- 

 sphere over our heads. 



The lecture concluded with an account of the observations of 

 Preyer upon the delicacy of pitch perception, and of the results of 

 Kohlrausch upon the estimation of pitch when the total number of 

 vibrations is small. In illustration of the latter subject an experi- 

 ment (after Lodge) was shown, in which the sound was due to the 

 oscillating discharge of a Leyden battery through coils of insulated 

 wire. Observation of the spark proved that the total number of 

 (aerial) vibrations was four or five. The effect upon the jiitch 

 of moving one of the coils so as to vary the self-induction was 

 very apparent. 



