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medium be transparent the intensity of illumination which a luminous point can produce on a surface directly exposed to it is inversely as the square of the distance. The word trans-See also:

PARENT, SIMON NAPOLEON (1855– )

parent implies that no light is absorbed or stopped. Whatever, therefore, leaves the source of light must in See also:

SUCCESSION (Lat. successio, from succedere, to follow after)

succession pass through each of a See also:

SERIES (a Latin word from serere, to join)

series of spherical surfaces described See also:

ROUND (O. Fr. rond, Lat. rotundus, the Fr. is the source also of Du. rond; Ger., Swed., Dan. and Nor. rond)

round the source as centre. The same amount of light falls perpendicularly on all these surfaces in succession. The amount received in a given See also:

time by a unit of surface on each is therefore inversely as the number of such See also:

units in each. But the surfaces of See also:

SPHERES, MUSIC OF THE

spheres are as the squares of their radii,—whence the proposition. (We assume here that the velocity of light is See also:

CONSTANT, BENJAMIN (1845-1902)

constant, and that the source gives out its light uniformly.) When the rays fall otherwise than perpendicularly on the surface, the illumination produced is proportional to the cosine of the See also:

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle of obliquity; for the See also:

AREA

area seen under a given spherical angle increases as the secant of the obliquity, the distance remaining the same. As a corollary to this we have the further proposition that the apparent brightness of a luminous surface (seen through a transparent homogeneous medium) is the same at all distances. The word brightness is here taken as a measure of the amount of light falling on the See also:

PUPIL (Lat. pupillus, orphan, minor, dim. of pupus, boy, allied to puer, from root pm- or peu-, to beget, cf. "pupa," Lat. for " doll," the name given to the stage intervening between the larval and imaginal stages in certain insects)

pupil per unit of spherical angle subtended by the luminous surface. The spherical angle subtended by any small surface whose See also:

PLANE

plane is at right angles to the See also:

LINE

line of sight is inversely as the square of the distance.

So also is the light received from it. Hence the brightness is the same at all distances. The word brightness is often used (even scientifically) in another sense from that just defined. Thus we speak of a See also:

bright See also:

STAR

star, of the question—When is See also:

VENUS

Venus at its brightest? &c. Strictly, such expressions are not defensible except for See also:

SOURCES

sources of light which (like a star) have no apparent surface, so that we cannot tell from what amount of spherical angle their light appears to come. In that See also:

case the spherical angle is, for want of knowledge, assumed to be the same for all, and therefore the brightness of each is now estimated in terms of the whole quantity of light we receive from it. The See also:

FUNCTION

function of a See also:

TELESCOPE

telescope is to increase the " apparent magnitude " of distant See also:

OBJECTS

objects; it does not increase the " apparent brightness." If we put out of See also:

account the loss of light by reflection at See also:

glass surfaces (or by imperfect reflection at metallic surfaces) and by absorption, and suppose that the magnifying See also:

POWER [WILLIAM GRATTAN] TYRONE (1797-1841)

power does not exceed the ratio of the See also:

APERTURE (from Lat. aperire, to open)

aperture of the See also:

OBJECT

object-glass to that of the pupil, under which See also:

CONDITION (Lat. condicio, from condicere, to agree upon, arrange; not connected with conditio, from condere, conditum, to put together)

condition the pupil will be filled with light, we may say that the " apparent brightness " is absolutely unchanged by the use of a telescope. In this statement, however, two reservations must be admitted. If the object under examination, like a fixed star, have no sensible apparent magnitude, the conception of " apparent brightness " is altogether inapplicable, and we are concerned only with the See also:

TOTAL

total quantity of light reaching the See also:

eye. Again, it is found that the visibility of an object seen against a See also:

black background depends not only upon the " apparent brightness " but also upon the apparent magnitude. If two or three crosses of different sizes be cut out of the same piece of See also:

white See also:

paper, and be erected against a black background on the further See also:

side of a nearly dark See also:

ROOM

room, the smaller ones become invisible in a light still sufficient to show the larger.

Under these circumstances a suitable telescope may of course bring also the smaller objects into view. The explanation is probably to be sought in imperfect See also:

ACTION

action of the See also:

lens of the eye when the pupil is dilated to the utmost. See also:

Lord See also:

RAYLEIGH, JOHN WILLIAM STRUTT

Rayleigh found that in a nearly dark room he became distinctly See also:

SHORT, FRANCIS JOB (1857– )

short-sighted, a defect of which there is no trace whatever in a moderate light. If this view be correct, the brightness of the See also:

IMAGE (Lat. imago, perhaps from the same root as imitari, copy, imitate)

image on the retina is really less in the case of a small than in the case of a large object, although the so-called apparent brightnesses may be the same. However this may be, the utility of a See also:

NIGHT

night-glass is beyond dispute. The See also:

general law that (apart from the accidental losses mentioned above) the " apparent brightness " depends only upon the area of the pupil filled with light, though often See also:

ill under-stood, has been established for a See also:

long time, as the following See also:

QUOTATION

quotation from See also:

Smith's Optics (See also:

Cambridge, 1738), p. 113, will show:— " Since the magnitude of the pupil is subject to be varied by various degrees of light, let NO be its semi-See also:

DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter when the object PL is viewed by the naked eye from the distance OP; and upon a plane that touches the eye at 0, let OK be the semi-diameter of the greatest area, visible through all the glasses to another eye at P, to be found as PL was; or, which is the same thing, let OK be the semi-diameter of the greatest area inlightened by a See also:

PENCIL (Lat. penicillus, brush, literally little tail)

pencil of rays flowing from P through all the glasses; and when this area is not less than the area of the pupil, the point P will appear just as bright through all the glasses as it would do if they were removed; but if the inlightened area be less than the area of the pupil, the point P will appear less bright through the glasses than if they were removed in the same proportion as the inlightened area is less than the pupil. And these proportions of apparent brightness would be accurate if all the incident rays were transmitted through the glasses to the eye, or if only an insensible See also:

PART

part of them were stopt." A very important fact connected with our See also:

PRESENT

present subject is: The brightness of a self-luminous surface does not depend upon its inclination to the line of sight. Thus a red-hot See also:

ball of See also:

IRON [symbol Fe, atomic weight 55.85 (0=16)]

iron, See also:

FREE

free from scales of See also:

OXIDE

oxide, &c., appears See also:

FLAT (a modification of O. Eng. flet, an obsolete word of Teutonic origin, meaning the ground beneath the feet)

flat in the dark; so, also, the See also:

sun, seen through mist, appears as a flat disk. This fact, however, depends ultimately upon the second law of See also:

THERMODYNAMICS (from Gr. Bepµos, hot, Siva trs, force)

thermodynamics (see See also:

RADIATION, THEORY OF

RADIATION). It may be .stated, however, in another See also:

FORM (Lat. forma)

form, in which its connexion with what precedes is more obvious—The amount of radiation, in any direction, from a luminous surface is proportional to the cosine of the obliquity. The flow of light (if we may so See also:

CALL (from Anglo-Saxon ceallian, a common Teutonic word, cf. Dutch kallen, to talk or chatter)

call it) in straight lines from the luminous point, with constant velocity, leads, as we have seen, to the expression nr 2 (where r is the distance from the luminous point) for the quantity of light which passes through unit of surface perpendicular to the See also:

ray in unit of time, µ being a quantity indicating the See also:

RATE

rate at which light is emitted by the source.

This represents the illumination of the surface on which it falls. The flow through unit of surface whose normal is inclined at an angle 0 to the ray is of course µr--2 See also:

cos 0, again representing the illumination. These are precisely the expressions for the See also:

GRAVITATION (from Lat. gravis, heavy)

gravitation force exerted by a particle of See also:

mass µ on a unit of See also:

MATTER

matter at distance r, and for its resolved part in a given direction. Hence we may employ an expression V 2:w-1 , which is exactly analogous to the gravitation or electric potential, for the purpose of calculating the effect due to any number of See also:

SEPARATE

separate sources of light. And the fundamental proposition in potentials, viz. that, if n be the See also:

EXTERNAL

external normal at any point of a closed surface, the integral fJ(dV/dn)dS, taken over the whole surface, has the value-47rµo, where po is the sum of the values of n for each source lying within the surface, follows almost intuitively from the See also:

mere See also:

CONSIDERATION (from Lat. considerare, to look at closely, examine, generally taken to be from con-, and the base seen in sidus, sideris, a star, the word being supposed to be originally an astrological or astronomical term)

consideration of what it means as regards light. For every source external to the closed surface sends in light which goes out again. But the light from an See also:

INTERNAL

internal source goes wholly out; and the amount per second from each unit source is 47r, the total area of the unit See also:

SPHERE (Gr. vclsa?pa, a ball or globe)

sphere surrounding the source. It is well to observe, however, that the See also:

ANALOGY (Gr. avaXo-yLa, proportion)

analogy is not quite See also:

COMPLETE

complete. To make it so, all the sources must See also:

lie on the same side of the surface whose illumination we are dealing with. This is due to the fact that, in See also:

order that a surface may be illuminated at all, it must be capable of scattering light, i.e. it must be to some extent opaque. Hence the illumination depends mainly upon those sources which are on the same side as that from which it is regarded. Though this See also:

PROCESS

process bears some resemblance to the See also:

HEAT (0. E. haktu, which like " hot," Old Eng. hat, is from the Teutonic type haita, hit, to be hot; cf. Ger. hitze, heiss; Dutch, hitte, heet, &c.)

heat analogy employed by Lord See also:

KELVIN, WILLIAM THOMSON, BARON (1824-1907)

Kelvin (See also:

Sir W.

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