64 Royal Society : — Prof. Reynolds on 



8 feet, and smaller still compared with what it is at greater 

 heights. 



To understand the way in which this variation in the velocity 

 affects the sound, it is necessary to consider that the velocity of 

 the waves of sound does depend on the velocity of the wind, 

 although not in a great degree. To fiud the velocity of the sound 

 with the wind we must add that of the wind to the normal velo- 

 city of sound, and against the wind we must subtract the velocity 

 of the wind from the 1100 feet per second (or whatever may be 

 the normal velocity of the sound) to find the actual velocity. 

 Now, if the wind is moving at 10 feet per second at the sur- 

 face of a meadow, and at 20 feet per second at a height of 8 feet, 

 the velocity of the sound against the wind will be 1090 feet 

 per second at the surface and 1080 feet per second at 8 feet 

 above the surface ; so that in a second the same wave of sound 

 will have travelled 10 feet further at the surface than at a height 

 of 8 feet. This difference of velocity would cause the wave to tip 

 up and proceed in an upward direction instead of horizontally. 

 For if we imagine the front of a wave of sound to be vertical to 

 start with, it will, after proceeding for one second against the wind, 

 be inclined at an angle of more than 45°, or half a right angle ; and 

 since sound-waves always move in a direction perpendicular to the 

 direction of the front (that is to say, if the waves are vertical they 

 will move horizontally and not otherwise), after one second the 

 wave would be moving upwards at an angle of 45° or more. Of 

 course, in reality, it would not have to proceed for one second 

 before it began to move upwards : the least forward motion would 

 be followed by an inclination of the front backwards, and by an 

 upward motion of the wave. A similar effect would be produced 

 in a direction opposite to that of the wind, only as the top of the 

 wave would then be moving faster than the bottom, the waves 

 would incline forwards and move downwards. In this way the 

 effect of the wind is to lift the waves which proceed to wind- 

 ward, and to bring those down which move with it. 



Thus the effect of wind is not to destroy the sound, but to raise 

 the ends of the wave, which would otherwise move along the ground, 

 to such a height that they pass over our heads. 



When the ends of the waves are raised from the ground they 

 will tend to diverge down to it, and throw off secondary ivaves, or, 

 as I shall call them, diverging waves, so as to reconstitute the gap 

 that is thus made. These secondary waves will be heard as a 

 continuation of the sound, more or less faint, after the primary 

 waves are altogether above our heads. [This phenomenon of di- 

 vergence presents many difficulties, and has only as yet been dealt 

 with for particular cases. It may, however, be assumed, from 

 what is known respecting it, that in the case of sound being lifted 

 up from the ground by refraction, or, what is nearly the same 

 thing, passing directly over the crest of a hill so that the ground 

 falls away from the rays of sound, diverging waves would be 

 thrown off very rapidly at first and for a considerable distance, de- 



