GRADUATION. . 99 GRADY. I step, from gradi, to walk). The art of laying oil scales of measurements, as the tape, protractor (q.v. ), or vernier (q.v.). The simplest i)roblem in graduation is the dividing of a straight line, such as the linear scale, or rule. Standard scales being abundant, it is only necessary to make a careful copy of an original. If the material used is wood or iron, the divisions may he marked off by the use of a dividing square and knife-edge. The dividing square is simply a piece of steel in the form of an L, one arm of which may be moved from one division of the scale to another, while the other arm serves to guide the knife in mark- ing the new scale. The original graduation of linear scales into equal divisions was performed either on the principle of bisection or of 'step- ping.' In the case of bisection, beam or exten- sion compasses (see CoMP.ssES) serve to de-. scribe an arc from each end of the line to be graduated, so as to locate the bisection point. The two arcs drawni by the compasses cannot be made to touch with sufficient precision for accu- rate dividing. The small inten'al between the arcs may be divided by the aid of a microscope and delicate compasses, thus approaching more nearly the bisection point of the original line. In the same way, each segment may be divided again, and so on. It is evident that all divisions cannot be effected by bisection, hence such instru- ments as the diagonal scale (q.v.) are employed. 'Stepping' is performed with delicately pointed compasses, which are adjusted as nearly as pos- sible to the length of a required division. Be- ginning at one end of the line, the compasses are turned round each leg alternately until the whole line is stepped off. If the last step falls short of or beyond the end, the compasses are adjusted accordingly, and the process is repeated until the desired accuracy is attained. The method of bisection is more accurate in practice, and was adopted by Graham (17'25), Bird (1767), Eams- den. Troughton (1809), and other eminent in- strument-makers in original graduation. Curved lines may also be graduated on this principle. Since the chord of an arc of 60° is equal to the radius of the circle, the circumference may be divided into six equal parts with a precision de- pending only on the delicacy of the instruments. Further division depends upon bisection. The amoiint of care, patience, skill, and delicacy of touch required in the original graduation of im- portant astronomical instruments is such that comparatively few men have been found com- petent for the task, and these have been almost as famous as the astronomers who have success- fully used the instruments. The necessity of ex- treme accuracy in graduating a scale will be understcKxl by considering the application thai is made of these divisions. The mariner, for ex- ample, determines his latitude by taking the meridian altitude of the sun. Fot this purpose he uses a sextant, the arc of whose limb corre- sponds to the cun'ed surface of the glolje. Whence the real error in latitude bears the same ratio to an error in the scale that the earth's radius bears to the radius of. the arc. If each degree occupied an arc of | of an inch, an error of j-^jj of an inch in a division would thus mislead the mariner to an extent of more than four statute miles as regards his position at sea. But a ship's quadrant is a rude instrument compared with astronomical transits for meas- uring celestial angular distances by means of a divided arc; in these, a deviation of a thousandth part of an inch is regarded as a serious error. Tlie methods of original graduation above described are used only for the largest and most important astronomical or gemletic instruments. Ordinary instruments are graduated by dividing- plates or engines, which co|>y and adapt a stand- ard set of divisions. The dividing-plate which is used for conunon purposes, such a.s dividing com- pass-rings, theodolites, and sextants, is a divided circle with a straight-edge, made movable on the axis or arbor of the plate in such a manner that its edge during every part of its revolution shall fall in the exact line from centre to cir- cumference. The ring, protractor, or other in- strument to be divided, is clamped upon the plate with its centre exactly coinciding with that of the plate, and the straight-edge is moved round, and made to halt at the required divisions on the circumference of the dividing-plate; and by using the steel straight-edge as a guide, corre- sponding divisions are marked off upon the con- centric arc of the instrument to be divided. TJie dividing-engine is a verj' complex machine, requir- ing the greatest accuracy and care in its con- struction. Among the styles of dividing-engines may be mentioned the English t^'pes of Ramsden (1777), Troughton (1793). Simms and Ross, the German types of Keichenbach, and the French tj'pe of Gambey. A detailed account of these would far exceed the limits of this article. Their principal parts consist of a large toothed circle, graduated with extreme care by original division ; a very carefully constructed endless screw works in these teeth, and is moved through any given number of revolutions, or any measured fraction of a revolution, by means of a treadle or other suitable power, thus making the requisite steps for each division, another part of the machine cutting a fine line at the moment of the halt of each step. These divisions are cut upon an arc of silver, gold, or platinum, which is soldered or inlaid upon the limb of the instrument, the precious metals being used on account of the ox- idation to which conuuon metals are liable. Consult: Bird, Method of Dividing Astronom- ical Instruments (London. 1707) : Ramsden. De- scription of an Engine for Dividing Mathematical Instruments (London, 1777) ; and "Memoir" of Troughton, in Phitosophical Transactions (Lon- don, 1809). For history of efforts at graduation and notes on the modern methods, consult Wat- kins, "The Ramsden Dividing Engine," in Smith- sonian Report (Washington, 1890). GRA'DUS AD PARNAS'SUM (Lat., steps to Parnassus). (1) A name applied to a Latin or C4reek dictionary, in Avhich the vowel quan- tities are marked, and which hence is useful in verse composition. (2) The name was also used as the title of a Latin work on composition and counterpoint by .7. J. Fux (1725), and of a French work on the art of piano-playing by de- menti (1817). GRA'DY, Henry Woodfex (1851-89). An American journalist and orator. He was bom at Athens. Ga., 1851. and after being educated at the L'niversity of Georgia at Athens, he began his work as a journalist in a series of letters on the resources of his native State, which attracted nnich attention. In 1880 he purchased an inter- est in and became editor of the Atlanta Constitu- tion, as which he remained till his death, contrib-
