We have followed the logical line of sequences from the fundamental premise to conclusions applied in practical mechanics. Every factor thus far considered is indisputable.

Sections of the Rectilineator in Adjustment

We now purpose to describe the embodiment of all theseprinciples of right-angulation and rectilineation in a tangible apparatus, the use and purpose of which can now be easily comprehended by the reader. The Koreshan geodetic apparatus called the Rectilineator (from rectus, right, and linea, line), an instrument for surveying a straight line, was invented by the writer in 1896, at the instance of the Founder of Koreshanity, for the purpose of demonstrating the premise of the Koreshan Cosmogony. This instrument is constructed so as to involve the factors of constancy, convenience of operation, and precision of adjustment, which we will briefly describe and illustrate.
The Rectilineator consists of a number of sections in the form of double T squares, each 12 feet in length, with
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braced and tensioned cross-arms 4 feet in length. The length of the cross-arms is to the length of the sections, as 1 is to 3.
The material of which the sections of the Rectilineator are constructed, is inch mahogany, seasoned for twelve years in the shops of the Pullman Palace Car Co., Pullman, Illinois.
The horizontal bar of each section is 8 inches in width, while the cross-arms, are five inches wide. Steel tension rods crossing the horizontal bar transversely and extending through the extremities of the cross-arms. are adjusted to maintain the constancy of the right angles.

Cross-arms of the Rectilineator in Accurate Adjustment

Finely trimmed brass facings at the extremities of the cross-arms constitute the adjusting surfaces. Through flanges on the facings, ingenious screws were placed for securing the adjustments, when made.
As will be seen from the cuts in this connection, each section was supported by two strongly built, platformed standards, with adjustable castings to receive the horizontal sections between the body of the castings and adjustable cleats with clamps and set screws. The sections rest in the castings edgewise, the cross-arms extendings perpendicularly, as shown in the picture.

Modus Operandi of the New Geodesy.

The principle involved in the operation of the Rectilineator, is as simple as that of placing two rectangular plates in contact, or laying two mechanic's squares together.
Indeed, from the foregoing the mind with a mechanical eye can at once understand the method without further description .
Supposing the first section accurately leveled and fastened to its standards by the clamps and screws, the reader is ready to imagine the adjustment of Section No.2 to No. 1.
This is accomplished by placing two standards in proper place in line with the preceding standards, and placing the castings at approximately the proper height.
Section No. 2 is placed in position in the castings; set screws are turned so as to raise or lower the horizontal axis to approximate coincidence with the middle line of the first section.

The brass facings are brought to within one fourth of an inch of contact. Operators of the set screws are directed to raise or lower the section to bring the hairlines on the two sections exactly coincidental; fine lines are read with the microscope and the section is carefully moved horizontally by the device for that purpose, until the brass facings are one fiftieth of an inch apart, as determined by a bristol card.

The precise adjustment is determined on the same principle that the thickness of paper is measured by the finest micrometers, differing only in the fact that the metal surfaces are adjustable, while the thickness of the celluloid card, 0.01 inch in thickness, is constant.
In measuring the thickness of sheets of paper, the fact that when two sheets of paper pass between the fingers of the micrometer with equal friction, proves the sheets to be of equal thickness.

The difference of a millionth of an inch can be determined in this way.
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So, in case of adjustment of the sections of the Rectilineator, when the same card passes between the brass surfaces at top and bottom of the cross-arms with equal friction, it proves that the adjustment is precise; that the brass surfaces of Section 2 are in adjustment with those of Section 1, and that consequently the hair-line extending the whole length of Section 2 is in line with the hair line on Section 1. The two sections are now ready for bolting; when bolted, the sections are firm and free from disturbance, while other adjustments are being made to Sections 2, 3, and so an. The same processes are repeated in adjusting Section 3 to Section 2. Only the first section is leveled, for the line to be extended is one which will not follow the curve of the earth, but one that will continue as a rectiline, the line which crosses at right angles the perpendicular at the point of beginning of the survey.
The straight line is forced by right-angulation, from the first section forward to the terminus of the line. Every succeeding adjustment being exactly like the first, necessitates the conclusion that every cross-arm is parallel with all others by virtue of actual contact, and that consequently the hair-line of each section is an extension of the hair-line of each preceding section. This conclusion is so simple, and so in keeping with our premise at the beginning of the argument, as to be absolutely conclusive.

So far we have taken nothing for granted, and have asserted only that which is known by every mathematician and mechanic to be true.
If we can know that right angles are equal, and they are invariable and constant in their geometrical functions, we can also know that the principles of right-angulation and mechanical rectilineation are one and the same.
The unique principles and points of the Rectilineator, -
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factors of certainty to be considered in the line of evidences and arguments previous to our final conclusion, may be summed up as follows:
It is constructed upon geometrical and mechanical principles.

Proceeds from a known basis of measurement with invariable results.
Compensates for contraction and expansion.
Eliminates atmospheric refraction and visual perspective.
Furnishes a constant basis of reference for levels, tests, and measurements, and for ascertaining ratio of curvature of the earth.

Methods of operation and and results obtained can be understood by the simplest mind.
It does not require a "scientist" to interpret the results.
It has two points of adjustment for each cross-arm -finely trimmed brass facings.
Adjustments are made secure from tampering hands by bolts; each adjustment is witnessed by every operator.
Standards are platformed, to obviate settling.

Other apparatus are mounted on tripods, terminating in sharp points extending into the ground.

A complete system of reversals of the sections corrects any possibleinaccuracies or deviation of right-angles in the cross-arms. This system makes impossible the charge of any predetermined plan to construct the instrument so as to run a curved line.
The sections were subjected to all the known crucial tests of right angles, and the lines were read with microscope.
In trial surveys of a given distance and return, the hair-line axis returned to hair-line on brass plate on firmly set stake at starting point, thus proving the perfection of the instrument and the possibility of absolutely accurate adjustments.
From the above, it will be seen that the principles upon which the Rectilineator is constructed, differentiate it from all other geodetic apparatus ever used, in the simple feature that it has two adjusting points for each cross-arm instead of one, - as the end of a rod.
Its object is to force a straight line instead of following one to measure its length.
It is not intended to survey a straight line as related to the right or left, but an air line from the vertical point of any given perpendicular, in accordance with the plans and specifications presented in the previous chapter.

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Following the line of argument from the fundamental premise to the embodiment of the principles in a Geodetic Apparatus, we are ready to present the facts of the actual demonstration achieved through its use. On the evening of March 17, 1897, the Rectilineator stood at the beginning of the line of survey, at Naples, Fla., ready for the first adjustment in the first and only geodetic survey ever made in the history of the world, to determine whether the earth is flat, convex, or concave

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