214 



THE REFRACTION OF SOUND. 



faster tliau at the line o of 07°, or the height of GOO feet ; and at this line 

 the same quantity faster than at the line ^9 of 64°, or the height of 900 

 feet. The result is that a vertical wave-front 900 feet deep would, at 

 the distance of one mile, be advanced at its lower part more than 51 feet 

 beyond its upper part, making an angle of about 3^°; and the corres- 

 ponding upward curvature of the lower sound-beams emanating from. 

 tn (the versed sine of this arc) would amount to about 150 feet. 



64" 



64c> 



670 



70O 



7=iO ! 1 



67° 



70^^ 



Fig. 5. — Thermal refraction. 



If the temperature of the lower strata of air were found to increase 

 only at half the rate above assumed, the lower sound-beams from m 

 would be lifted one hundred and fifty feet in about two miles. If the 

 differences of temperature were reduced to one-fourth, this amount of 

 upward tilt would be reached in about four miles, &c. 



From this it is apparent that temperature-refraction — the upward 

 " dishing" of the lower sheet of sound by the overheating of the lower 

 air — is not only a real phenomenon, but that in quantity it introduces 

 a very considerable amount of disturbance in the direction of sound, 

 and thus imi)airs seriously its audibility at any great distance on the 

 surface of the earth. 



In further illustration of the same i^rinciple, no less notable is the 

 converse effect of an excess of cooling in the lower strata, occasionally 

 noticed. Professor Keynolds, continuing his researches " On the re- 

 fraction of sound," during the summer of 1875, found that, on the 19th 

 of August, " after three weeks of cold and windy weather," the sea 

 and the adjacent air being chilled considerably below the average or 

 upper temperature, sound passing over the water reached the observers 

 in a boat with such remarkable clearness that " guns, and on one occa- 

 sion the barking of a dog, on the shore, eight miles distant, were dis- 

 tinctly heard, as were also the paddles of a steamer fifteen miles dis- 

 tant. The day was perfectly calm ; there was no wind; the sky was 

 quite clear, and the sun shining with great power." The significant 

 circumstance is recorded that " all the time distant objects loomed con- 

 siderably, i. e., appeared lifted." In this case, " the diminution in the 

 temperature of the air being downward, the sound instead of being 



