936 
to curve upwards from the earth. Hence each ray, which deviates 
ever so little from the horizontal direction, will depart faster and 
faster from the earth, and that is the reason for the relatively low 
audibility of sounds in the free air under normal conditions. A wind 
e. g. from the SW., increasing upwards, may counteract this tem- 
perature-effect, and lead to an increase upwards of the velocity of 
sound for propagation in north-easterly direction — the sound-rays 
are curved towards the earth: with a linear variation of the velo- 
city of sound the radius of curvature in each point of the orbit is 
7. 
Bes if V, means the velocity of sound in the summit of the orbit 
c 
and ¢ the variation in velocity per unit of length. The sound may 
then return to the earth up to great distances in north-easterly 
direction, after a path through the atmosphere with small frietion 
and relatively small loss of intensity. 
If we then suppose, that at a certain height the increase of wind- 
velocity ends or changes in a decrease, (resp. that the SW.-wind 
changes into a NW.-wind or into a wind of still more northerly 
direction), then the ray, the summit of which just lies at that height, 
will be the last to return to the earth. A slightly steeper ray is 
curved upwards above this level and cannot return to the earth 
for the next future. If we assume at a greater height another in- 
crease of the wind from the SW., then once more a curvature 
towards the earth may be found and at great distances the ray 
may reach the earth. 
Towards the SW. the curvature of the ray from the earth is 
increased by a SW.-wind. Hence very little sound will reach the 
earth there. But if at a higher level a strong wind from NE. occurs, 
then a second region of audibility may be found at a greater distance. 
For a direction perpendicular to that of the wind as a first approxi- 
mation no change in the normal propagation is found. 
From a theoretical standpoint little can be opposed to this mode 
of explanation; the suppositions as to the increase of wind with 
height, which have been made, are sometimes to be regarded as 
not improbable. But we know of no case, where, on the basis of 
measurements or even estimates of windvelocity at great height above 
the place of observation the proof was obtained, that the peculiari- 
ties of the propagation of sound may be explained entirely by the 
variations of wind. 
§ 3. An entirely different aspect was opened by Von prem Bornr’s *) 
supposition, that the appearance of silent regions ought to be ascribed, 
1) Physikalische Zeitschrift, 11 p. 483, 1910. 
