February 9, 1894. 
have suggested, that such inaudibility is mainly, if not 
wholly, dependent upon causes acting in only one direc- 
“tion. If then it should be ascertained that independent 
sounds may be projected from a point just within the 
proximal boundary of a pseudumbral area to a point 
beyond its distal boundary, it would of itself be a demons- 
tration that the fog signal’s sounds become either refracted 
or annulled at the proximal boundary of the area. 
The frequent, if not the usual, recovery of the fog 
signal’s sounds in strong intensity beyond the distal 
boundary of a pseudumbral area seems to show that there 
has been no permanent annulment of those sounds either 
at the proximal boundary or elsewhere. It also seems to 
indicate that their restoration is at most only in part due 
to such diffusion and coalescence of sound waves of the 
fog signal as quickly restricts the extent of a montumbral 
area, and makes those sounds audible beyond its distal 
boundary. It therefore becomes desirable to investigate 
the air above pseudumbral areas with a view to learning 
whether the fog signal’s sounds pass there uninterruptedly 
to the distal side of the area. The investigations by 
balloon which have been proposed by both Mr. Johnson 
and Major Livermore will evidently be the means of 
testing this question, and they will doubtless aid in other 
ways to increase our knowledge of the acoustic conditions 
which prevail in pseudumbral areas.* 
The preceding paragraphs are largely suggestive of 
scientific results yet to be attained. The facts now to be 
mentioned are suggestive of dangers to navigation to be 
avoided or guarded against. Last autumn, while a mem- 
ber of the party of investigation whose operations were 
described by Mr. A. B. Johnson in Sczence for January 5th 
of the present year, I made some observations of echoes 
of the sounds of fog signals which are of special interest 
in this connection. The most important of these ob- 
servations were made upon Great Gull Island, at the 
eastern end of Long Island Sound, and the echoes were 
those of the fog signal, a siren, which is connected with 
the lighthouse on Little Gull Island, about half a mile 
from my point of observation. There was no fog at the 
time these observations were made, but the siren’s sounds 
were given regularly that their variations of audibility 
might be studied in the surrounding region. 
The echoes were received from the sails of several 
schooners which were standing in the offing with all sails 
set and close hauled by the wind. The vessels varied in 
distance from me and from the siren from half a mile to 
nearly two miles. The wind was light, there was perfect 
silence around me, and the echoes reached me with almost 
startling distinctness. In timbre, or quality, they were 
exact reproductions of the siren’s sounds; and in duration 
and time-interval they also agreed with them. I estimated 
the intensity of the echoes at from 1 to 3 ina scale of to, 
the latter number representing the full intensity of the 
siren’s sounds. The angles of incidence and reflection by 
which they reached me were from 20, to somewhat more 
than 4o degrees. 
Considering the intensity and distinctness of those 
echoes, their identity of timbre, time-length and time 
interval with those of the direct sounds of the siren, the 
distances from which they were reflected, and the broad 
angles of incidence and reflection by which they reached 
me, I was impressed with the belief that such echoes, 
when heard within either pseudumbral or montumbral 
areas, may be a source of danger to passing vessels. The 
following diagram will show how sail-echoes of a fog 
signal may be a source of danger to a vessel traversing a 
montumbral area in a fog, and it also illustrates the 
3Since the foregoing paragraphs were written Major Livermore has informed me 
that in experiments lately performed under his direction the sounds of a bell and of a 
steamer’s whistle were projected both into and out of pseudumbral areas, thus 
demonstrating in large part what I have suggested, 
SCIENCE: 61 
character of montumbral areas as they have already been 
described. 
A, represents an elevated island ; B, a small island with lighthouse and fog signal, 
and C,a montumbral area, the seat of an acoustic shadow caused by the elevated 
island. D, represents a schooner with all sails set and close hauled. #, represents 
another vessel, within the montumbral area, where of course the direct sounds of the 
fog signal are inaudible. Those sounds, however, reach the sails of the vessel at D, 
and are reflected to the vessel at 2, as an echo. To persons on board the vessel at Z, 
the sounds of the fog signal seem to come from the direction of D. 
Sail-echoes of a fog signal which are recovered beyond 
the distal boundary of a montumbral area may, perhaps, 
also be reflected back into it, but lateral reflections, such 
as are represented by the diagram, are probably more 
likely to occur. 
It cannot be denied that the permanent conditions 
necessary for the casting of an acoustic shadow of a fog 
signal’s sounds across a navigable channel, or a usual 
track of vessels, are not common, but such conditions do 
exist in connection with certain of the fog signals which 
have been established along our coasts. Neither can it 
be denied that the occurrence of such a combination of 
permanent and adventitious conditions for reflecting the 
sounds of a fog signal from the sails of vessels into a 
montumbral area as is represented by the foregoing 
diagram is likely to be rare. Still, there is an undeniable 
probability that such cases may occur at any time, and it 
is also undeniable that they may be attended with danger 
whenever they do occur. 
If my assumption is correct that a pseudumbral area is 
one of inaudibility of only such sounds as are projected 
towards that side of it which faces the neighboring fog 
signal it may legitimately be assumed that sail-echoes of 
the fog signal’s sounds may be projected into such an 
area just as they may: be projected into a montumbral 
area. ‘That is, if a pseudumbral area should be a short 
one, sail-echoes of the neighboring fog signal may be pro- 
jected into it laterally in the same manner that they are 
represented by the foregoing diagram as being projected 
into a montumbral area. Recovered sounds of the fog 
signal, upon the distal side of the pseudumbral area, may 
also be echoed back into that area from the sails of 
vessels. Such echoes may enter a pseudumbral area from 
any point of the compass within a range of, perhaps, one 
half the horizon. ‘To persons on board a vessel traversing 
one of these areas during a fog those echoes might 
readily be mistaken for the direct sounds of the fog 
signal, and the true location of the latter would in every 
case be falsely indicated. 
The conditions under which echoes occur are number- 
less, and their observation has from time immemorial 
been prominent among the practical duties of mariners. 
They habitually use echoes of permanent objects as aids, 
