CHAPTER VI.
DIVISION OF THE CIRCLE AND METHODS EMPLOYED IN TAKING ANGLES—DIVIDING ENGINE—SURFACES FOR GRADUATION—VERNIER—VARIOUS SECTIONS—READING MICROSCOPES—SHADES—MICROMETERS—CLAMP AND TANGENT MOTIONS—OF LIMBS—OF AXES—USE AND WEAR—DIFFERENCE OF HYPOTENUSE AND BASE.
304.—Division of the Circle.—Sexagesimal Division.—All true surveying instruments depend, as their special function, upon taking the direction, or angular position, of surrounding objects or definite parts of the surface of the earth from positions which are at first accurately measured or ascertained. The instruments required for such work must possess an accurately divided circle or arc, with means of subdividing the visible divisions of this to greater closeness than any possible method of drawing lines simply would permit. The lines upon the circle in general practice in Great Britain are divided into degrees, which are subdivided to 30, 20, 10, or 5 minutes, according to the size of the instrument, and arranged for further subdivisions by means of a vernier into minutes or 30, 20, or 10 seconds of arc. Upon large circles, say of 10 and 12 inches diameter, and with modern 5, 6, and 8 inch diameters, angular displacements in the direction of the telescope are ultimately read off with a microscope by means of a screw with divided head, termed a micrometer, placed tangentially to the divided circle; or by a series of lines placed at equal distances apart in front of an eye-piece or within a microscope; but in the ordinary portable instruments, or those that a surveyor can personally carry about the country, the ultimate subdivisions of the circle are still generally made by a vernier scale only, which will presently be described, although the smaller modern micrometer reading instruments are slowly but surely coming into favour for all high class work.
305.—Centesimal Division.—Ten to fifteen years ago on the Continent generally, and in America occasionally, the division of the circle into 400-grades and ½-grades, and the subdivision of these decimally to centigrades, appeared to be coming more and more into use, particularly with the more extended use of the tacheometer. Under this system it will be seen that the right angle subtends 100 grades. This division, with its centesimal parts, was found to blend conveniently with logarithmetical calculation and to permit the free use of the slide rule with great saving of time over ordinary calculation, but it is now very little used.
The decimal division of the ordinary degree of 90 to the quadrant greatly facilitates the calculation compared with what is necessary with the sexagesimal division into minutes and seconds, and the reading of the verniers is much simpler and less liable to errors; moreover, the mental conversion of the sexagesimal division into decimals of the same degrees is much simpler than the conversion into the centesimal degrees of 100 to the quadrant.
306.—Dividing Engine.—This important tool is used for cutting the graduations on all surveying instruments. If possible a position should be secured for it on a ground floor at a mile or more distance from any railway, and at a good distance from roads upon which there is heavy traffic, as small vibrations are sufficient to cause unpleasant working and some error in the division of large instruments. For very accurate work some makers divide at night for the sake of stillness. The principles of construction of this machine, as at present in general use, were invented by Jesse Ramsden, of which an account was printed by the Board of Longitude in 1777. Refinements of detail have been added to the invention, and the steady action of steam or electric power has been applied in place of the foot, but otherwise the machine remains practically the same. Therefore a brief description of this machine as originally invented will be sufficient for the purposes of this work, which is not intended to fully describe the tools used in the manufacture of instruments.
307.—Ramsden's Engine consists of a circular brass surface plate, made generally of 36 inches diameter. This plate is supported from below upon a hollow vertical axis, which moves in an adjustable collar placed at its upper end and in a conical point or pivot at its base. The pivot rests in a cup of oil and supports the weight of the plate and axis, so that this part rotates with little friction. The outer edge of the surface plate is cut with 2160 teeth or threads, into which an endless or tangent screw works, so that the plate can be revolved any desired quantity by means of the screw. Six turns of the tangent screw moves the plate 1°. The head of the tangent screw is divided as a micrometer into 60 parts; therefore the movement of one of the divisions of this head revolves the plate 10″ of an arc. A ratchet wheel of 60 teeth is attached to the tangent screw, and so arranged that by reciprocating motion applied to a rack which works into it the circle can be advanced any multiple of 10″. Motion is given to the tangent screw by a catgut over a pulley worked by the foot. The work is centred and clamped down upon the surface plate. While the divisions are being cut this surface plate remains for the time quite stationary.
308.—The dividing knife is attached to a swinging frame having a reciprocating motion. The forward extent of its swing is regulated by a detent wheel with teeth of varied heights, which, as they are brought by the mechanism consecutively forward, stop the knife at a definite position; so that the cuts upon the circle—technically the limb—are regulated for lengths to represent 10 degrees, 5 degrees, degrees and parts. In the use of this dividing machine the divider who worked it had alternately to press his foot upon a treadle and then pull a cord attached to the dividing knife frame. These motions are now performed by self-acting mechanism. For full particulars and details of the dividing engine see Troughton's Memoir, Phil. Trans., 1809: Memoirs of the Royal Astronomical Soc., vol. v. p. 325; vol. viii. p. 141; vol. ix. pp. 17 and 35. For various plans that have been tried see Holtzapffel's Turning and Mechanical Manipulation, pp. 651–955.