70 Scientific Intelligence. 



the rate at which the vibrations of the fork die down (say to one : 

 half). In this way the distance of audibility may be reduced to 

 30 metres, and the results are less liable to be disturbed by 

 atmospheric irregularities. If s be the proportional condensation 

 in the waves which are just capable of exciting audition, the 

 results may be expressed : 



c frequency = 256 s = 6*0 X lCr 9 



cj " = 384 s = 4-6 X 10~ 9 



c" " =512 s — 4-6 X 10~ 9 



showing that the ear is capable of recognizing vibrations which 

 involve far less changes of pressure than the total pressure out- 

 standing in our highest vacua. 



In such 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 kilometers! 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 ex- 

 cess 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 doubt- 

 less to be found principally in atmospheric refraction due to vari- 

 ation 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 atmosphere 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 pitch of moving one of the coils so as to vary the self- 

 induction was very apparent. — Royal Institution of Great Brit- 

 ain^ April 9, 1897. 



