the Refraction of Sound by the Atmosphere. 73 



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 ex- 

 poses the fallacies of several theories advanced to account for it. 

 Amongst others there are some remarks by Humboldt, in which 

 he says that the difference 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 differ- 

 ence of 1 degree in the 100 feet would cause the rays of sound, 

 otherwise horizontal, to move on a circle, the radius of which by 

 the previous rule =1100 . J^-2-= 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 eleva- 

 tion 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 diverging sound would be audible. From an elevation of 

 15 feet, however, the direct sound might be heard to a distance of 

 •36, or ^ mile further, so that in all it could be heard 1*72 (l|)mile. 



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

 sound would be heard to 2-4 miles from an elevation of 15 feet, or 1*4 

 times what it is with the clear sky. These results have been ob- 

 tained by taking the extreme variations of temperature at the sur- 

 face of the earth. At certain times, however, in the evening, or 

 when it was raining, the variation would be much less than this, in 

 which case the direct sound would be heard to much greater dis- 

 tances. 



[So far I have only spoken of the direct or geometrical rays of 

 sound, that is, I have supposed the edge of the sound to be definite, 

 and not fringed with diverging rays ; but, as has been already 

 explained, the sound would diverge downwards, and from this cause 

 would be heard to a considerable distance beyond the point at which 

 the direct rays first left the ground. From this point, however, 

 the sound would become rapidly fainter until it was lost. The 



