Refraction of Sound by the Atmosphere. 543 



" When the sky was partially cloudy the decline of temperature 



In the first 100 feet was 0-9 



* * * * 



From 2900 to 5000 0-3 for every 100 feet. 



" The decline of temperature near the earth with a partially clear sky 

 is nearly double that with a cloudy sky. 



" In some cases, as on July 30th, the decline of temperature in the first 

 100 feet was as large as 1-1." 



We may say, therefore, that when the sky is clear the variation of 

 temperature as we proceed upwards from 1 to 3000 feet will be more 

 than double what it is when the sky is cloudy. And since for such small 

 variations the variation in the velocity of sound, that is the refraction, is 

 proportional to the temperature, this refraction will be twice as great with 

 a clear sky as when the sky is cloudy. 



This is the mean difference, and there are doubtless exceptional cases 

 in which the variations are both greater and less than those given; during 

 the night the variations are less than during the day, and again in winter 

 than in summer. 



This reasoning at once suggested an explanation of the well-known 

 fact that sounds are less intense during the day than at night. This is a 

 matter of common observation, and has been the subject of scientific 

 inquiry. F. De La Roche discusses the subject, and exposes the fal- 

 lacies of several theories advanced to account for it. Amongst others 

 there are some remarks by Humboldt, in which he says that the dif- 

 ference is not due to the quietness of the night, for he had observed 

 the same thing near the torrid zone, where the day seemed quieter than 

 the night, which was rendered noisy with insects. 



It is, however, by the experiments of Prof. Tyndall that this fact has 

 been fully brought to light; and from their definite character they afford 

 an opportunity of applying the explanation, and furnish a test of its 

 soundness. 



Neglecting the divergence of the bottom of the waves, a difference of 

 1 degree in the 100 feet would cause the rays of sound, otherwise hori- 

 zontal, to move on a circle, the radius of which by the previous rule 

 = 1100 . 4Jp.= 110,000 feet. A variation of one half this would cause 

 them to move on a circle of 220,000 feet radius. From the radii of these 

 circles we can calculate the range of the sound from different elevations. 



With a clear sky, i. e. with a radius 110,000 feet from an elevation of 

 235 feet, the sound would be audible with full force to 1*36 mile ; the 

 direct sound would then be lifted above the surface, and only the di- 

 verging sound would be audible. From an elevation of 15 feet, however, 

 the direct sound might be heard to a distance of *36, or 3 mile further, 

 so that in all it could be heard 1-72 (1|) mile. 



With a cloudy sky, i. e. with a radius 220,000 feet, the direct sound 



