F

24.5

In the formula, therefore, for the magnifying power of the Microscope as a whole

(f and being the focal lengths of the objective and ocular respectively), N is in the one case 17.8 and in the other 31.3, assuming to be 25 mm.

Those who are interested in optical formula may like to have before them the method by which (1) the focal length of the objective and (2) the distances of its posterior focal plane are determined, according to the improved methods of Prof. Abbe, of which we hope to give a more detailed account later.

(1) To determine the focal length ƒ of the combination, we require to know only the focal lengths f, and f2 of the two lenses, and the position of their anterior and posterior focal planes, whence we derive f according to the formula

fifa

(8 being the distance of the posterior focal plane of the first lens † from the anterior focal plane of the second lens).

Thus suppose in fig. 59 that we have given fi

= 24.8 mm. and

f2 = 48.4 mm., we require only to determine & to solve the equation.

=

We can determine & from the distances (supposed to be given) of the focal planes from the respective lenses, the distance of the posterior focal plane of the first lens F1* =24.5 mm. and that of the anterior focal plane of the second lens F2 46.3 mm. For the diagram shows that if from the total distance between F,* and the front of the second lens (which is made up of the variable distance between the lenses d and the quantity 24.5), we deduct the distance 46.3 mm. of the focal plane F, from the second lens we shall have the distance 8.

† The first lens being a plano-concave the posterior focal plane (i. e. which relates to the posterior medium, or to the image) is in front of the lens, and not, as with convex lenses, at the back.

Thus, according as the lenses are closed or open (d 52 mm.),

= 44 mm. or

(2) The second step is to find the distance of the posterior focal plane F* of the combination, which being deducted from 10 in. gave

us A.

=

*

This distance, as the diagram shows, is made up of two quantities, one being the distance of the posterior focal plane F2 of the second lens, which is supposed to be given, and 48.1 mm., and the other, an unknown quantity, which we will call (*. This unknown quantity may be determined from the known quantities of f, and 8 by the formula

according as the lenses are open or closed.

Adding these values of * to 48.1 we get the figures given above as the distance of the posterior focal plane from the back lens, i. e. 153.6 or 125.7.

The focal length of the objective and the distance of its posterior focal plane are thus very readily found, without elaborate calculations, by simply knowing the focal lengths and the position of the focal planes of the separate lenses, data which can be obtained very simply and without the necessity of knowing anything about the formulæ on which the objective is constructed or the refractive index of the glass of which its lenses are made. We hope, as we have said, to return to this subject hereafter and in more detail.

Queen's Spot-lens Mounting.t-In order to overcome as far as possible the difficulty J. W. Queen and Co. have felt in fitting the spot-lens to instruments of various patterns (some with movable substage and some with fixed tube, the latter at varying distances from the upper surface of the stage), they have devised the following mount:

The tube A (figs. 61 and 62) is made of standard size to fit the

+ Micr. Bulletin, i. (1884) p. 11 (3 figs.).

usual English and American substage or accessory tubes. The tube B carries a third tube C (blackened inside), sliding easily within it. Securely mounted in the latter tube is the spot-lens, which thus may be accurately focused upon the object; and when once adjusted for any stand, there is no occasion to alter it. If the small tubes be only 1/2 in. or 5/8 in. in length, the focusing range is a long one.

FIG. 60.

FIG. 61.

FIG. 62.

4

Fig. 60 shows the instrument as fitted to a Microscope which has the fixed tube beneath the stage. By reversing, as shown in fig. 61, the same mount may be used equally well in the movable substage of larger instruments.

They have also applied the same device to the usual substage Society-screw adapter, for carrying achromatic condenser or objective used as such (fig. 62).

The inside diameter of the tube C in this case is made 1 in., which will exclude very few objectives. It may, of course, be used, as the other, either in Microscopes with fixed stage tubes, or with movable substage.

Paraboloid as an Illuminator for Homogeneous-Immersion Objectives.*-A. J. Moore attempts "to make two comparatively inexpensive pieces of apparatus take the place and do the work of any first-class wide-angled immersion condenser. These accessories are the ordinary parabola and the hemispherical lens."

Ordinarily the former is a dark-ground illuminator, but when the aperture of the objective exceeds that of the parabola, the effect is simply that of a dry condenser, in which the central rays are stopped out. But even at its best the light cannot traverse the slide at a greater angle than 41° from the axis; and it is rarely, if ever, even so great as this. Now, if the light reflected by the parabola could be converted into a glass (or balsam) angle without altering its angular direction, it would be amply sufficient to give light to the objective at the widest balsam angle now used in the best homogeneousimmersion objectives. This may be done by using, under the slide, a hemispherical lens,† whose radius is less than that of the concavity of the parabola, making optical contact by the immersion fluid. This is to be accurately centered and the parabola brought up so close that the hemispherical lens will occupy the concavity. When properly adjusted, it will be obvious that those rays which are transmitted by the parabola impinge normally to the surface of the hemispherical

The Microscope,' iv. (1884) pp. 27-30 (1 fig.).

This was described and figured by Mr. F. H. Wenham, Trans. Micr. Soc. Lond., iv. (1856) pp. 57-8 (1 fig.).—ED.

lens, and hence are not refracted; that is, they traverse the same path in the lens that they had upon the parabola. The effect, then, is that of the wide-angled immersion condenser with the central rays stopped out.

Although this may be very desirable for some objects, it is not generally so, and it becomes necessary to limit the direction from which the light comes. This may be very easily accomplished by the use of a cardboard diaphragm. This may be made by cutting a circle of blackened cardboard, the diameter of the inside of the mounting of the parabola, so that when pushed home against the glass surface the circle will be held friction-tight. By cutting small holes in this card the light may be regulated; and it should be kept well in mind that when the holes are cut in the outer edge of the card, the light, although oblique, will be more nearly central than when admitted to the reflecting surface through a hole nearer the centre; but should the hole be too near the centre of the card the light will not be transmitted at all, owing to the fact that it will strike the top of the concavity of the parabola. A good guide to go by is a circle upon the card whose diameter is the same as that of the top of the concavity. The most of the oblique light may then be obtained by cutting the holes near this line. Holes may be cut at various angles to each other, to effect the resolution of the various sets of lines by which some objects are marked.

FIG. 63.

The author adds: "The chief objection to this method of illumination is, that central light cannot be obtained; but this, of itself, is of no particular account, as the parabola may be removed from the substage when it is desired. As to the performance of this arrangement, I can speak in the highest terms; the resolution of the diatoms of Möller's balsamed plate being easily accomplished; and when the full operation of the parabola was used, the dots of No. 18 showed better than I have ever seen them by any other method of illumination.”

Paraboloid for Rotating Illumination in Azimuth. We have a paraboloid with an arrangement shown in section in fig. 63. The bottom of the fitting is closed by a brass box in which is a rhomboidal prism, the lower face of which is over an oblong slot in the centre of the lower plate of the box, while the upper face is towards the side of the upper plate, and just beneath the outer zone of the paraboloid. Over the upper face is a tube 1 in. high (the horizontal section of which is shown in fig. 64). Axial rays are, by means of the prism, made to fall on a part of the outer zone of the paraboloid, and by rotating the box can be brought into any azimuth of the latter.

FIG. 64.

Horizontal Position of the Microscope. *-Mr. H. J. Slack considers that the usual position of a Microscope with a tube slanting a little and the head leaning forward to look down it, is all very well for a short examination of any object, but not at all desirable for continuous work. A better plan is to get a carpenter to make a light stool 2 ft. long and 14 in. wide, standing on four legs, the length of which should be determined by that of the Microscope it is intended to use and the height at which the observer sits. His own stool is 7 in. high, and when placed on an ordinary table brings a full-sized Microscope with its tube in a horizontal position at a convenient height for the eye of an observer sitting in an ordinary chair. The late Mr. Lobb, who was skilful in exhibiting troublesome objects, always used his Microscope in this position; but as far as Mr. Šlack knows, it is seldom adopted. When the instrument is in position as described, the substage mirror should be turned out of the way, and the lamp placed so that its flame is exactly opposite the axis of the instrument, and can be seen in the middle of the field on looking through it. If the objects to be watched are large enough for a low power, the light may be softened by placing under the slide a piece of foreign post paper saturated with spermaceti. For high powers, an achromatic condenser is desirable, and one of the smallest central stops is usually the most useful for displaying fine cilia, or delicate whips, as well as for lighting up without glare the interior of various creatures. If all is arranged properly, the manners and customs of infusoria may be watched for hours without more fatigue than reading a well-printed book. A tenth part of the time spent with the head leaning forward in the usual way is far more exhausting.

Flögel's Dark Box.-Dr. J. H. L. Flögel some fourteen years ago devised the dark box, shown in fig. 65, to put over the Microscope and shut out all extraneous light. It is open behind and has an aperture in front to admit light to the mirror. From back to front it measures 20-25 cm., and in width 60-80 cm. ; its height depends upon the stand to be used.† He now adds a few words in the interest of those microscopists who may wish to have similar boxes made. ‡

The principal thing is the right position of the aperture by which the light is admitted; its upper edge must lie exactly at the level of the stage-not lower, in order that the full light from the window may be used; and not higher, in order that light may not fall from above on the stage, which would do away with most of the advantages of the box. The Microscope is put as far as possible in the box, so that the edge of the stage touches it, and, in order that there may be sufficient room for the head of the observer in this position, the anterior portion of the box is bowed out. On the right and left of the

+ Dr. L. Dippel considers this plan preferable to a darkened room with an opening in the shutter to admit light. The contrast between the illuminated field and the dark room is too great. The pupil of the eye is now enlarging and now contracting, and injurious results must inevitably follow. Das Mikroskop,' 1882, PP. 751-2 (1 fig.).

Zool. Anzeig., vi. (1883) pp. 566-7.