Factors involved in the Measurement of Meridian Arc in the
The Koreshan Geodetic Expedition. (4)

Factors involved in the Measurement of Meridian Arc in the Florida Coast Survey.   www.rolf-keppler.de 

HAVING demonstrated the principles of rectilineation and shown how they are to be applied geodetically, it now devolves upon us to show the actual relation that the rectiline surveyed by such processes, sustains to the actual meridian are 8.5 miles in length. The relations of the chord and are we have already considered, the principles of which belong to the direct processes of demonstration which we have introduced and maintained from the premise.

We must now deal with the factors involved in the processes of relating a tangibly constructed chord to the great arc of 25 000 miles circumference.
In order that these factors may be thoroughly understood, and the strength and character of our evidences appreciated, it is necessary that the reader consider our work of preparation upon which the accuracy of the survey depended, our preliminary surveys, and the methods employed in obtaining accurate measurements of the Gulf level, which is subject to daily tides.


Naples, a beautiful winter resort on the Florida westcoast,
(longitude 81° 55' 25" west, latitude 26° 4' 30" north,) was selected as the Operating Station for the following reasons:
The coast line, north and south, was comparatively straight for a number of miles; the climate admitted of operations during the winter months, and the site was near the Koreshan Co-operative and Communistic Colony at Estero, Lee Co., Fla. The Geodetic Staff of the Koreshan Unity reached the Operating Station January 2, 1897, with apparatus, and all appurtenances and instruments, and plans of operations, which required five months, careful observations and accurate work to execute.
Details of observations on the water's surface, by means of the telescope, have been presented in the preceding chapters.

Accuracy of the Rectilineator Proved.

In the direct line of logical sequences, demonstration of the accuracy of the apparatus employed, is demanded; this is absolutely necessary to definite conclusions. It is easy to be seen that if the earth is concave, only accurate apparatus could determine it to be so.

The duty that we owed to the Founder of the Koreshan System, to ourselves, and to the world, demanded precision, and herein we found a powerful incentive to the greatest possible accuracy.
Caution forced us to be sure that such an apparatus would admit of practical and precise work, so that months of our time, as well as mental and physical energy, might not be thrown away in a futile attempt to settle the question.
It was necessary to submit the apparatus to the most crucial tests that could be devised in mechanical science.
It was a new apparatus, and if it was inaccurate, it must be made accurate; our operators must be drilled and skilled by actual experience with
the apparatus, before precise adjustments could be expected; for "practice makes perfect." Several weeks were devoted to practice manipulation of the apparatus and trial surveys.

Proof of mathematical results is obtained in reversing the operations, and referring the final results to the first.
The cross-arms on several sections must be proven to be at right angles with the longitudinal hair-line or axis of the sections of the apparatus.
The inventor and mechanical experts devoted four weeks to test and adjustment of the right angles; six series of tests were applied, and each section was reversed, end for end, and turned over fifty times on the special platform with mechanical devices for measurement and reference.
Points and the finest possible lines engraved on steel and brass plates, to which adjustments were referred, were read by means of the microscope; in this way, the very slightest variation of angles could be detected.
When the hair-line of each section, in the different positions of reversals in which they could be placed, fell upon the same point under the microscope, it was a mechanical demonstration that the cross-arms were at absolute right-angles with the hair-line on the horizontal bar.

System of Reversals and Final Tests.

During the mechanical tests of the apparatus and trial surveys, an ingenious system of reversals of the sections for use in actual survey, was invented at the Operating Station by Rev. R. M. Castle, of the Geodetic Staff, and member of the Visiting and Investigating Committee, and witness of important operations. This system consisted in turning over each section at its every alternate adjustment; in this way any inaccuracy in the right-angled cross-arms, whether great or small, would in the course of a few adjustments,
be made to correct itself.
The proposition is self-evident, and resulted in the geometrical and mechanical certainty of obviating the effect of any cross-arm varying from absolute right-angles, and prevented any errors arising from such a source.
The Check Record Books of the Staff show that this system of reversals was faithfully applied throughout the entire line of survey.

After all the adjustments were completed, and the system of reversals was devised for application, and before the actual line of survey was commenced, the apparatus was subjected to one of the most crucial tests possible to impose upon it.
A single hat connects two points. By means of approximate right angles, we might extend a line from a given point to another; but so long as the right angles are an unknown quantity, they cannot constitute a basis of reference of the results. In the case of our apparatus, the cross-arms themselves were being subjected to test.
The fact that we extend a line for a given distance proves nothing, unless there is a basis of proof preceding the survey;
without the final test, a slight deviation might remain, which escaped other methods. To ascertain whether or not there was, to what extent, and in what direction a trial line has deviated, we must mechanically relate the results to the point from which the line was projected.
On so large a scale, this can only be done by taking the last adjustment in the forward line, as the first adjustment in the return, and retrace the direction to the beginning; if there had been a deviation from a rectilinear course, it would be shown when the original point was reached; if it returned to the same point, the cross-arms were at right angles, and the apparatus absolutely accurate.
228 feet were measured; a stake was fixed at the beginning, with brass plate bearing
p. 104
fine line coincidental with the horizontal hair-line of the apparatus.

19 forward adjustments were made, and the direction retraced;
at the last return adjustment, the section was found to be in exactly the same place as originally, with the hair-line precisely over the fine line on the brass plate.

The results were determined by observations with the microscope; the apparatus returned to the same point, after traversing the space of 456 feet, without a deviation of 0.0001 of an inch.
This test was in accordance with the plans of critics on the field of observations, representing the Copernican System, who were doing all in their power to prove the instrument inaccurate.

The test was applied, and the demonstration places the fact that the apparatus was accurate and capable of surveying an accurate air line, beyond all doubt or denial!

Preparation for the Geodetic Survey.

For several weeks previous to the beginning of the geodetic operations, the numerous tourists from the North and from Europe, and the residents of Naples, standing upon Col. Haldeman's long dock, saw two 15 foot, 2x6 inch perpendicular stakes outlined against the southern horizon.
They marked historic points along the line of the first survey that determined the true contour and ratio of curvature of the earth's surface.
From the fixed stake on the approach of the Naples dock, the dignified stakes marked the direction of the meridian line.
Standing in the long line like sentinels of success, were the lesser stakes that indicated shorter intervals of space.
We had conducted a coast survey; with surveyor's instruments, a line or path along which the Rectilineator was to be moved section by section in precise adjustments, had been measured, and eighths of miles marked
by stakes, for 4.5 miles down the coast.

As the air line was to be straight, and as the shore line was a little irregular, the land elevation above the water level varied from 3 to 5 feet.
Excavations were necessary, and much other work of similar character, to remove all obstructions and dear the way for convenient and uninterrupted operations when the adjustments began.
We refer to these incidental preparations, in connection with all other factors involved in obtaining the results, to give something of an idea of the magnitude of the undertaking we had before us, to show that care was taken to attain accuracy;
that we were faithful and persistent in the execution of our plans; that we understood what was required to determine the facts involved in the question, geometrically, mathematically, practically, and mechanically; to manifest to the reader that we faithfully detail the entire proceeding all of the obstacles and difficulties, and how they were removed, as well as demonstration of principles and facts of measurements – to prove not only that the survey was made, and made honestly, and success achieved, but also to show that in consideration of the fact that it was the first attempt in the history of the world to make such a survey, its accomplishment is a marvel!

Prof. Morrow's System of Uniform Tide Measures.

We have shown through definition of the laws of hydrostatics, that the contour of the water's surface conforms to the general contour of the earth's surface;
consequently, its natural level constitutes the definite curve to which all our geodetic measurements must be referred;
that is, after relating that curve to a tangible air line or rectiline, the arc of the water surface is considered as the curve measured,
from which measurements we are to deduce a definite ratio of curvature.
The fact that it is impossible to operate on the water's surface and only on the land, necessitated the employment of a system of hypsometry for the measurements of the altitude of the surveyed line at every eighth division of a mile throughout the line of survey.

The average difference of tide levels on the Florida, coast is about 3.5 feet.
The mean tide level is a point midway between high and low tide levels.
It was necessary to ascertain this point with all possible precision, which we did by means of a tide register, consisting of a caisson, with perforations, and a tide staff measure, set in the Gulf, so that its bottom was below the level of low tide, and its top above the level of high tide.

pegel.gif (9623 Byte)
Transferring 128-inch Vertical Altitude to Naples Beach-Cross-sectional View, Looking South.

The perforations admitted the water from beneath at normal pressure, and prevented wave fluctuations; thus the water in the caisson was perfectly still, and only rose and fell, with the Gulf tide level.
When the mean tide level was obtained, it was marked upon the stationary tide register and became the fixed point to which all other measurements of water level were referred, as we will show.

We desired to project a line from the vertical altitude of 128 inches above a definite instead of a fluctuating level; consequently, by means of the tide staff extending
vertically from the caisson, that altitude was transferred to the land elevation where the survey began, by application of the principles of right angles, as in the Cross-sectional View.
The geodetic level was adjusted to cause the vertical angle to intersect the tide staff at altitude of 128 inches; we then had 128 inches altitude as a fixed point on the beach, as the altitude of the commencement of the air line.
As the mean tide level in the stationary tide register became a known and fixed quantity, it was taken as a basis of reference for the measure of the altitude of the air line at all station points along the entire line.

Mittleres Gezeitenniveau (19839 Byte)
Process of Referring all Measurements to Stationary Caisson-Land Elevation, Looking East.

We may illustrate this process of referring all other tide measurements to the original, by diagramming tide staff on stationary register, and tide staff on portable register at any other given point.
XY is the mean tide level, which is marked as a fixed point on staff A, the top of which is the altitude of 128 inches above mean tide level, which is also indicated on the beach as shown on preceding page. The tide staff A is divided into feet and inches.
Now what we desire to make clear to the reader, is how we could obtain the same vertical altitude with accuracy, at any other point along the line, by measurement of altitude staff B with the Gulf level constantly varying from the mean tide level.
We will take the measurement on tide staff A, for instance.
At the time of measurement, say 2 miles from the beginning, suppose the water level was 12 inches above mean tide level, leaving 116 inches of tide staff A., extending above the water at the stationary caisson.
The line PQ will represent the 116-inch measure on the staff.
Now if staff B, with inches marked from the vertical point the same as A, be fastened to Register B, 116 inches above the line PQ, it will have the same vertical altitude as A.
The water level in caisson A, as indicated on the staff A, was received at B by means of our Code of Signals, so that the adjustment of staff B at the proper altitude, or corresponding height above the water, was made at the same instant. In this way, no matter whether the measurements were taken at high or low tide, or at any water level between the two extremes, the results were accurate, because the fixed point at A was the constant and unvarying basis of reference.
When the vertical altitude of staff R was ascertained, the corresponding vertical angle was transferred to the land elevation, the same as illustrated in the cross-sectional view of the first tide measure.

Measurements of same vertical attitude above the water were made for 25 points along the beach from the beginning to the extremity of the line;
when completed, the 128-inch uniform vertical altitude of the 25 tide staffs, necessarily formed a line parallel with the water's surface, as in the above diagram. XY is the water's continuous surface
at mean tide level; the curved line PQ, represents the 128-inch vertical altitude of the tide staffs.
XY was our datum line, to which the altitude of the air line above the water at every successive eighth of a mile tide staff was referred.
The hypsometric principles involved in these measurements by means of the tide staffs are scientific, and the process admitted of accurate measurements.
With the line PQ established as a fixed line parallel with the mean tide level or datum line, measurements were made from the upper line of reference with equal accuracy; the upper datum line was constantly above the water, and on the land elevation, while the lower datum line was sometimes beneath the tide waters; we found it more convenient therefore, to measure from the vertical points than from the datum line beneath the vertical points.
When our datum lines were established, the preparations for the survey were complete.
The ground elevation on the beach on which the line was extended, was on the average about 4.5 feet above mean tide level; at the beginning of the survey, the highest land elevation, the hair line on the apparatus measured 53 inches above the ground.

Levels, Plumbs, Appurtenances, and Records.

Inasmuch as the Geodetic Survey was extended through space by means of right angles, regardless of any other method of determination of a straight line, and regardless of the consequences, it is obvious that it was not extended by any leveling process.
By reference to cut No. 4, Plate 1, it will be seen that the rectiline would vary from the water level in ever-increasing angles from the beginning to the end of the line. If the earth were convex, the line at the end of 4 miles would be higher than at the beginning,
and the angles would be divergent from the beginning; if concave, convergent from the beginning.
We used levels for two purposes: First, to level the first section; second, to ascertain and record the variation of the sections from the water horizontal at given points along the coast.
By reference to the "Comprehensive View of the Air Line," the reader will understand how the plumb-line should hang with reference to the right-angled bars first, if the earth were convex; second, if it were flat; and third, on the basis of the concavity.
The leveling of the first section was the point for the exercise and application of the greatest skill and accuracy;
he first section must be accurately leveled !
For this purpose we applied one of the finest and most sensitive spirit levels obtainable. In connection with this we had our 12-foot Mercurial Geodetic Level, invented by the writer, especially for this survey.
Being 12 feet in length, it was susceptible of being used with great accuracy and precision.
Applied to the first section, the spirit and mercurial levels agreed.
The plumb was also applied to the cross-arms of the first section, as additional corroboration.
The horizon was also observed in relation to the long straight-edge formed by a number of adjustments, and the straight-edge was perfectly parallel with the clear-cut water line of the Gulf of Mexico, viewed from a point three or four rods back of the appapatus, so as to place the under edge of the straight-edge and the water line in apparent contiguity.
The leveling was a careful, painstaking, and successful work, witnessed by every member of the staff, and finallypronounced perfect at 8 : 5o on the morning of March 18, 1897.
From thence the line was projected on the basis of the principles which we have demonstrated.
Constantly at the hand of the writer, moved along the line as the work progressed, was the convenient chest with thermometer, microscope, calipers, rules, compass, spirit level, triangles, protractor, telescope, thumb bolts, adjusting gauges, celluloid test card, etc., and the books of the staff, for the purpose of making the most accurate observations and measurements, and recording the same on the field of operations in the presence of all the witnesses.
Every item of adjustment, test, observation, and measurement was checked in the Check Record Book, and described in detail in the Daily Record Book, to which are appended the signatures of all operators and witnesses.
The facts of preparation, measurements, and survey contained in this work are taken today from the records, attested and sworn to by the entire Geodetic Staff and the Investigating Committee.

Personnel of the Staff, Investigating Committee, and Corps of Witnesses.

In our line of argument, it is necessary to introduce the Operator and witnesses, that the reader may judge of the character of the testimony concerning the facts observed; and to this end we publish the names of all those connected in any way with the experiments and survey conducted on the Florida coast.
The operations and observations were not witnessed by the Operating Staff alone.
Appended to this work are the statesments of the Visiting and Investigating Committee, concerning the facts observed when the air line was projected into the water on May 5, 1897, and the repetition of the same on May 8;
also the sworn statesments of the Operators and Watchman concerning the precautions taken to prevent any one tampering with the
apparatus or its adjustments.
In the list of Operating Staff, we briefly mention the position each occupied, and the class of work to which each was assigned:

Division A.
Prof. U. G. Morrow, Geodesist, head of the Expedition; Inventor of the Rectilineator; in charge of the Field Operations, Experiments, and Observations; director of Hypsometric Operations; special Newspaper Correspondent; directed and tested every Adjustment and Measurement of the entire Survey, and personally checked same in the Record Books.

[Now follows a list of all the persons participating in the measurement.] These names can be found in the book "The Cellular Cosmogony".

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