Bismarck daily tribune. [volume] (Bismarck, Dakota [N.D.]) 1881-1916, 1907-08-17
. THE LIMIT or VISION.
How Far Can the Normal Eye See on
Land or on Seat


How Far Can the Normal Eye See on
Land or on Sea
There is absolutely no limit to the
normal vision il the sight be unob-
structed. Yet we can see the stars,
which are trillions of miles away.
while we cannot see q tree twenty
miles distant. Why? It is true that
all objects diminish IN apparent size
in a direct proportion to distance. but
that is not the only reason. The chief
reason is that our vision is obstrueted
by the curvature of the earth. a writ.
er in Popular Science News gives some
figures to show how great this curya-.
ture is. All
1t Is often a matter of interest and
Importance to know how far We can
see from any given height or, con-
versely. how far one must be above
the earth to see an object at a given
distance. The exact calculation Of
these figures would require the use Of
very complex formulate, but for prac-
tical use two very simple rules will
suffice.
The distance In miles at which an
object upon the surface OF the earth
Is visible is equal to the square root
of one and one half times the height of
the observer in feet above the surface
and conversely
The height in feet to which an OBJ
server must be placed to see a distinct
object is equal to two-thirds the square
Of the distance In miles. For instance,
if the observer is In the rigging Of a
ship 100 feet above the water, how far
distant is the horizon that Is, how far
could all object floating in the water
be visible before being hidden by the
convexity of the earth? One and one
half times 100 Is $50, and the square
root Of $50 is approximately twelve and
one-half; therefore the horizon is
twelve and one half miles distant
AS the deck of smaller vessels, like
pleasure yachts, is rarely more than
ten feet above the water, 1t follows
that the limit Of vision from that point
is less than four miles in every direc-
ton.
An illustration of the second rule
may be given as follows: a building is
thirty three miles away. How high a
hill must one climb in order to be able
to see it? AS the square Of the dis
lance equals 1899 and two-thirds Of
that number equals 726, 1t follows that
we must climb hill 726 feet high be-
fore we are able to see the building,
even with the most powerful telescope.
Usually, however, the height OF the
object as well as that of the observ-
er must be taken into consideration,
but this simply requires the duplica-
ton Of the problem. For Instance,
the Washington monument is 552 feet
high. At what height must an OBJ.
server fifty miles away be in order to
see the top Of it? Supposing the OBJ
server to stand upon the ground, we
find by the first rule that he could
just see the top twenty nine miles
away, and to overcome the remaining
twenty-one miles, due to the convexity
of the earth, he would by rule second
have to climb to the height Of 294 feet.
If we apply similar calculations to
the Eiffe1 tower, the highest artificial
structure in the world, we obtain some
interesting results. Assuming the
height to be just / ,O00 feet, we find.
that, standing at the top, we enjoy q
circle of vision bounded by horizon
thirty mine miles distant and that If
another similar tower should ever be
erected it could be placed over seven
ty-eight miles away before the rays
of the electric lights on their summits
would be eclipsed BY the intervening
earth.
From the summit of Mount Everest
in the Himalayas $4,000 feet, one
could see nearly 200 miles, provided
the air was clear enough, which would
| rarely be the case.