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Micrographia by Robert Hooke

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But because all transparent _mediums_ are not _Homogeneous_ to one another,
therefore we will next examine how this pulse or motion will be propagated
through differingly transparent _mediums_. And here, according to the most
acute and excellent Philosopher _Des Cartes_, I suppose the sign of the
angle of inclination in the first _medium_ to be to the sign of refraction
in the second, As the density of the first, to the density of the second.
By density, I mean not the density in respect of gravity (with which the
refractions or transparency of _mediums_ hold no proportion) but in respect
onely to the _trajection_ of the Rays of light, in which respect they only
differ in this; that the one propagates the pulse more easily and weakly,
the other more slowly, but more strongly. But as for the pulses themselves,
they will by the refraction acquire another propriety, which we shall now
endeavour to explicate.

We will suppose therefore in the first Figure ACFD to be a physical Ray, or
ABC and DEF to be two Mathematical Rays, _trajected_ from a very remote
point of a luminous body through an _Homogeneous_ transparent _medium_ LLL,
and DA, EB, FC, to be small portions of the orbicular impulses which must
therefore cut the Rays at right angles; these Rays meeting with the plain
surface NO of a _medium_ that yields an easier _transitus_ to the
propagation of light, and falling _obliquely_ on it, they will in the
_medium_ MMM be refracted towards the perpendicular of the surface. And
because this _medium_ is more easily _trajected_ then the former by a
third, therefore the point C of the orbicular pulse FC will be mov'd to H
four spaces in the same time that F the other end of it is mov'd to G three
spaces, therefore the whole refracted pulse GH shall be _oblique_ to the
refracted Rays CHK and GI; and the angle GHC shall be an acute, and so much
the more acute by how much the greater the refraction be, then which
nothing is more evident, for the sign of the inclination is to the sign of
refraction as GF to TC the distance between the point C and the
perpendicular from G on CK, which being as four to three, HC being longer
then GF is longer also then TC, therefore the angle GHC is less than GTC.
So that henceforth the parts of the pulses GH and IK are mov'd ascew, or
cut the Rays at _oblique_ angles.

It is not my business in this place to set down the reasons why this or
that body should impede the Rays more, others less: as why Water should
transmit the Rays more easily, though more weakly than air. Onely thus much
in general I shall hint, that I suppose the _medium_ MMM to have less of
the transparent undulating subtile matter, and that matter to be less
implicated by it, whereas LLL I suppose to contain a greater quantity of
the fluid undulating substance, and this to be more implicated with the
particles of that _medium_.

But to proceed, the same kind of _obliquity_ of the Pulses and Rays will
happen also when the refraction is made out of a more easie into a more
difficult _mediu_; as by the calculations of GQ & CSR which are refracted
from the perpendicular. In both which calculations 'tis _obvious_ to
observe, that always that part of the Ray towards which the refraction is
made has the end of the _orbicular pulse_ precedent to that of the other
side. And always, the oftner the refraction is made the same way, Or the
greater the single refraction is, the more is this unequal progress. So
that having found this odd propriety to be an inseparable concomitant of a
refracted Ray, not streightned by a contrary refraction, we will next
examine the refractions of the Sun-beams, as they are suffer'd onely to
pass through a small passage, _obliquely_ out of a more difficult, into a
more easie _medium_.

Let us suppose therefore ABC in the second Figure to represent a large
_Chimical Glass-body_ about two foot long, filled with very fair Water as
high as AB, and inclin'd in a convenient posture with B towards the Sun:
Let us further suppose the top of it to be cover'd with an _opacous_ body,
all but the hole ab, through which the Sun-beams are suffer'd to pass into
the Water, and are thereby refracted to cdef, against which part, if a
Paper be expanded on the outside, there will appear all the colours of the
Rain-bow, that is, there will be generated the two principal colours,
_Scarlet_ and _Blue_, and all the _intermediate_ ones which arise from the
composition and dilutings of these two, that is, cd shall exhibit a
_Scarlet_, which toward d is diluted into a _Yellow_; this is the
refraction of the Ray, ik, which comes from the underside of the Sun; and
the Ray ef shall appear of a deep _Blue_, which is gradually towards e
diluted into a pale _Watchet-blue_. Between d and e the two _diluted_
colours. _Blue_ and _Yellow_ are mixt and compounded into a _Green_; and
this I imagine to be the reason why _Green_ is so acceptable a colour to
the eye, and that either of the two extremes are, if intense, rather a
little offensive, namely, the being plac'd in the middle between the two
extremes, and compounded out of both those, _diluted_ also, or somewhat
qualifi'd, for the _composition_, arising from the mixture of the two
extremes _undiluted_, makes a _Purple_, which though it be a lovely colour,
and pretty acceptable to the eye, yet is it nothing comparable to the
ravishing pleasure with which a curious and well tempered _Green_ affects
the eye. If removing the Paper, the eye be plac'd against cd, it will
perceive the lower side of the Sun (or a Candle at night which is much
better, because it offends not the eye, and is more easily manageable) to
be of a deep _Red_, and if against ef it will perceive the upper part of
the luminous body to be of a deep _Blue_; and these colours will appear
deeper and deeper, according as the Rays from the luminous body fall more
_obliquely_ on the surface of the Water, and thereby suffer a greater
refraction, and the more distinct, the further cdef is removed from the
trajecting hole.

So that upon the whole, we shall find that the reason of the _Phaenomena_
seems to depend upon the _obliquity_ of the _orbicular pulse_, to the Lines
of Radiation, and in particular, that the Ray cd which constitutes the
_Scarlet_ has its inner parts, namely those which are next to the middle of
the luminous body, precedent to the outermost which are contiguous to the
dark and _unradiating_ skie. And that the Ray ef which gives a _Blue_, has
its outward part, namely, that which is contiguous to the dark side
precedent to the pulse from the innermost, which borders on the bright
_area_ of the luminous body.

We may observe further, that the cause of the _diluting_ of the colours
towards the middle, proceeds partly from the wideness of the hole through
which the Rays pass, whereby the Rays from several parts of the luminous
body, fall upon many of the same parts between c and f as is more manifest
by the Figure: And partly also from the nature of the refraction it self,
for the vividness or strength of the two terminating colours, arising
chiefly as we have seen, from the very great difference that is betwixt the
outsides of those _oblique undulations_ & the dark Rays circumambient, and
that disparity betwixt the _approximate_ Rays, decaying gradually: the
further inward toward the middle of the luminous body they are remov'd, the
more must the colour approach to a white or an undisturbed light.

Upon the calculation of the refraction and reflection from a Ball of Water
or Glass, we have much the same _Phaenomena_, namely, an _obliquity_ of the
undulation in the same manner as we have found it here. Which, because it
is very much to our present purpose, and affords such an _Instancia
crucis_, as no one that I know has hitherto taken notice of, I shall
further examine. For it does very plainly and positively distinguish, and
shew, which of the two _Hypotheses_, either the _Cartesian_ or this is to
be followed, by affording a generation of all the colors in the Rainbow,
where according to the _Cartesian Principles_ there should be none at all
generated. And secondly, by affording an instance that does more closely
confine the cause of these _Phaenomena_ of colours to this present
_Hypothesis_.

And first, for the _Cartesian_, we have this to object against it, That
whereas he says (_Meteorum Cap. 8. Sect. 5._) _Sed judicabam unicam
(refractione scilicet) ad minimum requiri, & quidem talem ut ejus effectus
alia contraria (refractione) non destruatur: Nam experientia docet si
superficies _NM_ & _NP_ (nempe refringentes) Parallelae forent, radios
tantundem per alteram iterum erectos quantum per unam frangerentur, nullos
colores depicturos_; This Principle of his holds true indeed in a prisme
where the refracting surfaces are plain, but is contradicted by the Ball or
Cylinder, whether of Water Or Glass, where the refracting surfaces are
Orbicular or Cylindrical. For if we examine the passage of any _Globule_ or
Ray of the primary _Iris_, we shall find it to pass out of the Ball or
Cylinder again, with the same inclination and refraction that it enter'd in
withall, and that that last refraction by means of the _intermediate_
reflection shall be the same as if without any reflection at all the Ray
had been twice refracted by two Parallel surfaces.

And that this is true, not onely in one, but in every Ray that goes to the
constitution of the Primary Iris; nay, in every Ray, that suffers only two
refractions, and one reflection, by the surface of the round body, we shall
presently see most evident, if we repeat the _Cartesian Scheme_, mentioned
in the tenth _Section_ of the eighth _Chapter_ of his _Meteors_, where
EFKNP in the third Figure[9] is one of the Rays of the Primary Iris, twice
refracted at F and N, and once reflected at K by the surface of the
Water-ball. For, first it is evident, that KF and KN are equal, because KN
being the reflected part of KF they have both the same inclination on the
surface K that is the angles FKT, and NKV made by the two Rays and the
Tangent of K are equal, which is evident by the Laws of reflection; whence
it will follow also, that KN has the same inclination on the surface N, or
the Tangent of it XN that the Ray KF has to the surface F, or the Tangent
of it FY, whence it must necessarily follow, that the refractions at F and
N are equal, that is, KFE and KNP are equal. Now, that the surface N is by
the reflection at K made parallel to the surface at F, is evident from the
principles of reflection; for reflection being nothing but an inverting of
the Rays, if we re-invert the Ray KNP, and make the same inclinations below
the line TKV that it has above, it will be most evident, that KH the
inverse of KN will be the continuation of the line FK, and that LHI the
inverse of OX is parallel to FY. And HM the inverse of NP is Parallel to EF
for the angle KHI is equal to KNO which is equal to KFY, and the angle KHM
is equal to KNP which is equal to KFE which was to be prov'd.

So that according to the above mentioned _Cartesian_ principles there
should be generated no colour at all in a Ball of Water or Glass by two
refractions and one reflection, which does hold most true indeed, if the
surfaces be plain, as may be experimented with any kind of prisme where the
two refracting surfaces are equally inclin'd to the reflecting; but in this
the _Phaenomena_ are quite otherwise.

The cause therefore of the generation of colour must not be what _Des
Cartes_ assigns, namely, a certain _rotation_ of the _Globuli aetherei_,
which are the particles which he supposes to constitute the _Pellucid
medium_, But somewhat else, perhaps what we have lately supposed, and shall
by and by further prosecute and explain.

But, First I shall crave leave to propound some other difficulties of his,
notwithstanding exceedingly ingenious _Hypothesis_, which I plainly confess
to me seem such; and those are,

First, if that light be (as is affirmed, _Diopt._ cap. 1. Sec. 8.) not so
properly a motion, as an action or propension to motion, I cannot conceive
how the eye can come to be sensible of the _verticity_ of a _Globule_,
which is generated in a drop of Rain, perhaps a mile off from it. For that
_Globule_ is not carry'd to the eye according to his formerly recited
Principle; and if not so, I cannot conceive how it can communicate its
_rotation_, or circular motion to the line of the _Globules_ between the
drop and the eye. It cannot be by means of every ones turning the next
before him; for if so, then onely all the _Globules_ that are in the odd
places must be turned the same way with the first, namely, the 3. 5. 7. 9.
11, &c. but all the _Globules_ interposited between them in the even
places; namely, the 2. 4. 6. 8. 10. &c. must be the quite contrary, whence,
according to the _Cartesian Hypothesis_, there must be no distinct colour
generated, but a confusion. Next, since the _Cartesian Globuli_ are
suppos'd (_Principiorum Philosoph._ Part. 3. Sec. 86.) to be each of them
continually in motion about their centers, I cannot conceive how the eye is
able to distinguish this new generated motion from their former inherent
one, if I may so call that other wherewith they are mov'd or _turbinated_,
from some other cause than refraction. And thirdly, I cannot conceive how
these motions should not happen sometimes to oppose each other, and then,
in stead of a _rotation_, there would be nothing but a direct motion
generated, and consequently no colour. And fourthly, I cannot conceive, how
by the _Cartesian Hypothesis_ it is possible to give any plausible reason
of the nature of the Colours generated in the thin _laminae_ of these our
_Microscopical Observations_; for in many of these, the refracting and
reflecting surfaces are parallel to each other, and consequently no
_rotation_ can be generated, nor is there any necessity of a shadow or
termination of the bright Rays, such as is suppos'd (_Chap._ 8. Sec. 5. _Et
praeterea observavi umbram quoque, aut limitationem luminis requiri:_ and
_Chap._ 8. Sec. 9.) to be necessary to the generation of any distinct
colours; Besides that, here is oftentimes one colour generated without any
of the other appendant ones, which cannot be by the _Cartesian Hypothesis_.

There must be therefore some other propriety of refraction that causes
colour. And upon the examination of the thing, I cannot conceive any one
more general, inseparable, and sufficient, than that which I have before
assign'd. That we may therefore see how exactly our _Hypothesis_ agrees
also with the _Phaenomena_ of the refracting round body, whether _Globe_ or
_Cylinder_, we shall next subjoyn our _Calculation_ or _Examen_ of it.

And to this end, we will calculate any two Rays: as for instance;[10] let
EF be a Ray cutting the _Radius_ CD (divided into 20. parts) in G 16. parts
distant from C, and ef another Ray, which cuts the same _Radius_ in g 17.
parts distant, these will be refracted to K and k, and from thence
reflected to N and n, and from thence refracted toward P and p; therefore
the Arch Ff will be 5.d 5'. The Arch FK 106.d 30'. the Arch fk 101.d 2'.
The line FG 6000. and fg 5267. therefore hf. 733. therefore Fc 980, almost.
The line FK 16024. and fk 15436. therefore Nd 196. and no 147 almost, the
line Nn 1019 the Arch Nn 5.d 51'. therefore the Angle Nno is 34.d 43'.
therefore the Angle Non is 139.d 56'. which is almost 50.d more than a
right Angle.

It is evident therefore by this _Hypothesis_, that at the same time that ef
touches f. EF is arrived at c. And by that time efkn is got to n, EFKN is
got to d and when it touches N, the pulse of the other Ray is got to o. and
no farther, which is very short of the place it should have arriv'd to, to
make the Ray np to cut the _orbicular pulse_ No at right Angles: therefore
the Angle Nop is an acute Angle, but the quite contrary of this will
happen, if 17. and 18. be calculated in stead of 16. and 17. both which
does most exactly agree with the _Phaenomena_: For if the Sun, or a Candle
(which is better) be placed about Ee, and the eye about Pp, the Rays EFef
at 16. and 17. will paint the side of the luminous object toward np _Blue_,
and towards NP _Red_. But the quite contrary will happen when EF is 17. and
ef 18. for then towards NP shall be a _Blue_, and towards np a _Red_,
exactly according to the calculation. And there appears the _Blue_ of the
Rainbow, where the two _Blue_ sides of the two Images unite, and there the
_Red_ where the two _Red_ sides unite, that is, where the two Images are
just disappearing; which is, when the Rays EF and NP produc'd till they
meet, make an Angle of about 41. and an half; the like union is there of
the two Images in the Production of the _Secundary Iris_, and the same
causes, as upon calculation may appear; onely with this difference, that it
is somewhat more faint, by reason of the duplicate reflection, which does
always weaken the impulse the oftner it is repeated.

Now, though the second refraction made at Nn be convenient, that is, do
make the Rays glance the more, yet is it not altogether requisite; for it
is plain from the calculation, that the pulse dn is sufficiently _oblique_
to the Rays KN and kn, as wel as the pulse fc is _oblique_ to the Rays FK &
fk. And therefore if a piece of very fine Paper be held close against Nn
and the eye look on it either through the Ball as from D, or from the other
side, as from B. there shall appear a Rainbow, or colour'd line painted on
it with the part toward X appearing _Red_, towards O, _Blue_; the same also
shall happen, if the Paper be placed about Kk, for towards T shall appear a
_Red_, and towards V a _Blue_, which does exactly agree with this my
_Hypothesis_, as upon the calculation of the progress of the pulse will
most easily appear.

Nor do these two observations of the colours appearing to the eye about p
differing from what they appear on the Paper at N contradict each other;
but rather confirm and exactly agree with one another, as will be evident
to him that examines the reasons set down by the ingenious. _Des Cartes_ in
the 12. _Sect._ of the 8. _Chapter of his Meteors_, where he gives the true
reason why the colours appear of a quite contrary order to the eye, to what
they appear'd on the Paper if the eye be plac'd in steed of the Paper: And
as in the Prisme, so also in the Water-drop, or Globe the _Phaenomena_, and
reason are much the same.

Having therefore shewn that there is such a propriety in the _prisme_ and
water _Globule_ whereby the pulse is made _oblique_ to the progressive, and
that so much the more, by how much greater the refraction is, I shall in
the next place consider, how this conduces to the production of colours,
and what kind of impression it makes upon the bottom of the eye; and to
this end it will be requisite to examine this _Hypothesis_ a little more
particularly.

First therefore, if we consider the manner of the progress of the pulse, it
will seem rational to conclude, that that part or end of the pulse which
precedes the other, must necessarily be somwhat more _obtunded_, or
_impeded_ by the resistance of the transparent _medium_, than the other
part or end of it which is subsequent, whose way is, as it were, prepared
by the other; especially if the adjacent _medium_ be not in the same manner
enlightned or agitated. And therefore (in the fourth _Figure_ of the sixth
_Iconism_) the Ray AAAHB will have its side HH more deadned by the
resistance of the dark or quiet _medium_ PPP, Whence there will be a kind
of deadness superinduc'd on the side HHH, which will continually increase
from B, and strike deeper and deeper into the Ray by the line BR; Whence
all the parts of the triangle, RBHO will be of a dead _Blue_ colour, and so
much the deeper, by how much the nearer they lie to the line BHH, which is
most deaded or impeded, and so much the more _dilute_, by how much the
nearer it approaches the line BR. Next on the other side of the Ray AAN,
the end A of the pulse AH will be promoted, or made stronger, having its
passage already prepar'd as 'twere by the other parts preceding, and so its
impression wil be stronger; And because of its _obliquity_ to the Ray,
there will be propagated a kind of faint motion into QQ the adjacent dark
or quiet _medium_, which faint motion will spread further and further into
QQ as the Ray is propagated further and further from A, namely, as far as
the line MA, whence all the triangle MAN will be ting'd with a _Red_, and
that _Red_ will be the deeper the nearer it approaches the line MA, and the
_paler_ or _yellower_ the nearer it is the line NA. And if the Ray be
continued, so that the lines AN and BR (which are the bounds of the _Red_
and _Blue diluted_) do meet and cross each other, there will be beyond that
intersection generated all kinds of _Greens_.

Now, these being the proprieties of every single refracted Ray of light, it
will be easie enough to consider what must be the result of very many such
Rays collateral: As if we suppose infinite such Rays _interjacent_ between
AKSB and ANOB, which arc the terminating: For in this case the Ray AKSB
will have its _Red_ triangle intire, as lying next to the dark or quiet
_medium_, but the other side of it BS will have no _Blue_, because the
_medium adjacent_ to it SBO, is mov'd or enlightned, and consequently that
light does destroy the colour. So likewise will the Ray ANOB lose its
_Red_, because the _adjacent medium_ is mov'd or enlightned, but the other
side of the Ray that is _adjacent_ to the dark, namely, AHO will preserve
its _Blue_ entire, and these Rays must be so far produc'd as till AN and BR
cut each other, before there will be any _Green_ produc'd. From these
Proprieties well consider'd, may be deduc'd the reasons of all the
_Phaenomena_ of the _prisme_, and of the _Globules_ or drops of Water which
conduce to the production of the Rainbow.

Next for the impression they make on the _Retina_, we will further examine
this _Hypothesis_: Suppose therefore ABCDEF, in the fifth _Figure_, to
represent the Ball of the eye: on the _Cornea_ of which ABC two Rays GACH
and KCAI (which are the terminating Rays of a luminous body) falling, are
by the refraction thereof collected or _converg'd_ into two points at the
bottom of the eye. Now, because these terminating Rays, and all the
_intermediate_ ones which come from any part of the luminous body, are
suppos'd by some sufficient refraction before they enter the eye, to have
their pulses made _oblique_ to their progression, and consequently each Ray
to have potentially _superinduc'd_ two proprieties, or colours, viz., a
_Red_ on the one side, and a _Blue_ on the other, which notwithstanding are
never actually manifest, but when this or that Ray has the one or the other
side of it bordering on a dark or unmov'd _medium_, therefore as soon as
these Rays are entred into the eye and so have one side of each of them
bordering on a dark part of the humours of the eye, they will each of them
actually exhibit some colour; therefore ADC the production of GACH will
exhibit a _Blue_, because the side CD is _adjacent_ to the dark _medium_
CQDC, but nothing of a _Red_, because its side AD is _adjacent_ to the
enlightned _medium_ ADFA: And all the Rays that from the points of the
luminous body are collected on the parts of the _Retina_ between D and F
shall have their _Blue_ so much the more _diluted_ by how much the farther
these points of collection are distant from D towards F; and the Ray AFC
the production of KCAI, will exhibit a _Red_, because the side AF is
adjacent to the dark or quiet _medium_ of the eye APFA, but nothing of a
_Blue_, because its side CF is _adjacent_ to the enlightned _medium_ CFDC,
and all the Rays from the intermediate parts of the luminous body that are
collected between F and D shall have their _Red_ so much the more diluted,
by how much the farther they are distant from F towards D.

Now, because by the refraction in the _Cornea_, and some other parts of the
eye, the sides of each Ray, which before were almost parallel, are made to
_converge_ and meet in a point at the bottom of the eye, therefore that
side of the _pulse_ which preceded before these refractions, shall first
touch the _Retina_, and the other side last. And therefore according as
this or that side, or end of the pulse shall be impeded, accordingly will
the _impressions_ on the _Retina_ be varied; therefore by the Ray GACH
refracted by the _Cornea_ to D there shall be on that point a stroke or
impression confus'd, whose weakest end, namely, that by the line CD shall
precede, and the stronger, namely, that by the line AD shall follow. And by
the Ray KCAI refracted to F, there shall be on that part a confus'd stroke
or impression, whose strongest part, namely, that by the line CF shal
precede, and whose weakest or impeded, namely, that by the line AF shall
follow, and all the intermediate points between F and D will receive
impressions from the _converg'd_ Rays so much the more like the impressions
on F and D by how much the nearer they approach that or this.

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