DISTANCE

, properly speaking, denotes the shortest line between two points, objects, &c.

Distance

, in Astronomy, as of the sun, planets, comets, &c.

The Real Distances are found from the parallaxes of the planets, &c. See Parallax, and Planet, and Transit. The distance of the earth from the sun has been determined at 95 millions of miles, by the late transits of Venus; and from this one real distance, and the several relative distances, by analogy are found all the other real distances, as in the table below.

The Proportional or Relative Distances of the planets are very well deduced from the theory of gravity: for Kepler has long since discovered, and Newton has demonstrated, that the squares of their periodical times are proportional to the cubes of their distances. Kepler's Epit. Astron. lib. 4; Newton's Principia, lib. 3, phæn. 4; and Gregory's Astron. book 1, prop. 40. If therefore the mean distance of the earth from the sun be assumed, or supposed 10000, we shall then, from the foregoing analogy, and the known periodical times, obtain the relative distances of the other planets: thus,

The Periodical Revolutions in Days and Parts. Mercury. Venus. Earth. Mars. Jupiter. Saturn. Herschel.

87 23/24224 17/24365 1/4686 23/244332 1/210759 7/2430445
Relative Mean Distances from the Sun.
3871723310000152375201095401190818
Real Distance in Millions of Miles.
376695145493 1/2903 1/21813

For the distances of the secondary planets from the centres of their respective primaries, see Satellites.

As to that of the fixed stars, as having no sensible parallax, we can do little more than guess at.

Distance of the Sun from the Moon's node, or apogee, is an arch of the ecliptic, intercepted between the sun's true place and the moon's node, or apogee. See Node.

Curtate Distance. See Curtate.

Distance of the Bastions, in Fortification, is the side of the exterior polygon.

Accessible Distances, in Geometry, are measured with the chain, decempeda or ten-foot rod, or the like.

Inaccessible Distances, are found by taking bearings to them, from the two extremities of a line whose length is given. Various ways of performing this may be seen in my Treatise on Mensuration, sect. 3, on Heights and Distances.

Distance

, in Geography, is the arch of a great circle intercepted between two places.

To find the distance of two places, A and B, far remote from each other. Assume two stations, C and D, from which both the places A and B may be seen; and there, with a theodolite, observe the quantity of the angles ACD, BCD, ADC, BDC, and measure any distance as AC.

Then, in the triangle ACD, there are given the angles ACD, ADC, and the side AC; to find the side CD.—Next, in the triangle BCD, there are given the angles BCD, BDC, and the side CD; to find the side BC.—Lastly, in the triangle ABC, there are given the angle ACB, and the sides AC, CB; to find the side AB, which is the distance sought.

And in these operations, the triangles may be computed either as plane triangles, or as spherical ones, as the case may require, or according to the magnitude of the distances.

The Distance of a remote object may also be found from its height. This admits of several cases, according as the distances are large or small, &c. 1st, Suppose that from the top of a tower at A, whose height AB is 120 feet, there be taken the angle BAC = 33°, and the angle BAD = 64° 1/2, to two trees, or other objects, C, D; to find the distance between them CD, and the distance of each from the bottom of the tower at B.

First, rad. : tang. [angle] BAD :: AB : BD =251.585,
next, rad. : tang. [angle] BAC :: AB : BC =77.929,
their difference is the dist.CD =173.656.
2d, Suppose
|

2d, Suppose it be required to find the distance to which an object can be seen, by knowing its altitude; ex. gr. the Pike of Teneriffe, whose height is accounted 3 miles above the level of the sea, supposing the circumference of the earth 25,000 miles, or the diameter 7958 miles. Let FG be the radius = 3979, EF = 3 the height of the mountain, and EI a tangent to the earth at the point H, which is the farthest distant point to which the top of the mountain E canbe seen. Here in the right angled triangle EGH, are given the hypothenuse EG = 3982, and the leg FG = 3979; to sind the other leg HE = 154 1/2 miles = the distance sought nearly. Or, rather, as EG : GH :: rad. : cosin. [angle] G=2° 13′ 1/2; then as 360° : 2° 13′ 1/2 :: 25,000 : 154 1/2 miles = the arch of dist. HF sought, the same as before.

3d, If the eye, instead of being in the horizon at H, were elevated above it at I, any known height, as suppose 264 feet, or (1/20)th of a mile, as on the top of a ship's mast, &c; then the mountain can be seen much farther off along the line IE, and the distance will be the two tangents IH and HE, or rather the two arcs KH and HF. Hence, as above, as IG : GH :: rad. cosin. [angle] IGH = 17′ 2/7; then as 360° : 17′ 2/7 :: 25,000 : 20 miles = the are KH : this added to the former are HF = 154 1/2, makes the whole are KF = 174 1/2 miles, for the whole distance to which the top of the mountain can be seen in this case.

Apparent Distance, in Optics, that distance which we judge an object is placed at when seen afar off, being usually very different from the true distance; because we are apt to think that all very remote objects, whose parts cannot well be distinguished, and which have no other object in view near them, are at the same distance from us, though perhaps the one is thousands of miles nearer than the other, as is the case with regard to the sun and moon.

M. De la Hire enumerates sive circumstances, which assist us in judging of the distance of objects; viz, their apparent magnitude, the strength of the colouring, the direction of the two eyes, the parallax of the objects, and the distinctness of their small parts. On the contrary, Dr. Smith maintains, that we judge of distance principally, or solely, by the apparent magnitude of objects; and concludes universally, that the apparent distance of an object seen in a glass, is to its apparent distance seen by the naked eye, as the apparent magnitude to the naked eye is to its apparent magnitude in the glass: But it was long since observed by Alhazen, that we do not judge of distance merely by the angle under which objects are seen; and Mr. Robins clearly shews that Dr. Smith's hypothesis is contrary to fact, in the most common and simple cases. Thus, if a double convex glass be held upright before some luminous object, as a candle, there will be seen two images, one erect, and the other inverted; the first is made simply by reflexion from the nearest surface; the second by reflexion from the farther surface, the rays undergoing a refraction from the first surface both before and after the reflexion. If this glass has not too short a focal distance, when it is held near the object, the inverted image will appear larger than the other, and also nearer; but if the glass be carried off from the object, though the eye remain as near to it as before, the inverted image will be diminished so much father than the other, that at length it will appear much less than it, but still nearer. Here, says Mr. Robins, two images of the same object are seen under one view, and their apparent distances immediately compared; and it is evident that those distances have no necessary connexion with the apparent magnitude. This experiment may be made still more convincing, by sticking a piece of paper on the middle of the lens, and viewing it through a short tube. He observes farther, that the apparent magnitude of very distant objects is neither determined by the magnitude of the angle only under which they are seen, nor is the exact proportion of that angle compared with their true distance, but is compounded also with a deception concerning that distance; so that if we had no idea of difference in the distance of objects, each would appear in magnitude proportional to the angle under which it was seen; and if our apprehension of the distance were always just, our idea of their magnitude would be unvaried, in all distances; but in proportion as we err in our conception of their distance, the greater angle suggests a greater magnitude. By not attending to this compound effect, Mr. Robins apprehends that Dr. Smith was led into his mistake.

Dr. Porterfield has made several remarks on the sive methods of judging concerning the distance of objects above recited from M. De la Hire; and he has also added to them one more, viz, the conformation of each eye. See Circle of Dissipation. This, he says, can be of no use to us, with respect to objects that are placed without the limits of distinct vision. But the greater or less confusion with which the object appears, as it is more or less removed from those limits, will assist the mind in judging of its distance: the more confused it appears, the farther will it be thought distant. However, this confusion has its limits; for when an object is placed at a certain distance from the eye, to which the breadth of the pupil bears no sensible proportion, the rays proceeding from a point in the object may be considered as parallel; in which case, the picture on the retina will not be sensibly more confused, though the object be removed to a much greater distance. The most universal, and often the most sure means of judging of the distance of objects, he says, is the angle made by the optic axes: our two eyes are like two different stations, by the assistance of which, distances are taken; and this is the reason why those persons who have lost the sight of one eye, so frequently miss their mark in pouring liquor into a glass, snuffing a candle, and such other actions as require that the distance be exactly distinguished. With respect to the method of judging by the apparent magnitude of objects, he observes that this can only serve when we are otherwise acquainted with their real magnitude. Thus he accounts for the deception to which we are liable in estimating distances, by any extraordinary magnitudes that terminate them; as, in travelling towards a large city, castle, or cathedral, we fancy they are nearer than they really are. Hence also, animals and small objects seen in a valley contiguous to large mountains, or on the top of a mountain or high building, appear exceedingly small. Dr. Jurin accounts for the last recited phenomenon, by observing that we have no distinct idea of | distance in that oblique direction, and therefore judge of them merely by their pictures on the eye.

Dr. Porterfield observes, with respect to the strength of colouring, that if we are assured they are of a similar colour, and one appears more bright and lively than the other, we judge that the brighter object is the nearer. When the small parts of objects appear confused, or do not appear at all, we judge that they are at a great distance, and vice versa; because the image of any object, or part of an object, diminishes as the distance of it increases. Finally, we judge of the distance of objects by the number of intervening bodies, by which it is divided into separate and distinct parts; and the more this is the case, the greater will the distance appear. Thus distances upon uneven surfaces appear less than upon a plane, because the inequalities do not appear, and the whole apparent distance is diminished by the parts that do not appear in it: and thus the banks of a river appear contiguous to a distant eye, when the river is low and not seen. Accidens de la Vue, pa. 358. Smith's Optics, vol. 1, pa. 52, and Rem. pa. 51. Robins's Tracts, vol. 2, pa. 230, 247, 251. Porterfield on the Eye, vol. 1, pa. 105, vol. 2, pa. 387. See Priestley's Hist. of Vision, pa. 205, and pa. 689.

Distance

, in Navigation, is the number of miles or leagues that a ship has sailed from any point or place. See Sailing.

Line of Distance, in Per- spective, is a right line drawn from the eye to the principal point: as the line OF, drawn between the eye at O, and the principal point F. As this is perpendicular to the plane, or table, it is therefore the distance of the eye from the table.

Point of Distance, in Perspective, is a point in the horizontal line at the same distance from the principal point, as the eye is from the same. Such are the points P and Q, in the horizontal line PQ, whose distance from the principal point F, is equal to that of the eye from the same F.

DISTINCT Base, in Optics, is that distance from the pole of a convex glass, at which objects, beheld through it, appear distinct and well defined: so that the Distinct base is the same with what is otherwise called the focus.

The Distinct base is caused by the collection of the rays proceeding from a single point in the object, into a single point in the representation: and therefore concave glasses, which do not unite, but scatter and dissipate the rays, can have no real Distinct base.

Distinct Vision. See Vision.

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ABCDEFGHKLMNOPQRSTWXYZABCEGLMN

Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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DISPERSION
DISSIPATION
DISSOLVENT
DISSOLUTION
DISSONANCE
* DISTANCE
DITCH
DITONE
DITTON (Humphrey)
DIVIDEND
DIVING