discover men. You may erect laboratories and endow them; you may
furnish them with all the appliances needed for inquiry; in so doing
you are but creating opportunity for the exercise of powers which come
from sources entirely beyond your reach. You cannot create genius by
bidding for it. In biblical language, it is the gift of God; and the
most you could do, were your wealth, and your willingness to apply it,
a million-fold what they are, would be to make sure that this glorious
plant shall have the freedom, light, and warmth necessary for its
development. We see from time to time a noble tree dragged down by
parasitic runners. These the gardener can remove, though the vital
force of the tree itself may lie beyond him: and so, in many a case
you men of wealth can liberate genius from the hampering toils which
the struggle for existence often casts around it.
Drawn by your kindness, I have come here to give these lectures, and
now that my visit to America has become almost a thing of the past, I
look back upon it as a memory without a single stain. No lecturer was
ever rewarded as I have been. From this vantage-ground, however, let
me remind you that the work of the lecturer is not the highest work;
that in science, the lecturer is usually the distributor of
intellectual wealth amassed by better men. And though lecturing and
teaching, in moderation, will in general promote their moral health,
it is not solely or even chiefly, as lecturers, but as investigators,
that your highest men ought to be employed. You have scientific genius
amongst you--not sown broadcast, believe me, it is sown thus
nowhere--but still scattered here and there. Take all unnecessary
impediments out of its way. Keep your sympathetic eye upon the
originator of knowledge. Give him the freedom necessary for his
researches, not overloading him, either with the duties of tuition or
of administration, nor demanding from him so-called practical
results--above all things, avoiding that question which ignorance so
often addresses to genius: 'What is the use of your work?' Let him
make truth his object, however unpractical for the time being it may
appear. If you cast your bread thus upon the waters, be assured it
will return to you, though it be after many days.
APPENDIX.
ON THE SPECTRA OF POLARIZED LIGHT.
Mr. William Spottiswoode introduced some years ago to the members of
the Royal Institution, in a very striking form, a series of
experiments on the spectra of polarized light. With his large Nicol
prisms he in the first place repeated and explained the experiments of
Foucault and Fizeau, and subsequently enriched the subject by very
beautiful additions of his own. I here append a portion of the
abstract of his discourse:--
'It is well known that if a plate of selenite sufficiently thin be
placed between two Nicol's prisms, or, more technically speaking,
between a polarizer and analyzer, colour will be produced. And the
question proposed is, What is the nature of that colour? is it
simply a pure colour of the spectrum, or is it a compound, and if
so, what are its component parts? The answer given by the wave
theory is in brief this: In its passage through the selenite plate
the rays have been so separated in the direction of their vibrations
and in the velocity of their transmission, that, when re-compounded
by means of the analyzer, they have in some instances neutralized
one another. If this be the case, the fact ought to be visible when
the beam emerging from the analyzer is dispersed by the prism; for
then we have the rays of all the different colours ranged side by
side, and, if any be wanting, their absence will be shown by the
appearance of a dark band in their place in the spectrum. But not
only so; the spectrum ought also to give an account of the other
phenomena exhibited by the selenite when the analyzer is turned
round, viz. that when the angle of turning amounts to 45°, all trace
of colour disappears; and also that when the angle amounts to 90°,
colour reappears, not, however, the original colour, but one
complementary to it.
'You see in the spectrum of the reddish light produced by the
selenite a broad but dark band in the blue; when the analyzer is
turned round the band becomes less and less dark, until when the
angle of turning amounts to 45° it has entirely disappeared. At this
stage each part of the spectrum has its own proportional intensity,
and the whole produces the colourless image seen without the
spectroscope. Lastly, as the turning of the analyzer is continued, a
dark band appears in the red, the part of the spectrum complementary
to that occupied by the first band; and the darkness is most
complete when the turning amounts to 90°. Thus we have from the
spectroscope a complete account of what has taken place to produce
the original colour and its changes.
'It is further well known that the colour produced by a selenite, or
other crystal plate, is dependent upon the thickness of the plate.
And, in fact, if a series of plates be taken, giving different
colours, their spectra are found to show bands arranged in different
positions. The thinner plates show bands in the parts of the
spectrum nearest to the violet, where the waves are shorter, and
consequently give rise to redder colours; while the thicker show
bands nearer to the red, where the waves are longer and consequently
supply bluer tints.
'When the thickness of the plate is continually increased, so that
the colour produced has gone through the complete cycle of the
spectrum, a further increase of thickness causes a reproduction of
the colours in the same order; but it will be noticed that at each
recurrence of the cycle the tints become paler, until when a number
of cycles have been performed, and the thickness of the plate is
considerable, all trace of colour is lost. Let us now take a series
of plates, the first two of which, as you see, give colours; with
the others which are successively of greater thickness the tints are
so feeble that they can scarcely be distinguished. The spectrum of
the first shows a single band; that of the second, two; showing that
the second series of tints is not identical with the first, but that
it is produced by the extinction of two colours from the components
of white light. The spectra of the others show series of bands more
and more numerous in proportion to the thickness of the plate, an
array which may be increased indefinitely. The total light, then, of
which the spectrum is deprived by the thicker plates is taken from a
greater number of its parts; or, in other words, the light which
still remains is distributed more and more evenly over the spectrum;
and in the same proportion the sum total of it approaches more and
more nearly to white light.
'These experiments were made more than thirty years ago by the
French philosophers, MM. Foucault and Fizeau.
'If instead of selenite, Iceland spar, or other ordinary crystals,
we use plates of quartz cut perpendicularly to the axis, and turn
the analyzer round as before, the light, instead of exhibiting only
one colour and its complementary with an intermediate stage in which
colour is absent, changes continuously in tint; and the order of the
colour depends partly upon the direction in which the analyzer is
turned, and partly upon the character of the crystal, _i.e._ whether
it is right-handed or left-handed. If we examine the spectrum in
this case we find that the dark band never disappears, but marches
from one end of the spectrum to another, or _vice versâ_, precisely
in such a direction as to give rise to the tints seen by direct
projection.
'The kind of polarization effected by the quartz plates is called
circular, while that effected by the other class of crystals is
called plane, on account of the form of the vibrations executed by
the molecules of æther; and this leads us to examine a little more
closely the nature of the polarization of different parts of these
spectra of polarized light.
'Now, two things are clear: first, that if the light be
plane-polarized--that is, if all the vibrations throughout the
entire ray are rectilinear and in one plane--they must in all their
bearings have reference to a particular direction in space, so that
they will be differently affected by different positions of the
analyzer. Secondly, that if the vibrations be circular, they will be
affected in precisely the same way (whatever that may be) in all
positions of the analyzer. This statement merely recapitulates a
fundamental point in polarization. In fact, plane-polarized light is
alternately transmitted and extinguished by the analyzer as it is
turned through 90°; while circularly polarized light [if we could
get a single ray] remains to all appearance unchanged. And if we
examine carefully the spectrum of light which has passed through a
selenite, or other ordinary crystal, we shall find that, commencing
with two consecutive bands in position, the parts occupied by the
bands and those midway between them are plane-polarized, for they
become alternately dark and bright; while the intermediate parts,
_i.e._ the parts at one-fourth of the distance from one band to the
next, remain permanently bright. These are, in fact, circularly
polarized. But it would be incorrect to conclude from this
experiment alone that such is really the case, because the same
appearance would be seen if those parts were unpolarized, _i.e._ in
the condition of ordinary lights. And on such a supposition we
should conclude with equal justice that the parts on either side of
the parts last mentioned (e.g. the parts separated by eighth parts
of the interval between two bands) were partially polarized. But
there is an instrument of very simple construction, called a
"quarter-undulation plate," a plate usually of mica, whose thickness
is an odd multiple of a quarter of a wave-length, which enables us
to discriminate between light unpolarized and circularly polarized.
The exact mechanical effect produced upon the ray could hardly be
explained in detail within our present limits of time; but suffice
it for the present to say that, when placed in a proper position,
the plate transforms plane into circular and circular into plane
polarization. That being so, the parts which were originally banded
ought to remain bright, and those which originally remained bright
ought to become banded during the rotation of the analyzer. The
general effect to the eye will consequently be a general shifting of
the bands through one-fourth of the space which separates each pair.
'Circular polarization, like circular motion generally, may of
course be of two kinds, which differ only in the direction of the
motion. And, in fact, to convert the circular polarization produced
by this plate from one of these kinds to the other (say from
right-handed to left-handed, or _vice versâ_), we have only to turn
the plate round through 90°. Conversely, right-handed circular
polarization will be changed by the plate into plane-polarization in
one direction, while left-handed will be changed into plane at right
angles to the first. Hence if the plate be turned round through 90°
we shall see that the bands are shifted in a direction opposite to
that in which they were moved at first. In this therefore we have
evidence not only that the polarization immediately on either side
of a band is circular; but also that that immediately on the one
side is right-handed, while that immediately on the other is
left-handed[28].
'If time permitted, I might enter still further into detail, and
show that the polarization between the plane and the circular is
elliptical, and even the positions of the longer and shorter axes
and the direction of motion in each case. But sufficient has,
perhaps, been said for our present purpose.
'Before proceeding to the more varied forms of spectral bands,
which I hope presently to bring under your notice, I should like to
ask your attention for a few minutes to the peculiar phenomena
exhibited when two plates of selenite giving complementary colours
are used. The appearance of the spectrum varies with the relative
position of the plates. If they are similarly placed--that is, as if
they were one plate of crystal--they will behave as a single plate,
whose thickness is the sum of the thicknesses of each, and will
produce double the number of bands which one alone would give; and
when the analyzer is turned, the bands will disappear and re-appear
in their complementary positions, as usual in the case of
plane-polarization. If one of them be turned round through 45°, a
single band will be seen at a particular position in the spectrum.
This breaks into two, which recede from one another towards the red
and violet ends respectively, or advance towards one another
according to the direction in which the analyzer is turned. If the
plate be turned through 45° in the opposite direction, the effects
will be reversed. The darkness of the bands is, however, not equally
complete during their whole passage. Lastly, if one of the plates be
turned through 90°, no bands will be seen, and the spectrum will be
alternately bright and dark, as if no plates were used, except only
that the polarization is itself turned through 90°.
'If a wedge-shaped crystal be used, the bands, instead of being
straight, will cross the spectrum diagonally, the direction of the
diagonal (dexter or sinister) being determined by the position of
the thicker end of the wedge. If two similar wedges be used with
their thickest ends together, they will act as a wedge whose angle
and whose thickness is double of the first. If they be placed in the
reverse position they will act as a flat plate, and the bands will
again cross the spectrum in straight lines at right angles to its
length.
'If a concave plate be used the bands will dispose themselves in a
fanlike arrangement, their divergence depending upon the distance of
the slit from the centre of concavity.
'If two quartz wedges, one of which has the optic axis parallel to
the edge of the refractory angle, and the other perpendicular to it,
but in one of the planes containing the angle (Babinet's
Compensator), the appearances of the bands are very various.
'The diagonal bands, besides sometimes doubling themselves as with
ordinary wedges, sometimes combine so as to form longitudinal
(instead of transverse) bands; and sometimes cross one another so as
to form a diaper pattern with bright compartments in a dark
framework, and _vice versâ_, according to the position of the
plates.
'The effects of different dispositions of the interposed crystals
might be varied indefinitely; but enough has perhaps been said to
show the delicacy of the method of spectrum analysis as applied to
the examination of polarized light.'
* * * * *
The singular and beautiful effect obtained with a circular plate of
selenite, thin at the centre, and gradually thickening towards the
circumference, is easily connected with a similar effect obtained with
Newton's rings. Let a thin slice of light fall upon the glasses which
show the rings, so as to cover a narrow central vertical zone passing
through them all. The image of this zone upon the screen is crossed by
portions of the iris-rings. Subjecting the reflected beam to prismatic
analysis, the resultant spectrum may be regarded as an indefinite
number of images of the zone placed side by side. In the image before
dispersion we have _iris-rings_, the extinction of the light being
nowhere complete; but when the different colours are separated by
dispersion, each colour is crossed transversely by its own system of
dark interference bands, which become gradually closer with the
increasing refrangibility of the light. The complete spectrum,
therefore, appears furrowed by a system of continuous dark bands,
crossing the colours transversely, and approaching each other as they
pass from red to blue.
In the case of the plate of selenite, a slit is placed in front of the
polarizer, and the film of selenite is held close to the slit, so that
the light passes through the central zone of the film. As in the case
of Newton's rings, the image of the zone is crossed by iris-coloured
bands; but when subjected to prismatic dispersion, the light of the
zone yields a spectrum furrowed by bands of complete darkness exactly
as in the case of Newton's rings and for a similar reason. This is the
beautiful effect described by Mr. Spottiswoode as the fanlike
arrangement of the bands--the fan opening out at the red end of the
spectrum.
* * * * *
_MEASUREMENT OF THE WAVES OF LIGHT._
The diffraction fringes described in Lecture II., instead of being
formed on the retina, may be formed on a screen, or upon ground glass,
when they can be looked at through a magnifying lens from behind, or
they can be observed in the air when the ground glass is removed.
Instead of permitting them to form on the retina, we will suppose them
formed on a screen. This places us in a condition to understand, even
without trigonometry, the solution of the important problem of
measuring _the length_ of a wave of light.
We will suppose the screen so distant that the rays falling upon it
from the two margins of the slit are sensibly parallel. We have
learned in Lecture II. that the first of the dark bands corresponds to
a difference of marginal path of one undulation; the second dark band
to a difference of path of two undulations; the third dark band to a
difference of three undulations, and so on. Now the angular distance
of the bands from the centre is capable of exact measurement; this
distance depending, as already stated, on the width of the slit. With
a slit 1.35 millimeter wide,[29] Schwerd found the angular distance of
the first dark band from the centre of the field to be 1'38"; the
angular distances of the second, third, fourth dark bands being twice,
three times, four times this quantity.
[Illustration: Fig. 57.]
Let A B, fig. 57, be the plate in which the slit is cut, and C D the
grossly exaggerated width of the slit, with the beam of red light
proceeding from it at the obliquity corresponding to the first dark
band. Let fall a perpendicular from one edge, D, of the slit on the
marginal ray of the other edge at _d_. The distance, C _d_, between
the foot of this perpendicular and the other edge is the length of a
wave of the light. The angle C D _d_, moreover, being equal to R C R',
is, in the case now under consideration, 1'38". From the centre D,
with the width D C as radius, describe a semicircle; its radius D C
being 1.35 millimeter, the length of this semicircle is found by an
easy calculation to be 4.248 millimeters. The length C _d_ is so small
that it sensibly coincides with the arc of the circle. Hence the
length of the semicircle is to the length C _d_ of the wave as 180° to
1'38", or, reducing all to seconds, as 648,000" to 98". Thus, we have
the proportion--
648,000 : 98 :: 4.248 to the wave-length C _d_.
Making the calculation, we find the wave-length for this particular
kind of light to be 0.000643 of a millimeter, or 0.000026 of an inch.
FOOTNOTES:
[Footnote 1: Among whom may be especially mentioned the late Sir
Edmund Head, Bart., with whom I had many conversations on this
subject.]
[Footnote 2: At whose hands it gives me pleasure to state I have
always experienced honourable and liberal treatment.]
[Footnote 3: One of the earliest of these came from Mr. John Amory
Lowell of Boston.]
[Footnote 4: It will be subsequently shown how this simple apparatus
may be employed to determine the 'polarizing angle' of a liquid.]
[Footnote 5: From this principle Sir John Herschel deduces in a simple
and elegant manner the fundamental law of reflection.--See _Familiar
Lectures_, p. 236.]
[Footnote 6: The low dispersive power of water masks, as Helmholtz has
remarked, the imperfect achromatism of the eye. With the naked eye I
can see a distant blue disk sharply defined, but not a red one. I can
also see the lines which mark the upper and lower boundaries of a
horizontally refracted spectrum sharp at the blue end, but ill-defined
at the red end. Projecting a luminous disk upon a screen, and covering
one semicircle of the aperture with a red and the other with a blue or
green glass, the difference between the apparent sizes of the two
semicircles is in my case, and in numerous other cases, extraordinary.
Many persons, however, see the apparent sizes of the two semicircles
reversed. If with a spectacle glass I correct the dispersion of the
red light over the retina, then the blue ceases to give a sharply
defined image. Thus examined, the departure of the eye from
achromatism appears very gross indeed.]
[Footnote 7: Both in foliage and in flowers there are striking
differences of absorption. The copper beech and the green beech, for
example, take in different rays. But the very growth of the tree is
due to some of the rays thus taken in. Are the chemical rays, then,
the same in the copper and the green beech? In two such flowers as the
primrose and the violet, where the absorptions, to judge by the
colours, are almost complementary, are the chemically active rays the
same? The general relation of colour to chemical action is worthy of
the application of the method by which Dr. Draper proved so
conclusively the chemical potency of the yellow rays of the sun.]
[Footnote 8: Young, Helmholtz, and Maxwell reduce all differences of
hue to combinations in different proportions of three primary colours.
It is demonstrable by experiment that from the red, green, and violet
_all_ the other colours of the spectrum may be obtained.
Some years ago Sir Charles Wheatstone drew my attention to a work by
Christian Ernst Wünsch, Leipzig 1792, in which the author announces
the proposition that there are neither five nor seven, but only three
simple colours in white light. Wünsch produced five spectra, with five
prisms and five small apertures, and he mixed the colours first in
pairs, and afterwards in other ways and proportions. His result is
that red is a _simple_ colour incapable of being decomposed; that
orange is compounded of intense red and weak green; that yellow is a
mixture of intense red and intense green; that green is a _simple_
colour; that blue is compounded of saturated green and saturated
violet; that indigo is a mixture of saturated violet and weak green;
while violet is a pure _simple_ colour. He also finds that yellow and
indigo blue produce _white_ by their mixture. Yellow mixed with bright
blue (Hochblau) also produces white, which seems, however, to have a
tinge of green, while the pigments of these two colours when mixed
always give a more or less beautiful green, Wünsch very emphatically
distinguishes the mixture of pigments from that of lights. Speaking of
the generation of yellow, he says, 'I say expressly _red and green
light_, because I am speaking about light-colours (Lichtfarben), and
not about pigments.' However faulty his theories may be, Wünsch's
experiments appear in the main to be precise and conclusive. Nearly
ten years subsequently, Young adopted red, green, and violet as the
three primary colours, each of them capable of producing three
sensations, one of which, however, predominates over the two others.
Helmholtz adopts, elucidates, and enriches this notion. (_Popular
Lectures_, p. 249. The paper of Helmholtz on the mixture of colours,
translated by myself, is published in the _Philosophical Magazine_ for
1852. Maxwell's memoir on the Theory of Compound Colours is published
in the _Philosophical Transactions_, vol. 150, p. 67.)]
[Footnote 9: The following charming extract, bearing upon this point,
was discovered and written out for me by my deeply lamented friend Dr.
Bence Jones, when Hon. Secretary to the Royal Institution:--