APPARENT

, that which is visible, or evident to the eye, or the understanding.

Apparent conjunction of the planets, is when a right line, supposed to be drawn through their centres, passes through the eye of the spectator, and not through the centre of the earth.—And, in general, the apparent conjunction of any objects, is when they appear or are placed in the same right line with the eye.

Apparent Altitude, Diameter, Distance, Horizon, Magnitude, Motion, Place, Time, &c. See the respective substantives, for the quantity and measure of it.

The apparent state of things, is commonly very different from their real state, either as to distance, figure, magnitude, position, &c, &c. Thus,

Apparent Diameter, or Magnitude, as for example of the heavenly bodies, is not the real length of the diameter, but the angle which they subtend at the eye, or under which they appear. And hence, the angle, or apparent extent, diminishing with the distance of the object, a very small object, as AB, may have the same apparent diameter as a very large one FG; and indeed the objects have all the same apparent diameter, that are contained in the same angle FEG. And if these are parallel, the real magnitudes are directly proportional to their distances.

But the apparent magnitude varies not only by the distance, but also by the position of it. So, if the object CD be changed from the direct position to the oblique one Cd, its apparent magnitude would then be only the angle CEd, instead of the angle CED.

If the eye E be placed between two parallels AB, CD, these parallels will appear to converge or come nearer and nearer to each other the farther they are continued out, and at last they will appear to coincide in that point where the sight terminates, which will happen when the optic angle BED becomes equal to about one minute of a degree, the smallest angle under which an object is visible.—Also the apparent magnitudes of the same object FG or BD, seen at different distances, that is the angles FEG, BED, are in a less ratio than the reciprocal ratio of the distances, or the distance increases in a greater ratio than the angle or apparent magnitude diminishes. But when the object is very remote, or the optic angle is very small, as one degree or thereabouts, the angle then varies nearly as the distance reciprocally.

But although the optic angle be the usual or sensible measure of the apparent magnitude of an object, yet habit, and the frequent experience of looking at distant objects, by which we know that they are larger than they appear, has so far prevailed upon the imagination and judgment, as to cause this too to have some share in our estimation of apparent magnitudes; so that these will be judged to be more than in the ratio of the optic angles.

The apparent magnitude of the same object, at the same distance, is different to different persons, and different animals, and even to the same person, when viewed in different lights, all which may be occasioned | by the different magnitudes of the eye, causing the optic angle to differ as that is greater or less: and since, in the same person, the more light there comes from an object, the less is the pupil of the eye, looking at that object; therefore the optic angle will also be less, and consequently the apparent magnitude of the object. Every one must have experienced the truth of this, by looking at another person in a room, and afterwards abroad in the sunshine, when he always appears smaller than in a room where the light is less. So also, objects up in the air, having more light coming from them than when they are upon the ground, or near it, may appear less in the former case than in the latter; like as the ball of the cross on the top of St. Paul's church, which is 6 feet in diameter, appears less than an object of the same diameter seen at the same distance below, near the ground. And this may be the chief reason why the sun and moon appear so much larger when seen in the horizon, where their beams are weak, then when they are raised higher, and their light is more bright and glaring.

Again, if the eye be placed in a rare medium, and view an object through a denser, as glass or water, having plane surfaces; the object will appear larger than it is: and contrariwise, smaller. And hence it is that fishes, and other objects, seen in the water, by an eye in the air, always appear larger than in the air.—In like manner, an object will appear larger when viewed through a globe of glass or water, or any convex spherical segments of these; and, on the contrary, it will appear smaller when viewed through a concave of glass or water.

Apparent Distance, is that distance which we judge an object to be from us, when seen afar off. This is commonly 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 visible objects near them, are at the same distance from us; though perhaps they may bethousands or millions of miles off; as in the case of the sun and moon. The apparent distances of objects are also greatly altered by the refraction of the medium through which they are seen.

Apparent Figure, is the figure or shape which an object appears under when viewed at a distance; and is osten very different from the true figure. For a straight line, viewed at a distance, may appear but as a point; a surface, as a line; and a solid, as a surface. Also these may appear of different magnitudes, and the surface and solid of different figures, according to their situation with respect to the eye: thus, the arch of a circle may appear a straight line; a square, a trapezium, or even a triangle; a circle, an ellipsis; angular magnitudes, round; and a sphere, a circle. Also all objects have a tendency to roundness and smoothness, or appear less angular, as their distance is greater: for, as the distance is increased, the smaller angles and asperities first disappear, by subtending a less angle than one minute; after these, the next larger disappear, for the same reason; and so on continually, as the distance is more and more increased; the object seeming still more and more round and smooth. So, a triangle, or square, at a great distance, shews only as a round speck; and the edge of the moon appears round to the eye, notwithstanding the hills and valleys on her surface. And hence it is also, that near objects, as a range of lamps, or such like, seen at a great distance, appear to be contiguous, and to form one uniform continued magnitude, by the intervals between them disappearing, from the smallness of the angles subtended by them.

Apparent Motion, is either that motion which we perceive in a distant body that moves, the eye at the same time being either in motion or at rest; or that motion which an object at rest seems to have, while the eye itself only is in motion.

The motions of bodies at a great distance, though really moving equally, or passing over equal spaces in equal times, may appear to be very unequal and irregular to the eye, which can only judge of them by the mutation of the angle at the eye. And motions, to be equally visible, or appear equal, must be directly proportional to the distances of the objects moving. Again, very swift motions, as those of the luminaries, may not appear to be any motions at all, but like that of the hour hand of a clock, on account of the great distance of the objects: and this will always happen, when the space actually passed over in one second of time, is less than about the 14000th part of its distance from the eye; for the hour hand of a clock, and the stars about the earth, move at the rate of 15 seconds of a degree in one second of time, which is only the 13751 part of the radius or distance from the eye. On the other hand, it is possible for the motion of a body to be so swift, as not to appear any motion at all; as when through the whole space it describes there constantly appears a continued surface or solid as it were generated by the motion of the object, like as when any thing is whirled very swiftly round, describing a ring, &c.

Also, the more oblique the eye is to the line which a distant body moves in, the more will the apparent motion differ from the true one. So, if a body revolve with an equable motion in the circumference of the circle ABCD &c, and the eye be at E in the plane of the circle; as the body moves from A to B and C, it seems to move slower and slower along the line ALK, till when the body arrives at C, it appears at rest at K; then while it really moves from C by D to F, it appears to move quicker and quicker from K by L to A, where its motion is quickest of all; after this it appears to move slower and slower from A to N while the body moves from F to H: there becoming stationary again, it appears to return from N to A in the straight line, while it really moves from H by I to A in the circle. And thus it appears to move in the line KN by a motion continually varying between the least, or nothing, at the extremes K and N, and the greatest of all at the middle point A. Or, if the motion be referred to the concave side of the circle, instead of the line KN, the appearances will be the same.

If an eye move directly forwards from E to O, &c; any remote object at rest at P, will appear to move the | contrary way, or from P to Q, with the same velocity. But if the object P move the same way, and with the same velocity as the eye; it will seem to stand still. If the object have a less velocity than the eye, it will appear to move back towards Q with the difference of the velocities; and if it move faster than the eye, it will appear to move forwards from Q, with the same difference of the velocities. And so likewise when the object P moves contrary to the motion of the eye, it appears to move backwards with the sum of the motions of the two. And the truth of all this is experienced by persons sitting in a boat moving on a river, or in a wheel-carriage when running fast, and viewing houses or trees, &c, on the shore or side of the road, or other boats or wheel-carriages also in motion.

Apparent Place of an object, in Optics, is that in which it appears, when seen in or through glass, water, or other refracting mediums; which is commonly different from the true place. So, if an object be seen in or through glass, or water, either plane or concave, it will appear nearer to the eye than its true place; but when seen through a convex glass, it appears more remote from the eye than the real place of it.

Apparent Place of the Image of an object, in Catoptrics, is that where the image of an object made by the reflexion of a speculum appears to be; and the optical writers, from Euclid downwards, give it as a general rule that this is where the reflected rays meet the perpendicular to the speculum drawn from the object: so that if the speculum be a plane, the apparent place of the image will be at the same distance behind the speculum as the eye is besore it; if convex, it will appear behind the glass nearer to the same; but if concave, it will appear before the speculum. And yet in some cases there are some exceptions to this rule, as is shewn by Kepler in his Paralipomena in Vitellionem, prop. 18. See also Wolfius Catoptr. § 51, 188, 233, 234.

Apparent Place of a Planet, &c, in Astronomy, is that point in the sursace of the sphere of the world, where the centre of the luminary appears from the surface of the earth.