Micrographia by Robert Hooke

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This Inflection may be mechanically explained, either by Monsieur _Des
Cartes_ principles by conceiving the Globuls of the third Element to find
less and less resistance against that side of them which is downwards, or
by a way, which I have further explicated in the Inquisition about Colours,
to be from an obliquation of the pulse of light, whence the under part is
continually promoted, and consequently refracted towards the perpendicular,
which cuts the Orbs at right angles. What the particular Figure of the
_Curve line_, describ'd by this way of light, is, I shall not now stand to
examine, especially since there may be so many sorts of it as there may be
varieties of the Positions of the _intermediat_ degrees of _density_ and
_rarity_ between the bottom and the top of the inflecting Medium.

I could produce many more Examples and Experiments, to illustrate and prove
this first Proposition, _viz._ that there is such a constitution of some
bodies as will cause inflection. As not to mention those I have observ'd in
_Horn_, _Tortoise-Shell_, _transparent Gums_, and _resinous Substances_:
The _veins_ of Glass, nay, of melted _Crystal_, found, and much complained
of by Glass-grinders, and others, might sufficiently demonstrate the truth
of it to any diligent Observator.

But that, I presume, I have by this Example given proof sufficient (_viz.
ocular demonstration_) to evince, that there is such a modulation, or
bending of the rayes of light, as I have call'd _inflection_, differing
both from _reflection_, and _refraction_ (since they are both made in the
superficies, this only in the middle); and likewise, that this is able or
sufficient to produce the effects I have ascribed to it.

It remains therefore to shew, that there is such a property in the Air, and
that it is sufficient to produce all the above mentioned _Phaenomena_, and
therefore may be the principal, if not the only cause of them.

First, That there is such a property, may be proved from this, that the
parts of the Air are some of them more condens'd, others more rarified,
either by the differing heat, or differing pressure it sustains, or by the
somewhat heterogeneous vapours interspers'd through it. For as the Air is
more or less rarified, so does it more or less refract a ray of light (that
comes out of a denser medium) from the perpendicular. This you may find
true, if you make tryal of this Experiment.

Take a small Glass-bubble, made in the form of that in the second Figure of
the 37. _Scheme_, and by heating the Glass very hot, and thereby very much
rarifying the included Air, or, which is better, by rarifying a small
quantity of water, included in it, into vapours, which will expel the most
part, if not all the Air, and then sealing up the small neck of it, and
letting it cool, you may find, if you place it in a convenient Instrument,
that there will be a manifest difference, as to the refraction.

As if in this second Figure you suppose A to represent a small sight or
hole, through which the eye looks upon an object, as C, through the
Glass-bubble B, and the second sight L; all which remain exactly fixt in
their several places, the object C being so cized and placed, that it may
just seem to touch the upper and under edge of the hole L: and so all of it
be seen through the small Glass-ball of rarified Air; then by breaking off
the small seal'd neck of the Bubble (without at all stirring the sights,
object, or glass) and admitting the external Air, you will find your self
unable to see the utmost ends of the object; but the terminating rayes AE
and AD (which were before refracted to G and F by the rarified Air) will
proceed almost directly to I and H; which alteration of the rayes (seeing
there is no other alteration made in the Organ by which the Experiment is
tryed, save only the admission, or exclusion of the condens'd Air) must
necessarily be caused by the variation of the _medium_ contain'd in the
Glass B; the greatest difficulty in the making of which Experiment, is from
the uneven surfaces of the bubble, which will represent an uneven image of
the object.

Now, that there is such a difference of the upper and under parts of the
Air is clear enough evinc'd from the late improvement of the _Torricellian_
Experiment, which has been tryed at the tops and feet of Mountains; and may
be further illustrated, and inquired into, by a means, which some whiles
since I thought of, and us'd, for the finding by what degrees the Air
passes from such a degree of Density to such a degree of Rarity. And
another, for the finding what pressure was requisite to make it pass from
such a degree of Rarefaction to a determinate Density: Which Experiments,
because they may be useful to illustrate the present Inquiry, I shall
briefly describe.

[16] I took then a small Glass-pipe AB, about the bigness of a Swans quill,
and about four foot long, which was very equally drawn, so that, as far as
I could perceive, no one part was bigger then another: This Tube (being
open at both ends) I fitted into another small Tube DE, that had a small
bore just big enough to contain the small Pipe, and this was seal'd up at
one, and open at the other, end; about which open end I fastned a small
wooden box C with cement, so that filling the bigger Tube, and part of the
box, with Quicksilver, I could thrust the smaller Tube into it, till it
were all covered with the Quicksilver: Having thus done, I fastned my
bigger Tube against the side of a wall, that it might stand the steadier,
and plunging the small Tube cleer under the _Mercury_ in the box, I stopt
the upper end of it very fast with cement, then lifting up the small Tube,
I drew it up by a small pully, and a string that I had fastned to the top
of the Room, and found the height of the _Mercurial Cylinder_ to be about
twenty nine inches.

Then letting down the Tube again, I opened the top, and then thrust down
the small Tube, till I perceived the Quicksilver to rise within it to a
mark that I had plac'd just an inch from the top; and immediately clapping
on a small piece of cement that I had kept warm, I with a hot Iron seal'd
up the top very fast, then letting it cool (that both the cement might grow
hard, and more especially, that the Air might come to its temper, natural
for the Day I try'd the Experiment in) I observ'd diligently, and found the
included Air to be exactly an Inch.

Here you are to take notice, that after the Air is seal'd up, the top of
the Tube is not to be elevated above the superficies of the Quicksilver in
the box, till the surface of that within the Tube be equal to it, for the
Quicksilver (as I have elsewhere prov'd) being more heterogeneous to the
Glass then the Air, will not naturally rise up so high within the small
Pipe, as the superficies of the _Mercury_ in the box, and therefore you are
to observe, how much below the outward superficies of the _Mercury_ in the
box, that of the same in the Tube does stand, when the top being open, free
ingress is admitted to the outward Air.

Having thus done, I permitted the _Cylinder_, or small Pipe, to rise out of
the box, till I found the surface of the Quicksilver in the Pipe to be two
inches above that in the box, and found the Air to have expanded it self
but one sixteenth part of an inch; then drawing up the small pipe, till I
found the height of the Quicksilver within to be four inches above that
without, I observed the Air to be expanded only 1/7 of an inch more then it
was at first, and to take up the room of 1-1/7 inch: then I raised the Tube
till the Cylinder was six inches high, and found the Air to take up 1-2/9
inches of room in the Pipe; then to 8, 10, 12. &c. the expansion of the Air
that I found to each of which Cylinders are set down in the following
Table; where the first row signifies the height of the _Mercurial
Cylinder_; the next, the expansion of the Air; the third, the pressure of
the _Atmosphere_, or the highest _Cylinder_ of _Mercury_, which was then
neer thirty inches: The last signifies the force of the Air so expanded,
which is found by substracting the first row of numbers out of the third;
for having found, that the outward Air would then keep up the Quicksilver
to thirty inches, look whatever of that height is wanting must be
attributed to the Elater of the Air depressing. And therefore having the
Expansion in the second row, and the height of the subjacent _Cylinder_ of
_Mercury_ in the first, and the greatest height of the _Cylinder_ of
_Mercury_, which of it self counterballances the whole pressure of the
_Atmosphere_; by substracting the numbers of the first row out of the
numbers of the third, you will have the measure of the _Cylinders_ so
deprest, and consequently the force of the Air, in the several Expansions,
registred.

The height of the The Expansion The height of The strength
Cylinder of Mercury, of the Air. the Mercury of the Elater
that, together with that counter- of the expanded
the Elater of the ballanc'd the Air.
included Air, Atmosphere.
ballanced the
pressure of the
Atmosphere.
---------- ---------- ---------- ----------
00 01 30 30
02 01-1/16 30 28
04 01-1/7 30 26
06 01-2/9 30 24
08 01-1/3 30 22
10 01-1/2 30 20
12 01-2/3 30 18
14 01-5/6 30 16
16 02-2/27 30 14
18 02-4/9 30 12
20 03 30 10
22 03-7/9 30 8
24 05-7/18 30 6
25 06-2/3 30 5
26 08-1/2 30 4
26-1/4 09-1/2 30 3-3/4
26-1/2 10-3/4 30 3-1/2
26-3/4 13 30 3-1/4
27 15-1/2 30 3

I had several other Tables of my Observations, and Calculations, which I
then made; but it being above a twelve month since I made them; and by that
means having forgot many circumstances and particulars, I was resolved to
make them over once again, which I did _August_ the second 1661. with the
very same Tube which I used the year before, when I first made the
Experiment (for it being a very good one, I had carefully preserv'd it:)
And after having tryed it over and over again; and being not well satisfied
of some particulars, I, at last, having put all things in very good order,
and being as attentive, and observant, as possibly I could, of every
circumstance requisite to be taken notice of, did register my several
Observations in this following Table. In the making of which, I did not
exactly follow the method that I had used at first; but, having lately
heard of Mr. _Townly_'s _Hypothesis_, I shap'd my course in such sort, as
would be most convenient for the examination of that _Hypothesis_; the
event of which you have in the latter part of the last Table.

The other Experiment was, to find what degrees of force were requisite to
compress, or condense, the Air into such or such a bulk.

The manner of proceeding therein was this: I took a Tube about five foot
long, one of whose ends was sealed up, and bended in the form of a
_Syphon_, much like that represented in the fourth Figure of the 37.
_Scheme_, one side whereof AD, that was open at A, was about fifty inches
long, the other side BC, shut at B, was not much above seven inches long,
then placing it exactly perpendicular, I pour'd in a little Quicksilver,
and found that the Air BC was 6-7/8 inches, or very near to seven; then
pouring in Quicksilver at the longer Tube, I continued filling of it till
the Air in the shorter part of it was contracted into half the former
dimensions, and found the height exactly nine and twenty inches; and by
making several other tryals, in several other degrees of condensation of
the Air, I found them exactly answer the former _Hypothesis_.

But having (by reason it was a good while since I first made) forgotten
many particulars, and being much unsatisfied in others, I made the
Experiment over again, and, from the several tryals, collected the former
part of the following Table: Where in the row next the left hand 24.
signifies the dimensions of the Air, sustaining only the pressure of the
_Atmosphere_, which at that time was equal to a _Cylinder_ of _Mercury_ of
nine and twenty inches: The next Figure above it (20) was the dimensions of
the Air induring the first compression, made by a _Cylinder_ of _Mercury_
5-3/16 high, to which the pressure of the _Atmosphere_ nine and twenty
inches being added, the elastick strength of the Air so comprest will be
found 34-3/16, &c.

_A Table of the Elastick power of the Air, both Experimentally and
Hypothetically calculated, according to its various Dimensions._

The dimensions The height The Mercurial The sum or What they
of the included of the Cylinder difference ought to
Air. Mercurial added, or of these be according
Cylinder taken from two to the
counter- the former. Cylinders. Hypothesis.
pois'd
by the
Atmosphere.
---------- ---------- ---------- ---------- ----------
12 29 + 29 = 58 58
13 29 + 24-11/16 = 53-11/16 53-7/13
14 29 + 20-3/16 = 49-3/16 49-5/7
16 29 + 14 = 43 43-1/2
18 29 + 9-1/8 = 38-1/8 38-2/3
20 29 + 5-3/16 = 34-3/16 34-4/5
24 29 0 = 29 29
48 29 - 14-5/8 = 14-3/8 14-1/2
96 29 - 22-1/8 = 6-7/8 7-2/8
192 29 - 25-5/8 = 3-3/8 3-5/8
384 29 - 27-2/8 = 1-6/8 1-7/16
576 29 - 27-7/8 = 1-1/8 1-5/24
768 29 - 28-1/8 = 0-7/8 0-[7-1/4]/8
960 29 - 28-3/8 = 0-5/8 0-[5-4/5]/8
1152 29 - 28-7/16 = 0-9/16 0-10/16

From which Experiments, I think, we may safely conclude, that the Elater of
the Air is reciprocal to its extension, or at least very neer. So that to
apply it to our present purpose (which was indeed the chief cause of
inventing these wayes of tryal) we will suppose a _Cylinder_ indefinitely
extended upwards, [I say a _Cylinder_, not a piece of a _Cone_, because, as
I may elsewhere shew in the Explication of Gravity, that _triplicate_
proportion of the shels of a Sphere, to their respective diameters, I
suppose to be removed in this case by the decrease of the power of Gravity]
and the pressure of the Air at the bottom of this _Cylinder_ to be strong
enough to keep up a _Cylinder_ of _Mercury_ of thirty inches: Now because
by the most accurate tryals of the most illustrious and incomparable Mr.
_Boyle_, published in his deservedly famous Pneumatick Book, the weight of
Quicksilver, to that of the Air here below, is found neer about as fourteen
thousand to one: If we suppose the parts of the _Cylinder_ of the
_Atmosphere_ to be every where of an equal density, we shall (as he there
deduces) find it extended to the height of thirty five thousand feet, or
seven miles: But because by these Experiments we have somewhat confirm'd
the hypothesis of the reciprocal proportion of the Elaters to the
Extensions we shall find, that by supposing this _Cylinder_ of the
_Atmosphere_ divided into a thousand parts, each of which being equivalent
to thirty five feet, or seven geometrical paces, that is, each of these
divisions containing as much Air as is suppos'd in a _Cylinder_ neer the
earth of equal diameter, and thirty five foot high, we shall find the
lowermost to press against the surface of the Earth with the whole weight
of the above mentioned thousand parts; the pressure of the bottom of the
second against the top of the first to be 1000 - 1 = 999. of the third
against the second to be 1000 - 2 = 998. of the fourth against the third to
be 1000 - 3 = 997. of the uppermost against the 999. or that next below it,
to be 1000 - 999 = 1. so that the extension of the lowermost next the
Earth, will be to the extension of the next below the uppermost, as 1. to
999. for as the pressure sustained by the 999. is to the pressure sustain'd
by the first, so is the extension of the first to the extension of the 999.
so that, from this hypothetical calculation, we shall find the Air to be
indefinitely extended: For if we suppose the whole thickness of the Air to
be divided, as I just now instanced, into a thousand parts, and each of
those under differing Dimensions, or Altitudes, to contain an equall
quantity of Air, we shall find, that the first _Cylinder_, whose Base is
supposed to lean on the Earth, will be found to be extended 35-35/999 foot;
the second equal Division, or _Cylinder_, whose _basis_ is supposed to lean
on the top of the first, shall have its top extended higher by 35-70/998
the third 35-105/997 the fourth 35-140/996 and so onward, each equal
quantity of Air having its dimensions measured by 35. and some additional
number exprest alwayes in the manner of a fraction, whose numerator is
alway the number of the place multipli'd by 35. and whose denominator is
alwayes the pressure of the _Atmosphere_ sustain'd by that part, so that by
this means we may easily calculate the height of 999. divisions of those
1000. divisions, I suppos'd; whereas the uppermost may extend it self more
then as high again, nay, perhaps indefinitely, or beyond the Moon; for the
Elaters and Expansions being in reciprocal proportions, since we cannot yet
find the _plus ultra_, beyond which the Air will not expand it self, we
cannot determine the height of the Air: for since, as we have shewn, the
proportion will be alway as the pressure sustain'd by any part is to 35. so
1000. to the expansion of that part; the multiplication or product
therefore of the pressure, and expansion, that is, of the two extream
proportionals, being alwayes equal to the product of the means, or 35000.
it follows, since that Rectangle or Product may be made up of the
multiplication of infinite diversities of numbers, that the height of the
Air is also indefinite; for since (as far as I have yet been able to try)
the Air seems capable of an indefinite Expansion, the pressure may be
decreased in _infinitum_, and consequently its expansion upwards indefinite
also.

There being therefore such a difference of density, and no Experiment yet
known to prove a _Saltus_, or skipping from one degree of rarity to another
much differing from it, that is, that an upper part of the Air should so
much differ from that immediately _subjacent_ to it, as to make a distinct
superficies, such as we observe between the Air and Water, &c. But it being
more likely, that there is a continual increase of rarity in the parts of
the Air, the further they are removed from the surface of the Earth: It
will hence necessarily follow, that (as in the Experiment of the salt and
fresh Water) the ray of Light passing obliquely through the Air also, which
is of very different density, will be continually, and infinitely
inflected, or bended, from a streight, or direct motion.

This granted, the reason of all the above recited _Phaenomena_, concerning
the appearance of the Celestial Bodies, will very easily be deduced. As,

First, The redness of the Sun, Moon, and Stars, will be found to be caused
by the inflection of the rays within the _Atmosphere_. That it is not
really in or near the luminous bodies, will, I suppose, be very easily
granted, seeing that this redness is observable in several places differing
in Longitude, to be at the same time different, the setting and rising Sun
of all parts being for the most part red:

And secondly, That it is not meerly the colour of the Air interpos'd, will,
I suppose, without much more difficulty be yielded, seeing that we may
observe a very great _interstitium_ of Air betwixt the Object, and the Eye,
makes it appear of a dead blew, far enough differing from a red, or yellow.

But thirdly, That it proceeds from the refraction, or inflection, of the
rays by the _Atmosphere_, this following Experiment will, I suppose,
sufficiently manifest.

Take a sphaerical Crystalline Viol, such as is describ'd in the fifth
Figure ABCD, and, having fill'd it with pure clear Water, expose it to the
Sun beams; then taking a piece of very fine _Venice_ Paper, apply it
against that side of the Globe that is opposite to the Sun, as against the
side BC, and you shall perceive a bright red Ring to appear, caus'd by the
refraction of the Rays, AAAA, which is made by the Globe; in which
Experiment, if the Glass and Water be very cleer, so that there be no Sands
nor bubbles in the Glass, nor dirt in the Water, you shall not perceive any
appearance of any other colour. To apply which Experiment, we may imagine
the _Atmosphere_ to be a great transparent Globe, which being of a
substance more dense then the other, or (which comes to the same) that has
its parts more dense towards the middle, the Sun beams that are tangents,
or next within the tangents of this Globe, will be refracted or inflected
from their direct passage towards the center of the Globe, whence,
according to the laws of refractions made in a triangular _Prism_, and the
generation of colour set down in the description of Muscovi-glass there
must necessarily appear a red colour in the _transitus_ or passage of those
tangent Rays. To make this more plain, we will suppose (in the sixth
_Figure_) ABCD, to represent the Globe of the _Atmosphere_, EFGH to
represent the opacous Globe of the Earth, lying in the midst of it, neer to
which, the parts of the Air, sustaining a very great pressure, are thereby
very much condens'd, from whence those Rays that are by inflection made
tangents to the Globe of the Earth, and those without them, that pass
through the more condens'd part of the _Atmosphere_, as suppose between A
and E, are by reason of the inequality of the _medium_, inflected towards
the center, whereby there must necessarily be generated a red colour, as is
more plainly shewn in the former cited place; hence whatsoever opacous
bodies (as vapours, or the like) shall chance to be elevated into those
parts, will reflect a red towards the eye; and therefore those evenings and
mornings appear reddest, that have the most store of vapours and halituous
substances exhaled to a convenient distance from the Earth; for thereby the
inflection is made the greater, and thereby the colour also the more
intense; and several of those exhalations being opacous, reflect several of
those Rays, which, through an _Homogeneous_ transparent _medium_ would pass
unseen; and therefore we see, that when there chances to be any clouds
situated in those Regions they reflect a strong and vivid red. Now, though
one great cause of the redness may be this inflection, yet I cannot wholly
exclude the colour of the vapours themselves, which may have something of
redness in them, they being partly nitrous; and partly fuliginous; both
which steams tinge the Rays that pass through them, as is made evident by
looking at bodies through the fumes of _Aqua fortis_ or spirit of _Nitre_
[as the newly mentioned Illustrious Person has demonstrated] and also
through the smoak of a Fire or Chimney.

Having therefore made it probable at least, that the morning and evening
redness may partly proceed from this inflection or refraction of the Rays,
we shall next shew how the Oval Figure will be likewise easily deduced.

Suppose we therefore, EFGH in the sixth _Figure_ of the 37. _Scheme_, to
represent the Earth; ABCD, the _Atmosphere_; EI, and EL, two Rays coming
from the Sun, the one from the upper, the other from the neather Limb,
these Rays, being by the _Atmosphere_ inflected, appear to the eye at E, as
if they had come from the points, N and O; and because the Ray L has a
greater inclination upon the inequality of the _Atmosphere_ then I,
therefore must it suffer a greater inflection, and consequently be further
elevated above its true place, then the Ray I, which has a less
inclination, will be elevated above its true place; whence it will follow,
that the lower side appearing neerer the upper then really it is, and the
two _lateral_ sides, _viz._ the right and left side, suffering no sensible
alteration from the inflection, at least what it does suffer, does rather
increase the visible Diameter then diminish it, as I shall shew by and by,
the Figure of the luminous body must necessarily appear somewhat
_Elliptical_.

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