GEODESY is the application of mechanical and other means for the purpose of determining measurements of the earth's surface, including not only that of its general contour as to whether it is concave, flat, or convex, but also of demonstrating the amount of curvation at any given point and in any given direction.
The Copernican system of astronomy assumes that the earth's surface is convex, and upon this
Perpendicular standards are placed at points where there is a quiet expanse of water large enough in area to extend a line six, seven, or more miles. Across these perpendicular standards the horizontal bar of the Rectilineator is adjusted. From this first adjustment the rectiline is extended in both directions, until the line meets the water at a distance proportionate to the height of the perpendicular standard.
By this operation we extend a chord from the top of the uprights, at right angles to two points at the surface of the water, as in diagram No. 4, Plate 1. The relation of the straight line to the arc determines the concavity of the earth as its true contour.
In diagram No. 3, Plate 1, we have an illustration of the optical effect of an observation made with a leveling instrument, which does not differ in principle from a corresponding observation made with the unaided eye. The straight surface over which the line of observation extends is represented A A A; B B B is the visual direction deviating in a gradual curve away from the straight line A A A. The mind is unconscious of this curvation of vision, hence the curved line appears to be straight as in the dotted line C C C, while the straight line A A A appears to rise gradually as the line D D D.
The point 1 in the line of vision appears to be at the point 2. The vanishing point is where. the extremity of the visual line at 1 seems to meet the line A A A, represented by the line D D D. Beyond this point the straight line A A A, appearing as the line D D D seems to convex away from the apparent line D D D.
diagram No. 3, Plate 1, we prove that a straight surface curves away from the line of vision, by the identical argument employed to prove the convexity of the earth. We can prove that a straight line bends four different ways, by the same argument used to sustain the convex theory of the earth.
Revolution in astronomy implies revolution in all things. The great Swedish Seer said: "Every dispensation proceeds as from an egg." We reiterate, that a scientific religion which must embrace scientific social organization, will proceed from an astronomical basis, the foundation of which is the Cellular Cosmogony. Life develops in the cell. When the world is forced to accept this proposition, all else follows readily.
In connection with the establishment of the fact, in the public mind, of the concavity of the surface of the earth, and next also in importance is the determination of the amplitude of the arc, or the radius of its curvature. This cannot be determined accurately by any process of surface triangulation, because there are too many factors entering into the process to insure accuracy.
The Rectilineator, extending its line from an given height of a prime vertical, approaches the normal curve of the surface at a proportionate ratio, which may be determined at any given point by two exact methods,--each acting as the verificator of the