60 
istence ; and when one is discovered its shape and ex- 
tent can be known only by special investigation. It 
is known, however, that the shape and extent of 
pseudumbral areas are very variable, and also that 
their location is uncertain as regards distance and direction 
from the fog signals whose sounds are inaudible within 
them. They are also very variable in outline, and the 
distinctness of the boundary of each is usually, if not 
always, variable in its different parts. That is, if the 
area may be propery designated as umbral, the term pen- 
umbral may not inappropriately be used to indicate the 
indefiniteness of certain portions of the boundaries of those 
areas. 
Furthermore, certain known facts indicate that all the 
conditions which characterize a pseudumbral area at one 
time may be absent from nearly or quite the whole area 
at another time. ‘These areas, therefore, unlike mon- 
tumbral_ areas, are always potentially, and apparently 
always actually, variable, not only in outline but in posi- 
tion and duration. Still, they frequently have sufficient 
permanence for systematic study; and Major W. R. Liver- 
more, Engineer in Charge of the First and Second United 
States Light House Districts, has successfully mapped 
some of them.* 
Experimental study of pseudumbral areas is necessarily 
made on board of vessels, and as the observer directs his 
course away from the fog signal, which is meanwhile kept 
regularly sounding, he becomes aware of having reached the 
proximal boundary of a pseudumbral area by the gradual, 
or often sudden, failure of the fog signal’s sounds to reach 
him. Continuing in that direction, if open water be there, 
he comes to the distal boundary of the area when the fog 
signal’s sounds are again heard, usually with little diminu- 
tion of their intensity. The biological terms, proximal 
and distal, are borrowed and applied to the nearer and 
opposite sides, respectively, of the area, with reference to 
the location of the fog signal. 
Although, as has already been mentioned, a consider- 
able part of the acoustic conditions which prevail in a 
pseudumbral area are, in effect, identical with conditions 
which characterize montumbral areas, two important 
differences between the conditions prevailing in the two 
areas respectively are known, besides the difference as to 
permanency just mentioned. First, in the case of a 
pseudumbral area there is no such interception or de- 
structive arrest of any portion of the fog signal’s sounds by 
a visible physical object as takes place in the case of a 
montumbral area. The inaudibility is caused by some 
invisible physical force or condition, but how that force 
acts, or what that condition really is, has long been the 
subject of wide differences of opinion and of earnest con- 
troversy. Second, independent sounds caz be projected 
from points within a pseudumbral area to the place of 
origin of the neighboring fog signal’s sounds, further 
mention of which fact will presently be made. 
The cases discussed under the head of Acoustic Rever- 
sibility by Professor Tyndall,‘ and some of those related 
by Professor Henry* concerning his experiments while he 
was Chairman of the United States Light House Board, 
agree with the foregoing statements, one of the latter 
cases being especially important in this connection. 
Many of Professor Henry’s experiments were made to 
ascertain the relation to one another of sounds responsively 
produced, such, for example, as those which he made with 
the whistles of steamers off Sandy Hook in 1874. He 
showed that sounds may be returned from an area in which 
similar reciprocal sounds, projected from other points, are 
inaudible, and he urged this fact against Professor 
‘Tyndall’s theory that the cause of such inaudibility is a 
1Tyndall, John ; Sound, 3rd edition, p. 403. 
*Henry, Joseph ; Researches in Sound, pp. 493, 501, 503, 510 and 547, 
SCIENCE: 
Vol. XXIII. No. 574 
flocculent condition of the atmosphere. The experiment 
which I wish particularly to refer to, however, was made 
with reference to the sounds of a stationary fog signal, 
and it is therefore of special interest to the subject of this 
article. The result of this experiment was the projection 
from within a pseudumbral area of the sounds of the 
whistle of the steamer upon which he was, making his ob- 
servations to the immediate vicinity of the neighboring 
fog signal. While the steamer was moving away from the 
fog signal, which was meanwhile kept regularly sounding, 
the steamer entered an area where the sounds of the fog 
signal became inaudible. The steamer’s whistle being then 
blown, its sounds were distinctly heard by observers 
standing beside the fog signal. 
Professor Henry died soon after the last of the ex- 
periments referred to were made, and they have not, to 
my knowledge, been continued. However, considering 
the facts which he then demonstrated, together with other 
facts concerning the acoustic conditions which are known 
to prevail in both pseudumbral and montumbral areas, I 
cannot doubt that sounds of any kind, if sufficiently in- 
tense for such distances, may be projected into or across 
pseudumbral areas as readily, and in the same manner, 
as into or across montumbral areas. That is, I think the 
facts now known warrant the opinion that a pseudumbral 
area is one of inaudibility only of sounds coming toward 
that side of it which faces the neighboring fog signal. 
The question may be raised whether the acoustic con- 
ditions which usually prevail in connection with pseudum- 
bral areas may not sometimes be complicated by the si- 
multaneous presence of such an additional force or con- 
dition as would make them areas of inaudibility of certain 
other sounds besides those of their neighboring fog 
signals. I am not aware of any fact which favors the 
supposition that such complications ever exist, nor do I 
now think they are to be expected. This statement, 
however, has no reference to the assumed inaudibility 
within the pseudumbral area of sounds which may be pro- 
jected from points within a short distance upon either 
side of the fog signal, because it is evident that, to a 
greater or less extent, such sounds are controlled by the 
same cause which controls the fog signal’s sounds. The 
question may also be raised whether the condition which 
produces inaudibility of the fog signal’s sounds, without 
reference to other sounds, may not also be complex. I 
am not, however, at present prepared to discuss the 
question of causes of inaudibility of sounds in pseudum- 
bral areas. Still, I think that exhaustive investigations 
concerning the relation of the sounds of fog signals to 
other sounds, in connection with pseudumbral areas, are 
likely to throw much light upon it. 
In view of the variability of those areas it is evidently 
desirable that various experiments showing such relation 
should be simultaneously made when one of them is 
discovered. For example, it is desirable that several 
vessels, each provided with the means of producing 
various penetrating sounds, should surround and traverse 
the pseudumbral area and attempt the projection of those. 
sounds into, from, and across it in all directions; the 
neighboring fog signal being meanwhile kept regularly 
sounding. As a matter of course all such experiments. 
should be accompanied by observations of all atmospheric. 
conditions, especially those which affect, or which are 
supposed to affect, the propagation of sounds. 
Such experiments would tend to show, among other 
things, what becomes of the sounds of a fog signal upon 
reaching the proximal boundary of a pseudumbral area. 
For example, if it should be ascertained that such sounds 
as I have indicated may be projected in various directions 
through the very space in whicl,a fog signal’s squnds,are 
at the same time inaudible, 7%. would demonstrate what 1 
