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Updated: May 29, 2025
In the month of December, 1882, I was in this part of the world again. During the six years that had elapsed since my last visit in 1876, a survey party had reached these ranges on a trigonometrical survey, and upon its return, the officer in charge reported having had some trouble and a collision with the natives of the Everard Range. I suppose my second visit occurred two years after that event.
He had learnt from ships returned from the Friendly Islands, that their King had recently conquered the Navigator Islands, which now paid tribute to him. The map of Matarai, and of the bay which bounds it on the north-east, completed by us with the utmost care from trigonometrical surveys, is attached to this volume, and renders any further description of the coast it embraces unnecessary.
I had only to prepare the fundamental data for him, explain what was wanted, write down the matters he was to start with, and he ground out day after day the most complicated algebraic and trigonometrical computations with untiring diligence and almost unerring accuracy. But a dark side of the picture showed itself very suddenly and unexpectedly in a few years.
Laplace says that the only observation which the history of astronomy offers us, made by the Greeks before the school of Alexandria, is that of the summer solstice of the year B.C. 432. by Meton and Euctemon. We have, for the first time, in that school, a combined system of observations made with instruments for the measurement of angles, and calculated by trigonometrical methods.
Whether the horizontality of the shelves or terrace-lines is really as perfect as has been generally assumed is a point which will require to be tested by a more accurate trigonometrical survey than has yet been made.
Now and then he would creep from the shyness which enveloped the inventive side of his nature, and would talk with her with unintelligible earnestness of these dreadful engines; of radial and initial hoop pressures, of drift angles, of ballistics, of longitudinal tensions, and would jot down trigonometrical formulae illustrated by diagrams until her brain reeled; or of his treatise on guns of large caliber just written and now in the printers' hands, and of the revolution in warfare these astounding machines would effect.
The celebrated Italian astronomer, Schiaparelli, took advantage of this opportunity to make a trigonometrical survey of the surface of Mars as coolly and confidently as if he were not taking his sights across a thirty-five-million-mile gulf of empty space and in the course of this survey he was astonished to perceive that the reddish areas, then called continents, were crossed in many directions by narrow, dusky lines, to which he gave the suggestive name of ``canals. Thus a kind of firebrand was cast into the field of astronomical speculation, which has ever since produced disputes that have sometimes approached the violence of political faction.
The topographical chart of the property and its environs was completed. It was executed on a considerable scale; the character of the particular localities was made intelligible by various colors; and by means of a trigonometrical survey the Captain had been able to arrive at a very fair exactness of measurement. He had been rapid in his work.
Acting on this reasoning, he got the master of a neighbouring school to give me after-time lessons in mathematics and geography; and, in the course of a few months, I was able to be inducted into the mysteries of great circle sailing and the art of taking lunars, much to the admiration of Sam, whom I'm afraid I often took a delight in puzzling with trigonometrical phrases that sounded full of portentous difficulty, albeit harmlessly easy.
The force required to move the thing up a slope is directly proportional not to the angle, but to the trigonometrical sine of that angle. To measure this, place the tricycle, or Otto a bicycle will not stand square to the road, and therefore cannot be used pointing in direction at right angles to the slope of the hill, so that it will not tend to move.
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