TO MAKE SMALL GLASS MICROSCOPIC GLOBULES.
Take two rods of glass, one in each hand, place their extremities close to each other, and in the purest part of the flame; when you perceive the ends to be fused, separate them from each other; the heated glass following each rod, will be finer, in proportion to the length it is drawn to, and the smallness of the rod; in this manner you may procure threads of glass of any degree of fineness. Direct the flame to the middle of the thread, and it will be instantly divided into two parts. When one of the threads is perfectly cool, place it at the extremity of the flame, by which it will be rendered round; and, if the thread of glass be very fine, an exceeding small globule will be formed. This thread may now be broke off from the rod, and a new one may be again drawn out as before, by the assistance of the other glass rod.
The small ball is now to be separated from the thread of glass; this is easily effected by the sharp edge of a piece of flint. The ball should be placed in a groove of paper, and another piece of paper be held over it, to prevent the ball from flying about and being lost. A quantity of globules ought to be prepared in this manner; they are then to be cleaned, and afterwards placed in the cavities of the tripoli, by means of a delicate pair of nippers. The globules are now to be melted a second time, in order to render them completely spherical; for this purpose, bring one of the cavities near the extremity of the flame, directing this towards the tripoli, which must be first heated; the cavity is then to be lowered, so that the flame may touch the glass, which, when it is red hot, will assume a perfect globular form; it must then be removed from the flame, and laid by; when cold, it should be cleaned, by rubbing between two pieces of white paper. Let it now be set in a brass cap, to try whether the figure be perfect. If the object be not well defined, the globule must be thrown away. Though, if it be large, it may be exposed two or three times to the flame. When a large globule is forming, it should be gently agitated by shaking the tripoli, which will prevent its becoming flat on one side. By attending to these directions, the greater part of the globules will be round and fit for use. In damp weather, notwithstanding every precaution, it will often happen, that out of forty globules, four or five only will be fit for use.
Mr. Stephen Gray, of the Charter-House, having observed some irregular particles within a glass globule, and finding that they appeared distinct and prodigiously magnified when held close to his eye, concluded, that if he placed a globule of water, in which there were any particles more opake than the water, near his eye, he should see those particles distinctly and highly magnified. This idea, when realized, far exceeded his expectation. His method was, to take on a pin a small portion of water which he knew had in it some minute animalculæ; this he laid on the end of a small piece of brass wire, till there was formed somewhat more than an hemisphere of water; on applying it then to the eye, he found the animalculæ most enormously magnified; for those which were scarce discernible with his glass globules, with this appeared as large as ordinary sized peas. They cannot be seen in day-time, except the room be darkened, but are seen to the greatest advantage by candle-light. Montucla observes, that when any objects are inclosed within this transparent globule, the hinder part of it acts like a concave mirror, provided they be situated between that surface and the focus; and that by these means they are magnified three times and an half more than they would be in the usual way. An extempore microscope may be formed, by taking up a small drop of water on the point of a pin, and placing it over a fine hole made in a piece of metal; but as the refractive power of water is less than that of glass, these globules do not magnify so much as those of the same size which are made of glass: this was also contrived by Mr. Gray. The same ingenious author invented another water microscope, consisting of two drops of water, separated in part by a thin brass plate, but touching near the center; which were thus rendered equivalent to a double convex lens of unequal convexities.
Dr. Hooke describes a method of using the single microscope, which seems to have a great analogy to the foregoing methods of Mr. Gray. “If you are desirous,” says he, “of obtaining a microscope with one single refraction, and consequently capable of procuring the greatest clearness and brightness any one kind of microscope is susceptible of; spread a little of the fluid you intend to examine, on a glass plate, bring this under one of your microscopic globules, then move it gently upwards, till the fluid touch the globule, to which it will soon adhere, and that so firmly, as to bear being moved a little backwards or forwards. By looking through the globule, you will then have a perfect view of the animalculæ in the drop.”[11]
[11] Hooke’s Lectures and Conjectures, p. 98.
Having laid before the reader the principal improvements that have been suggested, or made in the single microscope, it remains only to point out those instruments of this kind, which, from the mode in which they are fitted up, seem best adapted for general use; the peculiar advantages of which, as well as the manner of using them, will be described in the [third chapter] of this work.
Fig. 1. [Plate VI.] A botanical microscope, contrived by Dr. Withering.
Fig. 2. [Plate VI.] A botanical microscope, by Mr. B. Martin, being the most universal pocket microscope.
Fig. 3. [Plate VI], represents that which was used by M. Lyonnet for dissecting the cossus.
Fig. 5. [Plate VI.] The tooth and pinion microscope, which is now generally substituted in the room of Wilson’s. Fig. 1. [Plate II. B].
Fig. 1. [Plate VII. B]. The aquatic microscope used by Mr. Ellis for investigating the nature of coralline, and recommended to botanists by Mr. Curtis, in his valuable publication, the “Flora Londinensis.”
Fig. 7. [Plate VIII.] A botanical magnifier, or hand megalascope, which by the different combinations of its three lenses produces seven different magnifying powers; when the three are used together, they are turned in, and the object viewed through the apertures in the sides.
Fig. 8. [Plate VIII.] A botanical magnifier, having one large lens and two small ones, but not admitting of more than three powers.
A compound microscope, as it consists of two, three, or more glasses, is more easily varied, and is susceptible of greater changes in its construction, than the single microscope. The number of the lenses, of which it is formed, may be increased or diminished, their respective positions may be varied, and the form in which they are mounted be altered almost ad infinitum. But among these varieties, some will be found more deserving of attention than others; we shall here treat of these only.
The three first compound microscopes deserving of notice, are those of Dr. Hooke, Eustachio Divinis, and Philip Bonnani. Dr. Hooke gives an account of his in the preface to his Micrographia, which has been already cited; it was about three inches in diameter, seven long, and furnished with four draw-out tubes, by which it might be lengthened as occasion required: it had three glasses—a small object glass, a middle glass, and a deep eye glass. Dr. Hooke used all the glasses when he wanted to take in a considerable part of an object at once, as by the middle glass a number of radiating pencils were conveyed to the eye, which would otherwise have been lost: but when he wanted to examine with accuracy the small parts of any substance, he took out the middle glass, and only made use of the eye and object lenses; for the fewer the refractions are, the clearer and more bright the object appears.
An account of Eustachio Divinis’s microscope was read at the Royal Society, in 1668.[12] It consisted of an object lens, a middle glass, and two eye glasses, which were plano convex lenses, and were placed so that they touched each other in the center of their convex surfaces; by which means the glass takes in more of an object, the field is larger, the extremities of it less curved, and the magnifying power greater. The tube, in which the glasses were inclosed, was as large as a man’s leg, and the eye glasses as broad as the palm of the hand. It had four several lengths; when shut up, it was sixteen inches long, and magnified the diameter of an object forty-one times; at the second length, ninety times; at the third length, one hundred and eleven times; at the fourth length, one hundred and forty-three times. It does not appear that E. Divinis varied the object lenses.
[12] Philos. Trans. No. 42.
Philip Bonnani published an account of his two microscopes in 1698;[13] both were compound; the first was similar to that which Mr. Martin published as new, in his Micrographia Nova,[14] in 1742. His second was like the former, composed of three glasses, one for the eye, a middle glass, and an object lens; they were mounted in a cylindrical tube, which was placed in an horizontal position; behind the stage was a small tube, with a convex lens at each end; beyond this was a lamp; the whole capable of various adjustments, and regulated by a pinion and rack; the small tube was used to condense the light on the object, and spread it uniformly over it according to its nature, and the magnifying power that was used.
[13] Bonnani Observationes circa Viventia.
[14] Micrographia Nova, by B. Martin, 4to.
If the reader attentively consider the construction of the foregoing microscopes, and compare them with more modern ones, he will be led to think with me, that the compound microscope has received very little improvement since the time of Bonnani. Taken separately, the foregoing constructions are equal to some of the most famed modern microscopes. If their advantages be combined, they are far superior to that of M. Dellebarre, notwithstanding the pompous eulogium affixed thereto by Mess. De L’Academie Royale des Sciences.[15]
[15] Memoires sur les Differences de la Construction et des Effets du Microscope, de M. L. F. Dellebarre, 1777.
From this period, to the year 1736, the microscope appears not to have received any considerable alteration, but the science itself to have been at a stand. The improvements which were making in the reflecting telescope, naturally led those who had considered the subject, to expect a similar advantage would accrue to microscopes on the same principles: accordingly we find two plans of this kind; the first was that of Dr. Robert Barker. This instrument is entirely the same as the reflecting telescope, excepting the distance of the two speculums, which is lengthened, in order to adapt it to those pencils of rays which enter the telescope diverging; whereas, from very distant objects, they come in a direction nearly parallel. But this was soon laid aside, not only as it was more difficult to manage, but also because it was unfit for any but very small or transparent objects: for the object being between the speculum and the image, would, if it were large and opake, prevent a due reflection of light on the object.
The second was contrived by Dr. Smith.[16] In this there were two reflecting mirrors, one concave and the other convex; the image was viewed by a lens. This microscope, though far from being executed in the best manner, performed, says Dr. Smith, very well, so that he did not doubt but that it would have excelled others, if it had been properly finished.
[16] Dr. Smith’s Optics, Remarks, p. 94.
As some years are more favourable to the fruits of the earth, so also some periods are more favourable to particular sciences, being rich in discovery, and cultivated with ardor. Thus, in the year 1738, Dr. Lieberkühn’s invention of the solar microscope was communicated to the public: the vast magnifying power which was obtained by this instrument, the colossal grandeur with which it exhibited the minima of nature, the pleasure which arose from being able to display the same object to a number of observers at the same time, by affording a new source of rational amusement, increased the number of microscopic observers, who were further stimulated to the same pursuits by Mr. Trembley’s famous discovery of the polype: the wonderful properties of this little animal, together with the works of Mr. Trembley, Baker, and my father, revived the reputation of this instrument.[17]
[17] Trembley Memoires sur les Polypes. Baker’s Microscope made Easy; Attempt towards an History of the Polype; Employment for the Microscope. Adams’s Micrographia Illustrata. Joblot’s Observations d’Histoire Naturelle.
Every optician now exercised his talents in improving, as he called it, the microscope; in other words, in varying its construction, and rendering it different from that sold by his neighbour. Their principal object seemed to be, only to subdivide the instrument, and make it lie in as small a compass as possible; by which means, they not only rendered it complex and troublesome in use, but lost sight also of the extensive field, great light, and other excellent properties of the more ancient instruments; and, in some measure, shut themselves out from further improvements on the microscope. Every mechanical instrument is susceptible of almost infinite combinations and changes, which are attended with their relative advantages and disadvantages: thus, what is gained in power, is lost in time; “he that loves to be confined to a small house, must lose the benefit of air and exercise.”
The microscope, nearly at the same period, gave rise to M. Buffon’s famous system of organic molecules, and M. Needham’s incomprehensible ideas concerning a vegetable force and the vitality of matter. M. Buffon has dressed up his system with all the charms of eloquence, presenting it to the mind in the most agreeable and lively colours, exerting the depths of erudition in the most interesting and seducing manner to establish his hypothesis, making us almost ready to adopt it against the dictates of reason, and the evidence of facts. But whether this great man was misled by the warmth of his imagination, his attachment to a favourite system, or the use of imperfect instruments, it appears but too evident, that he was not acquainted with the objects whose nature he attempted to investigate; and it is probable, that he never saw[18] those which he supposed he was describing, continually confounding the animalculæ produced from the putrifying decomposition of animal substances, with the spermatic animalculæ, although they are two kinds of beings, differing in form and nature; so that the beautiful fabric attempted to be raised on his hypothesis, vanishes before the light of truth and well conducted experiments.
[18] Porro Buffonius, ut cum illustris viri venia dicam, omnino non videtur vermiculos seminales vidisse. Diuturnitas enim vitæ quam suis corpusculis tribuit, ostendit non esse nostra animalcula (id est, spermatica) quibus brevis et paucarum horarum vita est. Haller Physiol. tom. 7.
After this period, the mind, either satisfied with the discoveries already made, which will be particularly described hereafter, or tired by its own exertions, sought for repose in other pursuits; so that for several years this instrument was again, in some measure, laid aside. In 1770, Dr. Hill[19] published a treatise, in which he endeavoured to explain the construction of timber by the microscope, and shew the number, the nature, and office of its several parts, their various arrangements and proportions in the different kinds; and point out a way of judging, from the structure of trees, the uses they will best serve in the affairs of life. So important a subject soon revived the ardor for microscopic pursuits, which seems to have been increasing ever since. About the same time, my father contrived an instrument for cutting the transverse sections of wood, in order that the texture thereof might be rendered more visible in the microscope, and consequently be better understood; this instrument was afterwards improved by Mr. Cumming. Another instrument for the same purpose, more certain in its effects, and more easily managed, is represented in Fig. 1. [Plate IX]; and will be described in one of the following chapters. Dr. Hill and Mr. Custance now endeavoured to bring back the microscope nearer to the old standard, to increase the field by the multiplication of the eye glasses, and to augment the light on the object, by condensing lenses; and in this they happily succeeded: Mr. Custance was unrivalled in his dexterity in preparing, and accuracy in cutting thin transverse sections of wood.
[19] Dr. Hill on the Construction of Timber.
In 1771, my father published a fourth edition of his Micrographia, in which he described the principal inventions then in use; particularly a contrivance of his own, for applying the solar microscope to the camera obscura, and illuminating it at night by a lamp, by which means a picture of microscopic objects might be exhibited in winter evenings.
It appears[20] from the testimony of M. Æpinus, that Dr. Lieberkühn had considerably improved the solar microscope, by adapting it to view opake objects. This contrivance was by some means lost. The knowledge, however, that such an effect had been produced, led Æpinus to attend to the subject himself, in which he in some measure succeeded, and would, no doubt, have brought it to perfection, if he had increased the size of his illuminating mirror. Some further improvements were made on this instrument by M. Ziehr; but the most perfect instrument of the kind, is that of Mr. B. Martin, who published an account of it in the year 1774.[21] The common solar microscope does not shew the surface of any object, whereas the opake solar microscope not only magnifies the object, but exhibits on a screen an expanded picture of its surface, with all its colours, in a most beautiful manner.
[20] Priestley’s Hist. of Optics, p. 743.
[21] Martin’s Description and Use of an Opake Solar Microscope. The merits and ingenuity in constructing and improving microscopes by this learned optician, seem to be unnoticed by our late author. The following pamphlets by Mr. B. Martin are, among others of his valuable publications, instances of his indefatigable industry. Description and Use of a Pocket Reflecting Microscope, with a Micrometer; 1739. Micrographia Nova, or a New Treatise on the Microscope; 1742. Description of a New Universal Microscope; a Postscript to his New Elements of Optics; 1759. Description of several Sorts of Microscopes, and the Use of the Reflecting Telescope, as an universal Perspective for viewing every Sort of Objects. Optical Essays; 1770. A Description and Use of a Proportional Camera Obscura, with a Solar Microscope adapted thereto, annexed to his Description of the Opake Solar Microscope above-mentioned. Description of a New Universal Microscope; 1776. Description and Use of a Graphical Perspective and Microscope; 1771. Microscopium Polydynamicum, or a New Construction of a Microscope; 1771. An Essay on the genuine Construction of a standard Microscope and Telescope; 1776. Microscopium Pantometricum, or a new Construction of a Micrometer adapted to the Microscope. The most essential articles in the above works will be hereafter described. Edit.
About the year 1774, I invented the improved lucernal microscope; this instrument does not in the least fatigue the eye: it shews all opake objects in a most beautiful manner; and transparent objects may be examined by it in various ways, so that no part of an object is left unexplored; and the outlines of all may be taken with ease, even by those who are most unskilled in drawing.
M. L. F. Dellebarre published an account of his microscope in the year 1777. It does not appear from this, that it was superior in any respect to those that were made in England, but was inferior in others; for those published by my father in 1771 possessed all the advantages of Dellebarre’s in a higher degree, except that of changing the eye glasses.
In 1784, M. Æpinus published a description of what he termed 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.
To render this still plainer, let us divest what has been said of the A’s and B’s, and of the references to figures. When objects are viewed through a flat or plane glass, the rays of light in passing through it, from the object to the eye, proceed in a strait direction and parallel to each other, and consequently the object appeared at the same distance as to the naked eye, neither enlarged or diminished. But if the glass be of a convex form, the rays of light change their direction in passing through the glass, and incline from the circumference towards the center of convexity, in an angle proportional to the convexity, and meet at a point at a less or greater distance from the glass, as it is more or less convex. The point where the rays thus meet is called the focus; when, therefore, the convexity is small, the focus is at a great distance, but when it is considerable, the focus is near; the magnifying power is in proportion to the change made in the rays, or the degree of convexity, by which we are enabled to see an object nearer than we otherwise could; and the nearer it is brought to the eye, the larger will be the angle under which it appears, and consequently the more it will be magnified.
The human eye is so constituted, that it can only have distinct vision, when the rays which fall on it are parallel, or nearly so; because the retina, on which the image is painted, is placed in the focus of the crystalline humor, which performs the office of a lens in collecting rays, and forming the image in the bottom of the eye.
As an object becomes perceptible to us, by means of the image thereof which is formed on the retina, it will, therefore, be seen in that direction, in which the rays enter the eye to form the image, and will always be found in the line, in which the axis of a pencil of rays flowing from it enters the eye. We from hence acquire a habit of judging the object to be situated in that line. Note; as the mind is unacquainted with the refraction the rays suffer before they enter the eye, it judges them to be in the line produced back, in which the axis of a pencil of rays flowing from it is situated, and not in that in which it was before the refraction.
If the rays, therefore, that proceed from an object, are refracted and reflected several times before they enter the eye, and these refractions or reflections change considerably the original direction of the rays which proceed from the object, it is clear, that it will not be seen in that line, which would come strait from it to the eye; but it will be seen in the direction of those rays which enter the eye, and form the image thereof on it.
We perceive the presence and figure of objects, by the impression each respective image makes on the retina; the mind, in consequence of these impressions, forms conclusions concerning the size, position, and motion of the object. It must however be observed, that these conclusions are often rectified or changed by the mind, in consequence of the effects of more habitual impressions. For example, there is a certain distance, at which, in the general business of life, we are accustomed to see objects: now, though the measure of the image of these objects changes considerably when they move from, or approach nearer to us, yet we do not perceive that their size is much altered; but beyond this distance, we find the objects appear to be diminished, or increased, in proportion as they are more or less distant from us.
For instance, if I place my eye successively at two, at four, and at six feet from the same person, the dimensions of the image on the retina will be nearly in the proportion of 1, of 1⁄2, of 1⁄3, and consequently they should appear to be diminished in the same proportion; but we do not perceive this diminution, because the mind has rectified the impression received on the retina. To prove this, we need only consider, that if we see a person at 120 feet distance, he will not appear so strikingly small, as if the same person should be viewed from the top of a tower, or other building 120 feet high, a situation to which we had not been accustomed.
From hence, also, it is clear, that when we place a glass between the object and the eye, which from its figure changes the direction of the rays of light from the object, this object ought not to be judged as if it were placed at the ordinary reach of the sight, in which case we judge of its size more by habit than by the dimensions of the images formed on the retina; but it must be estimated by the size of the image in the eye, or by the angle formed at the eye, by the two rays which come from the extremity of the object.
If the image of an object, formed after refraction, be greater or less than the angle formed at the eye, by the rays proceeding from the extremities of the object itself, the object will appear also proportionably enlarged or diminished; so that if the eye approach to or remove from the last image, the object will appear to increase or diminish, though the eye should in reality remove from it in one case, or approach toward it in the other; because the image takes place of the object, and is considered instead of it.
The apparent distance of an object from the eye, is not measured by the real distance from the last image; for, as the apparent distance is estimated principally by the ideas we have of their size, it follows, that when we see objects, whose images are increased or diminished by refraction, we naturally judge them to be nearer or further from the eye, in proportion to the size thereof, when compared to that with which we are acquainted. The apparent distance of an object is considerably affected by the brightness, distinctness, and magnitude thereof. Now as these circumstances are, in a certain degree, altered by the refraction of the rays, in their passing through different mediums, they will also, in some measure, affect the estimation of the apparent distance.
In the theory of vision it is necessary to be cautious not to confound the organs of vision with the being that perceives, or with the perspective faculty. The eye is not that which sees, it is only the organ by which we see. A man cannot see the satellites of Jupiter but by a telescope. Does he conclude from this, that it is the telescope that sees those stars? By no means; such a conclusion would be absurd. It is no less absurd to conclude, that it is the eye that sees. The telescope is an artificial organ of sight, but it sees not. The eye is a natural organ of sight, by which we see; but the natural organ sees as little as the artificial.
The eye is a machine, most admirably contrived for refracting the rays of light, and forming a distinct picture of objects upon the retina; but it sees neither the object nor the picture. It can form the picture after it is taken out of the head, but no vision ensues. Even when it is in its proper place, and perfectly sound, it is well known, that an obstruction in the optic nerve takes away vision, though the eye has performed all that belongs to it.[25]
[25] Reid on the Intellectual Powers of Man, p. 78.