Daily Yellowstone journal., 1890-01-25
HOW FAR CAN WE SECT
Simple Rules by Which to Calcuiats the
I.anse of Vision.

Range Of Vision.
TEe,e il absolutely no limit 10 the
normal vision, If the sight be uuob-
structed. Yet We can see The stars,
which are trillious OF miles away.
while we cannot sec a tree twenty
miles distant Why! 1t is true that
all objects diminish in apparent size
in n direct proportion to distance, but
that is not The only reason. The chief
reason is that our vision Is DISTRACTED
by the curvature of the oar.h. \
writer in Popular science News gives
some figures 10 show how great this
curvature is.
II is often a matter OF interest and
importance 10 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 formula, but for prac-
teal use, two very simple rules will
suffice.
The distance in rifles at which an
object upon the surface of the earth is
visible is equal 10 the square root of
one and "A half times the height of the
observer in feet above the surface, and
conversely.
The height in feet 10 which an OBJ
server must be placed TO see IA distant
object is equal 10 two-thirds the
square OF the distance in miles. For
instance: The observer j, in the rig.
ging of a ship 100 feet above the
water. how far distant is the horizon.
that is. how far could an object
floating ia the wafer be visible before
being hidden by the convcxity of the
earth. One and onc-half times 100 is
$50, and the square root Of 1870 is, ap.
proyimatcly, l2s. therefore the horizon
is ~ miles distant,
As the deck Of smaller vessels, like
pleasure yachts, is rarely more than
ten feet above the water, it follows
that the limit OF vision from that point
is less than four mics in every direc.
ton.
An illustration OF the second rule
may be given Us foliows: A building is
50 miles away; how high "a hill must
one climb in order To be- able To see it,
As the square of the distance equals
lOS9, and two-thirds of that number
equals 12G. il follows that We must
climb a hill 40 feet high before we
are able To see Tie building, even with
the most powerful telescope.
Usually, however. the height of the
object, as well as that of the observer.
must be taken into consideration, but
this simply requires the duplication Of
the problem. For instance: The
Washington monument is 5J2 feet
high; at what height must an observer
fifty miles away bc in order to see the
top of 1t; Surprising the observer TO
stand upon the ground, we find by the
first rule that he could just see the
top 20 miles away, and To overcome
the remaining q mil 5, due Ia the
conveXIty of the earth, he would by
rule second have toclimb 10 the height
Of pa feet.
If we apply similar calculations 70
the Eilfel tower, the highest artificial
structure in the world, We obtain some
interesting results. Assuming the
height 10 be just loo feet, We lind
that, standing at the top, W. enjoy a
circle of vision bounded by a horizon
80 miles distant. and that if another
similar tower should ever be erected,
it could be placed over Is miles away
before Inc rays of the electric lights
on their sumuats would be- eclipscd
by the intervening earth.
From the summit of Mount Everest
in the IIimalayas (21.O0O feet one
could sec nearly 200 miles, provided
the air was clear enough, which
would rarely DC the case.