C. GENERAL PHYSICS. 189 



perature of the air must produce this effect; for every de- 

 gree of temperature between 32 and 70 adds nearly one 

 foot per second to the velocity of sound. Mr. Glaisher's bal- 

 loon observations show that when the sun is shining with a 

 clear sky the variation from the surface is 1 Fahr. for every 

 hundred feet, and that with a cloudy sky 0.5, or half what 

 it is with a clear sky. Hence it is shown that "rays" of 

 sound, otherwise horizontal, will be refracted upward in the 

 form of circles, the radii of which are 110,000 feet with a 

 clear sky and 220,000 with a cloudy sky that is to say, 

 the refraction on bright, hot days will be double what it is 

 on dull days, and still more under exceptional circumstances, 

 and comparing day with night. 



It is then shown by calculation that the greatest refrac- 

 tion (110,000 radius) is sufficient to render sound from a cliff 

 235 feet high inaudible on the deck of a ship at one and 

 three fourths of a mile, except such sound as might reach the 

 observer by divergence from the waves passing over his 

 head ; whereas when the refraction is least (220,000 radius) 

 that is, when the sky is cloudy the range would be extend- 

 ed to two and a half miles, w T ith a similar extension for the 

 diverging waves, and under exceptional circumstances the 

 extension would be much greater. It is hence inferred that 

 the phenomenon which Professor Tyndall observed on the 

 3d of July and other days (namely, that when the air was 

 still and the sun was hot he could not hear guns and other 

 sounds from the cliffs, 235 feet high, more than two miles, 

 whereas when the sky was clouded the range of the sounds 

 was extended to three miles, and, as evening approached, 

 much farther) was due, not to the stoppage or reflection of 

 the sound by clouds of invisible vapor, as Professor Tyndall 

 has supposed, but to the sounds being lifted over his head 

 by refraction in the manner described ; and that, had lie 

 been able to ascend thirty feet up the mast, he might at any 

 time have extended the range of the sounds by a quarter of 

 a mile at least. 



THE MECHANICAL EQUIVALENT OF SOUND. 



In paper No. 7 of his " Researches in Acoustics," Pro- 

 fessor Mayer gives an experimental research on the deter- 

 mination of the mechanical equivalent of a given sound. 



