GUNTER (Edmund)

, an excellent English ma-| thematician, was born in Hertfordshire in 1581. He was educated at Westminster school under Dr. Busby, and from thence was elected to Christ-church College, Oxford, in 1599, where he took the degree of master of arts in 1606, and afterwards entered into holy orders; and in 1615 he took the degree of bachelor of divinity. But being particularly distinguished for his mathematical talents, when Mr. Williams resigned the professorship of astronomy in Gresham College, London, Mr. Gunter was chosen to succeed him, the 6th of March, 1619; where he greatly distinguished himself by his lectures and writings, and where he died in 1626, at only 45 years of age, to the great loss of the mathematical world.

Mr. Gunter was the author of many useful inventions and works. About the year 1606, he merited the title of an inventor, by the new projection of his Sector, which he then described in a Latin treatise, not printed however till some time afterwards.—In 1618 he had invented a small portable quadrant, for the more easy finding the hour and azimuth, and other useful purposes in astronomy.—And in 1620 or 1623, he published his Canon Triangulorum, or Table of Artificial Sines and Tangents, to the radius, 10,000,000 parts, to every minute of the quadrant, being the first tables of this kind published; together with the first 1000 of Briggs's logarithms of common numbers, which were in later editions extended to 10,000 numbers.—In 1622, he discovered, by experiment made at Deptford, the variation or changeable declination of the magnetic needle; his experiment shewing that the declination had changed by 5 degrees in the space of 42 years; and the same was confirmed and established by his successor Mr. Gellibrand.—He applied the logarithms of numbers, and of fines and tangents, to straight lines drawn on a scale or rule; with which proportions in common numbers and trigonometry were resolved by the mere application of a pair of compasses; a method founded on this property, that the logarithms of the terms of equal ratios are equidisserent. This was called Gunter's Proportion, and Gunter's Line; and the instrument, in the form of atwo-foot scale, is now in common use for navigation and other purposes, and is commonly called the Gunter. He also greatly improved the Sector and other instruments for the same uses; the description of all which he published in 1624.—He introduced the common measuring chain, now constantly used in land-surveying, which is thence called Gunter's Chain.—Mr. Gunter drew the lines on the dials in Whitehall-garden, and wrote the description and use of them, by the direction of prince Charles, in a small tract; which he afterwards printed at the desire of king James, in 1624.—He was the first who used the word co-sine, for the sine of the complement of an arc. He also introduced the use of Arithmetical Complements into the logarithmical arithmetic, as is witnessed by Briggs, cap. 15, Arith. Log. And it has been said that he first started the idea of the Logarithmic Curve, which was so called, because the segments of its axis are the logarithms of the corresponding ordinates.

His works have been collected, and various editions of them have been published; the 5th is by Mr. William Leybourn, in 1673, containing the Defcription and Use of the Sector, Cross-staff, Bow, Quadrant, and other instruments; with several pieces added by Samuel Foster, Henry Bond, and William Leybourn.

Gunter's Chain, the chain in common use for measuring land, according to true or statute measure; so called from Mr. Gunter its reputed inventor.

The length of the chain is 66 feet, or 22 yards, or 4 poles of 5 1/2 yards each; and it is divided into 100 links, of 7.92 inches each.

This Chain is the most convenient of any thing for measuring land, because the contents thence computed are so easily turned into acres. The reason of which is, that an acre of land is just equal to 10 square chains, or 10 chains in length and 1 in breadth, or equal to 100000 square links. Hence, the dimensions being taken in chains, and multiplied together, it gives the content in square chains; which therefore being divided by 10, or a figure cut off for decimals, brings the content to acres; after which the decimals are reduced to roods and perches, by multiplying by 4 and 40. But the better way is to set the dimensions down in links as integers, considering each chain as 100 links; then, having multiplied the dimensions together, producing square links, divide these by 100000, that is, cut off five places for decimals, the rest are acres, and the decimals are reduced to roods and perches, as before.

Ex. Suppose in measuring a rectangular piece of ground, its length be 795 links, and its breadth 480 links.

	795
	480
	63600
	3180
Ac.	3.81600
	4
Ro.	3.264
	40
Per.	10.560

So the content is 3 ac. 3 roods 10 perches.

Gunter's Line, a Logarithmic line, usually graduated upon scales, sectors, &c; and so called from its inventor Mr. Gunter.

This is otherwise called the line of lines, or line of numbers, and consists of the logarithms transferred upon a ruler, &c, from the tables, by means of a scale of equal parts, which therefore serves to resolve problems instrumentally, in the same manner as logarithms do arithmetically. For, whereas logarithms resolve proportions, or perform multiplication and division, by only addition and subtraction, the same are performed on this line by turning a pair of compasses over this way or that, or by sliding one slip of wood by the side of another, &c.

This line has been contrived various ways, for the advantage of having it as long as possible. As, first, on the two feet ruler or scale, by Gunter. Then, in 1627 the logarithms were drawn by Wingate, on two separate rulers, sliding against each other, to save the use of compasses in resolving proportions. They were also in 1627 applied to concentric circles by Oughtred. Then in a spiral form by Mr. Milburne of Yorkshire, about the year 1650. Also, in 1657, on the present common sliding rule, by Seth Partridge.

Lastly, Mr. William Nicholson has proposed another disposition of them, on concentric circles, in the Philos. Trans. an. 1787, pa. 251. His instrument is equivalent| to a straight rule of 28 1/2 inches long. It consists of three concentric circles, engraved and graduated on a plate of about 1 1/2 inch in diameter. From the centre proceed two legs, having right-lined edges in the direction of radii; which are moveable either singly, or together. To use this instrument; place the edge of one leg at the antecedent of any proportion, and the other at the consequent, and fix them to that angle: the two legs being then moved together, and the antecedent leg placed at any other number, the other leg gives its consequent in the like position or situation on the lines.

The whole length of the line is divided into two equal intervals, or radii, of 9 larger divisions in each radius, which are numbered from 1 to 10, the 1 standing at the beginning of the line, because the logarithm of 1 is 0, and the 10 at the end of each radius; also each of these 9 spaces is subdivided into 10 other parts, unequal according to the logarithms of numbers; the smaller divisions being always 10ths of the larger; thus, if the large divisions be units or ones, the smaller are tenth-parts; if the larger be tens, the smaller are ones; and if the larger be 100's, the smaller are 10's; &c.

Use of Gunter's Line. 1. To find thē product of two numbers. Extend the compasses from 1 to either of the numbers, and that extent will reach the same way from the other number to the product. Thus, to multiply 7 and 5 together; extend the compasses from 1 to 5, and that extent will reach from 7 to 35, which is the product.

2. To divide one number by another. Extend the compasses from the divisor to 1, and that extent will reach the same way from the dividend to the quotient. Thus, to divide 35 by 5; extend the compasses from 5 to 1, and that extent will reach from 35 to 7, which is the quotient.

3. To find a 4th Proportional to three given Numbers; as suppose to 6, 9, and 10. Extend from 6 to 9, and that extent will reach from 10 to 15, which is the 4th proportional sought. And the same way a 3d proportional is found to two given terms, extending from the 1st to the 2d, and then from the 2d to the 3d.

4. To find a Mean Proportional between two given numbers, as suppose between 7 and 28. Extend from 7 to 28, and bisect that extent; then its half will reach from 7 forward, or from 28 backward, to 14, the mean proportional between them.—Also, to extract the square root, as of 25, which is only finding a mean proportional between 1 and the given square 25, bisect the distance between 1 and 25, and the half will reach from 1 to 5, the root sought.—In like manner the cubic or 3d root, or the 4th, 5th, or any higher root, is found, by taking the extent between 1 and the given power; then take such part of it as is denoted by the index of the root, viz, the 3d part for the cube root, the 4th part for the 4th root, and so on, and that part will reach from 1 to the root sought.

If the Line on the Scale or Ruler have a slider, this is to be used instead of the compasses.

Gunter's Quadrant, is a quadrant made of wood, brass, or some other substance; being a kind of stereographic prejection on the plane of the equinoctial, the eye being supposed in one of the poles: so that the tropic, ecliptic, and horizon, form the arches of circles, but the hour circles other curves, drawn by means of several altitudes of the sun, for some particular latitude every day in the year.

The use of this instrument, is to find the hour of the day, the sun's azimuth, &c, and other common problems of the sphere or globe; as also to take the altitude of an object in degrees. See Quadrant.

Gunter's Scale, usually called by seamen the Gunter, is a large plain scale, having various lines upon it, of great use in working the cases or questions in Navigation.

This Scale is usually 2 feet long, and about an inch and a half broad, with various lines upon it, both natural and logarithmic, relating to trigonometry, navigation, &c.

On the one side are the natural lines, and on the other the artificial or logarithmic ones. The former side is first divided into inches and tenths, and numbered from 1 to 24 inches, running the whole length near one edge. One half the length of this side consists of two plane diagonal scales, for taking off dimensions to three places of figures. On the other half or foot of this side, are contained various lines relating to trigonometry, in the natural numbers, and marked thus, viz,

Rumb,	the rumbs or points of the compass,
Chord,	the line of chords,
Sine,	the line of sines,
Tang.	the tangents,
S. T.	the semitangents,

and at the other end of this half are

Leag.	leagues, or equal parts,
Rumb.	another line of rumbs,
M. L.	miles of longitude,
Chor.	another line of chords.

Also in the middle of this foot are L. and P. two other lines of equal parts. And all these lines on this side of the scale serve for drawing or laying down the figures to the cases in trigonometry and navigation.

On the other side of the scale are the following artisicial or logarithmic lines, which serve for working or resolving those cases; viz,

S. R.	the fine rumbs,
T. R.	the tangent rumbs,
Numb.	line of numbers,
Sine,	Sines,
V. S.	the versed sines,
Tang.	the tangents,
Meri.	Meridional parts.
E. P.	Equal parts.

The late Mr. John Robertson, librarian to the Royal Society, greatly improved this scale, both as to size and accuracy, for the use of mariners. He extended it to 30 inches long, 2 inches broad, and half an inch thick; upon which the several lines are very accurately laid down by Messrs. Nairne and Blunt, ingenious instrument makers. Mr. Robertson died before his improved scales were published; but the account and description of them were supplied and drawn up by his friend Mr. William Mountaine, and published in 1778.

GUTTÆ, or Drops, in Architecture, are ornaments in form of little bells or cones, used in the Doric order, on the architrave, below the tryglyphs. There are usually fix of them.|