DISCOVERY OF THE LAW OF DISPERSION BY REFRACTION.
EARLY attempts were made to account for the colors of the rainbow,
and various other phenomena in which colors are seen to arise from
transient and unsubstantial combinations of media. Thus Aristotle
explains the colors of the rainbow by supposing[9\9] that it is
light seen through a dark medium: "Now," says he, "the bright seen
through the dark appears red, as, for instance, the fire of green
wood seen through the smoke, and the sun through mist. Also[10\9]
the weaker is the light, or the visual power, and the nearer the
color approaches to the black; becoming first red, then green, then
purple. But[11\9] the {59} vision is strongest in the outer circle,
because the periphery is greater;--thus we shall have a gradation
from red, through green, to purple, in passing from the outer to the
inner circle." This account would hardly have deserved much notice,
if it had not been for a strange attempt to revive it, or something
very like it, in modern times. The same doctrine is found in the
work of De Dominis.[12\9] According to him, light is white: but if
we mix with the light something dark, the colors arise,--first red,
then green, then blue or violet. He applies this to explain the
colors of the rainbow,[13\9] by means of the consideration that, of
the rays which come to the eye from the globes of water, some go
through a larger thickness of the globe than others, whence he
obtains the gradation of colors just described.
[Note 9\9: _Meteor._ iii. 3, p. 373.]
[Note 10\9: Ib. p. 374.]
[Note 11\9: Ib. p. 375.]
[Note 12\9: Cap. iii. p. 9. See also Göthe, _Farbenl._ vol. ii.
p. 251.]
[Note 13\9: Göthe, p. 263.]
Descartes came far nearer the true philosophy of the iridal colors.
He found that a similar series of colors was produced by refraction
of light bounded by shade, through a prism;[14\9] and he rightly
inferred that neither the curvature of the surface of the drops of
water, nor the reflection, nor the repetition of refraction, were
necessary to the generation of such colors. In further examining the
course of the rays, he approaches very near to the true conception
of the case; and we are led to believe that he might have
anticipated Newton in his discovery of the unequal refrangibility of
different colors, if it had been possible for him to reason any
otherwise than in the terms and notions of his preconceived
hypotheses. The conclusion which he draws is,[15\9] that "the
particles of the subtile matter which transmit the action of light,
endeavor to rotate with so great a force and impetus, that they
cannot move in a straight line (whence comes refraction): and that
those particles which endeavor to revolve much more strongly produce
a red color, those which endeavor to move only a little more
strongly produce yellow." Here we have a clear perception that
colors and unequal refraction are connected, though the cause of
refraction is expressed by a gratuitous hypothesis. And we may add,
that he applies this notion rightly, so far as he explains
himself,[16\9] to account for the colors of the rainbow.
[Note 14\9: _Meteor._ Sect. viii. p. 190.]
[Note 15\9: Sect. vii. p. 192.]
[Note 16\9: _Meteor._ Sect. ix.]
It appears to me that Newton and others have done Descartes
injustice, in ascribing to De Dominis the true theory of the
rainbow. There are two main points of this theory, namely, the
showing that a _bright_ circular band, of a certain definite
diameter, arises from the {60} great intensity of the light returned
at a certain angle; and the referring the different _colors_ to the
_different quantity of the refraction_; and both these steps appear
indubitably to be the discoveries of Descartes. And he informs us
that these discoveries were not made without some exertion of
thought. "At first," he says,[17\9] "I doubted whether the iridal
colors were produced in the same way as those in the prism; but, at
last, taking my pen, and carefully calculating the course of the
rays which fell on each part of the drop, I found that many more
come at an angle of forty-one degrees, than either at a greater or a
less angle. So that there is a bright bow terminated by a shade; and
hence the colors are the same as those produced through a prism."
[Note 17\9: Sect. ix. p. 193.]
The subject was left nearly in the same state, in the work of
Grimaldi, _Physico-Mathesis, de Lumine, Coloribus et Iride_,
published at Bologna in 1665. There is in this work a constant
reference to numerous experiments, and a systematic exposition of
the science in an improved state. The author's calculations
concerning the rainbow are put in the same form as those of
Descartes; but he is further from seizing the true principle on
which its coloration depends. He rightly groups together a number of
experiments in which colors arise from refraction;[18\9] and
explains them by saying that the color is brighter where the light
is denser: and the light is denser on the side from which the
refraction turns the ray, because the increments of refraction are
greater in the rays that are more inclined.[19\9] This way of
treating the question might be made to give a sort of explanation of
most of the facts, but is much more erroneous than a developement of
Descartes's view would have been.
[Note 18\9: Prop. 35, p. 254.]
[Note 19\9: Ib. p. 256.]
At length, in 1672, Newton gave[20\9] the true explanation of the
facts; namely, that light consists of rays of different colors and
different refrangibility. This now appears to us so obvious a mode
of interpreting the phenomena, that we can hardly understand how
they can be conceived in any other manner; but yet the impression
which this discovery made, both upon Newton and upon his
contemporaries, shows how remote it was from the then accepted
opinions. There appears to have been a general persuasion that the
coloration was produced, not by any peculiarity in the law of
refraction itself but by some collateral circumstance,--some
dispersion or variation of density of the light, in addition to the
refraction. Newton's discovery consisted in {61} teaching distinctly
that the law of refraction was to be applied, not to the beam of
light in general, but to the colors in particular.
[Note 20\9: _Phil. Trans._ t. vii. p. 3075.]
When Newton produced a bright spot on the wall of his chamber, by
admitting the sun's light through a small hole in his
window-shutter, and making it pass through a prism, he expected the
image to be round; which, of course, it would have been, if the
colors had been produced by an equal dispersion in all directions;
but to his surprise he saw the image, or _spectrum_, five times as
long as it was broad. He found that no consideration of the
different thickness of the glass, the possible unevenness of its
surface, or the different angles of rays proceeding from the two
sides of the sun, could be the cause of this shape. He found, also,
that the rays did not go from the prism to the image in curves; he
was then convinced that the different colors were refracted
separately, and at different angles; and he confirmed this opinion
by transmitting and refracting the rays of each color separately.
The experiments are so easy and common, and Newton's interpretation
of them so simple and evident, that we might have expected it to
receive general assent; indeed, as we have shown, Descartes had
already been led very near the same point. In fact, Newton's
opinions were not long in obtaining general acceptance; but they met
with enough of cavil and misapprehension to annoy extremely the
discoverer, whose clear views and quiet temper made him impatient
alike of stupidity and of contentiousness.
We need not dwell long on the early objections which were made to
Newton's doctrine. A Jesuit, of the name of Ignatius Pardies,
professor at Clermont, at first attempted to account for the
elongation of the image by the difference of the angles made by the
rays from the two edges of the sun, which would produce a difference
in the amount of refraction of the two borders; but when Newton
pointed out the calculations which showed the insufficiency of this
explanation, he withdrew his opposition. Another more pertinacious
opponent appeared in Francis Linus, a physician of Liege; who
maintained, that having tried the experiment, he found the sun's
image, when the sky was clear, to be round and not oblong; and he
ascribed the elongation noticed by Newton, to the effect of clouds.
Newton for some time refused to reply to this contradiction of his
assertions, though obstinately persisted in; and his answer was at
last sent, just about the time of Linus's death, in 1675. But
Gascoigne, a friend of Linus, still maintained that he and others
had seen what the Dutch physician had described; and Newton, who was
pleased with the candor of {62} Gascoigne's letter, suggested that
the Dutch experimenters might have taken one of the images reflected
from the surfaces of the prism, of which there are several, instead
of the proper refracted one. By the aid of this hint, Lucas of Liege
repeated Newton's experiments, and obtained Newton's result, except
that he never could obtain a spectrum whose length was more than
three and a half times its breadth. Newton, on his side, persisted
in asserting that the image would be five times as long as it was
broad, if the experiment were properly made. It is curious that he
should have been so confident of this, as to conceive himself
certain that such would be the result in all cases. We now know that
the dispersion, and consequently the length, of the spectrum, is
very different for different kinds of glass, and it is very probable
that the Dutch prism was really less dispersive than the English
one.[21\9] The erroneous assumption which Newton made in this
instance, he held by to the last; and was thus prevented from making
the discovery of which we have next to speak.
[Note 21\9: Brewster's _Newton_, p. 50.]
Newton was attacked by persons of more importance than those we have
yet mentioned; namely, Hooke and Huyghens. These philosophers,
however, did not object so much to the laws of refraction of
different colors, as to some expressions used by Newton, which, they
conceived, conveyed false notions respecting the composition and
nature of light. Newton had asserted that all the different colors
are of distinct kinds, and that, by their composition, they form
white light. This is true of colors as far as their analysis and
composition by refraction are concerned; but Hooke maintained that
all natural colors are produced by various combinations of two
primary ones, red and violet;[22\9] and Huyghens held a similar
doctrine, taking, however, yellow and blue for his basis. Newton
answers, that such compositions as they speak of are not
compositions of simple colors in his sense of the expressions. These
writers also had both of them adopted an opinion that light
consisted in vibrations; and objected to Newton that his language
was erroneous, as involving the hypothesis that light was a body.
Newton appears to have had a horror of the word _hypothesis_, and
protests against its being supposed that his "theory" rests on such
a foundation.
[Note 22\9: Brewster's _Newton_, p. 54. _Phil. Trans._ viii. 5084,
6086.]
The doctrine of the unequal refrangibility of different rays is
clearly exemplified in the effects of lenses, which produce images
more or {63} less bordered with color, in consequence of this
property. The improvement of telescopes was, in Newton's time, the
great practical motive for aiming at the improvement of theoretical
optics. Newton's theory showed why telescopes were imperfect,
namely, in consequence of the different refraction of different
colors, which produces a _chromatic_ aberration: and the theory was
confirmed by the circumstances of such imperfections. The false
opinion of which we have already spoken, that the dispersion must be
the same when the refraction is the same, led him to believe that
the imperfection was insurmountable,--that _achromatic_ refraction
could not be obtained: and this view made him turn his attention to
the construction of reflecting instead of refracting telescopes. But
the rectification of Newton's error was a further confirmation of
the general truth of his principles in other respects; and since
that time, the soundness of the Newtonian law of refraction has
hardly been questioned among physical philosophers.
It has, however, in modern times, been very vehemently controverted in
a quarter from which we might not readily have expected a detailed
discussion on such a subject. The celebrated Göthe has written a work
on _The Doctrine of Colors_, (_Farbenlehre_; Tübingen, 1810,) one main
purpose of which is, to represent Newton's opinions, and the work in
which they are formally published, (his _Opticks_,) as utterly false
and mistaken, and capable of being assented to only by the most blind
and obstinate prejudice. Those who are acquainted with the extent to
which such an opinion, promulgated by Göthe, was likely to be widely
adopted in Germany, will not be surprised that similar language is
used by other writers of that nation. Thus Schelling[23\9] says:
"Newton's _Opticks_ is the greatest proof of the possibility of a
whole structure of fallacies, which, in all its parts, is founded upon
observation and experiment." Göthe, however, does not concede even so
much to Newton's work. He goes over a large portion of it, page by
page, quarrelling with the experiments, diagrams, reasoning, and
language, without intermission; and holds that it is not reconcileable
with the most simple facts. He declares,[24\9] that the first time he
looked through a prism, he saw the white walls of the room still look
white, "and though alone, I pronounced, as by an instinct, that the
Newtonian doctrine is false." We need not here point out how
inconsistent with the Newtonian doctrine it was, to expect, as Göthe
expected, that the wall should be all over colored various colors.
{64}
[Note 23\9: _Vorlesungen_, p. 270.]
[Note 24\9: _Farbenlehre_, vol. ii. p. 678.]
Göthe not only adopted and strenuously maintained the opinion that
the Newtonian theory was false, but he framed a system of his own to
explain the phenomena of color. As a matter of curiosity, it may be
worth our while to state the nature of this system; although
undoubtedly it forms no part of the _progress_ of physical science.
Göthe's views are, in fact, little different from those of Aristotle
and Antonio de Dominis, though more completely and systematically
developed. According to him, colors arise when we see through a dim
medium ("ein trübes mittel"). Light in itself is colorless; but if
it be seen through a somewhat dim medium, it appears yellow; if the
dimness of the medium increases, or if its depth be augmented, we
see the light gradually assume a yellow-red color, which finally is
heightened to a ruby-red. On the other hand, if darkness is seen
through a dim medium which is illuminated by a light falling on it,
a blue color is seen, which becomes clearer and paler, the more the
dimness of the medium increases, and darker and fuller, as the
medium becomes more transparent; and when we come to "the smallest
degree of the purest dimness," we see the most perfect violet.[25\9]
In addition to this "doctrine of the dim medium," we have a second
principle asserted concerning refraction. In a vast variety of
cases, images are accompanied by "accessory images," as when we see
bright objects in a looking-glass.[26\9] Now, when an image is
displaced by refraction, the displacement is not complete, clear and
sharp, but incomplete, so that there is an accessory image along
with the principal one.[27\9] From these principles, the colors
produced by refraction in the image of a bright object on a dark
ground, are at once derivable. The accessory image is
semitransparent;[28\9] and hence that border of it which is pushed
forwards, is drawn from the dark over the bright, and there the
yellow appears; on the other hand, where the clear border laps over
the dark ground, the blue is seen;[29\9] and hence we easily see
that the image must appear red and yellow at one end, and blue and
violet at the other.
[Note 25\9: _Farbenlehre_, § 150, p. 151.]
[Note 26\9: Ib. § 223.]
[Note 27\9: Ib. § 227.]
[Note 28\9: Ib. § 238.]
[Note 29\9: Ib. § 239.]
We need not explain this system further, or attempt to show how
vague and loose, as well as baseless, are the notions and modes of
conception which it introduces. Perhaps it is not difficult to point
out the peculiarities in Göthe's intellectual character which led to
his singularly unphilosophical views on this subject. One important
{65} circumstance is, that he appears, like many persons in whom the
poetical imagination is very active, to have been destitute of the
talent and the habit of geometrical thought. In all probability, he
never apprehended clearly and steadily those relations of position
on which the Newtonian doctrine depends. Another cause of his
inability to accept the doctrine probably was, that he had conceived
the "composition" of colors in some way altogether different from
that which Newton understands by composition. What Göthe expected to
see, we cannot clearly collect; but we know, from his own statement,
that his intention of experimenting with a prism arose from his
speculations on the roles of coloring in pictures; and we can easily
see that any notion of the composition of colors which such
researches would suggest, would require to be laid aside, before he
could understand Newton's theory of the composition of light.
Other objections to Newton's theory, of a kind very different, have
been recently made by that eminent master of optical science, Sir
David Brewster. He contests Newton's opinion, that the colored rays
into which light is separated by refraction are altogether simple
and homogeneous, and incapable of being further analysed and
modified. For he finds that by passing such rays through colored
media (as blue glass for instance), they are not only absorbed and
transmitted in very various degrees, but that some of them have
their color altered; which effect he conceives as a further analysis
of the rays, one component color being absorbed and the other
transmitted.[30\9] And on this subject we can only say, as we have
before said, that Newton has incontestably and completely
established his doctrine, so far as analysis and decomposition _by
refraction_ are concerned; but that with regard to any other
analysis, which absorbing media or other agents may produce, we have
no right from his experiments to assert, that the colors of the
spectrum are incapable of _such_ decomposition. The whole subject of
the colors of objects, both opake and transparent, is still in
obscurity. Newton's conjectures concerning the causes of the colors
of natural bodies, appear to help us little; and his opinions on
that subject are to be separated altogether from the important step
which he made in optical science, by the establishment of the true
doctrine of refractive dispersion.
[Note 30\9: This latter fact has, however, been denied by other
experimenters.]
[2nd Ed.] [After a careful re-consideration of Sir D. Brewster's
asserted analysis of the solar light into three colors by means of
{66} absorbing media, I cannot consider that he has established his
point as an exception to Newton's doctrine. In the first place, the
analysis of light into _three_ colors appears to be quite arbitrary,
granting all his experimental facts. I do not see why, using other
media, he might not just as well have obtained other elementary
colors. In the next place, this cannot be called an _analysis_ in
the same sense as Newton's analysis, except the relation between the
two is shown. Is it meant that Newton's experiments prove nothing?
Or is Newton's conclusion allowed to be true of light which has not
been analysed by absorption? And where are we to find such light,
since the atmosphere absorbs? But, I must add, in the third place,
that with a very sincere admiration of Sir D. Brewster's skill as an
experimenter, I think his experiment requires, not only limitation,
but confirmation by other experimenters. Mr. Airy repeated the
experiments with about thirty different absorbing substances, and
could not satisfy himself that in any case they changed the color of
a ray of given refractive power. These experiments were described by
him at a meeting of the Cambridge Philosophical Society.]
We now proceed to the corrections which the next generation
introduced into the details of this doctrine.