Chapter M: L. F. Dellebarre published an account of his microscope in the year (2)

From these principles, the following general rule for ascertaining the magnifying power of single lenses, is deduced. Place a small thin transparent object on the stage of the microscope, adjust the lens till the object appears perfectly distinct, then measure the distance accurately between the lens and the object, reduce the measure thus found to the hundredths of an inch, and calculate how many times this measure is contained in eight inches, first reducing the eight inches into hundredths, which will give you the number of times the diameter of the object is magnified; which number multiplied into itself, or squared, gives the apparent superficial magnitude of the object.

As only one side of an object can be viewed at a time, it is sufficient, in general, to know how much the surface thereof is magnified: but when it is necessary to know how many minute objects are contained in a larger, as for instance, how many given animalculæ are contained in the bulk of a grain of sand, then we must cube the first number, by which means we shall obtain the solidity or magnified bulk.

The foregoing rule has been also applied to estimate the magnifying power of the compound microscope. To this application, Mr. Magny, in the “Journal d’Economie pour le mois d’Aout 1753,” has made several objections: one or two of these I shall just mention; the first is the difficulty of ascertaining with accuracy the precise focus of a small lens; the second is the want of a fixed or known measure, with which to compare the focus when ascertained. These considerations, though apparently trifling, will be found of importance in the calculations which are relative to deep magnifiers. To this it may be further added, that the same standard or fixed measure cannot be assumed for a short-sighted, that is used for a well-constituted eye. To obviate these difficulties, and some errors in the methods which were recommended by Mess. Baker and Needham, Mr. Magny offers the following

PROPOSITION. All convex lenses of whatsoever foci, double the apparent diameter of an object, provided that the object be at the focus of the glass on one side, and the eye be at the same distance, or on the focus of the glass, at the opposite side.

EXPERIMENT. Take a double convex lens, of six or eight inches focus, and fix it as at A, Fig. 1, Plate II. A, into the piece A, which is fixed perpendicular to the rule F G, and may be slid along it by means of its socket: the rule is divided into inches and parts. Paste a piece of white paper, two or three tenths of an inch broad, and three inches long, on the board D; draw three lines with ink on this piece of paper, so as to divide it into four equal parts, taking care that the middle of the paper corresponds with the center of the lens. There is also a sliding eye-piece, which is represented at e.

Take this apparatus into the darkest part of the room, but opposite to the window; direct the glass towards any remarkable and distant object which is out of doors, and move the sliding piece B, until the image of the object on the paper be sharp and clear. The distance between the face of the paper and the lens (which is shewn on the side of the rule by the divisions thereon) is the focus of the glass; now set the eye-piece e E to the same distance on the other side of the glass, then with one eye close to the sight at e, look at the magnified image of the lines, and with the other eye at the lines themselves: the image, seen by means of the glass, and expressed in the figure by the dotted lines, will be double the breadth of the same object seen by the natural eye. This will be found to be true, whatsoever is the focus of the lens with which the experiment is made.

This experiment is rendered more simple to those who are not accustomed to observe with both eyes at the same time, by making use of half a lens, and placing the diameter perpendicular to the rule, as they may then readily view the magnified image and real object with the same glance of the eye, and thus compare them together with ease and accuracy.

Let the angle A F B, Fig. 3. Plate II. A, represent that which is formed at the naked eye, by the rays of light which pass from the extremities of the object, and unite at the eye in the point F. The angle D F E is formed of the two rays, which at first proceeded parallel to each other from the extremities of the object, but that were afterwards so refracted, or bent, by passing through the glass, as to unite at its focal point F. C O is equal to the focal distance of the lens on the side next the object, C F equal thereto on the side next the eye, F O the distance of the eye.

From the allowed principles of optics, it is evident, that the object would appear double the size to the eye at C, than it would to the eye when placed at F; because the distance F O is double the distance C O. We have only to prove then, that the angle A C B is equal to the angle I F K, in order to establish the proposition.

The optical axis is perpendicular to the glass and the surface of the object. The rays A I, B K, which flow from the points A B are parallel to each other, and perpendicular to the glass, till they arrive at it; they are then refracted and proceed to F, where they form the triangle I F K, resting on the base I K: now as C F is equal to C O, and I K is equal to A B, the two triangles A C B, I F K are similar, and consequently the angle at C is equal to the angle F. If the visual rays are continued to the surface of the object, they will form the triangle D F E, equiangled to the triangle A B C; and therefore, as C O is to A B, so is F D to D E; and consequently, the apparent diameter of the object seen through the lens is double the size that it is when viewed by the naked eye. No notice is here taken of the double refraction of the rays, as it does not affect the demonstration.

If you advance towards M, half the focal distance, the apparent diameter will be only increased one-third. If, on the contrary, the point of sight is lengthened to double the distance of its focus, then the magnified diameter will appear to be three times that of the real object. Mr. Magny concludes from hence, that there is an impropriety in estimating the magnifying power of the eye glass of compound microscopes, by seeing how often its focus is contained in eight or ten inches; and to obviate these defects, he recommends two methods to be used, which reciprocally confirm each other.

The first and most simple method to find how much any compound microscope magnifies an object, is the same which is described by Dr. Hooke in his Micrographia, and is as follows: place an accurate scale, which is divided into very minute parts of an inch, on the stage of your microscope; adjust the microscope, till these divisions appear distinct; then observe with the other eye how many divisions of a rule, similarly divided and held at the stage, are included in one of the magnified divisions: for if one division, as seen with one eye through the microscope, extend to thirty divisions on the rule, which is seen by the naked eye, it is evident, that the diameter of the object is increased or magnified thirty times.

For this purpose, we often use a small black ebony rule, (see Fig. 4. Plate II. A,) three or four tenths of an inch broad, and about seven inches long; at each inch is fixed a piece of ivory, the first inch is entirely of ivory, and subdivided into ten equal parts.

2. A piece of glass, Fig. 2, fixed in a brass or ivory slider; on the diameter of this are drawn two parallel lines, about three-tenths of an inch long; each tenth being divided, one into three, the second into four, the third into five parts. To use this, place the glass, Fig. 2, on the middle of the stage, and the rule, Fig. 4, on one side, but parallel to it; then look into the microscope with one eye, keeping the other open, and observe how many parts one-tenth of a line in the microscope takes in upon the parts of the rule seen by the naked eye. For instance, suppose with a fourth magnifier that one-tenth of an inch magnified answers in length to forty-tenths or parts on the rule, when seen by the naked eye, then this magnifier increases the diameter of the object forty times.

This mode of actual admeasurement is, without doubt, the most simple that can be used; by it we comprehend, as it were, at one glance, the different effects of combined glasses; it saves the trouble, and avoids the obscurity that attends the usual modes of calculation; but many persons find it exceedingly difficult to adopt this method, because they have not been accustomed to observe with both eyes at once. We shall therefore proceed to describe another method, which has not this inconvenience.

OF THE NEEDLE MICROMETER.

Fig. 8. Plate II. A, represents this micrometer. The first of this kind was made by my father, and was described by him in his Micrographia Illustrata. It consists of a screw, which has fifty threads to an inch; this screw carries an index, which points to the divisions on a circular plate, which is fixed at right angles to the axis of the screw. The revolutions of the screw are counted on a scale, which is an inch divided into fifty parts; the index to these divisions is a flower de luce marked upon the slider, which carries the needle point across the field of the microscope. Every revolution of the micrometer screw measures ¹⁄₅₀ part of an inch, which is again subdivided by means of the divisions on the circular plate, as this is divided into twenty equal parts, over which the index passes at every revolution of the screw; by which means, we obtain with ease the measure of one-thousandth part of an inch; for 50, the number of threads on the screw in one inch, being multiplied by 20, the divisions on the circular plate, are equal to 1000; so that each division on the circular plate shews that the needle has either advanced or receded one-thousandth part of an inch.

To place this micrometer on the body of the microscope, open the circular part F K H, Fig. 8. Plate II. A, by taking out the screw G, throw back the semicircle F K which moves upon a joint at K, then turn the sliding tube of the body of the microscope, so that the small holes which are in both tubes may exactly coincide, and let the needle g of the micrometer have a free passage through them; after this, screw it fast upon the body by the screw G.

The needle will now traverse the field of the microscope, and measure the length and breadth of the image of any object that is applied to it. But further assistance must be had, in order to measure the object itself, which is a subject of real importance; for though we have ascertained the power of the microscope, and know that it is so many thousand times, yet this will be of little assistance towards ascertaining an accurate idea of its real size; for our ideas of bulk being formed by the comparison of one object with another, we can only judge of that of any particular body, by comparing it with another whose size is known: the same thing is necessary, in order to form an estimate by the microscope; therefore, to ascertain the real measure of the object, we must make the point of the needle pass over the image of a known part of an inch placed on the stage, and write down the revolutions made by the screw, while the needle passed over the image of this known measure; by which means we ascertain the number of revolutions on the screw, which are adequate to a real and known measure on the stage. As it requires an attentive eye to watch the motion of the needle point, as it passes over the image of a known part of an inch on the stage, we ought not to trust to one single measurement of the image, but ought to repeat it at least six times; then add the six measures thus obtained together, and divide their sum by six, or the number of trials; the quotient will be the mean of all the trials. This result is to be placed in a column of a table, next to that which contains the number of the magnifiers.

By the assistance of the sectoral scale, we obtain with ease a small part of an inch. This scale is shewn at Fig. 5, 6, 7. Plate II. A, in which the two lines c a c b, with the side a b, form an isosceles triangle; each of the sides is two inches long, and the base one-tenth of an inch. The longer sides may be of any given length, and the base still only of one-tenth of an inch. The longer lines may be considered as the line of lines upon a sector opened to one-tenth of an inch. Hence, whatever number of equal parts ca cb are divided into, their transverse measure will be such a part of one-tenth as is expressed by their divisions. Thus, if it be divided into ten equal parts, this will divide the inch into one-hundred equal parts; the first division next c will be equal to one-hundredth part of an inch, because it is the tenth part of one-tenth of an inch. If these lines be divided into twenty equal parts, the inch will be by those means divided into two hundred equal parts. Lastly, if a b c a be made three inches long, and divided into one-hundred equal parts, we obtain with ease the one-thousandth part. The scale is represented as solid at Fig. 6, but as perforated at Fig. 5 and 7; so that the light passes through the aperture, when the sectoral part is placed on the stage.

To use this scale, first fix the micrometer, Fig. 8. Plate II. A, to the body of the microscope; then fit the sectoral scale, Fig. 7, in the stage, and adjust the microscope to its proper focus or distance from the scale, which is to be moved till the base appears in the middle of the field of view; then bring the needle point g, Fig. 8, by turning the screw L, to touch one of the lines c a exactly at the point answering to 20 on the sectoral scale. The index a of the micrometer, Fig. 8, is to be set to the first division, and that on the dial plate to 20, which is both the beginning and end of its divisions; we are then prepared to find the magnifying power of every magnifier in the compound microscope which we are using.

EXAMPLE. Every thing being prepared agreeable to the foregoing directions, suppose you are desirous of ascertaining the magnifying power of the lens marked No. 4; turn the micrometer screw, until the point of the needle has passed over the magnified image of the tenth part of one inch; then the division, where the two indices remain, will shew how many revolutions, and parts of a revolution, the screw has made, while the needle point traversed the magnified image of the one-tenth of an inch; suppose the result to be twenty-six revolutions of the screw, and fourteen parts of another revolution, this is equal to 26 multiplied by 20, added to 14; that is, 534 thousandth parts of an inch.

The twenty-six divisions found on the strait scale of the micrometer, while the point of the needle passed over the magnified image of one-tenth part of an inch, were multiplied by 20, because the circular plate C D, Fig. 8, is divided into twenty equal parts; this produced 520; then adding the fourteen parts of the next revolution, we obtain 534 thousandth parts of an inch, or 5-tenths and 34-hundredth parts of another tenth, which is the measure of the magnified image of 1-tenth of an inch, at the aperture of the eye glasses, or at their foci. Now if we suppose the focus of the two eye-glasses to be one inch, the double thereof is two inches; or if we reckon in the thousandth part of an inch, we have two thousand parts for the distance of the eye from the needle point of the micrometer. Again, if we take the distance of the image from the object at the stage at six inches, or six thousandths, and add thereto two thousand, double the distance of the focus of the eye glass, we shall have eight thousand parts of an inch for the distance of the eye from the object; and as from the proposition, page 51, we gather that the glasses double the image, we must double the number 534 found upon the micrometer, which then makes 1068: then, by the following analogy, we shall obtain the number of times the microscope magnifies the diameter of the object; say, as 240, the distance of the eye from the image of the object, is to 800, the distance of the eye from the object, so is 1068, double the measure found on the micrometer, to 3563, or the number of times the microscope magnifies the diameter of the object. By working in this manner, the magnifying power of each lens used with the compound microscope may be easily found, though the result will be different in different compound microscopes, varying, according to the combination of the lenses, their distance from the object, and one another, &c.

Having discovered the magnifying power of the microscope, with the different object lenses that are used therewith, our next subject is to find out the real size of the objects themselves, and their different parts; this is easily effected, by finding how many revolutions of the micrometer-screw answer to a known measure on the sectoral scale, or other object placed on the stage; from the number thus found, a table should be constructed, expressing the value of the different revolutions of the micrometer with that object lens, by which the primary number was obtained. Similar tables must be constructed for each object lens. By a set of tables of this kind, the observer may readily find the measure of any object he is examining; for he has only to make the needle point traverse over this object, and observe the number of revolutions the screw has made in its passage, and then look into his table for the real measure which corresponds to this number of revolutions, which is the measure required.

ACCOUNT OF GLASS, PEARL, &c. MICROMETERS, BY THE EDITOR.

Having seen some glass, &c. micrometers with exquisite fine divisions, for the purposes of applying to microscopes and telescopes; and in accuracy, being equivalent to the micrometer just described by our author, I judge, some account of their application and uses here will be very acceptable to the curious and inquisitive reader. A particular description of these as made by the ingenious Mr. Coventry, has been already given in the Encyclopædia Britannica, Vol. XI. p. 708.

The singular dexterity which Mr. Coventry and others now possess, of cutting by an engine fine parallel lines upon glass, pearl, ivory, and brass, at such minute distances as, by means of a microscope, are proved to be from the 100th to the 5000dth part of an inch, render this sort of micrometer the easiest and most accurate means of obtaining the exact natural size of the object to be magnified, and how many times that object is magnified. Mr. B. Martin, and other opticians, many years ago applied divided slips of glass, ivory, and horn to the body, in the focus of the eye glass of microscopes; but the thickness of the whole medium of the glass was found to diminish the distinct view of the object: ivory and horn, from their variable texture, were found to expand and contract too readily to be commodious. It is therefore to Mr. Cavallo that we are indebted for the happy thought of adapting slips of divided pearl to telescopes, to ascertain their power, &c. which substance the opticians now find to be the best for microscopical micrometers. It possesses a sufficient degree of transparency, when made about the thickness of writing paper; is a steady substance; admits very easily of the finest graduations, and is generally made in breadth about the 20th part of an inch.

Fig. 9. Plate II. A, is a representation of this scale, with divisions of the 200ths of an inch, every fifth and tenth division being left longer than the others, which only go to about the middle. If the eye glass of the microscope or telescope, to which this micrometer is to be applied, magnify very much, its divisions may be proportionably minute.

To measure by this micrometer the size of an object in a single microscope, nothing more is required than to lay it on the micrometer, and adjust it to the focus of the magnifier, noticing how many divisions it covers or coincides with. Supposing the parallel lines to be the 1000dths of an inch, and the object covers two divisions, its real size is the 500th of an inch; if five, 200th of an inch, &c.

To find how much the object is magnified, is not so easily done by the single, as by the compound microscope, as has been before explained. The following simple method has been adopted by Mr. Coventry, and which may be considered tolerably accurate. Adjust a micrometer under the microscope, suppose 100th of an inch of divisions, with a small object on it, if square, the better; notice how many divisions one side of the object covers, suppose ten; then cut a piece of white paper something larger than the magnified appearance of the object; fix one eye on the object through the microscope, and the other at the same time on the paper, lowering it down till the object and the paper appear level and distinct: then cut the paper till it appear exactly the size of the magnified object; the paper being then measured, suppose an inch square: now, as the object under the magnifier, which appeared to be one inch square, was in reality only ten hundredths, or the tenth of an inch, the experiment proves that it is magnified ten times in length, one hundred times in superficies, and one thousand times in cube, which is the magnifying power of the glass; and in the same manner a table may be made of the power of all the other glasses.

In using the compound microscope, the real size of the object is found by the same method as in the single; but to demonstrate the magnifying power to greater certainty, adopt the following method. Lay a two-feet rule on the stage, and a micrometer level with its surface, (an inch suppose, divided into 100 parts:) with one eye see how many of those parts are contained in the field of the microscope, suppose 50; and with the other, at the same time, look for the circle of light in the field of the microscope, which with a little practice will soon appear distinct; mark how much of the rule, from the center of the stage, is intersected by the circle of light, which will be half the diameter of the field. Suppose eight inches; consequently the whole diameter will be sixteen. Now, as the real size of the field by the micrometers appeared to be only 50 hundredths, or half an inch, and as half an inch is only one 32d part of 16 inches, it shews the magnifying power to be 32 times in length, 1024 superficies, and 32768 in cube or bulk. For accuracy, as well as for comparative observations, the rule should always be a certain distance from the eye; eight inches in general is a proper distance.

Another way, and the most easy for finding the magnifying power of compound microscopes, is by using two micrometers of the same divisions; one adjusted under the magnifier, the other fixed in the body of the microscope in the focus of the eye glass. Notice how many divisions of the micrometer in the body are seen in one division of the micrometer under the magnifier, which again must be multiplied by the power of the eye glass. Example: Ten divisions of the micrometer in the body are contained in one division under the magnifier; so far the power is increased ten times: now, if the eye glass be one inch focus, such glass will of itself magnify about eight times in length, which, with the ten times magnified before, will be eight times ten, or 80 times in length, 6400 superficies, and 512000 cube.

Fig. 10. Plate II. A, represents the field of view of the compound microscope, with the pearl micrometer, as applied to the aperture in the body, called the eye stop; and a magnified micrometer that is laid on the stage, shewing that one of the latter contains ten of the former.

A set of ivory and glass micrometers, about six in number, besides one or two pearl ones for the eye stops, are generally packed up with the best sort of microscopes made by Messrs. W. and S. Jones, Opticians, Holborn. They are divided into lines and squares, from the 100th to the 1000dth parts of an inch; and, besides measuring the magnifying powers of microscopes, are generally found useful in measuring the diameters, proportions, &c. of opake and transparent objects, even of the minutest kind. The smallest divisions of the glass micrometer to be useful, are those divided into the 4000dth part of an inch; and as these may be crossed again with an equal number of lines in the same manner, they form squares of the SIXTEEN MILLIONTH part of an inch surface, each square of which appearing under the microscope true and distinct. And, even small as this is, animalculæ are found so minute as to be contained in one of these squares!

Glass micrometers with squares, applied to the solar microscope, divide the objects into squares on the screen in such a manner, as to render a drawing from it very easy; and are employed with great advantage in the lucernal microscope.

The micrometers are constructed with moveable frames or tubes, so as to be either applied or taken away in the readiest manner.

For the uses of the pearl micrometer as applied to the telescope, see Mr. Cavallo’s pamphlet descriptive of its use, 8vo. 1793, and the Philosophical Transactions for 1791.

CHAP. III.

A DESCRIPTION OF THE MOST APPROVED MICROSCOPES, AND THE METHOD OF USING THEM.

In the preceding chapter I have endeavoured to give a comprehensive view of the theory of the microscope, and the principles on which the wonderful effects of this instrument depend. I shall now proceed to describe the various instruments themselves, their apparatus, and the most easy and ready mode of applying them to use; selecting for description those that, from some peculiar advantage in their construction, or from the reputation of the authors who have recommended and used them, are in most general use. What is said of these will, I hope, be sufficient to enable the reader to manage any other kind that may fall in his way.

DESCRIPTION OF ADAMS’S IMPROVED AND UNIVERSAL LUCERNAL MICROSCOPE. Fig. 1. Plate III.

This microscope was originally thought of, and in part executed by my father; I have, however, so improved and altered it, both in construction and form, as to render it altogether a different instrument. The approbation it has received from the most experienced microscopic observers, as well as the great demand I have had for them, has fully repaid my pains and expenses, in bringing it to its present state of perfection.

As the far greater part of the objects which surround us are opake, and very few sufficiently transparent to be examined by the common microscopes, an instrument that could be readily applied to the examination of opake objects, has always been a desideratum. Even in the examination of transparent objects, many of the fine and more curious portions are lost, and drowned as it were in the light which must be transmitted through them; while different parts of the same object appear only as dark lines or spots, because they are so opake, as not to permit any light to pass through them. These difficulties, as well as many more, are obviated in the lucernal microscope; by which opake objects of various sizes may be seen with ease and distinctness; the beautiful colours with which most of them are adorned, are rendered more brilliant, without in the least changing their natural teints. The concave and convex parts of an object retain also their proper form.

The facility with which all opake objects are applied to this instrument is another considerable advantage, and almost peculiar to itself; as the texture and configuration of the more tender parts are often hurt by previous preparation, every object may be examined by this instrument, first as opake, and afterwards, if the texture will admit of it, as transparent.

The lucernal microscope does not in the least fatigue the eye; the object appears like nature itself, giving ease to the sight, and pleasure to the mind: there is also in the use of this instrument, no occasion to shut that eye which is not directed to the object.

A further advantage peculiar to this microscope is, that by it the outlines of every object may be taken, even by those who are not accustomed to draw; while those who can draw well, will receive great assistance, and execute their work with more accuracy, and in less time than they would otherwise have been able to have performed it in. Most of the designs for this work were taken with the lucernal microscope; and I hope the accuracy with which they are executed, will be deemed a sufficient testimony in favour of the instrument. In this point of view it will, I think, be found of great use to the anatomist, the botanist, the entomologist, &c. as it will enable them not only to investigate the object of their researches, but to convey to others accurate delineations of the subject they wish to describe.

By the addition of a tin lanthorn, transparent objects may be shewn on a screen, as by the solar microscope.

Transparent objects may be examined with this instrument in three or four different modes; from a blaze of light almost too great for the eye to bear, to that which is perfectly easy to it.

When this instrument is fitted up in the best way, it is generally accompanied with a small double and single microscope.

Fig. 1. Plate III. represents the IMPROVED LUCERNAL MICROSCOPE, mounted to view opake objects; A B C D E is a large mahogany pyramidical box, about fourteen inches long, and six inches square at its larger end, which forms the body of the microscope; it is supported firmly on the brass pillar F G, by means of the socket H, and the curved piece I K.