941 
until several days after the siege of Antwerp, and that, with a view 
to a preliminary account in the press, suggestion or mistakes in 
dates appear not quite impossible, whereas in our country there can 
be no question of such a thing. 
If we consider that on later occasions also the lightships “Schouwen- 
bank” and ‘Maas’ sent in reports, we are entitled to say that the 
inner circle has been verified over 180°, the outer one over more 
than 90°. 
It is this symmetry with regard to the source of sound which 
speaks immediately against every effort to explain this silent region 
by influence of wind. Any wind, which keeps the same direction 
over a certain distance, must form a limit of the area of audibility, 
which is less curved than the circle round the source of sound 
through the point, where the ray that has the same direction as the 
wind reaches the surface once more.') No trace of such a thing is 
shown here. We shall see afterwards, that also meteorological obser- 
vations do not give any reason to ascribe the reappearance of the 
sound at 160 K.M. and farther to the influence of the wind. 
Whereas this seemed to be in support of Von Dem Bornn’s view, 
the distance was somewhat at variance with that view. Indeed, 
Von prem borne calculated that the shortest distance at which the 
rays curved back by the high atmosphere shouid reach the surface, 
was 114 K.M. 
One might be inclined to think that meteorological circumstances 
might be the reason why another value for the minimum distance 
was found. In calculating the influences to be expected, it soon 
appears that these influences will be hardly perceptible. We return 
to this question in § 8 and will see first, whether the silent region 
was shown also on other days, and whether other distances were 
observed on these occasions. The various dates will be treated 
in succession. 
§ 6. October 17%. The initial position of the battle has been 
assumed according to a report of the ‘Drathning Sophia’, who 
reported to have been at 3°45’ E. Long. and 53°3' N. Lat. when 
1) Indeed, for a direction making an angle © with the wind, the velocity of sound 
V at the level of the maximum windvelocity v becomes Ve = Vj + Vcos¢; hence 
the initial angle of the ray, which becomes horizontal at this level, is determined by 
sin ag ese When ¢ grows, sina, increases and every element of the 
orbit is longer the more v increases. For a definite value of 9, 2» may become 
imaginary: in that case the area of abnormal audibility, belonging to this wind- 
distribution, is enclosed within a definite sector. 
