Sacramento daily record-union. [volume] (Sacramento [Calif.]) 1875-1891, 1883-10-17
MATHEMATICAL GEOGRAPHY.


In the Medina (Ohio) News, gives the fol-
lowing, which will be of much interest to
most readers
We will make inquiry az to the direction
of the earth axis. Many persons suppose
that the north pole is elevated per Sc, and
the south pole depressed. Now, toward
what part OF the heavens does the northern
part Of the earth's axis point The an
swer viii be that it points toward the
north. Yes, but does it point north near
the horizon, or does it point considerably
above the horizon Let US investigate.
The earth's axis points very nearly toward
the north star Ii we were at the equator
the horizon and the earths axis would be
parallel, and we should see the north star
due north in the horizon. Ii we should
come one degree north the star would seem
to rise one degree above the horizon. Ii
we come ten degrees north, the star would
seem to rise ten degrees; If forty-five de-
grees, the star would be half way between
the horizon and zenith. If we should stop
at Medina, the north star would be Al de-
grees, minutes, and 81 seconds above the
horizon, because Medina is so many de.
prees, minutes and seconds in north lati-
tude.
So you see the direction of the eaIth's
axis and the position of the pole of the
heavens depend on the position of the OBJ
server. If ne is thirty degrees north, the
north star will be thirty degrees above the
horizon, and if he should go to the north
pole the north star would be exactly over
head, aud while the earth turned around
IN one direction, all the heavenly bodies
would seem to move horizontally in the
opposite direction.
Well, the north pole is elevated, then,
is it not No, not per Sc. 1t is only ele-
waited relatively to US who live in the north
ern hemisphere. The same phenomena OBJ
tain il the southern hemisphere. II one
should 90 ten degrees south from the equa-
tor, the south pole of the heavens and the
south star, if there is one, would be ten
degrees above the heavens, and SO on.
Neither pole is elevated or depressed
generally, only relatively. Let no one pass
hastily over the point discussed above,
thinking it unimportant. | assure you it
is the open sesame to arriving at a some
what familiar acquaintance with either
mathematical geography or astronomy
Our second inquiry follows the first as
naturally as effect follows cause. 1t is in
reference TO the apparent daily motion of
the sun. In the summer the sun at sun
rise is far away in the northeast. But az
it climbs the morning sky it seems to
swing far southwark, go that at noon it is
never less than eighteen degrees and some
minutes south of our zenith. In the after
noon it makes its way back again to the
north. What causes this curious swinging
to and fro north and south Are the
phenomena the same at all places, here and
at Hudson's Bay, at the equator and in
Chile Not at all. At the equator there is
no such swinging south in the forenoon and
north in the afternoon. II person at the
equator sees the sun rise in the east, at
noon it IS exactly overhead, and sets exactly
west. If it rises a little north of east, it
Is north at noon. and sets little north of
west. But at Hudson's Bay the sun seems
further north at sunrise and further sonth
at noon than at Medina Strange as it may
seem, the further one goes north, the fur
ther north the sun seems at sunrise, and
the further south at noon. In South
America these phenomena are reversed. In
their summer the sun rises far in the
south, but of noon it is north of them.
Again ! ask what causes this apparent
swinging to and fro of the sun q? For it is
only apparent. The sun is no farther
north at sunrise than at noon. | have
stated above that north of the equator the
north pole of the heavens and the northern
part of she earth's axis are elevated above
the horizon equal to the latitude of any
given place. At Medina the earth's axis
makes an angle with the horizon of little
over a. degrees. OF course the plane of
the orbit of the suns apparent daily mo.
hon is at right angles to the axis. 1t will
be seen. then, that the plane of the orbit
of the suns daily motion westward is
tipped from perpendicular to the horizon
4 degrees toward the south, and this
makes the sun seem each day to veer to
the south IN the forenoon, and to the north
ia the afternoon.
CURIosITIEs OF MATHEMATICAL GEOGRA.
PLY.
If two stakes be set five miles Tor any
other distance) apart, in an equal distance
from the equator, and the same latitude,
then another stake be set midway between
them and exactly in range, the middle
stake is farther from the equator than the
other stakes.
If two places be equally distant from
the equator the shortest route from one to
the other is all of it farther north than
either of the places. Let it be remem-
bered that the shortest route between two
places on the earth's surface is part of a
great circle of the earth, and that no part
of great circle comedies with parallel
of latitude.
A person wishes to go from Oregon,
where the forty 6fth parallel intersects the
Pacific Ocean, to where the same parallel
meets the Bay OF Fundy. The shortest
route between these two places is not along
the parallel. Following the line of lati-
tude, the distance is ,, 7S3 miles but fol.
lowing great circle, north of the parallel,
the distance is only ., 723 miles-60 miles
less than following along the parallel. The
middle Of the shortest route is 236 miles
north of the parallel, Well, this is
strange" says one 81 do not quite be-
heve that circling round 236 miles north
makes the distance go miles less than keep
ing straight along the parallel" Well,
truth will remain truth whether believed
or not. When l speak of straight line,
mean straight except conforming to the
curvature of the earth-such line as is
made when a small cord is drawn tight be-
tween two places on the earth's surface.
Were the earths surface smooth like ice,
and two points taken on the same parallel,
few miles apart, and cord drawn tight
between them, this would be straight
line, and it would also be part of great
circle it would be the shortest route be-
tween the two points, and the entire route
would be further north than either of the
two points. If a person in north latitude
starts in direction at right angles to
meridian, that is, if he starts due east and
keeps on IL that straight line he will in 80
degrees cross the equator, and in going 80
degrees further he will be as far south of
the equator as he was north of it when he
started.
If in north latitade line be run due east
to an object mile off, and then from this
object line be run mile due west, this
last line viii not run back to the point of
starting but will run a little south of it.