Ottumwa tri-weekly courier. [volume] (Ottumwa, Iowa) 1903-1916, 1910-04-05
he lunar eclipse. But Mr. Graves asks

the lunar eclipse But Mr.. Graves asks
emphatically for proof of the concave
proposition, and he wants it without
any of the hypothesis that he uses SO
plentifully. He shall have it.
First, let us state principle in
hydrostatics that will be a necessary
factor in the demonstration-namely
water at rest is always level, with its
surface every where at right angles
to the gravic ravs. The water level
therefore conforms exactly to the
earth's curvature. be it convex or
concave; and a test Of the curvature
Of the waters surface is a true test
of the earth's curvature.
Second. let us get clear in our minds
the relations of circle and straight
line tangent thereto The line touches
the circle at only one point; has a
definite ratio of departure from the
adjacent arc in either direction, and is
exactly at right angles to that radius
of the circle which terminates at the
point of contact of the tangent Now
let us consider two lines, one on each
side of the tangent line, and exactly
parallel to it. The one inside the Cir
Gle will cut the radius at right angles,
and strike the arc on either side at
equal distances. The one outside the
circle will cut the produced radius at
right angles, and will depart from the
arc equally on either side. Let us now
make concrete application OF these
geometrical relations. The circle IS
the eartk's circumference, described In
any direction at mean sea level. The
tangent line is a straight line touch
ing the extremity of given radius in
that circumference, and at right angles
to it. The straight lines on either side
of the tangent line, and parallel to it
must be surveyed by some mechanical
process, if we are to determine geo
metrically the direction of the earth's
curvature.
Suppose we survey them both on
paper-and see which one of them fits
the actual survey made by the Kore-
shan Geodetic staff on the Gulf Coast
of Florida in 1897. Take first the
parallel line exterior to the circle:
which would place it above the surface
of a convex earth. We start at the
point where the line cuts the produced
radius-at the top of a perpendicular.
bay ~ l6SI dUcfO LIN "oSCA ~ -, e~AA>~
survey a. geometrically straight line
at right angles to that perpendicular.
Our line, parallel to the water level
at the starting point. will depart from
that level at constantly acceleating
ratio; the plumb-bob will hang back
wards from the right angle more and
more at each succeeding observation,
and indicating downward converg-
ance of the gravic rays; and the
angular drop okthe horizon below the
line will continually increase. Now
take the parallel line interior to the
circle; which would place it above the
surface Of the concave earth. We start
at the point where the line cuts the
radius at the top of a perpendicular,
ten feet above sea level, and survey
a straight line at right angles to that
perpendicular. Our line. parallel to the
water level at the starting point, will
approach that level at constantly &C
celebrating ratio; the nlumb-bob will
hang forwards more and more from
the right angle at each successive OBJ
servation. thus indicating a downward
divergence of the gravic rays, and the
angular rise of the horizon above the
l