951 
the results for October 8*> are very much in favour of that explanation. 
When pe QUPRVAIN') maintains, that even in this case the proof 
has not been given that the silent region shows a circular form, 
this can only refer to the absence of reporis from the southern 
battlefields. But he forgets to remark that already the semi-circular 
form following from the reports obtained, nay, even a circular form 
over 90°, comes into conflict with what ought to be expected in 
the case of a wind influence, sufficient to make the sounds return 
to the earth at 160 KM. distance from the source. 
As may appear from what precedes, we are of opinion, that the 
two explanations of the silent region, which we shall call for the 
sake of brevity the physical and the meteorological explanation, are 
both true and ought to be applied in combination. The question then 
arises: how is the path of the rays changed speaking generally, e.g. 
in case g, when the air is not at rest or large irregularities of the 
temperature gradient occur? 
We leave on one side at this moment the rays, starting with a small 
elevation, which will contribute most to the audibility in the first 
region, and shall concentrate our attention on the rays in the neigh- 
bourhood of 25° zenithdistance, which reach the surface again at 
the border of the silent region. Secondly we have in mind, that 
disturbances by wind and temperature will be confined almost wholly 
to the first 10 KM., at least in the temperate zone; in the strato- 
sphere no great variations of wind or temperature occur. Then we 
may also perceive, without going into details, that even very heavy 
disturbances in the lower strata can exert only little influence on 
the position of the silent region. E.g. if we take an increase of wind 
of 0.5 M. per 100 M., as pr QvERVAIN assumes in his case, then the 
velocity of sound at 10 KM. height is increased by 50 M. for 
horizontal propagation in the direction of the wind, but only by 
30 sin 25° or 21 M. for a ray of about 25° zenithsdistance. The 
velocities of sonnd in case y at the height of 10 KM. are thus 
changed in the proportion 1: 1.07, which changes the elevation there 
only from 22°37’ into 24°13’. Nevertheless this might have a rather 
great influence on the limit of the silent region, were it not that 
for the further propagation the rôle of the ray with initial angle 
of 25° is taken up by the ray, which starts with 23° 30’ and enters 
the stratosphere at an angle of 22°37’. The entire change in the 
total horizontal path of the rays with minimum distance will hence 
1) Die Umschau, 19, No. 27, 1915. Here a case of a very widespread audibility 
of roar of cannons in the Sundgau on December 25th 1914 is described, in which 
the propagation is rather unsymmetrical and the silent region of little importance. 
