1

In this formula AB is successively made equal to 100, 95, etc., BC inches, and ƒ equals one fourth the minimum value of AC. By a table of reciprocals the calculation is easily made by subtracting the reciprocal of AB from the reciprocal of f, and the reciprocal of the difference gives BC. Construct two curves on the same sheet of paper with the same abscissas AB, and ordinates equal to the observed and computed values of BC, respectively, and their agreement proves the correctness of the formula.

use.

79. MICROscope.

Apparatus. The importance of this instrument renders it desirable that each student should devote considerable time to its For this reason, in a large laboratory two or three microscopes should be procured, and it is well to have them from different makers, so that the student may be accustomed to all forms. For example, a "Student's Microscope," by Tolles or Zentmayer, to represent the American instrument, a binocular "Popular Microscope," by Beck, for the English, and a third instrument by Nachet or Hartnack, for the Continental form. The latter is very cheap and good, but not having the Microscropical Society's screw, common objectives cannot be used on it without an adapter. It is also well, if it can be afforded, to have one first-class microscopestand for work of a higher nature. The usual appurtenances described below should be added, but need not be duplicated, also a number of objectives and objects.

The following description will serve for all the common forms of instrument. A brass tube or body is attached to a heavy stand, so that it can be set at an angle, or moved up or down. In its lower end the objectives are screwed, and the ye-pieces slide into the upper end. The objectives are made of three achromatic lenses, by which a short focus is attained, with great freedom from aberration. The eye-piece is of the form known as the negative eye-piece, and consists of two plano-convex lenses, with their plane surfaces turned upwards. Below is placed the stage, on which the object is laid and kept in place, either by a ledge, or by spring clips. In the larger stands the object may be moved by two racks and pinions in directions at right angles, or revolved by turning the stage. It is very desirable that this rotation should take place around the axis of the instrument, as is done in the English, but not in the American instrument mentioned above. Under the stage is the diaphragm, a plate of brass with a number of

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circular holes in it of different sizes, to admit light more or less obliquely. Below it is a mirror, plane on one side, and concave on the other, by which light may be reflected upon the object.

It is very important that the body of the instrument may be raised and lowered with precision. There are generally two adjustments to effect this, one the coarse adjustment to move it rapidly, which is commonly a rack and pinion, or a simple sliding motion effected by hand, and a fine adjustment which is used for getting the exact focus, and is made in a variety of ways. One of the best is by a movable nose-piece, or the lower end of the tube made free to slide, and acted on by a lever, which may be moved by a screw. In a second form, the screw acts directly on a part of the tube itself, and sometimes the stage is raised or lowered. If the tube is moved, it should be raised only by the screw, the lowering being effected by a spring, so as to prevent the objective from being pressed forcibly against the object.

To show the use of each instrument used in connection with the microscope, one or more objects should be selected suited to each, and numbered as in the following examples. They may then be distributed among the various microscopes, according to the means or requirements of each laboratory. In this way a student acquires à better knowledge of the apparatus, and of the proper objects to which each appliance is best suited, than he could attain in weeks of unsystematic work. It is also well to examine several of the objects described below, with various methods of illumination, to learn how much their appearance may be thus altered. When studying a new object it should always be illuminated in various ways, and viewed first with a low, and afterwards with a higher power. There is, however, no more common mistake than to suppose that objects will be seen better, the higher the power. On account of the difficulty with which they are used, the want of distinctness and of sufficient illumination, the highest magnifying powers must be reserved for special occasions, and the lower powers commonly employed, especially in the preliminary observation of common objects. To save the eyes, it is better, at first, not to use a microscope very long at a time, and for the same reason, they should both be kept open. If possible, sometimes one eye should be used, and sometimes the other.

The applications of the microscope have been so extensive that it is impossible in a short article like the present, to give more than a general description of the most important. The student who wishes to make a specialty of this instrument is therefore referred at once to some of the works devoted especially to this subject. For instance, the treatises of Carpenter, Hogg and Beale, particularly the work by the latter author, entitled "How to Work with the Microscope." The same remarks apply with even more force to Experiments 80 and 81.

Experiment. 1. Ordinary Method of using the Microscope. Set the microscope in an inclined position, at such an angle that it can be used with comfort. The tube carries an objective below, by means of which an enlarged image of the object is formed, and magnified a second time by the eye-piece. Slip into the upper end of the tube the lowest power eye-piece, that is, the longest. The objectives are contained in brass, cylindrical boxes, with screw covers. They must be handled with care, as they are very expensive; the higher powers consist of very minute lenses, and the glass surfaces must never be touched, lest they be tarnished or scratched; the lower surface, which is plane, is particularly exposed to injury. Remove the cover of an objective whose focus is one or two inches, and screw it into the tube. Now turn the mirror so that the light from the window shall be reflected along the axis of the instrument, and on looking in, a bright circle of light will be visible.

Place object No. 1, eye of a fly, on the stage, and raise or lower the tube until it is distinctly visible. The distance between the objective and object should be somewhat less than the focal length of the former. Notice that the eye is composed of a multitude of facets, like the meshes of a net, each one containing a separate lens. Sketch some of them in your note book. Try the other eye-piece, which will give a somewhat higher power. Then remove the objective, putting it back in its box, and replace it by one whose focal length is 4 inch. The use of this is attended with somewhat greater difficulty. It must be brought very near the object, but not in contact, or it would very likely be scratched, or even broken. It is therefore safest to bring it as near as possible without touching, by the coarse adjustment, then looking through the instrument to withdraw it until the distance is about right, and finally focus exactly, by the fine adjustment. A great increase of magnifying power is thus attained; add to the description and drawing whatever additional is visible. Do the same with a second object, foot of the Dytiscus.

2. Diaphragm. Immediately under the stage is a brass plate pierced with a number of holes of different sizes. Its object is to vary the amount of light and the direction in which it comes. When a small aperture is used, all the light comes in nearly the

same direction, and thus renders the shadows of minute objects more distinct. The structure of delicate objects is thus sometimes brought out very beautifully, where a large aperture conceals everything. To show this, try object No. 2, proboscis of a horse-fly, and see how much more distinct the fine hairs at the end are, with the small aperture. Also the diatom Isthmia nervosa, in which the markings, although perfectly distinct with a small aperture, almost disappear when the diaphragm is turned so as to admit a large cone of light.

3. Oblique Illumination. Microscope objectives are made so that they will transmit rays of light not only along their axis, but also when falling obliquely on them, that is, they will receive a cone, the angle of whose vertex is called the angular aperture of the objective. For the higher powers this angle is sometimes very great, 170°, 175°, or even 177°. With them, instead of placing the mirror immediately underneath, it may be placed on one side, and the object illuminated obliquely. A better plan is by an Amici's prism which is placed below the object, and throws the rays obliquely like the mirror. The advantage in this case is like that of a diaphragm, only greater, shadows being strongly cast, and very delicate structure rendered visible. This effect is well shown with many diatoms, minute siliceous shells, on which are markings or very fine parallel lines, used frequently as tests. Try the quarter inch objective on specimens No. 3, Pleurosigma formosum and Pleurosigma hippocampus. First use direct light and then an oblique illumination, and see how much more distinctly the markings are visible in the second case.

4. Opaque Objects. Some objects, especially those of large size, cannot be rendered transparent, and sometimes the surface only of a body is to be examined. In this case remove the mirror from below its object, and place it above on a stand, turning it so that the light shall be thrown down upon the object. A second method is to use for the same purpose a large lens of short focus called a condenser. If the observer is facing the window, it is generally necessary in this case, to place the object nearly horizontal, in order to get light upon it. Try both these methods on objects No. 4, wing of a butterfly, and section of bone or tooth, viewing the latter also by transmitted light.

5. Lieberkuhn. Another method of illuminating opaque objects is by a parabolic mirror, with a hole in its centre, through which the objective is passed. This device, called a lieberkuhn, is used on small opaque objects, the light being thrown from the mirror below upon the lieberkuhn, and by it reflected upon the object. Try specimen, No. 4, wing of butterfly, thus illuminated, also some common objects, as a bit of paper, a steel scale, etc.

6. Wenham's Parabolic Condenser. This consists of a block of glass, plane below and parabolic above. It is placed, instead of the diaphragm, just below the object, which is at its focus, so that all light reflected upon it by the mirror below, will fall on the object illuminating it obliquely. The central rays are cut off by a circle of metal attached to the condenser. Objects are thus shown bright on a dark background, sometimes producing an excellent effect, though generally more beautiful than useful. See No. 6, Arachnoidiscus Ehrenbergii.

7. Achromatic Condenser. The mirror below the object is commonly plane on one side, and concave on the other, the former reflecting light on a given point from various directions, the latter concentrating that received from a single point. The second form is more commonly used, especially with artificial light, as any point may thus be selected as the source of illumination. The same effect is much better attained by placing below the object an objective similar to that above it, which allows only those rays parallel to its axis to pass through both. As it costs too much to duplicate all the objectives, each may be used as an achromatic condenser to that of next lowest power. This is a very favorite method of illumination, especially when using high powers on dif ficult objects. Try it on No. 7, fragment of hair and Surirella gemma.

8. Polariscope. One other method of illumination remains to be described; namely, that by polarized light. To use this to the greatest advantage, Experiment 88 should first be performed. The light is polarized by a Nicol's prism, placed under the object to be examined instead of the diaphragm, and a second prism or analyzer is placed above it, either slipping it over the eye-piece, or screwing it onto, and just above, the objective. On rotating either analyzer or polarizer, the field becomes dark when their planes are at right