§ 1. There is reason to believe that the ancients were more familiar
with optics than with any other branch of physics; and this may be due
to the fact that for a knowledge of external things man is indebted to
the sense of vision in a far greater degree than to other senses. That
light travels in straight lines--or, in other words, that an object is
seen in the direction in which it really lies--must have been realized
in very remote times. The antiquity of mirrors points to some
acquaintance with the phenomena of reflection, and Layard's discovery of
a convex lens of rock-crystal among the ruins of the palace of Nimrud
implies a knowledge of the burning and magnifying powers of this
instrument. The Greeks were acquainted with the fundamental law of
reflection, viz. the equality of the angles of incidence and reflection;
and it was Hero of Alexandria who proved that the path of the ray is the
least possible. The lens, as an instrument for magnifying objects or for
concentrating rays to effect combustion, was also known. Aristophanes,
in the _Clouds_ (c. 424 B.C.), mentions the use of the burning-glass to
destroy the writing on a waxed tablet; much later, Pliny describes such
glasses as solid balls of rock-crystal or glass, or hollow glass balls
filled with water, and Seneca mentions their use by engravers. A
treatise on optics ([Greek: Katoptrika]), assigned to Euclid by Proclus
and Marinus, shows that the Greeks were acquainted with the production
of images by plane, cylindrical and concave and convex spherical
mirrors, but it is doubtful whether Euclid was the author, since neither
this work nor the [Greek: Optika], a work treating of vision and also
assigned to him by Proclus and Marinus, is mentioned by Pappus, and more
particularly since the demonstrations do not exhibit the precision of
his other writings.
Reflection, or catoptrics, was the key-note of their explanations of
optical phenomena; it is to the reflection of solar rays by the air that
Aristotle ascribed twilight, and from his observation of the colours
formed by light falling on spray, he attributes the rainbow to
reflection from drops of rain. Although certain elementary phenomena of
refraction had also been noted--such as the apparent bending of an oar
at the point where it met the water, and the apparent elevation of a
coin in a basin by filling the basin with water--the quantitative law of
refraction was unknown; in fact, it was not formulated until the
beginning of the 17th century. The analysis of white light into the
continuous spectrum of rainbow colours by transmission through a prism
was observed by Seneca, who regarded the colours as fictitious, placing
them in the same category as the iridescent appearance of the feathers
on a pigeon's neck.
§ 2. The aversion of the Greek thinkers to detailed experimental inquiry
stultified the progress of the science; instead of acquiring facts
necessary for formulating scientific laws and correcting hypotheses, the
Greeks devoted their intellectual energies to philosophizing on the
nature of light itself. In their search for a theory the Greeks were
mainly concerned with vision--in other words, they sought to determine
how an object was seen, and to what its colour was due. Emission
theories, involving the conception that light was a stream of concrete
particles, were formulated. The Pythagoreans assumed that vision and
colour were caused by the bombardment of the eye by minute particles
projected from the surface of the object seen. The Platonists
subsequently introduced three elements--a stream of particles emitted by
the eye (their "divine fire"), which united with the solar rays, and,
after the combination had met a stream from the object, returned to the
eye and excited vision.
In some form or other the emission theory--that light was a longitudinal
propulsion of material particles--dominated optical thought until the
beginning of the 19th century. The authority of the Platonists was
strong enough to overcome Aristotle's theory that light was an activity
([Greek: energeia]) of a medium which he termed the _pellucid_ ([Greek:
diaphanes]); about two thousand years later Newton's exposition of his
corpuscular theory overcame the undulatory hypotheses of Descartes and
Huygens; and it was only after the acquisition of new experimental facts
that the labours of Thomas Young and Augustin Fresnel indubitably
established the wave-theory.
§ 3. The experimental study of refraction, which had been almost
entirely neglected by the early Greeks, received more attention during
the opening centuries of the Christian era. Cleomedes, in his _Cyclical
Theory of Meteors_, c. A.D. 50, alludes to the apparent bending of a
stick partially immersed in water, and to the rendering visible of coins
in basins by filling up with water; and also remarks that the air may
refract the sun's rays so as to render that luminary visible, although
actually it may be below the horizon. The most celebrated of the early
writers on optics is the Alexandrian Ptolemy (2nd century). His
writings on light are believed to be preserved in two imperfect Latin
manuscripts, themselves translations from the Arabic. The subjects
discussed include the nature of light and colour; the formation of
images by various types of mirrors, refractions at the surface of glass
and of water, with tables of the angle of refraction corresponding to
given angles of incidence for rays passing from air to glass and from
air to water; and also astronomical refractions, i.e. the apparent
displacement of a heavenly body due to the refraction of light in its
passage through the atmosphere. The authenticity of these manuscripts
has been contested: the _Almagest_ contains no mention of the _Optics_,
nor is the subject of astronomical refractions noticed, but the
strongest objection, according to A. de Morgan, is the fact that their
author was a poor geometer.
§ 4. One of the results of the decadence of the Roman empire was the
suppression of the academies, and few additions were made to scientific
knowledge on European soil until the 13th century. Extinguished in the
West, the spirit of research was kindled in the East. The accession of
the Arabs to power and territory in the 7th century was followed by the
acquisition of the literary stores of Greece, and during the following
five centuries the Arabs, both by their preservation of existing works
and by their original discoveries (which, however, were but few), took a
permanent place in the history of science. Pre-eminent among Arabian
scientists is Alhazen, who flourished in the 11th century. Primarily a
mathematician and astronomer, he also investigated a wide range of
optical phenomena. He examined the anatomy of the eye, and the functions
of its several parts in promoting vision; and explained how it is that
we see one object with two eyes, and then not by a single ray or beam as
had been previously held, but by two cones of rays proceeding from the
object, one to each eye. He attributed vision to emanations from the
body seen; and on his authority the Platonic theory fell into disrepute.
He also discussed the magnifying powers of lenses; and it may be that
his writings on this subject inspired the subsequent invention of
spectacles. Astronomical observations led to the investigation of
refraction by the atmosphere, in particular, astronomical refraction; he
explained the phenomenon of twilight, and showed a connexion between its
duration and the height of the atmosphere. He also treated _optical
deceptions_, both in direct vision and in vision by reflected and
refracted light, including the phenomenon known as the _horizontal
moon_, i.e. the apparent increase in the diameter of the sun or moon
when near the horizon. This appearance had been explained by Ptolemy on
the supposition that the diameter was actually increased by refraction,
and his commentator Theon endeavoured to explain why an object appears
larger when viewed under water. But actual experiment showed that the
diameter did not increase. Alhazen gave the correct explanation, which,
however, Friar Bacon attributes to Ptolemy. We judge of distance by
comparing the angle under which an object is seen with its supposed
distance, so that if two objects be seen under nearly equal angles and
one be supposed to be more distant than the other, then the former will
be supposed to be the larger. When near the horizon the sun or moon,
conceived as very distant, are intuitively compared with terrestrial
objects, and therefore they appear larger than when viewed at
elevations.
§ 5. While the Arabs were acting as the custodians of scientific
knowledge, the institutions and civilizations of Europe were gradually
crystallizing. Attacked by the Mongols and by the Crusaders, the Bagdad
caliphate disappeared in the 13th century. At that period the Arabic
commentaries, which had already been brought to Europe, were beginning
to exert great influence on scientific thought; and it is probable that
their rarity and the increasing demand for the originals and
translations led to those forgeries which are of frequent occurrence in
the literature of the middle ages. The first treatise on optics written
in Europe was admitted by its author Vitello or Vitellio, a native of
Poland, to be based on the works of Ptolemy and Alhazen. It was written
in about 1270, and first published in 1572, with a Latin translation of
Alhazen's treatise, by F. Risner, under the title _Thesaurus opticae_.
Its tables of refraction are more accurate than Ptolemy's; the author
follows Alhazen in his investigation of lenses, but his determinations
of the foci and magnifying powers of spheres are inaccurate. He
attributed the twinkling of stars to refraction by moving air, and
observed that the scintillation was increased by viewing through water
in gentle motion; he also recognized that both reflection and refraction
were instrumental in producing the rainbow, but he gave no explanation
of the colours.
The _Perspectiva Communis_ of John Peckham, archbishop of Canterbury,
being no more than a collection of elementary propositions containing
nothing new, we have next to consider the voluminous works of Vitellio's
illustrious contemporary, Roger Bacon. His writings on light,
_Perspectiva_ and _Specula mathematica_, are included in his _Opus
majus_. It is conceivable that he was acquainted with the nature of the
images formed by light traversing a small orifice--a phenomenon noticed
by Aristotle, and applied at a later date to the construction of the
camera obscura. The invention of the magic lantern has been ascribed to
Bacon, and his statements concerning spectacles, the telescope, and the
microscope, if not based on an experimental realization of these
instruments, must be regarded as masterly conceptions of the
applications of lenses. As to the nature of light, Bacon adhered to the
theory that objects are rendered visible by emanations from the eye.
The history of science, and more particularly the history of inventions,
constantly confronts us with the problem presented by such writings as
Friar Bacon's. Rarely has it been given to one man to promote an
entirely new theory or to devise an original instrument; it is more
generally the case that, in the evolution of a single idea, there comes
some stage which arrests our attention, and to which we assign the
dignity of an "invention." Furthermore, the obscurity that surrounds the
early history of spectacles, the magic lantern, the telescope and the
microscope, may find a partial solution in the spirit of the middle
ages. The natural philosopher who was bold enough to present to a prince
a pair of spectacles or a telescope would be in imminent danger of being
regarded in the eyes of the church as a powerful and dangerous magician;
and it is conceivable that the maker of such an instrument would
jealously guard the secret of its actual construction, however much he
might advertise its potentialities.[3]
§ 6. The awakening of Europe, which first manifested itself in Italy,
England and France, was followed in the 16th century by a period of
increasing intellectual activity. The need for experimental inquiry was
realized, and a tendency to dispute the dogmatism of the church and to
question the theories of the established schools of philosophy became
apparent. In the science of optics, Italy led the van, the foremost
pioneers being Franciscus Maurolycus (1494-1575) of Messina, and
Giambattista della Porta (1538-1615) of Naples. A treatise by Maurolycus
entitled _Photismi de Lumine et Umbra prospectivum radiorum incidentium
facientes_ (1575), contains a discussion of the measurement of the
intensity of light--an early essay in photometry; the formation of
circular patches of light by small holes of any shape, with a correct
explanation of the phenomenon; and the optical relations of the parts of
the eye, maintaining that the crystalline humour acts as a lens which
focuses images on the retina, explaining short- and long-sight (myopia
and hyper-metropia), with the suggestion that the former may be
corrected by concave, and the latter by convex, lenses. He observed the
spherical aberration due to elements beyond the axis of a lens, and also
the caustics of refraction (diacaustics) by a sphere (seen as the bright
boundaries of the luminous patches formed by receiving the transmitted
light on a screen), which he correctly regarded as determined by the
intersections of the refracted rays. His researches on refraction were
less fruitful; he assumed the angles of incidence and refraction to be
in the constant ratio of 8 to 5, and the rainbow, in which he recognized
four colours, orange, green, blue and purple, to be formed by rays
reflected in the drops along the sides of an octagon. Porta's fame rests
chiefly on his _Magia naturalis sive de miraculis rerum naturalium_, of
which four books were published in 1558, the complete work of twenty
books appearing in 1589. It attained great popularity, perhaps by reason
of its astonishing medley of subjects--pyrotechnics and perfumery,
animal reproduction and hunting, alchemy and optics,--and it was several
times reprinted, and translated into English (with the title _Natural
Magick_, 1658), German, French, Spanish, Hebrew and Arabic. The work
contains an account of the camera obscura, with the invention of which
the author has sometimes been credited; but, whoever the inventor, Porta
was undoubtedly responsible for improving and popularizing that
instrument, and also the magic lantern. In the same work practical
applications of lenses are suggested, combinations comparable with
telescopes are vaguely treated and spectacles are discussed. His _De
Refractione, optices parte_ (1593) contains an account of binocular
vision, in which are found indications of the principle of the
stereoscope.
§ 7. The empirical study of lenses led, in the opening decade of the
17th century, to the emergence of the telescope from its former
obscurity. The first form, known as the Dutch or Galileo telescope,
consisted of a convex and a concave lens, a combination which gave erect
images; the later form, now known as the "Keplerian" or "astronomical"
telescope (in contrast with the earlier or "terrestrial" telescope)
consisted of two convex lenses, which gave inverted images. With the
microscope, too, advances were made, and it seems probable that the
compound type came into common use about this time. These single
instruments were followed by the invention of binoculars, i.e.
instruments which permitted simultaneous vision with both eyes. There is
little doubt that the experimental realization of the telescope, opening
up as it did such immense fields for astronomical research, stimulated
the study of lenses and optical systems. The investigations of
Maurolycus were insufficient to explain the theory of the telescope, and
it was Kepler who first determined the principle of the Galilean
telescope in his _Dioptrice_ (1611), which also contains the first
description of the astronomical or Keplerian telescope, and the
demonstration that rays parallel to the axis of a plano-convex lens come
to a focus at a point on the axis distant twice the radius of the curved
surface of the lens, and, in the case of an equally convex lens, at an
axial point distant only once the radius. He failed, however, to
determine accurately the case for unequally convex lenses, a problem
which was solved by Bonaventura Cavalieri, a pupil of Galileo.
Early in the 17th century great efforts were made to determine the law
of refraction. Kepler, in his _Prolegomena ad Vitellionem_ (1604),
assiduously, but unsuccessfully, searched for the law, and can only be
credited with twenty-seven empirical rules, really of the nature of
approximations, which he employed in his theory of lenses. The true
law--that the ratio of the sines of the angles of incidence and
refraction is constant--was discovered in 1621 by Willebrord Snell
(1591-1626); but was published for the first time after his death, and
with no mention of his name, by Descartes. Whereas in Snell's manuscript
the law was stated in the form of the ratio of certain lines,
trigonometrically interpretable as a ratio of cosecants, Descartes
expressed the law in its modern trigonometrical form, viz. as the ratio
of the sines. It may be observed that the modern form was independently
obtained by James Gregory and published in his _Optica promota_ (1663).
Armed with the law of refraction, Descartes determined the geometrical
theory of the primary and secondary rainbows, but did not mention how
far he was indebted to the explanation of the primary bow by Antonio de
Dominis in 1611; and, similarly, in his additions to the knowledge of
the telescope the influence of Galileo is not recorded.
§ 8. In his metaphysical speculations on the system of nature, Descartes
formulated a theory of light at variance with the generally accepted
emission theory and showing some resemblance to the earlier views of
Aristotle, and, in a smaller measure, to the modern undulatory theory.
He imagined light to be a pressure transmitted by an infinitely elastic
medium which pervades space, and colour to be due to rotatory motions of
the particles of this medium. He attempted a mechanical explanation of
the law of refraction, and came to the conclusion that light passed more
readily through a more highly refractive medium. This view was combated
by Pierre de Fermat (1601-1665), who, from the principle known as the
"law of least time," deduced the converse to be the case, i.e. that the
velocity varied inversely with the refractive index. In brief, Fermat's
argument was as follows: Since nature performs her operations by the
most direct routes or shortest paths, then the path of a ray of light
between any two points must be such that the time occupied in the
passage is a minimum. The rectilinear propagation and the law of
reflection obviously agree with this principle, and it remained to be
proved whether the law of refraction tallied.
Although Fermat's premiss is useless, his inference is invaluable, and
the most notable application of it was made in about 1824 by Sir William
Rowan Hamilton, who merged it into his conception of the "characteristic
function," by the help of which all optical problems, whether on the
corpuscular or on the undulator theory, are solved by one common
process. Hamilton was in possession of the germs of this grand theory
some years before 1824, but it was first communicated to the Royal Irish
Academy in that year, and published in imperfect instalments some years
later. The following is his own description of it. It is of interest as
exhibiting the origin of Fermat's deduction, its relation to
contemporary and subsequent knowledge, and its connexion with other
analytical principles. Moreover, it is important as showing Hamilton's
views on a very singular part of the more modern history of the science
to which he contributed so much.
"Those who have meditated on the beauty and utility, in theoretical
mechanics, of the general method of Lagrange, who have felt the power
and dignity of that central dynamical theorem which he deduced, in the
_Mécanique analytique_ ..., must feel that mathematical optics can
only then attain a coordinate rank with mathematical mechanics ...,
when it shall possess an appropriate method, and become the unfolding
of a central idea.... It appears that if a general method in deductive
optics can be attained at all, it must flow from some law or
principle, itself of the highest generality, and among the highest
results of induction.... [This] must be the principle, or law, called
usually the Law of Least Action; suggested by questionable views, but
established on the widest induction, and embracing every known
combination of media, and every straight, or bent, or curved line,
ordinary or extraordinary, along which light (whatever light may be)
extends its influence successively in space and time: namely, that
this linear path of light, from one point to another, is always found
to be such that, if it be compared with the other infinitely various
lines by which in thought and in geometry the same two points might be
connected, a certain integral or sum, called often _Action_, and
depending by fixed rules on the length, and shape, and position of the
path, and on the media which are traversed by it, is less than all the
similar integrals for the other neighbouring lines, or, at least,
possesses, with respect to them, a certain _stationary_ property. From
this Law, then, which may, perhaps, be named the LAW OF STATIONARY
ACTION, it seems that we may most fitly and with best hope set out, in
the synthetic or deductive process and in the search of a mathematical
method.
"Accordingly, from this known law of least or stationary action I
deduced (long since) another connected and coextensive principle,
which may be called by analogy the LAW OF VARYING ACTION, and which
seems to offer naturally a method such as we are seeking; the one law
being as it were the last step in the ascending scale of induction,
respecting linear paths of light, while the other law may usefully be
made the first in the descending and deductive way.
"The former of these two laws was discovered in the following manner.
The elementary principle of straight rays showed that light, under the
most simple and usual circumstances, employs the direct, and therefore
the shortest, course to pass from one point to another. Again, it was
a very early discovery (attributed by Laplace to Ptolemy), that, in
the case of a plane mirror, the bent line formed by the incident and
reflected rays is shorter than any other bent line having the same
extremities, and having its point of bending on the mirror. These
facts were thought by some to be instances and results of the
simplicity and economy of nature; and Fermat, whose researches on
maxima and minima are claimed by the Continental mathematicians as the
germ of the differential calculus, sought anxiously to trace some
similar economy in the more complex case of refraction. He believed
that by a metaphysical or cosmological necessity, arising from the
simplicity of the universe, light always takes the course which it can
traverse in the shortest time. To reconcile this metaphysical opinion
with the law of refraction, discovered experimentally by Snellius,
Fermat was led to suppose that the two lengths, or _indices_, which
Snellius had measured on the incident ray prolonged and on the
refracted ray, and had observed to have one common projection on a
refracting plane, are inversely proportional to the two successive
velocities of the light before and after refraction, and therefore
that the velocity of light is diminished on entering those denser
media in which it is observed to approach the perpendicular; for
Fermat believed that the time of propagation of light along a line
bent by refraction was represented by the sum of the two products, of
the incident portion multiplied by the index of the first medium and
of the refracted portion multiplied by the index of the second medium;
because he found, by his mathematical method, that this sum was less,
in the case of a plane refractor, than if light went by any other than
its actual path from one given point to another, and because he
perceived that the supposition of a velocity inversely as the index
reconciled his mathematical discovery of the minimum of the foregoing
sum with his cosmological principle of least time. Descartes attacked
Fermat's opinions respecting light, but Leibnitz zealously defended
them; and Huygens was led, by reasonings of a very different kind, to
adopt Fermat's conclusions of a velocity inversely as the index, and
of a _minimum time_ of propagation of light, in passing from one given
point to another through an ordinary refracting plane. Newton,
however, by his theory of emission and attraction, was led to conclude
that the velocity of light was _directly_, not _inversely_, as the
index, and that it was _increased_ instead of being _diminished_ on
entering a denser medium; a result incompatible with the theorem of
the shortest time in refraction. This theorem of shortest time was
accordingly abandoned by many, and among the rest by Maupertuis, who,
however, proposed in its stead, as a new cosmological principle, that
_celebrated law of least action_ which has since acquired so high a
rank in mathematical physics, by the improvements of Euler and
Lagrange."
§ 9. The second half of the 17th century witnessed developments in the
practice and theory of optics which equal in importance the
mathematical, chemical and astronomical acquisitions of the period.
Original observations were made which led to the discovery, in an
embryonic form, of new properties of light, and the development of
mathematical analysis facilitated the quantitative and theoretical
investigation of these properties. Indeed, mathematical and physical
optics may justly be dated from this time. The phenomenon of
_diffraction_, so named by Grimaldi, and by Newton _inflection_, which
may be described briefly as the spreading out, or deviation, from the
strictly rectilinear path of light passing through a small aperture or
beyond the edge of an opaque object, was discovered by the Italian
Jesuit, Francis Maria Grimaldi (1619-1663), and published in his
_Physico-Mathesis de Lumine_ (1665); at about the same time Newton made
his classical investigation of the spectrum or the band of colours
formed when light is transmitted through a prism,[4] and studied
_interference_ phenomena in the form of the colours of thin and thick
plates, and in the form now termed _Newton's rings_; _double
refraction_, in the form of the dual images of a single object formed by
a rhomb of Iceland spar, was discovered by Bartholinus in 1670;
Huygens's examination of the transmitted beams led to the discovery of
an absence of symmetry now called _polarization_; and the finite
velocity of light was deduced in 1676 by Ole Roemer from the comparison
of the observed and computed times of the eclipses of the moons of
Jupiter.
These discoveries had a far-reaching influence upon the theoretical
views which had been previously held: for instance, Newton's
recombination of the spectrum by means of a second (inverted) prism
caused the rejection of the earlier view that the prism actually
manufactured the colours, and led to the acceptance of the theory that
the colours were physically present in the white light, the function of
the prism being merely to separate the physical mixture; and Roemer's
discovery of the finite velocity of light introduced the necessity of
considering the momentum of the particles which, on the accepted
emission theory, composed the light. Of greater moment was the
controversy concerning the emission or corpuscular theory championed by
Newton and the undulatory theory presented by Huygens (see section II.
of this article). In order to explain the colours of thin plates Newton
was forced to abandon some of the original simplicity of his theory; and
we may observe that by postulating certain motions for the Newtonian
corpuscles all the phenomena of light can be explained, these motions
aggregating to a transverse displacement, translated longitudinally, and
the corpuscles, at the same time, becoming otiose and being replaced by
a medium in which the vibration is transmitted. In this way the
Newtonian theory may be merged into the undulatory theory. Newton's
results are collected in his _Opticks_, the first edition of which
appeared in 1704. Huygens published his theory in his _Traité de
lumière_ (1690), where he explained reflection, refraction and double
refraction, but did not elucidate the formation of shadows (which was
readily explicable on the Newtonian hypothesis) or polarization; and it
was this inability to explain polarization which led to Newton's
rejection of the wave theory. The authority of Newton and his masterly
exposition of the corpuscular theory sustained that theory until the
beginning of the 19th century, when it succumbed to the assiduous skill
of Young and Fresnel.
§ 10. Simultaneously with this remarkable development of theoretical and
experimental optics, notable progress was made in the construction of
optical instruments. The increased demand for telescopes, occasioned by
the interest in observational astronomy, led to improvements in the
grinding of lenses (the primary aim being to obtain forms in which
spherical aberration was a minimum), and also to the study of
achromatism, the principles of which followed from Newton's analysis and
synthesis of white light. Kepler's supposition that lenses having the
form of surfaces of revolution of the conic sections would bring rays to
a focus without spherical aberration was investigated by Descartes, and
the success of the latter's demonstration led to the grinding of
ellipsoidal and hyperboloidal lenses, but with disappointing results.[5]
The grinding of spherical lenses was greatly improved by Huygens, who
also attempted to reduce chromatic aberration in the refracting
telescope by introducing a stop (i.e. by restricting the aperture of the
rays); to the same experimenter are due compound eye-pieces, the
invention of which had been previously suggested by Eustachio Divini.
The so-called Huygenian eye-piece is composed of two plano-convex lenses
with their plane faces towards the eye; the field-glass has a focal
length three times that of the eye-glass, and the distance between them
is twice the focal length of the eye-glass. Huygens observed that
spherical aberration was diminished by making the deviations of the rays
at the two lenses equal, and Ruggiero Giuseppe Boscovich subsequently
pointed out that the combination was achromatic. The true development,
however, of the achromatic refracting telescope, which followed from the
introduction of compound object-glasses giving no dispersion, dates from
about the middle of the 18th century. The difficulty of obtaining lens
systems in which aberrations were minimized, and the theory of Newton
that colour production invariably attended refraction, led to the
manufacture of improved specula which permitted the introduction of
reflecting telescopes. The idea of this type of instrument had
apparently occurred to Marin Mersenne in about 1640, but the first
reflector of note was described in 1663 by James Gregory in his _Optica
promota_; a second type was invented by Newton, and a third in 1672 by
Cassegrain. Slight improvements were made in the microscope, although
the achromatic type did not appear until about 1820, some sixty years
after John Dollond had determined the principle of the achromatic
telescope (see ABERRATION, TELESCOPE, MICROSCOPE, BINOCULAR INSTRUMENT).
§ 11. Passing over the discovery by Ehrenfried Walther Tschirnhausen
(1651-1708) of the caustics produced by reflection ("catacaustics") and
his experiments with large reflectors and refractors (for the
manufacture of which he established glass-works in Italy); James
Bradley's discovery in 1728 of the "aberration of light," with the
subsequent derivation of the velocity of light, the value agreeing
fairly well with Roemer's estimate; the foundation of scientific
photometry by Pierre Bouguer in an essay published in 1729 and expanded
in 1760 into his _Traité d'optique sur la graduation de la lumière_; the
publication of John Henry Lambert's treatise on the same subject,
entitled _Photometria, sive de Mensura et Gradibus Luminis, Colorum et
Umbrae_ (1760); and the development of the telescope and other optical
instruments, we arrive at the closing decades of the 18th century.
During the forty years 1780 to 1820 the history of optics is especially
marked by the names of Thomas Young and Augustin Fresnel, and in a
lesser degree by Arago, Malus, Sir William Herschel, Fraunhofer,
Wollaston, Biot and Brewster.
Although the corpuscular theory had been disputed by Benjamin Franklin,
Leonhard Euler and others, the authority of Newton retained for it an
almost general acceptance until the beginning of the 19th century, when
Young and Fresnel instituted their destructive criticism. Basing his
views on the earlier undulatory theories and diffraction phenomena of
Grimaldi and Hooke, Young accepted the Huygenian theory, assuming, from
a false analogy with sound waves, that the wave-disturbance was
longitudinal, and ignoring the suggestion made by Hooke in 1672 that the
direction of the vibration might be transverse, i.e. at right angles to
the direction of the rays. As with Huygens, Young was unable to explain
diffraction correctly, or polarization. But the assumption enabled him
to establish the principle of interference,[6] one of the most fertile
in the science of physical optics. The undulatory theory was also
accepted by Fresnel who, perceiving the inadequacy of the researches of
Huygens and Young, showed in 1818 by an analysis which, however, is not
quite free from objection, that, by assuming that every element of a
wave-surface could act as a source of secondary waves or wavelets, the
diffraction bands were due to the interference of the secondary waves
formed by each element of a primary wave falling upon the edge of an
obstacle or aperture. One consequence of Fresnel's theory was that the
bands were independent of the nature of the diffracting edge--a fact
confirmed by experiment and therefore invalidating Young's theory that
the bands were produced by the interference between the primary wave and
the wave reflected from the edge of the obstacle. Another consequence,
which was first mathematically deduced by Poisson and subsequently
confirmed by experiment, is the paradoxical phenomenon that a small
circular disk illuminated by a point source casts a shadow having a
bright centre.
§ 12. The undulatory theory reached its zenith when Fresnel explained
the complex phenomena of polarization, by adopting the conception of
Hooke that the vibrations were transverse, and not longitudinal.[7]
Polarization by double refraction had been investigated by Huygens, and
the researches of Wollaston and, more especially, of Young, gave such an
impetus to the study that the Institute of France made double refraction
the subject of a prize essay in 1812. E. L. Malus (1775-1812) discovered
the phenomenon of polarization by reflection about 1808 and investigated
metallic reflection; Arago discovered circular polarization in quartz in
1811, and, with Fresnel, made many experimental investigations, which
aided the establishment of the Fresnel-Arago laws of the interference of
polarized beams; Biot introduced a reflecting polariscope, investigated
the colours of crystalline plates and made many careful researches on
the rotation of the plane of polarization; Sir David Brewster made
investigations over a wide range, and formulated the law connecting the
angle of polarization with the refractive index of the reflecting
medium. Fresnel's theory was developed in a strikingly original manner
by Sir William Rowan Hamilton, who interpreted from Fresnel's analytical
determination of the geometrical form of the wave-surface in biaxal
crystals the existence of two hitherto unrecorded phenomena. At
Hamilton's instigation Humphrey Lloyd undertook the experimental search,
and brought to light the phenomena of external and internal conical
refraction.
The undulatory vibration postulated by Fresnel having been generally
accepted as explaining most optical phenomena, it became necessary to
determine the mechanical properties of the aether which transmits this
motion. Fresnel, Neumann, Cauchy, MacCullagh, and, especially, Green and
Stokes, developed the "elastic-solid theory." By applying the theory of
elasticity they endeavoured to determine the constants of a medium which
could transmit waves of the nature of light. Many different allocations
were suggested (of which one of the most recent is Lord Kelvin's
"contractile aether," which, however, was afterwards discarded by its
author), and the theory as left by Green and Stokes has merits other
than purely historical. At a later date theories involving an action
between the aether and material atoms were proposed, the first of any
moment being J. Boussinesq's (1867). C. Christiansen's investigation of
anomalous dispersion in 1870, and the failure of Cauchy's formula
(founded on the elastic-solid theory) to explain this phenomenon, led to
the theories of W. Sellmeier (1872), H. von Helmholtz (1875), E.
Ketteler (1878), E. Lommel (1878) and W. Voigt (1883). A third class of
theory, to which the present-day theory belongs, followed from Clerk
Maxwell's analytical investigations in electromagnetics. Of the greatest
exponents of this theory we may mention H. A. Lorentz, P. Drude and J.
Larmor, while Lord Rayleigh has, with conspicuous brilliancy, explained
several phenomena (e.g. the colour of the sky) on this hypothesis.
For a critical examination of these theories see section II. of this
article; reference may also be made to the _British Association
Reports_: "On Physical Optics," by Humphrey Lloyd (1834), p. 35; "On
Double Refraction," by Sir G. G. Stokes (1862), p. 253; "On Optical
Theories," by R. T. Glazebrook (1885), p. 157.
§ 13. _Recent Developments._--The determination of the velocity of light
(see section III. of this article) may be regarded as definitely
settled, a result contributed to by A. H. L. Fizeau (1849), J. B. L.
Foucault (1850, 1862), A. Cornu (1874), A. A. Michelson (1880), James
Young and George Forbes (1882), Simon Newcomb (1880-1882) and Cornu
(1900). The velocity in moving media was investigated theoretically by
Fresnel; and Fizeau (1859), and Michelson and Morley (1886) showed
experimentally that the velocity was increased in running water by an
amount agreeing with Fresnel's formula, which was based on the
hypothesis of a stationary aether. The optics of moving media have also
been investigated by Lord Rayleigh, and more especially by H. A.
Lorentz, who also assumed a stationary aether. The relative motion of
the earth and the aether has an important connexion with the phenomenon
of the aberration of light, and has been treated with masterly skill by
Joseph Larmor and others (see AETHER). The relation of the earth's
motion to the intensities of terrestrial sources of light was
investigated theoretically by Fizeau, but no experimental inquiry was
made until 1903, when Nordmeyer obtained negative results, which were
confirmed by the theoretical investigations of A. A. Bucherer and H. A.
Lorentz.
Experimental photometry has been greatly developed since the pioneer work
of Bouguer and Lambert and the subsequent introduction of the photometers
of Ritchie, Rumford, Bunsen and Wheatstone, followed by Swan's in 1859,
and O. R. Lummer and E. Brodhun's instrument (essentially the same as
Swan's) in 1889. This expansion may largely be attributed to the increase
in the number of artificial illuminants--especially the many types of
filament- and arc-electric lights, and the incandescent gas light. Colour
photometry has also been notably developed, especially since the
enunciation of the "Purkinje phenomenon" in 1825. Sir William Abney has
contributed much to this subject, and A. M. Meyer has designed a
photometer in which advantage is taken of the phenomenon of contrast
colours. "Flicker photometry" may be dated from O. N. Rood's
investigations in 1893, and the same principle has been applied by
Haycraft and Whitman. These questions--colour and flicker
photometry--have important affinities to colour perception and the
persistence of vision (see VISION). The spectrophotometer, devised by De
Witt Bristol Brace in 1899, which permits the comparison of similarly
coloured portions of the spectra from two different sources, has done
much valuable work in the determination of absorptive powers and
extinction coefficients. Much attention has also been given to the
preparation of a standard of intensity, and many different sources have
been introduced (see PHOTOMETRY). Stellar photometry, which was first
investigated instrumentally with success by Sir John Herschel, was
greatly improved by the introduction of Zöllner's photometer, E. C.
Pickering's meridian photometer and C. Pritchard's wedge photometer.
Other methods of research in this field are by photography--photographic
photometry--and radiometric method (see PHOTOMETRY, CELESTIAL).
The earlier methods for the experimental determination of refractive
indices by measuring the deviation through a solid prism of the
substance in question or, in the case of liquids, through a hollow prism
containing the liquid, have been replaced in most accurate work by other
methods. The method of total reflection, due originally to Wollaston,
has been put into a very convenient form, applicable to both solids and
liquids, in the Pulfrich refractometer (see REFRACTION). Still more
accurate methods, based on interference phenomena, have been devised.
Jamin's interference refractometer is one of the earlier forms of such
apparatus; and Michelson's interferometer is one of the best of later
types (see INTERFERENCE). The variation of refractive index with density
has been the subject of much experimental and theoretical inquiry. The
empirical rule of Gladstone and Dale was often at variance with
experiment, and the mathematical investigations of H. A. Lorentz of
Leiden and L. Lorenz of Copenhagen on the electromagnetic theory led to
a more consistent formula. The experimental work has been chiefly
associated with the names of H. H. Landolt and J. W. Brühl, whose
results, in addition to verifying the Lorenz-Lorentz formula, have
established that this function of the refractive index and density is a
colligative property of the molecule, i.e. it is calculable additively
from the values of this function for the component atoms, allowance
being made for the mode in which they are mutually combined (see
CHEMISTRY, PHYSICAL). The preparation of lenses, in which the refractive
index decreases with the distance from the axis, by K. F. J. Exner, H.
F. L. Matthiessen and Schott, and the curious results of refraction by
non-homogeneous media, as realized by R. Wood may be mentioned (see
MIRAGE).
The spectrum of white light produced by prismatic refraction has engaged
many investigators. The infra-red or heat waves were discovered by Sir
William Herschel, and experiments on the actinic effects of the
different parts of the spectrum on silver salts by Scheele, Senebier,
Ritter, Seebeck and others, proved the increased activity as one passed
from the red to the violet and the ultra-violet. Wollaston also made
many investigations in this field, noticing the dark lines--the
"Fraunhofer lines"--which cross the solar spectrum, which were further
discussed by Brewster and Fraunhofer, who thereby laid the foundations
of modern spectroscopy. Mention may also be made of the investigations
of Lord Rayleigh and Arthur Schuster on the resolving power of prisms
(see DIFFRACTION), and also of the modern view of the function of the
prism in analysing white light. The infra-red and ultra-violet rays are
of especial interest since, although not affecting vision after the
manner of ordinary light, they possess very remarkable properties.
Theoretical investigation on the undulatory theory of the law of
reflection shows that a surface, too rough to give any trace of regular
reflection with ordinary light, may regularly reflect the long waves, a
phenomenon experimentally realized by Lord Rayleigh. Long waves--the
so-called "residual rays" or "_Rest-strahlen_"--have also been isolated
by repeated reflections from quartz surfaces of the light from zirconia
raised to incandescence by the oxyhydrogen flame (E. F. Nichols and H.
Rubens); far longer waves were isolated by similar reflections from
fluorite (56 µ) and sylvite (61 µ) surfaces in 1899 by Rubens and E.
Aschkinass. The short waves--ultra-violet rays--have also been studied,
the researches of E. F. Nichols on the transparency of quartz to these
rays, which are especially present in the radiations of the mercury arc,
having led to the introduction of lamps made of fused quartz, thus
permitting the convenient study of these rays, which, it is to be noted,
are absorbed by ordinary clear glass. Recent researches at the works of
Schott and Genossen, Jena, however, have resulted in the production of a
glass transparent to the ultra-violet.
Dispersion, i.e. that property of a substance which consists in having a
different refractive index for rays of different wave-lengths, was first
studied in the form known as "ordinary dispersion" in which the
refrangibility of the ray increased with the wave-length. Cases had been
observed by Fox Talbot, Le Roux, and especially by Christiansen (1870)
and A. Kundt (1871-1872) where this normal rule did not hold; to such
phenomena the name "anomalous dispersion" was given, but really there is
nothing anomalous about it at all, ordinary dispersion being merely a
particular case of the general phenomenon. The Cauchy formula, which was
founded on the elastic-solid theory, did not agree with the experimental
facts, and the germs of the modern theory, as was pointed out by Lord
Rayleigh in 1900, were embodied in a question proposed by Clerk Maxwell
for the Mathematical Tripos examination for 1869. The principle, which
occurred simultaneously to W. Sellmeier (who is regarded as the founder
of the modern theory) and had been employed about 1850 by Sir G. G.
Stokes to explain absorption lines, involves an action between the
aether and the molecules of the dispersing substance. The mathematical
investigation is associated with the names of Sellmeier, Hermann
Helmholtz, Eduard Ketteler, P. Drude, H. A. Lorentz and Lord Rayleigh,
and the experimental side with many observers--F. Paschen, Rubens and
others; absorbing media have been investigated by A. W. Pflüger, a great
many aniline dyes by K. Stöckl, and sodium vapour by R. W. Wood. Mention
may also be made of the beautiful experiments of Christiansen (1884) and
Lord Rayleigh on the colours transmitted by white powders suspended in
liquids of the same refractive index. If, for instance, benzol be
gradually added to finely powdered quartz, a succession of beautiful
colours--red, yellow, green and finally blue--is transmitted, or, under
certain conditions, the colours may appear at once, causing the mixture
to flash like a fiery opal. Absorption, too, has received much
attention; the theory has been especially elaborated by M. Planck, and
the experimental investigation has been prosecuted from the purely
physical standpoint, and also from the standpoint of the physical
chemist, with a view to correlating absorption with constitution.
Interference phenomena have been assiduously studied. The experiments
of Young, Fresnel, Lloyd, Fizeau and Foucault, of Fresnel and Arago on
the measurement of refractive indices by the shift of the interference
bands, of H. F. Talbot on the "Talbot bands" (which he insufficiently
explained on the principle of interference, it being shown by Sir G. B.
Airy that diffraction phenomena supervene), of Baden-Powell on the
"Powell bands," of David Brewster on "Brewster's bands," have been
developed, together with many other phenomena--Newton's rings, the
colours of thin, thick and mixed plates, &c.--in a striking manner, one
of the most important results being the construction of interferometers
applicable to the determination of refractive indices and wave-lengths,
with which the names of Jamin, Michelson, Fabry and Perot, and of Lummer
and E. Gehrcke are chiefly associated. The mathematical investigations
of Fresnel may be regarded as being completed by the analysis chiefly
due to Airy, Stokes and Lord Rayleigh. Mention may be made of Sir G. G.
Stokes' attribution of the colours of iridescent crystals to periodic
twinning; this view has been confirmed by Lord Rayleigh (_Phil. Mag._,
1888) who, from the purity of the reflected light, concluded that the
laminae were equidistant by the order of a wave-length. Prior to 1891
only interference between waves proceeding in the same direction had
been studied. In that year Otto H. Wiener obtained, on a film 1/20th of
a wave-length in thickness, photographic impressions of the stationary
waves formed by the interference of waves proceeding in opposite
directions, and in 1892 Drude and Nernst employed a fluorescent film to
record the same phenomenon. This principle is applied in the Lippmann
colour photography, which was suggested by W. Zenker, realized by
Gabriel Lippmann, and further investigated by R. G. Neuhauss, O. H.
Wiener, H. Lehmann and others.
Great progress has been made in the study of diffraction, and "this
department of optics is precisely the one in which the wave theory has
secured its greatest triumphs" (Lord Rayleigh). The mathematical
investigations of Fresnel and Poisson were placed on a dynamical basis
by Sir G. G. Stokes; and the results gained more ready interpretation by
the introduction of "Babinet's principle" in 1837, and Cornu's graphic
methods in 1874. The theory also gained by the researches of Fraunhofer,
Airy, Schwerd, E. Lommel and others. The theory of the concave grating,
which resulted from H. A. Rowland's classical methods of ruling lines of
the necessary nature and number on curved surfaces, was worked out by
Rowland, E. Mascart, C. Runge and others. The resolving power and the
intensity of the spectra have been treated by Lord Rayleigh and Arthur
Schuster, and more recently (1905), the distribution of light has been
treated by A. B. Porter. The theory of diffraction is of great
importance in designing optical instruments, the theory of which has
been more especially treated by Ernst Abbe (whose theory of microscopic
vision dates from about 1870) by the scientific staff at the Zeiss
works, Jena, by Rayleigh and others. The theory of coronae (as
diffraction phenomena) was originally due to Young, who, from the
principle involved, devised the _eriometer_ for measuring the diameters
of very small objects; and Sir G. G. Stokes subsequently explained the
appearances presented by minute opaque particles borne on a transparent
plate. The polarization of the light diffracted at a slit was noted in
1861 by Fizeau, whose researches were extended in 1892 by H. Du Bois,
and, for the case of gratings, by Du Bois and Rubens in 1904. The
diffraction of light by small particles was studied in the form of very
fine chemical precipitates by John Tyndall, who noticed the polarization
of the beautiful cerulean blue which was transmitted. This subject--one
form of which is presented in the blue colour of the sky--has been most
auspiciously treated by Lord Rayleigh on both the elastic-solid and
electromagnetic theories. Mention may be made of R. W. Wood's
experiments on thin metal films which, under certain conditions,
originate colour phenomena inexplicable by interference and diffraction.
These colours have been assigned to the principle of optical resonance,
and have been treated by Kossonogov (_Phys. Zeit._, 1903). J. C. Maxwell
Garnett (_Phil. Trans_. vol. 203) has shown that the colours of coloured
glasses are due to ultra-microscopic particles, which have been
directly studied by H. Siedentopf and R. Zsigmondy under limiting
oblique illumination.
Polarization phenomena may, with great justification, be regarded as the
most engrossing subject of optical research during the 19th century; the
assiduity with which it was cultivated in the opening decades of that
century received a great stimulus when James Nicol devised in 1828 the
famous "Nicol prism," which greatly facilitated the determination of the
plane of vibration of polarized light, and the facts that light is
polarized by reflection, repeated refractions, double refraction and by
diffraction also contributed to the interest which the subject excited.
The rotation of the plane of polarization by quartz was discovered in
1811 by Arago; if white light be used the colours change as the Nicol
rotates--a phenomenon termed by Biot "rotatory dispersion." Fresnel
regarded rotatory polarization as compounded from right- and left-handed
(dextro- and laevo-) circular polarizations; and Fresnel, Cornu, Dove
and Cotton effected their experimental separation. Legrand des Cloizeaux
discovered the enormously enhanced rotatory polarization of cinnabar, a
property also possessed--but in a lesser degree--by the sulphates of
strychnine and ethylene diamine. The rotatory power of certain liquids
was discovered by Biot in 1815; and at a later date it was found that
many solutions behaved similarly. A. Schuster distinguishes substances
with regard to their action on polarized light as follows: substances
which act in the isotropic state are termed _photogyric_; if the
rotation be associated with crystal structure, _crystallogyric_; if the
rotation be due to a magnetic field, _magnetogyric_; for cases not
hitherto included the term _allogyric_ is employed, while optically
inactive substances are called _isogyric_. The theory of photogyric and
crystallogyric rotation has been worked out on the elastic-solid
(MacCullagh and others) and on the electromagnetic hypotheses (P. Drude,
Cotton, &c.). Allogyrism is due to a symmetry of the molecule, and is a
subject of the greatest importance in modern (and, more especially,
organic) chemistry (see STEREOISOMERISM).
The optical properties of metals have been the subject of much
experimental and theoretical inquiry. The explanations of MacCullagh and
Cauchy were followed by those of Beer, Eisenlohr, Lundquist, Ketteler
and others; the refractive indices were determined both directly (by
Kundt) and indirectly by means of Brewster's law; and the reflecting
powers from [lambda] = 251 µµ to [lambda] = 1500 µµ were determined in
1900-1902 by Rubens and Hagen. The correlation of the optical and
electrical constants of many metals has been especially studied by P.
Drude (1900) and by Rubens and Hagen (1903).
The transformations of luminous radiations have also been studied. John
Tyndall discovered calorescence. Fluorescence was treated by John
Herschel in 1845, and by David Brewster in 1846, the theory being due to
Sir G. G. Stokes (1852). More recent studies have been made by Lommel,
E. L. Nichols and Merritt (_Phys. Rev._, 1904), and by Millikan who
discovered polarized fluorescence in 1895. Our knowledge of
phosphorescence was greatly improved by Becquerel, and Sir James Dewar
obtained interesting results in the course of his low temperature
researches (see LIQUID GASES). In the theoretical and experimental study
of radiation enormous progress has been recorded. The pressure of
radiation, the necessity of which was demonstrated by Clerk Maxwell on
the electromagnetic theory, and, in a simpler manner, by Joseph Larmor
in his article RADIATION in these volumes, has been experimentally
determined by E. F. Nichols and Hull, and the tangential component by J.
H. Poynting. With the theoretical and practical investigation the names
of Balfour Stewart, Kirchhoff, Stefan, Bartoli, Boltzmann, W. Wien and
Larmor are chiefly associated. Magneto-optics, too, has been greatly
developed since Faraday's discovery of the rotation of the plane of
polarization by the magnetic field. The rotation for many substances was
measured by Sir William H. Perkin, who attempted a correlation between
rotation and composition. Brace effected the analysis of the beam into
its two circularly polarized components, and in 1904 Mills measured
their velocities. The Kerr effect, discovered in 1877, and the Zeeman
effect (1896) widened the field of research, which, from its intimate
connexion with the nature of light and electromagnetics, has resulted in
discoveries of the greatest importance.
§ 14. _Optical Instruments._--Important developments have been made in
the construction and applications of optical instruments. To these three
factors have contributed. The mathematician has quantitatively analysed
the phenomena observed by the physicist, and has inductively shown what
results are to be expected from certain optical systems. A consequence
of this was the detailed study, and also the preparation, of glasses of
diverse properties; to this the chemist largely contributed, and the
manufacture of the so-called _optical glass_ (see GLASS) is possibly the
most scientific department of glass manufacture. The mathematical
investigations of lenses owe much to Gauss, Helmholtz and others, but
far more to Abbe, who introduced the method of studying the aberrations
separately, and applied his results with conspicuous skill to the
construction of optical systems. The development of Abbe's methods
constitutes the main subject of research of the present-day optician,
and has brought about the production of telescopes, microscopes,
photographic lenses and other optical apparatus to an unprecedented
pitch of excellence. Great improvements have been effected in the
stereoscope. Binocular instruments with enhanced stereoscopic vision, an
effect achieved by increasing the distance between the object glasses,
have been introduced. In the study of diffraction phenomena, which led
to the technical preparation of gratings, the early attempts of
Fraunhofer, Nobert and Lewis Morris Rutherfurd, were followed by H. A.
Rowland's ruling of plane and concave gratings which revolutionized
spectroscopic research, and, in 1898, by Michelson's invention of the
echelon grating. Of great importance are interferometers, which permit
extremely accurate determinations of refractive indices and
wave-lengths, and Michelson, from his classical evaluation of the
standard metre in terms of the wave-lengths of certain of the cadmium
rays, has suggested the adoption of the wave-length of one such ray as a
standard with which national standards of length should be compared.
Polarization phenomena, and particularly the rotation of the plane of
polarization by such substances as sugar solutions, have led to the
invention and improvements of polarimeters. The polarized light employed
in such instruments is invariably obtained by transmission through a
fixed Nicol prism--the polarizer--and the deviation is measured by the
rotation of a second Nicol--the analyser. The early forms, which were
termed "light and shade" polarimeters, have been generally replaced by
"half-shade" instruments. Mention may also be made of the microscopic
examination of objects in polarized light, the importance of which as a
method of crystallographic and petrological research was suggested by
Nicol, developed by Sorby and greatly expanded by Zirkel, Rosenbusch and
others.
BIBLIOGRAPHY.--There are numerous text-books which give elementary
expositions of light and optical phenomena. More advanced works, which
deal with the subject experimentally and mathematically, are A. B.
Bassett, _Treatise on Physical Optics_ (1892); Thomas Preston, _Theory
of Light_, 2nd ed. by C. F. Joly (1901); R. W. Wood, _Physical Optics_
(1905), which contains expositions on the electromagnetic theory, and
treats "dispersion" in great detail. Treatises more particularly
theoretical are James Walker, _Analytical Theory of Light_ (1904); A.
Schuster, _Theory of Optics_ (1904); P. Drude, _Theory of Optics_,
Eng. trans. by C. R. Mann and R. A. Millikan (1902). General treatises
of exceptional merit are A. Winkelmann, _Handbuch der Physik_, vol.
vi. "Optik" (1904); and E. Mascart, _Traité d'optique_ (1889-1893); M.
E. Verdet, _Leçons d'optique physique_ (1869, 1872) is also a valuable
work. Geometrical optics is treated in R. S. Heath, _Geometrical
Optics_ (2nd ed., 1898); H. A. Herman, _Treatise on Geometrical
Optics_ (1900). Applied optics, particularly with regard to the theory
of optical instruments, is treated in H. D. Taylor, _A System of
Applied Optics_ (1906); E. T. Whittaker, _The Theory of Optical
Instruments_ (1907); in the publications of the scientific staff of
the Zeiss works at Jena: _Die Theorie der optischen Instrumente_, vol.
i. "Die Bilderzeugung in optischen Instrumenten" (1904); in S.
Czapski, _Theorie der optischen Instrumente_, 2nd ed. by O. Eppenstein
(1904); and in A. Steinheil and E. Voit, _Handbuch der angewandten
Optik_ (1901). The mathematical theory of general optics receives
historical and modern treatment in the _Encyklopädie der
mathematischen Wissenschaften_ (Leipzig). Meteorological optics is
fully treated in J. Pernter, _Meteorologische Optik_; and
physiological optics in H. v Helmholtz, _Handbuch der physiologischen
Optik_ (1896) and in A. Koenig, _Gesammelte Abhandlungen zur
physiologischen Optik_ (1903).
The history of the subject may be studied in J. C. Poggendorff,
_Geschichte der Physik_ (1879); F. Rosenberger, _Die Geschichte der
Physik_ (1882-1890); E. Gerland and F. Traumüller, _Geschichte der
physikalischen Experimentierkunst_ (1899); reference may also be made
to Joseph Priestley, _History and Present State of Discoveries
relating to Vision, Light and Colours_ (1772), German translation by
G. S. Klügel (Leipzig, 1775). Original memoirs are available in many
cases in their author's "collected works," e.g. Huygens, Young,
Fresnel, Hamilton, Cauchy, Rowland, Clerk Maxwell, Stokes (and also
his _Burnett Lectures on Light_), Kelvin (and also his _Baltimore
Lectures_, 1904) and Lord Rayleigh. Newton's _Opticks_ forms volumes
96 and 97 of Ostwald's Klassiker; Huygens' _Über d. Licht_ (1678),
vol. 20, and Kepler's _Dioptrice_ (1611), vol. 144 of the same series.
Contemporary progress is reported in current scientific journals, e.g.
the _Transactions_ and _Proceedings_ of the Royal Society, and of the
Physical Society (London), the _Philosophical Magazine_ (London), the
_Physical Review_ (New York, 1893 seq.) and in the _British
Association Reports_; in the _Annales de chimie et de physique and
Journal de physique_ (Paris); and in the _Physikalische Zeitschrift_
(Leipzig) and the _Annalen der Physik und Chemie_ (since 1900:
_Annalen der Physik_) (Leipzig). (C. E.*)