If held in a horizontal position it serves as an ordinary pocket compass and thus indicates the magnetic meridian in the plane of which it should be held when used to ascertain dip.
CHAPTER XII.
INSTRUMENTS TO MEASURE SUBTENSE OR TANGENTIAL ANGLES TO ASCERTAIN DISTANCES—HISTORICAL NOTES OF THE METHOD—PRINCIPLES INVOLVED—STADIUM MEASUREMENT, DIRECT AND BY THE ORDINARY TELESCOPE—CORRECTIONS FOR REFRACTION OF THE OBJECT-GLASS—STANLEY'S SUBTENSE DIAPHRAGM—ANALLATIC TELESCOPE OF PORRO—TACHEOMETERS—STADIUM—FIELD-BOOK—OMNIMETER AND ITS FIELD-BOOK—BAKEWELL's SUBTENSE ARRANGEMENT.
553.—Direct Subtense Measurement of Distances, by an Instrument, depends upon our powers of measuring the image of a distant staff or stadium, or the divisions marked thereon as they appear at the focus of the telescope. If the stadium is placed at right angles to the direction of one of two sight lines which subtend a given angle, the number of units divided upon the stadium cut by these lines will be proportional to units of length of base or cotangent for a constant focus of the telescope; so that if we can measure at a fixed angle the number of equal units of measurement of a stadium correctly, we can obtain its exact distance; and whether this method is more or less exact than chain measurement will depend entirely upon the perfection with which either of these operations may be practically performed.
554.—The Origin of the Invention of Subtense Surveying was thought to be due to Wm. Green, an optician of Great Moulton Street, London, who was awarded a premium for its invention by the Society of Arts in 1778. He published a pamphlet giving a description of his method in 1778.[28] This subject he pressed upon the notice of professional men at the time, and his method has continued in use in this country ever since. His refracting telescope, which alone has remained in use, formed part of the theodolite. A micrometer was placed in the focus of the eye-piece of the telescope, which revolved a quarter turn in its axis to read angles vertically or horizontally. He constructed his micrometer with lines fixed at a given distance apart, and by a second method with the lines adjustable. For this adjustment a fine line was ruled upon one side of two pieces of glass. The ruled sides were placed face to face, so as to be at the same focus. One of the lines was adjustable by a micrometer screw. His staff was 20 links in length by 4 inches in width, divided decimally into 1000. His description of the manner of using his instrument will give a general idea of working the others which have been derived from it—tacheometers, omnimeters, etc.—and this is worthy of note, as the invention, though generally attributed to him, was not his:—
555.—"To find the contents of a field with either of the instruments described, let the telescope be placed so that the observer may see all its angles from his station. If near the centre of the field the better. The person who carries the scale (staff) is to go all round the field, stopping at every angle, and to place the scale at right angles to the axis of the telescope (passing) from corner to corner (from right to left if required) with the help of a signal by the observer. After the distances all round the field are taken (by measurement of the image of the micrometer) and all the angles included betwixt them, with the theodolite, plot it out in the usual manner, e.g., with a nonius protractor. Describe a circle, and on this circle set off all the angles from the centre through each point upon the circumference. Set off the length of every line by a scale of equal parts. These points will give the limits of the field, which may be laid out in trapeziums, triangles, etc., and measured from the same scale of equal parts. The surveyor will comprehend how easily the contents of the field are found by trigonometrical calculation, since by this method there are two sides and one included angle given.
"The common method of measuring with the chain, besides the inaccuracies to which it is liable, does only give the length of the surface of the ground between two objects, and therefore not its proper distance, unless the surface be straight and no object to hinder its being measured from one end to the other. How often this is practicable I leave to the consideration of those who are most accustomed to measure lines, and doubt not that upon the whole they will find the telescope method has besides ease, accuracy, and universality, necessity itself to recommend it."
He points out the utility of the system for levelling, as "both distance and inclination may be taken at the same time." He finds by experiment that the accuracy of the method exceeds that which he could reasonably expect by calculations deduced from theory, by several circumstances in its favour being inseparable from it.