February 2, 1894. 
SCIENCE: 
PUBLISHED BY N. D. 6. HODGES, 874 BROADWAY, NEW YORK. 
SUBSCRIPTIONS TO ANY PART OF THE WORLD, $3.50 A YEAR. 
To any contributor, on request in advance, one hundred copies of the issue con- 
taining his article will be sent without charge. More copies will be supplied at about 
cost, also if ordered in advance. Reprints are not supplied, as for obvious reasons 
we desire to circulate as many copies of Science as possible. Authors are, however, 
at perfect liberty to have their articles reprinted elsewhere. For illustrations, 
drawings in black-and white suitable for photo-engraving should be supplied by the 
contributor. Rejected manuscripts will be returned to the authors only when the 
Whatever is intended for 
insertion must be authenticated by the name and address of the writer; not necessa- 
rily for publication, but as a guaranty of good faith. We do not hold ourselves 
responsible for any view or opinions expressed in the communications of our corres- 
pondents. > 
Attention is called to the ‘‘ Wants’’ column. 
requisite amount of postage accompanies the manuscript. 
It is invaluable to those who use it 
in soliciting information or seeking new positions. The name and address of 
applicants should be given in full, so that answers may go directly to them. The 
“*Exchange”’ column is likewise open. 
THE RELATION OF THE SOUNDS OF FOG 
SIGNALS TO OTHER SOUNDS. 
BY CHARLES A. WHITE, SMITHSONIAN INSTITUTION, WASH- 
INGTON, D. C. 
Ir is now generally known that within the range of 
possible audibility of most, if not all, the fog signals which 
the various civilized governments have established along 
their coasts, each usually in connection with a lighthouse, 
there are certain areas within which the sound of these 
signals are inaudible. It is also known that areas of more 
or less complete inaudibility of sounds, when projected 
from certain directions, sometimes occur upon the land ; 
but only these which occur upon the water will be specially 
referred to in this article, and they will be discussed only 
with reference to their relation to stationary fog signals. 
Such acoustic conditions being a constant menace to navi- 
‘gation during a fog, the various governments concerned 
have instituted inquiry into the character and limitations 
of those areas and, incidentally, into their causes. Our 
own government has been, and still is, active in experi- 
mental studies of this kind, but the records do not show 
that any of those studies have been more than incidentally 
directed to that particular phase of the subject which is 
indicated by the title of this article. 
The areas cf inaudibility referred to are of two kinds, 
each area of both kinds bearing a similar special relation 
to a neighboring fog signal. One of these kinds is made 
such in every case by a true acoustic shadow of a sta- 
tionary visible object, usually a small elevated island, or 
a ridge of land running out into the water, at, or near, 
one side of which the fog signal is located. That is, such 
an area is simply one which an essentially permanent 
acoustic shadow occupies. 
The areas of inaudibility of the other kind occur in 
broad open waters. ‘here is never any visible indication 
of their presence, and in connection with, or near, none 
of them is there any visible object above the water surface, 
and therefore nothing which could cast a true acoustic 
shadow there. Whatever may be the cause or causes of 
inaudibility of the sounds of the neighboring fog signal 
in areas of this kind, it is evident that at least a consider- 
able part of the acoustic conditions prevailing in them are 
in effect identical with conditions which characterize the 
other kind. That is, certain of the effects produced with- 
in these areas are the same as those which are produced 
by a true acoustic. shadow in each of the first mentioned 
kind of areas. 
SCHEIN CGE: 59 
It is impracticable to discuss these areas and to compare 
each kind with the other without applying to each kind a 
distinctive name. I have therefore selected for the first 
mentioned kind the name montumbral, and for the second, 
the name pseudumbral, areas. ‘The first name is selected 
because the areas to which it is applied are in every case 
made such by the acoustic shadow of a hill or ridge. The 
second name is selected because the acoustic conditions 
which prevail in the kind of areas to which it is applied 
are, as has just been mentioned, largely identical with 
those which are produced in the other kind by true 
acoustic shadows. 
The elevated island or ridge which lies between a fog 
signal and a montumbral area casts an acoustic shadow 
over the latter just as at night it casts an optic shadow 
over the same area by intercepting the light from the 
lighthouse with which the fog signal is connected. The 
bounderies of a montumbral area are therefore determined 
by the profile outline of the elevated island or ridge which 
causes it, but they are modified and restricted, as com- 
pared with those of an optic shadow, by the great lateral 
diffusion of the sound waves, and by their tendency to 
soon coalesce beyond any object which may separate or 
obstruct them. That is, the lateral boundaries of an 
optic shadow diverge beyond the intercepting object, 
while those of an acoustic shadow have a strong tendency 
to converge there. The diagram which follows further 
on approximately illustrates the character of a montumbal 
area besides other conditions which sometimes may be 
connected with it, as will presently be explained. 
It will thus been seen that what I designate as mon- 
tumbral areas are in each case identical in outline with 
an acoustic shadow which is necessarily permanent, or 
only slightly varying as to its boundaries with changes of 
atmospheric conditions. Beyond this, montumbral areas, 
unlike pseudumbral areas, as will presently be shown, are 
not potentially variable. Acoustic shadows occur under a 
great variety of conditions, but montumbral areas as I 
have defined them are not numerous. 
Excepting the absence of the direct sounds of the fog 
signal within a montumbral area the acoustic conditions 
prevailing there are normally the same as are those which 
prevail on all the water surface adjacent to it. That is, 
in case no other acoustic shadows are cast there by other 
objects, intercepting other neighboring sounds, it is an 
area of inaudibility only of the sounds of the neighboring 
fog signal and of such other sounds as may be projected 
from points within a limited distance upon either side of 
the fog signal. This inaudibility is caused by a complete 
interception or destructive arrest, by the adjacent elevated 
island or ridge, of a portion of the sounds which the fog 
signal projects towards it. All other sounds of whatso- 
ever kind, if sufficiently intense for such distances, may, 
with the following exceptions, be projected from, into, or 
across the area in any direction. 
The exceptions are that, because the elevated island or 
ridge intervenes, sounds connot be projected to points 
adjacent to its other side from points within the montum- 
bral area, and of course such sounds cannot reach the 
place of origin of the neighboring fog signal's sounds. 
Also, the projection of other sounds than those of the 
neighboring fog signal into the montumbral area from 
points at such distances at either side of the fog signal as 
accord with the length of the elevated island or ridge, will 
be more or less completely prevented by the presence of 
the latter, just as it prevents the projection of the fog 
signal’s sounds into that area. 
Pseudumbral areas are of more frequent occurrence than 
are montumbral areas, and in various ways they are more 
important. Still, their discovery is always empirical 
because there is never any visible indication of their ex- 
