Extracted text
Editorial transcription, lightly normalized from the scan. Line-break hyphenation, spacing, capitalization, and unmistakable OCR errors have been repaired; the claims remain those of The Flaming Sword.
EDITOR FLAMING SWORD:—I have had two letters from Samuel Blodgett since I wrote you. In his last letter he sends the following:
"If they were honest they would be glad to have attention called to the suspicious spots, so as to give an opportunity for explanations. But here is a very important one that they skipped; and as long as it is too hard a nut for them to crack at headquarters, perhaps you will condescend to try and help them out. They say that vision curves upward at the rate of 13 inches to the mile, and yet Prof. Morrow used it for 1¾ miles of his 4-mile survey, and came out just where he would if he had used the rectilineator, or looked over a straight line all the way. If this is true, such a result could not have happened. Will you figure out where he should have hit the Gulf with the vision curving up at that ratio? And, if he could use the projected vision for nearly half the way, why could he not have been equally successful in using it the whole distance? This is too much for Teed & Co.; now please try your hand.—SAMUEL BLODGETT."
I do not know that you take the position he claims. If you do, you will kindly publish his criticism and then "floor" him. If you do not hold to what he criticises, kindly clear up the quesiton. I cannot answer him unless I know your position. No base is named in his quotation; hence I must find out from your writings if you enjoy the position he criticises. Hoping to see his criticism in THE SWORD, and your reply, I am,—R. O. S., Monroe, Wis.
So we are face to face with an inexplicable difficulty! We have met a number of this kind from the western attorney—notably the one concerning the earth's curvature, according to which we should have hit the Gulf at a distance of about fifteen miles, on which we so quickly silenced him. The critic had the misfortune to "run amuck" the Editor of THE FLAMING SWORD on the question of admissible language, and a part of a letter of his was excluded. The above points were wrapped up in ungentlemanly insinuations, and we fed them to the office cat. Of course, ever since that time, we did not dare answer them! We have before us now a letter from him which we would publish if it were not personally insulting, in which the Editor of THE SWORD is informed that the critic knew that he was "dealing with a wary cuss,"—advising us to "make a clean breast, and leave the rotten concern," because we could "do better than be the menial of an obsessed lunatic." Failing in his attempt to overthrow the facts of the Koreshan premise, and smarting in chagrin, he resorts to this kind of language; but we are not dealing in this kind of ware, and so he refused to continue his arguments. We answer his criticism now because it is trimmed down to respectable terms and size, and because we bear him no ill-will.
The question is, How is it, if vision curves upward at the ratio of 13 inches to the mile, did the visual line—projected 1.75 miles into the Gulf of Mexico, in the Florida survey—strike the water where a straight line would have terminated? This reminds us of the reply the student gave the professor when asked to describe a crab. "It is a large red fish." "Correct," said the professor, "except that it is not large, it is not red, neither is it a fish!" The projected visual line did not strike the Gulf at the point where a straight line projected from the 2.375 mile air-line station would have terminated, neither did the visual line which completed the survey, curvate 13 inches to the mile.
The article from which our critic gets his information concerning the Florida survey, was written in the general terms of newspaper reports, without going into the details; this was reserved for the book we are now publishing. In the reports sent out from the field of operations before the more definite measurements on the shore-line alongside the visual projection, we said the distance from the beginning was "about four miles." According to the calculated ratio of the earth's curvature, beginning 128 inches above the water level, the rectiline, as line A in the diagram, should have terminated at b, in exactly 4 miles; while in practical operations, concluding with the visual line C, the survey terminated at the surface of the Gulf at d, in a little over 4.125 miles from the starting point.
[Printed figure, spanning the first two columns of p. 12, captioned "Diagram of Florida Geodetic Air Line, from 2-mile Station to Gulf Surface, showing difference between Rectiline, Telescopic Visual Projection, and Visual Curvilineation from Unaided Eye."]
According to the recorded and tabulated facts of the measurements from which our ratio is deduced, the air line cut the stakes at the last few stations a little lower than the calculated ratio would indicate, showing either a little more rapid curve of the earth in that vicinity, or a swell in the Gulf due to the crowding of the waters into the Pass in its entrance to the Bay of Naples. If it were not a swell, an absolutely straight line would have terminated at a point a little short of 4 miles, making a still greater difference between the points of the termination of an absolute rectiline and the visual line projected beyond the Pass. The calculated curvature for 4 miles is 128 inches; for 4.125 miles, 136.125 inches, making a difference of 8 inches between the probable rectiline and the visual line in a little over 1.75 miles. If the rectiline would have terminated a little short of 4 miles, say 3.875 miles, the difference would be about 15 inches.
We will give you for him, the results obtained by "figuring out" where we should have "hit the Gulf" in our survey with the visual line E, curving upward at the rate of 13 inches to the mile, in 1.75 miles: multiplying the square of the distance by 13 inches, gives 39 inches. The distance from the beginning of the survey at which the earth would curve 39 inches above the 4 mile point is 4.56 miles, represented in the diagram by the intersection of the line E with the arc XY at f. The 13-mile ratio must be taken as curving from the external tangent, and not as curving at that ratio of divergence from the earth's surface. The ratio of perspective elongation is 5 inches to the mile in excess of the earth's upward curvature.
But why did not the line terminate at 4.56 miles instead of 4.125 miles if the vision curves 13 inches to the mile? The fact that the telescope extends the horizon point, admitting of vision of objects apparently below the horizon to the naked eye, proves that a different ratio of the general direction of the visual energy obtains when the telescope is employed; If to the naked eye it is 13 inches to the mile, through a powerful instrument, such as we used, the ratio would be much less, and would nearly conform to the figures given of the difference between the terminal point of the visual line and the calculated distance. Besides the observations were made at high tide, while our datum arc was mean tide level; had our visual projection been made at mean tide it would have extended to a more distant point. We came out about right, you see!
Why could we not use the visual line throughout the whole distance of 4.125 miles, if we could use it successfully for 1.875 miles? Viewed over a leveled straight-edge, the horizon appears to drop below the visual line a few seconds of a degree. The curve of vision in excess of that of the earth is about 5 inches to the mile; in 4 miles, according to this ratio, the visual line would rise 80 inches above the earth—starting parallel, and both curving upward, the earth 8 inches, and the visual line 5 inches in excess of the ratio, to the mile. The difference of ratio would accelerate in proportion to the square of the distance. A straight line if extended on a concave surface, converging with the surface at a given distance, will sustain different angles to the curvating surface at given points, because the water level constantly changes in its relation to the chord as the distance increases from the starting point; so that at the end of 2.375 miles the angle is decided and distinct, covering a greater number of seconds of a degree than the apparent drop of the horizon, and consequently, the visual line would extend below the horizon. If the air line had been level at the 2.375 mile station, the visual line from that point, beginning parallel with the water's surface, would have extended above the horizon the same as at the beginning.
The angle of convergence of the air line at the 2.375 mile station, for the length of 12 feet was .115 inch. This is very nearly the legitimate angle according to geometrical and mathematical calculation, which would make it about .09. For the space of 66 feet, the angle measured 5.57 inches; 660 feet is 55 times 12 feet, making the angle for the longer distance proportionably about the same. This angle measured anywhere, at any time, would project a line below the horizon, subject to the test of anyone—for we here give the figures for altitude of observation about 5 feet above the water. It's the angle-worm that catches the fish!
We might ask a question as logical as the one just answered: Why, if you can hit a spot with a gun at a given angle at a distance of 10 feet, can you not with equal accuracy, hit the same spot with the gun placed at a different angle? If you make the angle of deviation large enough, one can project a visual line to a point nearly 200 miles away, below the horizon, from an altitude of 25,000 feet.
Ask our friend if he has any more "suspicious spots" that we are afraid of. This one was rather dim; he tried to paint it darker, but his re-marks were neither indelible nor infallible; they were all in his eye, and not on us!
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The source scans remain the record. This page preserves the periodical's argument and reported observations without presenting its conclusions as independently established results. The claims remain attributed to The Flaming Sword.
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The Flaming Sword · Vol. 12, No. 46 · · PDF pp. 11-12