The Saint Paul globe. (St. Paul, Minn.) 1896-1905, 1902-10-05

A few months ago the editor Of a
great magazine sought to secure an
authoritative statement concerning the
flying machine. Is it possible for man
ever to navigate the air by means of
wings? The editor secured the serv-
ices of one Of the greatest mathema-
ticians of the world, Dr. Simon New
comb, of the United States naval OBJ
servatory, who made a popular ex-
position of the subject, showing clear
ly the impracticability of any scheme
to enable men to fly. The learned pro-
fessor did not draw upon any prin-
ciple of mathematics beyond what is
contained generally in the practical
arithmeticS taught in the schools. Yet
1t would seem that the mass of the
people were not possessed of a ready
and practical knowledge of the laws
which he stated. 1t is indeed surpris-
ing how many educated and generally
practical people have failed to master
some Of the simple relations of sur
faces and solids. Almost everybody
can tell you the circumference and
the area of circle If you will give
him the diameter; but how many can
tell the area Of a globe? This area is
exactly equal to that of the convex
surface of cylinder inclosing the
globe; that is to say, it is equal to the
ence.
If you have two globes, one a foot in
diameter and the other three feet, the
large one will be twenty-seven times
the size of the small one. But if you
wish to paint these globes you will find
that the large one will require only
nine times as much paint as the small
one. If the large globe be four feet in
diameter it will be SiXty-four times as
large as the small one! but it will have
only sixteen times as large surface.
The law is, that similar solids are to
each other as the cubes of their CORE
spending linear dimensions, while their
surfaces are to each other as the
squares of such dimensions.
Many who are cogniZant of this law
in its application to globes and cubes
seem not to be aware of it's application
to other figures, such as statues, col
umns, ETC. Yet it will apply to any
similar figures. Where two statues,
for example, are alike except that one
is larger than the other, 1t is necessary
only to compare two corresponding di-
mansions in order to compute readily
their relative sizes. Take, for instance,
the length of the little finger nail on
the left hand. If in one of the statues
this is twice as long as in the other,
the statue is eight times as large; and
If the statues are to be painted, it will
require four times as much paint, for
it's surface will be four times as large
as the surface of the smaller one.
Let an inventor work upon his fly
ing machine and announce his sue
cess. 1t will not be at all incredible.
Inventors generally work upon small
models of the machines they con-
trive. Let us say that the small
model is really d success. The poor
inventor feels that his problem Is
solved. All he has now to do is to
build his machine upon a large scale.
He makes the wings, let us say, ten
times as long as those of his model.
He thus secures one hundred times as
much wing surface for the support of
the machine and it's load; but at the
same time he has increased the weight
to one thousand times that of the
model. This is the deadly law of
mathematics that utilities his efforts
to attain any practical results. The
power Of atmospheric displacement,
like the wing surface, is multiplied by
one hundred, while the. weight of the
machine is multiplied by one thous-
and ~
We See this principle illustrated in