935 
5. (Fig. 7). The explosion of the gunpowder-magazine at Wiener- 
Neustadt on June 7 1912 (200.000 KG.), investigated by J. N. Dorr’). 
Here the inner region of audibility is developed almost exclusively 
eastward and extends there to 120—140 KM., neglecting isolated 
reports; the outer region lies exclusively on the westside, where it 
forms almost half a circle, beginning at 160 KM. and reaching so 
far as 300 KM. 
For want of space in Figs. 2, 3 and 4, here and there a group 
of reports is indicated by a single cross and a number; the same occurs 
in Fig. 7, on account of the mode of representation chosen by Dorr. 
§ 2. Part of the irregularities in the propagation of sound in the 
above cases can be accounted for by the nature of the surface. The 
propagation mostly in one direction, so far as the inner region is 
concerned, may sometimes be easily explained by the presence of 
mountains, which prohibit propagation in a definite direction. 
Besides, it is long since the theory in elementary form was 
proposed, which ascribes the abnormal propagation of sound to the 
influence of variations in temperature and wind-velocity in the 
superposed layers of air in the atmosphere. Usually the starting 
point has been the supposition, that the velocity of sound in moving 
air is equal to the vector-sum of the velocity of sound in air at rest 
and the velocity of the wind, whereas the influence of temperature 
was allowed for in the usual way. 
FustwHara’) has treated the problem by drawing up the hydrodynamic 
equations for sound motion in a moving medium. The solution, 
however, meets with such difficulties that he was obliged to content 
himself with an approximation for the case of the simplest supposi- 
tions: a windvelocity in the same direction at all heights, and 
increasing or decreasing uniformly with height, and an equally linear 
variation of the velocity of sound on account of the variation in 
temperature. It appears that in this case the solution practically 
agrees with the supposition mentioned above. 
Even without going into particulars or calculations, it is easy to 
see how, by certain suppositions about the vertical distribution of 
wind-velocity, peculiarities of the propagation of sound, especially 
the silent region, may be explained. 
The influence of temperature, which in the mean decreases upwards, 
is a decrease of the velocity of sound, which causes the sound-rays 
1) Wien. Sitzungs Berichte lla. 122, p. 1683, 1913. Meteorologische Zeitschrift’ 
32 p. 207, 1915. 
3) le. p. 24. 
