new-invented microscopes, in a letter to the Academy of Sciences at
Petersburgh;[22] they are nothing more than an application of the
achromatic perspective to microscopic purposes. Now it has been long
known to every one who is the least versed in optics, that any telescope
is easily converted into a microscope, by removing the object glass to a
greater distance from the eye glasses; and that the distance of the
image varies with the distance of the object from the focus, and is
magnified more as its distance from the object is greater: the same
telescope may, therefore be successively turned into a microscope, with
different magnifying powers. Mr. Martin had also shewn, in his
description and use of a polydynamic microscope, how easily the small
achromatic perspective may be applied to this purpose. Botanists might
find some advantage in attending to this instrument; it would assist
them in discovering small plants at a distance, and thus often save them
from the thorns of the hedge, and the dirt of a ditch.
[22] Description des Nouveaux Microscopes inventes par M. Æpinus.
Fig. 1. Plate III, represents the improved lucernal microscope.
Fig. 1. Plate IV. The improved compound and single microscope.
Fig. 2. Plate IV. The best universal compound microscope.
Fig. 3. Plate IV, is what is usually called Culpeper’s, or the common
three pillared compound microscope.
Fig. 1. Plate V, represents Martin’s solar opake microscope.
Fig. 4. Plate VI, is a picture of the common solar microscope.
Fig. 1. Plate VII. A, is Cuff’s common compound microscope.
Fig. 3. Plate VIII. Martin’s new microscopic telescope, or convenient
portable apparatus for a traveller.
We cannot conclude this chapter better than with the following
observations on the microscope. We are indebted to it for many
discoveries in natural history; but let us not suppose that the Creator
intended to hide these objects from our observation. It is true, this
instrument discovers to us as it were a new creation, new series of
animals, new forests of vegetables; but he who gave being to these, gave
us an understanding capable of inventing means to assist our organs in
the discovery of their hidden beauties. He gave us eyes adapted to
enlarge our ideas, and capable of comprehending a universe at one view,
and consequently incapable of discerning those minute beings, with which
he has peopled every atom of the universe. But then he gave properties
and qualities to matter of a particular kind, by which it would procure
us this advantage, and at the same time elevated the understanding from
one degree of knowledge to another, till it was able to discover these
assistances for our sight.
It is thus we should consider the discoveries made by those instruments,
which have received their birth from an exertion of our faculties. It is
to the same power, who created the objects of our admiration, that we
are ultimately to refer the means of discovering them. Let no one,
therefore, accuse us of prying deeper into the wonders of nature, than
was intended by the great author of the universe. There is nothing we
discover by their assistance, which is not a fresh source of praise; and
it does not appear that our faculties can be better employed, than in
finding means to investigate the works of God.
From a partial consideration of these things, we are very apt to
criticise what we ought to admire; to look upon as useless what perhaps
we should own to be of infinite advantage to us, did we see a little
farther; to be peevish where we ought to give thanks; and at the same
time to ridicule those who employ their time and thoughts in examining
what we were, i. e. some of us most assuredly were created and appointed
to study. In short, we are too apt to treat the Almighty worse than a
rational man would treat a good mechanic, whose works he would either
thoroughly examine, or be ashamed to find any fault with them. This is
the effect of a partial consideration of nature; but he who has candor
of mind, and leisure to look farther, will be inclined to cry out:
How wond’rous is this scene! where all is form’d
With number, weight, and measure! all design’d
For some great end! where not alone the plant
Of stately growth; the herb of glorious hue,
Or food-full substance! not the laboring steed,
The herd, and flock that feed us; not the mine
That yields us stores for elegance and use;
The sea that loads our table, and conveys
The wanderer man from clime to clime, with all
Those rolling spheres, that from on high shed down
Their kindly influence; not these alone,
Which strike ev’n eyes incurious, but each moss,
Each shell, each crawling insect, holds a rank
Important in the plan of Him, who fram’d
This scale of beings; holds a rank, which lost,
Would break the chain, and leave behind a gap
Which nature’s self would rue. Almighty Being,
Cause and support of all things, can I view
These objects of my wonder; can I feel
These fine sensations, and not think of thee?
Thou who dost thro’ th’ eternal round of time,
Dost thro’ th’ immensity of space exist
Alone, shalt thou alone excluded be
From this thy universe? Shall feeble man
Think it beneath his proud philosophy
To call for thy assistance, and pretend
To frame a world, who cannot frame a clod?--
Not to know thee, is not to know ourselves--
Is to know nothing--nothing worth the care
Of man’s exalted spirit:--all becomes,
Without thy ray divine, one dreary gloom,
Where lurk the monsters of phantastic brains,
Order bereft of thought, uncaus’d effects,
Fate freely acting, and unerring chance.
Where meanless matter to a chaos sinks,
Or something lower still, for without thee
It crumbles into atoms void of force,
Void of resistance--it eludes our thought.
Where laws eternal to the varying code
Of self-love dwindle. Interest, passion, whim,
Take place of right and wrong, the golden chain
Of beings melts away, and the mind’s eye
Sees nothing but the present. All beyond
Is visionary guess--is dream--is death.[23]
[23] Stillingfleet’s Miscellaneous Tracts.
CHAP. II.
OF VISION; OF THE OPTICAL EFFECT OF MICROSCOPES, AND OF THE MANNER OF
ESTIMATING THEIR MAGNIFYING POWERS.
The progress that has been made in the science of optics, in the last
and present century, particularly by Sir Isaac Newton, may with
propriety be ranked among the greatest acquisitions of human knowledge.
And Mess. Delaval and Herschel have shewn by their discoveries, that the
boundaries of this science may be considerably enlarged.
The rays of light, which minister to the sense of sight, are the most
wonderful and astonishing part of the inanimate creation; of which we
shall soon be convinced, if we consider their extreme minuteness, their
inconceivable velocity, the regular variety of colours they exhibit, the
invariable laws according to which they are acted upon by other
substances, in their reflections, inflections, and refractions, without
the least change of their original properties; and the facility with
which they pervade bodies of the greatest density and closest texture,
without resistance, without crouding or disturbing each other. These, I
believe, will be deemed sufficient proofs of the wonderful nature of
these rays; without adding, that it is by a peculiar modification of
them, that we are indebted for the advantages obtained by the
microscope.
The science of optics, which explains and treats of many of the
properties of those rays of light, is deduced from experiments, on which
all philosophers are agreed. It is impossible to give an adequate idea
of the nature of vision, without a knowledge of these experiments, and
the mathematical reasoning grounded upon them; but as to do this would
alone fill a large volume, I shall only endeavour to render some of the
more general principles clear, that the reader, who is unacquainted with
the science of optics, may nevertheless be enabled to comprehend the
nature of vision by the microscope. Some of the most important of these
principles may be deduced from the following very interesting
experiment.
Darken a room, and let the light be admitted therein only by a small
hole; then, if the weather be fine, you will see on the wall, which is
facing the hole, a picture of all those exterior objects which are
opposite thereto, with all their colours, though these will be but
faintly seen. The image of the objects that are stationary, as trees,
houses, &c. will appear fixed; while the images of those that are in
motion, will be seen to move. The image of every object will appear
inverted, because the rays cross each other in passing through the small
hole. If the sun shine on the hole, we shall see a luminous ray proceed
in a strait line, and terminate on the wall. If the eye be placed in
this ray, it will be in a right line with the hole and the sun: it is
the same with every other object which is painted on the wall. The
images of the objects exhibited on the same plane, are smaller in
proportion as the objects are further from the hole.
Many and important are the inferences which may be deduced from the
foregoing experiment, among which are the following:
1. That light flows in a right line.
2. That a luminous point may be seen from all those places to which a
strait line can be drawn from the point, without meeting with any
obstacle; and consequently,
3. That a luminous point, by some unknown power, sends forth rays of
light in all directions, and is the center of a sphere of light, which
extends indefinitely on all sides; and if we conceive some of these rays
to be intercepted by a plane, then is the luminous point the summit of a
pyramid, whose body is formed by the rays, and its base by the
intercepting plane. The image of the surface of an object, which is
painted on the wall, is also the base of a pyramid of light, the apex of
which is the hole; the rays which form this pyramid, by crossing at the
hole, form another, similar and opposite to this, of which the hole is
also the summit, and the surface of the object the base.
4. That an object is visible, because all its points are radiant points.
5. That the particles of light are indefinitely small; for the rays,
which proceed from the points of all the objects opposite to the hole,
pass through it, though extremely small, without embarrassing or
confounding each other.
6. That every ray of light carries with it the image of the object from
which it was emitted.
The nature of vision in the eye may be imperfectly illustrated by the
experiment of the darkened room; the pupil of the eye being considered
as the hole through which the rays of light pass, and cross each other,
to paint on the retina, at the bottom of the eye, the inverted images of
all those objects which are exposed to the sight, so that the diameters
of the images of the same object are greater, in proportion to the
angles formed at the pupil, by the crossing rays which proceed from the
extremities of the object; that is, the diameter of the image is
greater, in proportion as the distance is less; or, in other words, the
apparent magnitude of an object is in some degree measured by the angle
under which it is seen, and this angle increases or diminishes,
according as the object is nearer to, or farther from the eye; and
consequently, the less the distance is between the eye and the object,
the larger the latter will appear.
From hence it follows, that the apparent diameter of an object seen by
the naked eye, may be magnified in any proportion we please; for, as the
apparent diameter is increased, in proportion as the distance from the
eye is lessenned, we have only to lessen the distance of the object from
the eye, in order to increase the apparent diameter thereof.[24] Thus,
suppose there is an object, A B, Plate I. Fig. 1, which to an eye at E
subtends or appears under the angle A E B, we may magnify the apparent
diameter in what proportion we please, by bringing our eye nearer to it.
If, for instance, we would magnify it in the proportion of F G to A B;
that is, if we would see the object under an angle as large as F E G, or
would make it appear the same length that an object as long as F G would
appear, it may be done by coming nearer to the object. For the apparent
diameter is as the distance inversely; therefore, if C D is as much less
than C E, as F G is greater than A B, by bringing the eye nearer to the
object in the proportion of C D to E D, the apparent diameter will be
magnified in the proportion of F G to A B; so that the object A B, to
the eye at D, will appear as long as an object F G would appear to the
eye at E. In the same manner we might shew, that the apparent diameter
of an object, when seen by the naked eye, may be infinite. For since
the apparent diameter is reciprocally as the distance of the eye, when
the distance of the eye is nothing or when the eye is close to the
object at C, the apparent diameter will be the reciprocal of nothing, or
infinite.
[24] Rutherforth’s System of Natural Philosophy, p. 330.
There is, however, one great inconvenience in thus magnifying an object,
without the help of glasses, by placing the eye nearer to it. The
inconvenience is, that we cannot see an object distinctly, unless the
eye is about five or six inches from it; therefore, if we bring it
nearer to our eye than five or six inches, however it may be magnified,
it will be seen confusedly. Upon this account, the greatest apparent
magnitude of an object that we are used to, is the apparent magnitude
when the eye is about five or six inches from it: and we never place an
object much within that distance; because, though it might be magnified
by these means, yet the confusion would prevent our deriving any
advantage from seeing it so large. The size of an object seems
extraordinary, when viewed through a convex lens; not because it is
impossible to make it appear of the same size to the naked eye, but
because at the distance from the eye which would be necessary for this
purpose, it would appear exceedingly confused; for which reason, we
never bring our eye so near to it, and consequently, as we have not been
accustomed to see the object of this size, it appears an extraordinary
one.
On account of the extreme minuteness of the atoms of light, it is clear,
a single ray, or even a small number of rays, cannot make a sensible
impression on the organ of sight, whose fibres are very gross, when
compared to these atoms; it is necessary, therefore, that a great number
should proceed from the surface of an object, to render it visible. But
as the rays of light, which proceed from an object, are continually
diverging, different methods have been contrived, either of uniting them
in a given point, or of separating them at pleasure: the manner of
doing this is the subject of dioptrics and catoptrics.
By the help of glasses, we unite in the same sensible point a great
number or rays, proceeding from one point of an object; and as each ray
carries with it the image of the point from whence it proceeded, all the
rays united must form an image of the object from whence they were
emitted. This image is brighter, in proportion as there are more rays
united; and more distinct, in proportion as the order, in which they
proceeded, is better preserved in their union. This may be rendered
evident; for, if a white and polished plane be placed where the union is
formed, we shall see the image of the object painted in all its colours
on this plane; which image will be brighter, if all adventitious light
be excluded from the plane on which it is received.
The point of union of the rays of light, formed by means of a glass
lens, &c. is called the FOCUS.
Now, as each ray carries with it the image of the object from whence it
proceeded, it follows, that if those rays, after intersecting each
other, and having formed an image at their intersection, are again
united by a refraction or reflection, they will form a new image, and
that repeatedly, as long as their order is not confounded or disturbed.
It follows also, that when the progress of the luminous ray is under
consideration, we may look on the image as the object, and the object as
the image; and consider the second image as if it had been produced by
the first as an object, and so on.
In order to gain a clear idea of the wonderful effects produced by
glasses, we must proceed to say something of the principles of
refraction.
Any body, which is so constituted as to yield a passage to the rays of
light, is called a MEDIUM. Air, water, glass, &c. are mediums of light.
If any medium afford an easy passage to the rays of light, it is called
a RARE MEDIUM; but if it do not afford an easy passage to these rays, it
is called a DENSE MEDIUM.
Let Z, Fig. 2. Plate I. be a rare medium, and Y a dense one; and let
them be separated by the plane surface G H. Let I K be a perpendicular
to it, and cutting it in C.
With the center C, and any distance, let a circle be described. Then let
A C be a ray of light, falling upon the dense medium. This ray, if
nothing prevented, would go forward to L; but because the medium Y is
supposed to be denser than Z, it will be bent downward toward the
perpendicular I K, and describe the line C B.
The ray A C is called the INCIDENT RAY; and the ray C B, the REFRACTED
RAY.
The angle A C I is called the ANGLE OF INCIDENCE, and the angle B C K is
called the ANGLE OF REFRACTION.
If from the point A upon the right line C I, there be let fall the
perpendicular A D, that line is called the sine of the angle of
incidence.
In the same manner, if from the point B, upon the right line I K, there
be let fall the perpendicular B E, that line will be the sine of the
angle of refraction.
The sines of the angles are the measures of the refractions, and this
measure is constant; that is, whatever is the sine of the angle of
incidence, it will be in a constant proportion to the sine of the angle
of refraction, when the mediums continue the same. A general idea of
refraction may be formed from the following experiments.
EXPERIMENT 1. Let A B C D, Fig. 3. Plate I. represent a vessel so
placed, with respect to the candle E, that the shadow of the side A C
may fall at D. Suppose the vessel to be now filled with water, and the
shadow will withdraw to d; the ray of light, instead of proceeding to D,
being refracted or bent to d. And there is no doubt but that an eye,
placed at d, would see the candle at e, in the direction of the
refracted ray d A. This is also confirmed by the following pleasing
experiment.
2. Lay a shilling, or any piece of money, at the bottom of a bason; then
withdraw from the bason, till you lose sight of the shilling; fill the
bason nearly with water, and the shilling will be seen very plainly,
though you are at the same distance from it.
3. Place a stick over a bason which is filled with water; then reflect
the sun’s rays, so that they may fall perpendicularly on the surface of
the water; the shadow of the stick will fall on the same place, whether
the vessel be empty or full.
What has been said of water, may be applied to any transparent medium,
only the power of refraction is greater in some than in others. It is
from this wonderful property, that we derive all the curious effects of
glass, which make it the subject of optics. It is to this we owe the
powers of the microscope and the telescope.
To produce these effects, pieces of glass are formed into given figures,
which, when so formed, are called lenses. The six following figures are
those which are most in use for optical purposes.
1. A PLANE GLASS, one that is flat on each side, and of an equal
thickness throughout. F, Fig. 13. Plate I.
2. A DOUBLE CONVEX GLASS, one that is more elevated towards the middle
than the edge. B, Fig. 13. Plate I.
3. A DOUBLE CONCAVE is hollow on both sides, or thinner in the middle
than at the edges. D, Fig. 13. Plate I.
4. A PLANO CONVEX, flat on one side, and convex on the other. A, Fig.
13. Plate I.
5. A PLANO CONCAVE, flat on one side, and concave on the other. C, Fig.
13. Plate I.
6. A MENISCUS, convex on one side, concave on the other. E, Fig. 13.
Plate I.
It has been already observed, that light proceeds invariably from a
luminous body, in strait lines, without the least deviation; but if it
happen to pass from one medium to another, it always leaves the
direction it had before, and assumes a new one. After having taken this
new direction, it proceeds in a strait line, till it meets with a
different medium, which again turns it out of its course.
A ray of light passing obliquely through a plane glass, will go out in
the same direction it entered, though not precisely in the same line.
The ray C D, Fig.4. Plate I. falling obliquely upon the surface of the
plane glass A B, will be refracted towards the glass in the direction D
E; but when it comes to E, it will be as much refracted the contrary
way. If the ray of light had fallen perpendicularly on the surface of
the plane glass, it would have passed through it in a strait line, and
not have been refracted at all.
If parallel rays of light, as a b c d e f g, Fig. 6. Plate I. fall
directly upon a convex lens A B, they will be so bent, as to unite in a
point C behind it. For the ray d D which falls perpendicularly upon the
middle of the glass, will go through it without suffering any
refraction: but those which go through the sides of the lens, falling
obliquely on its surface, will be so bent, as to meet the central ray at
C. The further the ray a is from the axis of the lens, the more
obliquely it will fall upon it. The rays a b c d e f g will be so
refracted, as to meet or be collected in the point C, called the
principal focus, whose distance, in a double convex lens, is equal to
the radius or semi-diameter of the sphere of the convexity of the lens.
All the rays cross the middle ray at C, and then diverge from it to the
contrary side, in the same manner as they were before converged.
If another lens, of the same convexity, as A B, Fig. 6. Plate I. be
placed in the rays, and at the same distance from the focus, it will
refract them, so that after going out of it, they will all be parallel
again, and go on in the same manner as they came to the first glass A B,
but on the contrary sides of the middle ray.
The rays diverge from any radiant point, as from a principal focus:
therefore, if a candle be placed at C, in the focus of the convex lens A
B, Fig. 6. Plate I. the rays diverging from it will be so refracted by
the lens, that after going out of it, they will become parallel. If the
candle be placed nearer the lens than its focal distance, the rays will
diverge more or less, as the candle is more or less distant from the
focus.
If any object, A B, Fig. 7. Plate I. be placed beyond the focus of the
convex lens E F, some of the rays which flow from every point of the
object, on the side next the glass, will fall upon it, and after passing
through it, they will be converged into as many points on the opposite
side of the glass; for the rays a b, which flow from the point A, will
converge into _a b_, and meet at C. The rays c d, flowing from the point
G, will be converged into _c d_, and meet at g; and the rays which flow
from B, will meet each other again at D; and so of the rays which flow
from any of the intermediate points: for there will be as many focal
points formed, as there are radiant points in the object, and
consequently they will depict on a sheet of paper, or any other
light-coloured body, placed at D g C, an inverted image of the object.
If the object be brought nearer the lens, the picture will be formed
further off. If it be placed at the principal focus, the rays will go
out parallel, and consequently form no picture behind the glass.