Omaha daily bee., 1916-06-06

treat upper when we see niRnIy IN the HoFtHoiH
sky7"
THAT Is what ! call delightful question, in
snct with imagination, yet not losing touch
with the realm Of fact In order to answer II we
must first make some estimates which cannot be
taken as accurate. although well within the limits
OF probability, and understated rather than over
stated
The four stars forming the figure Of the
Great Dipper" are Alpha, Beta, Gamma and
Delta Ursae MAJORS, their common designation.
Ursae MAJORS being cast in the form OF the
aristocratic genitiye Of "Ursa Major"
To perform the calculation required we must
first know the distance Of these stars from the
earth This has not yet been definitely aseer-
tanned, but as they are all four moving with APP
proximately the same velocity through space, II
Is probable assumption that their respective dis
tanccs about equal, and we shall be clearly on
the safe side Of error If we call their common
paraax one-ffh OF a second OF arc.
This corresponds TO a distance OF 95OO0OO0,-
100000 niles in round numbers. The establish
ment Of this distance gives rs the needed lever.
age for working our problem, and the rest VIII
be as easy as the rule Of three
The figure formed by the four stars represents
side view of the bowl OF dpper, in the form
OF trapezoid, the upper line OF which is about
ten degrees in length, the lower line about eight
degrees while the height Of the figure is FIVE de-
grees. The upper and lower lines are not pre-
cisely parallel, but no serious error will be in
troduced H. for simpcity's sake, we assume them
to be 50.
The first step now is the Transformation Of
these angular measures into miles, using the dis
lance from the earth as a basis for the calcula-
ton. Take the upper line OF the figure, ten de-
grees in length We know that the apparent or
| angular, diameter Of any object varies directly
as IFS actual, or linear, diameter, and inversely
as its distance
Thus II line one foot long be placed so that
its ends are at a distance OF one foot from the
eye, its apparent length will be 93 degrees. II
removed to twice the distance the apparent length
will be haved, and so on.
| Conversely, II the apparent length OF any line
Is one degree we know that its distance is 3.5
times its actual or linear, length. II the apparent
| length is ten degrees, the distance is 573 times
| its actual length.
Now the stars marking the upper line Of the
celestial dipper are ten degrees apart and since
their distance from US is 9S0000000 100000 miles,
it follows that the real distance between them is
! 9s 900 900 100000 divided by S73. This gives for
| the length OF the upper edge OF the dipper To-
| $4,000 100000 miles very nearly
| The lower edge, or bottom line, OF the dpper
is eight-tenths OF this or l52o40000 100000 miles
The height is one-half Of the upper line, or
8,2o0000,000000 miles. Adding together the upper
and lower lines and multiplying their sum by
half the height or 4l4s,000000000 we get for
the area OF the entire trapezod whose corners
are marked by the four stars, lZ370l ,OO0OOOOO0,-
| 100000 100000 square miles, throwing away the
least significant figures
But we are not yet done for 1t is required
TO find the cubic volume OF dipper whose pro-
| file covers the enormous space just mentioned.
| For this purpose We must make an estimate OF
the width OF the dippers bottom, assuming that
| its sides straight and vertical.
| II they construct celestial dppers on the plan
OF terrestrial scoop, may assume the width
10 be about two-thirds the length or say 1000
| 000000000 miles. We then multiply the area OF
the side by the width OF the bottom tfor who
would refuse so slight an arithmetical labor TO
oblige lady who loves the romance Of astron-
omy), and obtain for final result the stupen-
dous amount OF one duodeeillion, three hundred
and sixty undecillions OF cubic miles
Perhaps you would like 70 see that in figures,
so here il is: ,3o000000000 0000 600 900 100000
| 00000000 100000 ! have cast aside as OF no conse-
quence more than seven hundred decillions, for
II is intellectual intoxicatlon to come into pos
! session, by ones own arithmetieal prowess, OF
an actual duodecillion and he whose patience has
achieved it understands the contempt OF sudden
wealth for such trhes as thousand dollar bills.
| Now that we have got the capacity Of the
Great Bears mighty dipper, let compare 1t with
some more comprehensive things. This earth
OF ours contains about 2o8,000000000 cubic miles
So, it would take about five oetillions of earths
packed and crushed into a mass to I'LL that SUI
per-capacious dpperl --
The volume Of the sun is about 34S0000 100000
100000 cubic miles. Then nearly four sextil-
lions Of suns. smashed like strawberries in gro
GERS basket would be required to brim the dip
per with solor neearl
! But let not the Great Bear boast too reck-
| essly OF his big dipper. Huge as it is, after all
it fills but a speek of space in the universe. 1t is
near enough to us TO make great showing in the
sky and parayze our minds with amazement
when we apply out petty measurements 10 II, but
II could dip but a spoonful from the Milky Way
II would be lost in the gorgeous blazoury OF the
Great Magellanie Cloud, and would drop. like
tin cup down a well, through the tremendous
opening OF the awful Coal Sack that yawns be-
side the constellation OF the Southern Cross, and
seems 10 have no bottom in the rayless blaekness
Of the inhnity beyondl