212 THE REFRACTION OF SOUND. 



wave-face backward that a line perpendicular to it would have an up- 

 ward direction of about 2° 21'; or, an arc described with a radius of 

 24.39 miles would represent approximately the upward curvature of a 

 horizontal sound-beam, whereby at the distance of a mile it would be 

 lifted up about 108 feet. A wave-front of sound moving in the direction 

 of the wiud would, of course, be correspondingly accelerated above, 

 and the beam bent downward in a similar arc. 



A wiud blowing along the face of an extended bluff or cliff, being re- 

 tarded near the same by friction, would, in a similar manner, cause a 

 sound originating near it to be laterally refracted toward the wall in 

 the direction of the wind, and from it in the opposite direction. 



When, from any cause, the upper wiud should move more sluggishly 

 than the lower wiud, as sometimes occurs, the lines of refraction above 

 indicated would be reversed, and we should have the exceptional case 

 of sound being favored by an opposing wind, and vice versa. 



This very simple principle of vental refraction has thus a wide prac- 

 tical range, and the variety of its applications is limited only by that 

 of the actual differences in force and direction of the winds. In short, 

 in the case of any divergence between the upper and lower currents, in 

 whatever direction, there will be but two lines of no refraction. In all 

 other directions, a positive or a negative resultant must to some degree 

 disturb the direction of the acoustic ray. 



In consequence of the slight internal friction (or " viscosity ") of air, 

 the shadow-line is not usually very sharply defined. Wave-impulses act- 

 ing laterally on the adjacent air cause the sound to be feebly heard within 

 the shadow-line ; and the sound-beam is thus practically diffracted 

 around an obstacle to an extent which is probably some function of its^^ 

 intensity or energy. The effect of this, in the case of a refracted beam, 

 is to diminish somewhat its apparent curvature, and thus to render an 

 uplifted sound sensible to a greater distance than it would be on a merely 

 geometrical theory, or without such marginal diffusion. 



From the same cause the following practical results follow : 1st. A 

 continuous sound, as of a horn or steam-whistle, requires at a distance 

 a short but appreciable interval (a second or more) to be heard with its 

 full power; 2d. Hence, with adverse winds^j sounds of single impulse,^ 

 as those of bells and guns, are more refracted than continuous sounds, 

 whose initial impulses are re-enforced by rhythmic successions, giving 

 them greater persistence of force and direction ; 3d. It is unnecessary to 

 add that sounds under such circumstances (with beams of convex cur- 

 vature) can be heard to a greater distance w hen originating from an ele- 

 vation, and also when observed from an elevation ; 4th. It is probable 

 that sounds of high pitch are more refracted than medium tones and 

 those of lower pitch. 



3. — REFRACTION FROM INEQUALITY OF TEMPERATURE. 



In 1874, Prof. Osborne Reynolds pointed out a third practical cause of 

 acoustic refraction in the differences of temperature to which advancing 



