544 Prof. O. Reynolds on the 



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 obtained by taking the 

 extreme variations of temperature at the surface 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 distances. 



[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. Prom this point, however, the sound would become 

 rapidly fainter until it was lost. The extension which divergence would 

 thus add to the range of the sound would obviously depend on the re- 

 fraction that is to say, when the direct rays were last refracted upwards, 

 the extension of the range due to divergence would be greatest. It is 

 difficult to say what the precise effect of this divergence would be ; but we 

 may assume that it would be similar to that which was found in the case 

 of wind, only the refraction being so much smaller the extension of the 

 range by divergence would be greater. On the whole the. results calcu- 

 lated from the data furnished by Mr. Grlaisher agree in a remarkable 

 manner with those observed ; for if we add | mile for the extension of 

 the range by divergence, the calculated distance with a clear sky would 

 be two miles from a cliff 235 feet high. September 1874.] 



Now Prof. Tyndall found that from the cliffs at the South Foreland, 

 235 feet high, the minimum range of sound was a little more than 

 2 miles, arid that this occurred on a quiet July day with hot sunshine. 

 The ordinary range seemed to be from 3 to 5 miles when the weather 

 was dull, although sometimes, particularly in the evening, the sounds 

 were heard as far as 15 miles. This was, however, only under very ex- 

 ceptional circumstances. Prof. Tyndall also found that the interposition 

 of a cloud was followed by an almost immediate extension of the range 

 of the sound. I extract the following passages from Prof. Tyndall's 

 Beport : 



" On June 2 the maximum range, at first only 3 miles, afterwards ran 

 up to about 6 miles. 



" Optically, June 3 was not at all a promising day ; the clouds were 

 dark and threatening, and the air filled with a faint haze ; nevertheless 

 the horns were fairly audible at 9 miles. An exceedingly heavy rain- 

 shower approached us at a galloping speed. The sound was not sensibly 

 impaired during the continuance of the rain. 



"July 3 was a lovely morning : the sky was of a stainless blue, the air 

 calm, and the sea smooth. I thought we should be able to hear a long 

 way off. We steamed beyond the pier end and listened. The steam- 

 clouds were there, showing the whistles to be active ; the smoke-puffs 





