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Article X. — Any Member or holder of second class stock, detected in mutilating the newspapers, pamphlets or books belonging to the Insti- tute shall be deprived of hir, right of membership, and the name of the ofTender shall be made public. Digitized by the Internet Archive in 2015 https://archive.org/details/treatiseonconstrOObeck_0 R.Beck, Dell: G.AJ]e:ii, S A TREATISE ON THE OF SMITH, BECK, AND BECK'S ACHEOMATiC MICROSCOPES BY RICHARD BECK. LONDON: FEINTED FOE SMITH, BECK, AND BECK, 31, COENHILL: PUBLISHED BY JOHN VAN VOORST, PATEENOSTEE, ROW. MDCCCLXy. PRINTED BY TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. THE GETTY CENTER LIBRARY INTRODUCTION, The purpose of this work is to give, by a clear and con- cise description, combined with superior illustrations, the most complete directions for the use of Smith, Beck, and Beck's Achromatic Microscopes and the accessory appa- ratus. The publication has been much delayed by various causes which it is unnecessary to explain at length. It may, however, be mentioned that a considerable amount of matter is now included in the work, which it could not have contained at a much earlier issue ; such, for instance, as a description of "Wenham's Binocular Body, the third- class Popular Microscope," and several new pieces of apparatus. By giving more time than was at first intended to the preparation of this treatise, the Author has been able to allude more particularly to some of the peculiar fea- tures connected with the illumination of objects under the Microscope. Great care has also been bestowed upon the delineation of test-objects; for, preceded as this work has been by many others upon the same subject, no one has given satisfactory evidence, by illustration, of 3 ^ (s>-b> iv INTRODUCTION. that superior performance which belongs especially to the English Microscopes. This treatise is strictly confined to the subjects already mentioned; for although the improvement of the Micro- scope is intimately connected with much that has been done by its aid, it is impossible in this work to make any satisfactory reference to that wide range of observation which is so continually extending with the increase of the power of the instrument. In concluding this introduction, the firm of Smith, Beck, and Beck have gratefully to acknowledge the assist- ance they have received, whilst improving the Microscope, from the suggestions or from the contrivances of many amateurs, and especially from those of the late Mr. George Jackson and Mr. Wenham. But it is not with a simple mention only that any author on the Achromatic Micro- scope is justified in passing over the name of Mr. Lister, all the manufacturers of the improved instrument in England being indebted to him for that theoretical and practical information at the outset, which has enabled them to advance it to its present state of perfection. Erom Mr. Lister's designs and suggestions various improvements were made in the arrangement and the appendages of the Microscope; but his attention was especially directed to the object-glasses, for the construc- tion of which he not only determined the principle, but also recommended those combinations of lenses which, either unaltered or with modifications, are adhered to at the present day by the best makers. INTRODUCTION. V Erom consideration for those who were engaged in the manufacture, he abstained from taking credit for these; and various misstatements since published having been allowed to pass without notice, his valuable services have lately been alluded to in a manner most superficial and erroneous. Upper Holloway, March 1865. CONTENTS. Page First- and Second-class Achromatic Microscopes 1-8 Microscope-Stands ; The Stage ; The Mirror ; The Sub- stage ; Revolving and Folding Bases ; Eyepieces ; Ob- ject-glasses ; Universal Screw ; -^th Object-glasses. Directions for use op Microscope ; Transmitted Illumination . 8-23 The Mirror ; The Diaphragm ; The Achromatic Condenser ; Tests for Object-glasses ; Adjustment for High Powers ; The Podura-scale ; Methods of measuring Aperture ; "Lined Objects" as Tests; Nobert's Lines; Obhque Illumination. Illumination from above 23-34 Side Condensing- Lenses ; Side Silver Reflector; Lieber- kuhns ; Forceps ; Opaque Disk-revolver ; Splinter of Lucifer Match ; Podura-scale ; Tarsus of Spider ; Feather of Pigeon ; Arachnoidiscus Japonicus. Dark-field Illumination 34-36 Erecting-Glass for Low Power and Dissection 36, 37 Polarized Light, as applied to the Microscope 37-48 Nicol's Prisms ; The Selenite Plate ; Darker's Retarding- plates of Selenite ; Darker's Selenite Stage ; Tourma- lines ; Polarizers for large objects ; Experiments with Double-image Prisms ; Crystals to show Rings. Wenham's Binocular Body for Achromatic Microscope 48-55 Sundry Apparatus 55-70 Live-boxes and Trough ; Screw Live -box ; Lever Com- pressor ; Wenham's Compressor ; Reversible Compress- VIU CONTENTS. Page ors ; Frog Plate ; Camera Lucida ; Micrometers ; Indi- cator ; Double and Quadruple Nosepieces ; Leeson's Goniometer; Maltwood's Finder; Microscope Lamps and Table. Cases tor First- and Second-class Microscopes 70-72 The Third-class Microscopes 73-92 The Popular Microscope ; Series of Object-glasses ; Descrip- tion of Stand ; Diaphragm ; Side Condenser ; Forceps ; Glass Plate ; Pliers ; Case ; Binocular Body ; Mechanical Stage ; Achromatic Condenser ; Lieberkuhns ; Dark Well ; Parabolic Eeflector ; Polarizing Apparatus ; Ca- mera Lucida ; Micrometer ; Live-box ; Trough ; The Educational Microscope ; Diaphragm ; Forceps ; Tray for extra Apparatus. The Fourth-class Microscope. The Universal 93-101 Object-glasses ; Eyepieces ; Forceps, Pliers, and Glass Plate ; Extra Apparatus and Box ; Mechanical Stage ; Combined Body ; Binocular Body. Single Microscopes and Magnifiers 102-113 Darwin's Dissecting Microscope and Apparatus ; Improved ditto, with Binocular arrangement ; Patent Achromatic Binocular Magnifiers and Stand ; Hand-magnifier and Stand for ditto ; Coddington Lenses. Instruments used in preparing Objects Knives ; Points ; Hooks ; Needle-holder ; Scissors ; For- ceps ; Quekett's Forceps ; Wood-cutting Machine. 113-119 Instruments and Materials used in mounting Objects 119-130 Glass and other Slips ; Cutting and Writing Diamonds ; Thin Glass ; The Disk-cutter ; Canada Balsam ; Brass Table and Lamp; Page's Forceps; Deane's Medium; Farrants' Medium ; Glass and other Cells ; Gold Size and Asphalt ; Cell-machine ; Glass Cells ; Labels ; Small Glass Bottles ; Case for Instruments and Materials. Cabinets and Microscopic Objects 130-134 A TREATISE ON ACHROMATIC MICROSCOPES. Description of Construction. A Compound Achromatic Microscope consists essentially of two parts, an object-glass and an eyepiece — so called be- cause they are respectively near the object and the eye when the instrument is in use. The object-glass screws, and the eyepiece slides, into opposite ends of a tube termed the " body," and upon the union of the two the magnifying power depends. The microscope-stand is an arrangement for carry- ing the body ; and is combined with a stage for holding or giving traverse to an object, and a mirror or some other provision for illumination. Microscope-Stands, Three microscope-stands are shown, one-third their size, in Plates II., III. & lY.; they differ from each other in con- struction, but the following explanations will apply to all. B 2 CONSTEUCTION OF STANDS. The joint at (A) allows the body (B) to be placed in a vertical, horizontal, or any intermediate position ; and for the adjustment of the focus of the object-glass, a quick motion is obtained by turning either of the large milled heads (C), a smaller one (D) giving a slow motion. The Stage. The stage has a ledge (F), upon which the object is most frequently merely placed, but if necessary it can be clamped by carefully bringing down the spring-piece (G); the ledge will slide up or down, and the object may be pushed side- ways*: these are the only provisions for moving the object in the plain stage (Plate IV. fig. 2) ; but in the other " stages with actions " this arrangement forms the coarse adjustment, — finer movements in directions at right angles to each other being effected by the milled heads (H, I) ; and that part also to which the ledge is attached will rotate. The Mirror. The mirror (K) is flat on one side and concave on the other ; it swings in a rotating semicircle (L), which will slide up and down the stem (M), or can be turned on either side. The Suhstage. As the mirror alone is insufficient for many kinds of illumination, some provision has to be made for holding vari- ous pieces of apparatus between the object and the mirror. In the first-class instruments a cylindrical fitting or " short * In the plain stage the spring-piece (G) is almost invariably used, to supply some slight resistance, and thereby to steady the side movement of the object, which is directly dependent upon the fingers. OBJECT-GLASSES. 3 body" (T) is mounted perfectly true with the body, and can be moved up or down by rack and pinion connected with the milled heads (U, Plates II. & III.). In the second-class instruments a short piece of tube (Plate IV. fig. 2, R), equally true in its position as in the former case, fits by a bayonet- catch into the bottom plate of the stage ; but it has no rack movement. The way in which the several pieces of appa- ratus fit into these substage receiving-pieces will be explained in each particular case. Revolving and Folding Bases. In the two first-class instruments there is a revolving fitting on the base (N), by which means the microscope can be turned round without being lifted from the table. Each of these stands can also be made exceedingly portable for their size by the application of a folding base and a removeable stage ; the exact dimensions of their cases under such circum- stances are specified in our priced catalogues. The Eyepieces. There are generally three eyepieces, distinguished by the numbers 1, 2, or 3 (see Plate V.) : but it is not unusual, in the examination of many object-glasses by test-objects, to employ eyepieces of still higher power, and we then supply a No. 4 or a No. 5 in addition ; the latter magnifies about twice as much as the No. 3, and the former is intermediate. The Object-glasses. The object-glasses (see Plate V.) are numerous, and vary in many particulars ; the list of them on page 5 may there- fore require a few explanations. B 2 4 OBJECT-GLASSES. The " focal length" is in each instance that of a single lens magnifying the same as the object-glass. The numbers given under " linear magnifying power " (or, as they are sometimes termed, " diameters ") must be squared, to give the superficial measurement or real increase of size. The magnifying power is increased with the same object- glass by changing the eyepiece from a lower to that of a higher power, the extreme range being from No. 1 to No. 5 ; and also when both the object-glass and the eyepiece are the same, by pulling out the draw-tube of the body. This tube, shown at full length in Plate II. fig. 3, serves several purposes, which will be alluded to further on ; it may, how- ever, be mentioned here, that the graduations of inches and tenths on this tube should generally be kept on the left-hand side. The " aperture " is the measurement in degrees of the cone of light admitted by each object-glass. The erecting-glass (Plate V. fig. 4) has a special notice at p. 36. Many particulars connected with the use of the object-glasses are supplied in other parts of this treatise; and we will only add here, in connexion with the list, that we have made most of these object-glasses for many years. The construction of some of them was for a long time peculiar to ourselves ; and although both this and their nomenclature have been copied by others, we are still persuaded that the attention we give to them in every respect obtains a large amount of favour with microscopists. Another list of object-glasses, which we term our Edu- cational Series, is given further on, in the description of our third-class instruments. 0BJECT-GLAS«E1S. 5 lAst of Achromatic Object-glasses, Focal length 3 inches 2 inches 1| inch 1^ inch inch Y% inch I inch ^ inch -1- inch J inch -J^ inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw -tube closed .... Ditto if drawn out, add for each inch Draw-tube closed ... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw- tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Draw-tube closed .... Ditto if drawn out, add for each inch Linear magnifying power nearly, with eyepieces No. l.No. 2.INo. 3. No. 4. No. 5 12 2 20 4 30 5 70 120 14 146 18 200 24 225 18 225 18 500 60 900 80 20 4 38 56 7 120 14 210 24 255 32 340 42 400 35 400 35 870 100 1570 150 40 6 70 100 12 220 25 370 34 460 48 590 63 700 60 700 60 1500 180 2750 300 48 7 85 12 120 15 270 27 460 46 560 60 720 85 860 80 860 80 1850 190 3450 350 74 10 130 15 190 22 410 48 710 70 890 80 1120 120 1450 130 1450 130 2800 370 4950 900 The list of magnifying powers, as given above, is only approximate ; but if the exact power of any object-glass be required, it may be easily obtained in the way described at page 63. 6 ONE-TWENTIETH OBJECT-GLASS. The " Universal Screw'' All the object-glasses in both lists are made with what is called the "universal screw" — a standard size which the principal microscope-makers of England have adopted for the attachment of the object-glass to the instrument. When this uniformity of screw was proposed by the Microscopical Society of London, we immediately approved the suggestion, and also established a series of gauges connected with Whit- worth's standard sizes, which have been found to answer most satisfactorily*. The -^th Object-glass, The most important addition we have made of late to our object-glasses is the 2^th. This high power is constructed for the examination of those objects which require the greatest amount of amplification, but not that extreme angle of aperture which involves the employment of the very thinnest glass and the most careful preparation of the object. The ■^th will adjust through any covering-glass not more than •005 in. thick ; and, when in focus, there is sufficient space between the front lens and the object to admit of its use in the examination of ordinary preparations : under these con- ditions it can be employed with the same facility as an object- glass of only half the power. In Plate XXIV. are illustrations of two objects, selected from the animal and vegetable kingdoms; these are shown as they appear under a ^th, with the No. 1 eyepiece, the linear magnifying power being about 900 linear. Fig. 1 is the under side of the head and thorax of the Demodex folli- * Quarterly Journal of Microscopical Science, July 1859, Remarks on the Universal Screw." By Richard Beck. (Read May 26th, 1859.) ONE-TWENTIETH OBJECT-GLASS. 7 culorum, a minute parasite infesting the sebaceous and hair- follicles of the human skin. They are easily obtained by pressing out the contents of the follicles on the sides or bridge of the nose : if this matter be gently stirred up with a small camel' s-hair pencil in a little olive oil, the parasites become disengaged, and should be removed to a small quantity of fresh oil, with a piece of thin glass placed over ; and under this pressure they will retain their life and correct appearance for one or two days. The legs are very short, apparently composed of three joints, and the last one is terminated by a single claw : each leg is moved in a very deliberate manner, and describes a semicircular course at its extremity ; during the backward stroke the claw is retracted, but it is jerked out again rapidly at the commencement of the forward movement. There are two organs (A, B) at the side of the head, which are perhaps palpi ; they are constantly moved up or down during life, and are apparently provided with two flaps as a means of clasping. The parts occupying the central portion of the head may represent the mandibles and a labium ; but this parasite is altogether a remarkable instance of the dif- ficulty of determining the exact organization of a transparent object. The magnifying power is abundantly sufficient for the purpose; but, owing to the refraction of the light through the denser parts, and the upper and the under sur- faces being equally apparent in the thinner parts, it has only been after an examination of many specimens for several days that we have been able to determine the structure so far as it is here shown, whilst we know there is still much left in perfect obscurity. Figs. 2 and 3 are respectively the front and profile views of the stinging-hairs from the stem of the common 8 MANAGEMENT OF THE LIGHT. nettle {TIrtica dioica). It appears at first sight somewhat surprising that these hairs, which are known to enter the skin with so sHght a touch, should have a blunt bulbous ex- tremity ; but this is the very provision for the peculiar effect they produce. When any slight pressure is brought upon the extremity of the hair, the bulbous part breaks off, leaving an exceedingly sharp-cutting point (see fig. 4), admirably adapted for entering the skin, at the same time making an aperture at the extremity of the hair, from which the contents of the cell escape and enter the puncture. When the hairs are young and unbroken, a beautiful circulation is visible. Objects of this class can be examined under the <^th with as much facility as under a ^th ; the conditions being such as to cause many high powers of large aperture to be per- fectly useless. Directions for Use of Microscope. — Management of the Light. For general purposes the body of the microscope is inclined as shown in the Plates, but this position is varied according to circumstances. The light should, if possible, be on the left of the observer : the best is that from a white cloud on a bright day ; but a most satisfactory efiect can be obtained from a wax or Palmer's candle if protected by a glass, a good oil-lamp, or an argand gas-burner, provided they are not more than 10 or 12 inches from the microscope: but with all the artificial means of illumination there should be some arrangement for raising or lowering the light, and for holding a shade as a protection to the eyes (see Description of Lamps). In the examination of an object choose the object-glass that appears best suited for it, remembering that in investi- THE DIAPHEAGM. 9 gation it is best to begin with the lower powers for a general view, and afterwards to ascend to the higher, which give greater detail of minute parts. The right management of the light is indispensable for obtaining beauty of picture and fine definition, and is only to be acquired by practice ; for the illumination must be varied with different objects, and often even with the same to exhibit every feature. Every microscopic object may be said to be either trans- parent or opaque : this is not strictly correct, as will be seen hereafter, but the distinction is made here for the sake of division. The Mirror. The illumination of a transparent object is most frequently produced by reflexion from the mirror (K) below, which should generally have its centre coincident with the axis of the body. The flat side is sometimes preferable when there is abundance of light by day; but artificial light almost always requires the concave mirror to condense the light to a focus upon the object. The Bia'phragm, With the i^-ths and lower powers the light is generally in excess, and has to be diminished by one of the smaller openings of the diaphragm (P), which is attached to the under part of the stage : its perforated plate will revolve, and each hole when central is stopped by a weak spring. If it be necessary to remove the diaphragm altogether, it will slide off at its fitting (Plate II. fig. 2, R); and the plain circular ring (S) which is then left call also be detached from its bayonet-fitting to the stage, by turning it in the direction of the arrow. 10 THE ACHROMATIC CONDENSER. With the higher powers there is seldom too much light ; but the diaphragm must often be removed altogether ; and the mirror requires the most careful adjustment by its dif- ferent movements, especially that by which it can be moved up or down on the stem (M), to ensure its exact focus being thrown upon the object. It must be borne in mind that by daylight the rays are parallel, and then the focus of a con- cave muTor will be much shorter than by an artificial light, which cannot be used advantageously at more than 10 or 12 inches from the microscope. The Achromatic Condenser, When the nicest illumination by the mirror fails to exhibit the structure of an object, or the best definition of an object- glass, an achromatic condenser must be employed : this is a combination of lenses by which the light is concentrated to a minute spot upon the object, without the colour and other defects w^hich would be produced by a single lens alone. Of the two mirrors, the flat one should be invariably used ; but as this gives a somewhat imperfect reflexion which interferes with the very best definition, a right-angle prism (Plate VI. fig. 4), which fits on the mirror-stem of the best instrument, is sometimes employed instead of the mirror; or the lamp may be placed at the end of the microscope, in a direct line with the body. In the first-class instruments (Stands Nos. 1 & 2) the achro- matic condenser is mounted, as shown in Plate VI. fig. 2, and fits by its tube {a) into the top of the cylindrical fitting (Plates 11. & III., T) under the stage ; in the second-class Stand, it slides by its fitting (Plate VI. fig. 1, h) into the short tube under the stage (Plate IV. fig. 2, R). When the achromatic condenser is in use, it must be central with THE ACHEOMATIC CONDENSEE. 11 the body of the microscope : this may be tested by screwing a low power on the instrument, and if the top of the con- densing-lens should not appear in the centre of the field of view, the necessary movements can be made by turning the small milled heads (c, c) ; and these, to be convenient for use with the right hand, should be in the position shown in the drawing. The change of object-glasses involved in this plan of centering may be obviated in the first-class microscopes by sliding into the lower end of the cylindrical fitting (Plates II. & III., T), the diaphragm (Plate VI. fig. 3), when its smallest opening should appear as a bright spot in the middle of the field of view (see fig. 7). The achromatic condenser may, however, be so eccentric as to require a larger opening in the diaphragm to be used first. Or if the spot of light does not appear defined on the edge (see fig. 5), the cylindrical fitting must be moved up or down by either of the milled heads (Plates II. and III., U). The small milled heads (c, c) are used under the same circumstances as before mentioned, and full illumination is obtained by turning on the largest opening of the diaphragm. The achromatic condenser in the second-class Stands will slide up and down in the circular ring (Plate IV. fig. 2, R) ; and if slightly rotated at the same time, the movement can be made very exactly. In the first-class Stands the cylinder (Plates II. & III., T) will rack up or down by turning either of the milled heads (U). This rackwork, if connected with the achromatic condenser, serves for the adjustment of its focus, which should generally be thrown upon the object. When such is the case, the image of the flame by artificial light, or of the window-bars or objects in the landscape by day, will be seen in the microscope at the same time as the object. Moving the mirror or right-angle prism will not alter the 12 TESTS FOE OBJECT-GLASSES. adjustments, and any particular cloud, or part of the flame, can be selected for the illumination. Another essential point is the aperture of the condensing-lenses ; this is reduced from 65 to 40 degrees by removing the front lens (Plate VI. figs. 1 & 2, d). But in the most complete arrangement a perforated plate (fig. 6) is inserted at the back of the lenses, as shown in fig. 2 ; in this position it can be rotated on its axis (^), and the openings near its circumference can be brought in succession behind the lenses, each aperture of the plate being stopped by a slight spring when central. Five of the openings vary the aperture from 90 to 45 degrees with the front lens [d]^ and without it from 50 to 25, whilst the other three apertures cut ofl" the rays of light in the centre and admit only those at the circumference. Some additional instructions for the use of the achromatic condenser will be found in those parts of this treatise where the higher powers, and test-objects, are considered. Tests for Object-glasses. The principal points on which an object-glass has to be examined are, the spherical and chromatic aberrations, the aperture, flatness of fleld, and workmanship. When the term "achromatic"* is applied to an object-glass, it is in- ferred that all the errors consequent upon the refraction of light through its lenses are reduced to a minimum; with such a result the object-glass is called " corrected." And in connexion with the spherical and chromatic aberrations, the term ''under-" or "over-corrected" is applied as the right point is exceeded or otherwise, — a single lens being regarded as " under-corrected." * Achromatic really signifies the absence of colour only. ADJUSTMENT FOE HIGH POWERS. 13 Spherical aberration, which is the extension of the focus of a lens, can be entirely corrected, so that an object shall appear sharp and defined in one decided plane ; whilst, with a proper object, the appearance a little within, or as much beyond, the point of distinct vision will be the same. It is impossible, so far as is yet known, entirely to correct chromatic aberration ; but this aberration or separation of light into various colours, with which every one is so familiar in connexion with prisms and single lenses, can, by a proper combination of lenses, be so far counteracted as to leave only a pale green, resulting from the union of blue and yellow, which is inoffensive and quite immaterial. Adjustment for High Powers. In the higher powers, both of these aberrations are con- siderably affected by variations of the thickness in the covers of objects; for if an achromatic object-glass be corrected for an object which is completely uncovered, a piece of thin glass or any fluid, placed between the object and the object- glass, will alter that correction and produce indistinctness. It is not perceptible in the lower powers, but in the higher powers the error caused by the thinnest covering-medium becomes injurious. To provide against this, the ^, \, and -g-Q object-glasses have a moveable collar divided into ten divi- i ■ 1 sions (c) (see accompanying figure), by turn- ^ —f^ ing which the distance is varied between the front lens and those behind it. "When the object is uncovered, 0 on the screw-collar should stand opposite the small screw {a), and the line on the small piece of brass {h) which is let into the tube [d) should coincide a e b Vhcov 1 5 d 14 THE PODURA-SCALE. with the line (e) engraved " uncovered" : this is as far as the collar will go in that direction. For covered objects the collar must be turned from the uncovered point, so that the numbers 1, 2, 3, &c. come in succession opposite the small screw. It is best in practice to have the object-glass on the microscope, move the collar a little at a time, focus for each alteration, and carefully watch the appearance of the object until the best definition is obtained. This mode of adjustment can be easily and very correctly made if the object be well known to the observer, or if its structure be simple and distinctly marked : the latter is peculiarly the case with the Podura-scale, and as it is easily obtained we consider it one of the very best tests. The Podura-Scale. The Frontispiece shows the correct appearance of a small but coarse specimen under different object-glasses with the No. 3 eyepiece ; but Plate VII. more directly refers to the matter now under consideration. Each of the first six figures in this Plate represents j^o^^ mohi square, con- sequently the magnifying power is about 1300 linear, ob- tained by the |^th object-glass and the third eyepiece. The illumination employed is that of a small lamp, close to the microscope, with its light reflected by the right-angle prism so as to pass through the achromatic condenser, which, besides being carefully centred and focused, is found to produce the best efiect in this case with the smallest aperture and without the front lens. c The light will be reflected most brilliantly when it is placed a little behind the right-angle prism, as shown in the annexed diagram ; a being the light, h the THE PODUEA-SCALE. 16 right-angle prism, and c the direction of the light passing to the achromatic condenser. Good daylight will answer quite as well ; and nearly the same results can be obtained with the concave mirror alone. The drawings referred to have been very carefully made by aid of the camera lucida (the use of this piece of appa- ratus is described at p. 61) ; and whilst some size and pro- minence have been given to the features, great care has been taken not to exaggerate any one of the appearances. Fig. 1 gives a representation of the markings when there are no errors in the object-glass. Its adjustment is known to be correct by the object presenting the same perfectly in- distinct appearance (fig. 2) when thrown a very little either within or beyond the focus, and also, when this is done, by each marking dividing equally, somewhat as shown in fig. 3. _ If the adjustment be incorrect, the 'appearances within and beyond the focus are never similar, but on the one side there will be strong lines (fig. 4), and on the other side a still greater indistinctness than that shown at fig. 2 (see fig. 5) ; whilst the best focus under such circumstances shows the markings in a general fog (fig. 6), without either the sharp black sides or the white central spot shown in fig. 1. The exactness with which an error in adjustment can be detected is one of the best qualities of a test ; and with this particular structure, using a ^th or \\h object-glass, a vari- ation of T^oo^h of an inch in the distance of the lenses, or about half a division on the screw-collar, can be easily de- tected by a practised eye. Any chromatic aberration, as excess of colour, will be im- mediately seen in the light spaces between the markings of this object. 16 ADJUSTMENT FOE HIGH POWEES. The spherical aberration should be entirely corrected so far as the adjustment by the screw-collar will work ; this varies in each object-glass: thus the i%ths has a range of about 2^ turns, equivalent to 25 divisions, and will correct for glass about -025 thick ; the ^th has 2 turns for glass measuring -02 ; and the one turn of the |-th will only adjust for a thick- ness of '012. Whilst on this subject, we would caution some persons against concluding that an object-glass with a move- able collar must necessarily possess an adjustment; we have seen many instances in which such an arrangement made no alteration in the correction, and other cases in which the alteration that was made exactly reversed the proper condi- tions. With such an object as the Podura-scale, it is not at all difficult to establish a rule for the adjustment which shall be entirely independent of the appearance presented by the object; for if, after such an adjustment as has just been made, we measure the thickness of the covering-glass, first by focusing its upper surface, which is almost sure to have dust or spots upon it, and then noticing how many divisions of the slow-motion milled head of the microscope it takes to bring the object in focus, a comparison of these divisions with those recorded in the former observation will supply the standard. As, for example, the Podura-scale shown in Plate VII. is covered with a piece of glass, and when the appearance is correct, the collar of the ^th object- glass is moved five divisions; and it takes six divisions on the slow-motion milled head to focus from the top to the under surface of the thin covering-glass-; so that if, with the same object-glass, the cover of another object measure 9 divisions of the slow-motion milled head, 7*9 divisions must be taken on the collar of the object-glass. If the body of the microscope be lengthened by pulling APERTUEE OF OBJECT-GLASSES. 17 out the draw-tube, some further correction is required for the i^ths : thus, for 1 inch drawn out, add two divisions on the collar, for 3 inches four, and for 4 inches five divisions. The object-glasses of higher power are not so much altered by lengthening the body ; but with the ^th and ^th, one division may be advantageously added for the first 3 inches drawn out. In the lower powers an object should not differ in appear- ance, or require any alteration of focus, if moved from the centre to the edge of the field of view. This " flatness of field " is not of so much importance in the higher powers, and it is seldom obtained in them, especially when the aper- ture is large ; but its absence the Podura-scale will show to a remarkable degree. Aperture, as before stated, is the measurement in degrees of the cone of light admitted by the object-glass; and the definition is dependent upon it, provided the object-glass is at the same time well corrected. In the lower powers it is difficult under such conditions to exceed a certain point, whereas in the higher powers it may be said there is no limit within about 170°; but it must be remembered that the use- fulness of an object-glass is destroyed when the range of adjustment, or the distance between the front of the object- glass and the object, is sacrificed to an increase of the angle of aperture. With the Podura-scale a larger aperture in the lower powers is evidenced by the mere fact of seeing the markings, and in the higher powers with the deeper eye- pieces it gives a remarkable blackness and brilliancy to the picture ; but, as a real test of aperture, the Podura-scale is not equal to many other objects, more especially to those siliceous valves of the Diatomacese which show lines under oblique illumination. After all, however, the only certain c 18 METHODS OF MEASTJEINa APEETUEE. mode .of ascertaining the aperture is by some mechanical means. Methods of measurmg Aperture. Of these the simplest is that known as Mr. Wenham's, in which, by merely holding an object-glass in front of a strong light, the angle of the cone of light issuing from the front lens can be measured by means of a divided semicircular card (see Plate VI. fig. 14); but care must be taken to keep the focus of the object-glass in the centre, and also in the plane of the semicircle. This plan, however, at the best, is only intended to give a general estimate within a few degrees. The aperture may be much more exactly measured by the instrument shown in Plate VI. fig. 12. This consists of a semicircular piece of wood about 8 inches in radius, divided into degrees on its edge (a, a), with a narrow slip of wood { f) carrying two V-pieces (^, h) turning on the centre {c). To use this, the body of the microscope (or some similar tube), with a shallow eyepiece, should be placed on the V-pieces, and there should be a small bright light in a line with the axis of the body, at a distance of about 6 feet. The object- glass to be measured is screwed on, and the point of its focus brought exactly over the centre [c) ; the side [d) of the nar- row slip is then kept flush with the side [e) of the semicir- cular board, whilst the whole apparatus is moved to the right on an imaginary centre, until half of the field of view is cut ofl" ; this is the zero-point, and if the semicircular board be then kept firm and the slip (/) only be moved to the left until the field of view is again bisected, the number of degrees indicated at the point {d) will be the aperture of the object-glass. NOBEHT'S LINES. 19 " Lined Objects " as Tests. " Lined objects," as such, are invariably examined by oblique illumination in a direction at right angles, or nearly so, to the lines to be observed. Plate VII. figs. 7, 9, 10, & 12 will illustrate this by show- ing the various appearances of the structure of Pleurosigma quadratum under the different directions of illumination as indicated by the arrows. That which constitutes the test in this class of objects is the mere fact of being able to sepa- rate lines, — a power in great measure depending upon the aperture of the object-glass. In Navicula rliomhoides (fig. 13) the lines which appear in the direction there shown are as nearly as can be counted 75,000 to the inch (the lines and the interspaces being equal), and an object-glass of less than 120° will not separate them. The specimens, however, of the same species of the Diato- macese differ so considerably in the distances of their lines that none of them are equal in value as a test to the object known as Nobert's lines (Plate VIII.). Noherfs Lines. This is a piece of glass upon which are ruled, with the most remarkable regularity, and in a way entirely peculiar to M. Nobert, of Barth, twenty bands of minute lines; these are again divided into four sets, but from the first to the last the distance between the lines in each band is on a gradually diminishing scale of from about 13,000 to 70,000 to the inch; the particulars are given exactly on the Plate, and the number of lines in each band varies from about eight to thirty-five. The following observation may be taken as an instance of their power to test the aperture of an object- 20 OBLIQUE ILLUMINATION. glass: — an ^th of 120° will show them all; but when cut down to 110° it will not separate the twentieth band, at 100° the seventeenth is the limit, at 80° the fourteenth, and at 60° the tenth. Oblique Illumination, The simplest way to obtain the necessary illumination for this class of observations is with the concave mirror, by turn- ing it considerably on one side and making use of the lengthening arm (Plates II. III. & IV., W.) ; when this method is pushed to an extreme, the focus of the mirror must be accurately thrown upon the object, and the lamp should not be nearer than 12 inches. If the object require a still greater obliquity of illumination, it may be obtained by an Amici prism (Plate VI. fig. 11) : the way in which the light passes through this is shown by the three lines {a^ d'), and it is necessary that the prism should be so mounted that its focus may be thrown very obliquely and yet accu- rately upon the object (c). When in use, the mounting of the prism fits by its tube (h) into the top of the cylindrical fitting of the first-class instruments ; in all the other micro- scopes it requires a separate stand. The prism itself can be rotated by the small milled head (d) in the semicircle (e) ; and this is attached to an arm (/), sliding in a dovetail box (^), which also turns on a centre at g ; so that by these movements, combined with the rack- work of the cylindrical fitting, every adjustment can be made. With the mirror or the Amici prism the object has almost always to be rotated either more or less, so that the lines may be at right angles to the direction of the illumination : this may be obviated by using Nachet's prism (fig. 10), but OBLIQUE ILLUMINATION. 21 then the obliquity of the illumination is limited ; the direc- tion the rays take in passing through this prism is shown in fig. 9, and it will there be observed that the emergent pencil (fig. 9, a) comes to a focus in the axis of the mounting, shown by the line b,c; therefore when the prism is rotated, the centering of the illumination remains the same, whilst the direction is altered. The whole piece of apparatus slides into the cylindrical fitting under the stage, the rackwork of which, in the first-class instruments, will give the requisite adjustment up or down, whilst in the second class this move- ment is made with the fingers, and the light must in both cases be reflected from the mirror below. The prism, when in its place, can be rotated by means of the milled edge (fig. 10, a); it can also be taken ofi" at a fitting at 5, if the inner surface require cleaning ; the other surfaces are all exposed. When the object is transparent, and the illumination is transmitted obliquely and on one side only, it is very seldom that reliance can be placed upon the appearance as a true indication of the structure. There is a striking example of this in the change the markings of Pleurosigma formosmn assume (Plate IX. fig.l, A, B, C, D) when only slight variations are made in the direction of the light ; and we may here state that the most correct way of viewing this peculiar structure of the Diatomacese is undoubtedly by illuminating with the largest aperture of the achromatic condenser very carefully centered, whilst the appearance is considerably improved, as shown in fig. 1, D, by using one of the stops (Plate VI. fig. 6, a, c) in the diaphragm of the condenser. Under this kind of illumination, Plate VII. fig. 11 shows the appearance of the markings on Pleurosigma quadratum; and the upper part of the same figure also illustrates how entirely the pre- 22 INJUEED CONDITION OF OBJECT-GLASSES. sence of moisture will obliterate the markings, as is very frequently the case with specimens that have been mounted for some time. It is quite possible for an object-glass, although correct in all the points hitherto mentioned, yet to be deficient in its performance from errors in workmanship ; these are very various, and the causes are often as difficult to detect; but the one most evident of all is when the surfaces of the lenses, the lenses themselves, or the brass cells in which they are mounted, are not true with each other, and the object-glass is said to be badly " centered." The Podura-scale (Plate VII.) will immediately show this fault, even if the error be small, by one side of each marking being darker than the other ; and the scale should be examined in a horizontal as well as a perpendicular position, for it is quite possible that an object-glass will show the markings well in one direction and not at all in the other : the scale itself, not being flat, may produce a similar appearance to that arising from bad cen- tering ; and so also will the illumination to a certain extent, if it be not central. While on this subject, we would add one word of caution as to the appearance of an object-glass: a small chip out of the edge of a lens, a scratch, or even a surface not thoroughly polished, does not necessarily affect the performance ; whereas if an object-glass be not clean (it may have been made for some years, and may require wiping at the hands of the maker, or the front lens may have been touched only by the finger), its definition will be considerably impaired, and by many it might be most unjustly condemned. We cannot also too strongly urge upon microscopists the care required in the use of the object-glasses, as only a slight blow or a fall may in a moment make the best glass utterly worthless. SIDE CONDENSINa-LENSES. 23 The subject of test-objects has received a large share of attention from English observers, not only from the earliest times of the microscope, but more especially during the recent improvements and up to the present day ; this diligent investigation, although somevs^hat fruitless in itself, has been of no little aid in perfecting the instrument for those who have used it as a means of research, and v^e strongly recom- mend every microscopist to test his own instrument : if the result be satisfactory, it will enable him as a scientific observer to be accurate and confident in his deduction ; or if he be only an amateur, he will pursue his recreation with pleasure and comfort. Illumination from above. Opaque objects require, of necessity, that the light be thrown upon them from above ; but this kind of illumination is fre- quently employed in the examination of many specimens which are more or less transparent, and when under such circumstances the term " opaque illumination" is used, it must be remembered that, although the appearance is exactly the reverse of that produced by light transmitted from below, the real condition of the object remains unchanged. Side Condensing-Lenses. The "bull's-eye" condenser (Plate X. fig. 7) and the smaller condensing-lenses (figs. 9 & 10) are the simplest means of obtaining illumination from above, by merely con- centrating the light to a focus and in an oblique direction upon the object; the best results, however, can only be obtained by some little care in the adjustments. When the bull's-eye is used alone for this purpose, its flat side should be next the object ; and the various means by which it can 24 SIDE SILVER EEFLECTOE. be brought into position are a ball-and-socket joint at fig. 7, A, a sliding horizontal tube at B, and a movement up or down on the perpendicular rod (C). The smaller condensing-lens (fig. 10) is shown as mounted for use with the first-class stands ; it fits by a square (a) into either of the two holes in the limb of the best instruments (Plates II. & III ), the rod (B) slides through a pipe (C), which has a ball-and-socket movement at D, and the lens swings in the semicircle (E). Fig. 9 shows the same lens mounted on a separate stand, with a ball-and-socket at (D), a draw-tube (F), and a sliding rod (B) carrying the lens at its extremity; this being the arrangement for the second-class instruments. When any of the condensers are in use, the lamp should not be more than 6 or 7 inches from the object, except when two of them are combined to increase the intensity of the illumination, and then the lamp may be moved 3 or 4 inches further ofi", with the flat side of the bull's-eye nearly close to it, so that the light is concentrated to about the diameter of the smaller condenser, and from it to the object. This kind of illumination must necessarily be one-sided ; for some pur- poses it may be advantageously so, in many instances it is abundantly sufiicient, and for large objects it is the only method available. Side Silver B^efiector. The light, if required, may be thrown more perpendicularly by the side silver reflector (Plate X. fig. 1) ; this, when in use, is generally attached by its square bar (A) to one of the holes on the right-hand side of the limb of the best instru- ments; it is most advantageously used when reflecting the light which has in the first instance been concentrated upon LIEBEEKIJHNS. 25 it by one of the condensers. The focus of the reflector, and therefore the right distance from the object, is a little more than an inch, and the particular position in which it may be wanted is obtained by the two ball-and-socket movements at D and E and by the sliding rod (B) ; the small screw (G), when tightened, will prevent the rod from turning round, which it has a tendency to do from the weight of the re- flector being on one side. For the second-class instruments the side silver reflector, with the movements just described, is mounted on abase and stem similar to that shown by fig. 9. Lieherkuhns. But the illumination which is the best for opaque objects, because it is not only the most brilliant, but also permits any alteration in the direction of the light, is that afforded by the Lieberkuhns; these are highly polished silver cups, sliding upon the fronts of the object-glasses, and reflecting to a focus the light thrown upon them by the mirror. They are supplied to the |^-inch and all the lower powers (see Plate X. fig. 11); but several things are essential to their proper use. The diaphragm under the stage must be in- variably removed, and neither the object nor the substance upon which it is mounted should stop any more light from the mirror than is really necessary ; for although a diameter of 6 or 7 tenths of an inch may make no obstruction with the 1^-inch Lieberkuhn, about 2 tenths is the largest size that the J-inch will admit of without impairing the illumination. If the object be too small or transparent, one of the dark wells (fig. 12, A, B, C) may be used as a background ; of these the largest is, of course, intended for the lowest power ; and they slide into the arm of the holder (fig. 12, D), which fits by 26 rOECEPS FOE HOLDING OBJECTS. its tube (E) into the cylindrical fitting under the stage. A dark well, when in use, should be brought as close behind the object as possible ; and it must also be central, or nearly so, with the body of the microscope. The direction of the illumination, when a Lieberkuhn is used, is regulated by moving the mirror, the flat side of which is generally used by daylight, and the concave is the best for artificial light ; but the most intense illumination is obtained by throwing parallel rays from the lamp upon the mirror by a condensing-lens, and the flat or concave side is in this case immaterial. The proper illumination of an object from above requires quite as much care as the most accurate treatment of trans- mitted light. Very slight variations in the illumination will entirely alter appearances ; and the adjustments of the higher powers require especial attention, as this mode of examining objects is often the most severe test of the performance of an object-glass. But a feature which is peculiar to this mode of illumina- tion is the change which almost always has to be made in the position of the object itself. Forceps for holding Objects, If the specimen be mounted permanently on a slip of glass, it is only capable of rotation by turning the top plate of the stage of the microscope on its fitting ; and this may be quite sufficient when the object is flat, and an exact analysis of its structure is unnecessary; but if otherwise, the forceps (Plate X. fig. 6) are generally used ; these fit by their pin (A) into a small socket (Plates II. III. & IV., Y) on the clamping- piece of the stage, and the object is either held between the points of the forceps at B, or it may be attached by a pin OPAQUE DISK-REVOLVEE. 27 or some other means to the cork end (C), the various move- ments of the forceps affording in either case considerable range for varying the position of the object. The three-pronged forceps (fig. 5) are for holding large or irregular-shaped objects, the specimen being placed between the three points A, B, and C, which are made to approach each other or spread out by sliding the piece (D) to which they are attached either up or down on the stem (E) ; the other movements being the same as those of the ordinary forceps (fig. 6) already described. It will be found by trial that many of the movements of these forceps are limited, and, except for objects that require but little alteration of position, there is considerable difficulty in turning an object about quickly and with certainty under moderately high powers. To obviate these difficulties, we have contrived a piece of apparatus termed an " opaque disk-revolver" ; its construction is as follows : — Opaque Disk-revolver. A brass plate (Plate X. fig. 2, A), which is adapted for clamping in the ordinary way upon the stage of the micro- scope, has a hole through it sufficiently large for a low-power Lieberkuhn. On the right side, at B, is attached a short upright stem, which turns at its base ; and at its top is another fitting, in which the arm (C) can be revolved by a milling at D. But the most important movement of all is the rotation of the small socket (E) at the extremity of the arm (C). This is accomplished by means of a fine chain which communicates with the milled head (F). The object is gummed upon a small disk (G) which fits into the socket (E), and with these arrangements, as many as five sides of a cube 28 OPAQUE DISK-REVOLVEE. may be examined with perfect ease, and without disturbing the position of the object on the disk. This fact is illustrated in Plate IX. figs. 3, 4, 5, 6, & 7, which represent the appearances of the cast skin from the head of the silkworm in five different positions, the whole of these being easily brought in succession under examination with the microscope by means of the disk-revolver just de- scribed, without moving the object from the disk or holder to which it was in this case gummed, on the side opposite to that shown in fig. 7. To preserve those objects that are permanent, the box (Plate X. fig. 4) may be used. It will contain twenty-four disks, and, the holes in which they fit being numbered, the objects may be easily registered ; the top of the box on the outside at A will also hold a paper label, and a wire fixed in the centre of the outside case of the box (B) serves as a guide when it is screwed or unscrewed to prevent the objects being rubbed off. The space between the inner and outer cases is also so arranged that, if a disk should become loose, there is no room for it to get quite free and shake about to the injury of the other specimens. Another apparatus for keeping the disks is shown in fig. 8, and consists of a brass plate capable of holding two dozen objects ; each hole is numbered, and the centre is occupied by a piece of paper as a label, which is held in its place by a brass mat and milled head. The plates may be placed one above the other, as they are kept the right distance apart by four pins at the corners ; and the usual plan is to pack three plates, together with the disk-revolver, in a small mahogany box by themselves. Each disk has a small groove on the edge to facilitate its being put on or taken off by the pliers (fig. 3), which are OBJECTS ILLUMINATED FEOM ABOVE. 29 specially made for the purpose, as the object is not unfre- quently injured when the fingers only are used. Having now described the various means of illuminating objects (whether opaque or otherwise) from above, we would draw attention to some of the results as shown in the dif- ferent illustrations. Objects illuminated from above. — Splinter of Lucifer Match. Plate XT. fig. 1 represents a part near the termination of an oblique fracture of a lucifer match, and shows the struc- ture of coniferous wood. We give this illustration more for its general beauty and superiority when compared with that of a section viewed as transparent, than as any remarkable test. It exhibits, however, very strikingly the necessity of illuminating in more than one direction ; for if the light be thrown in a line with the medullary rays they are almost invisible. To exhibit this object, Lieberkuhn illumination is much the best, and with it there is no difficulty in showing, by one adjustment of the light, the longitudinal woody tissue, the transverse medullary rays, and the beautiful coniferous glands. Podura-Scale, The advantage of a one-sided illumination from above, and the extent to which it may be carried, are shown by an exa- mination of the Podura-scale (a test already alluded to as the best for transmitted light) under a |^th with the 3rd eyepiece. It is necessary that the object be uncovered ; for, with the ob- lique illumination that is required under such a power, a thin glass cover is the most perfect reflector ; but, without this, quite sufficient light can be obtained by means of the usual large and small condensing-lenses combined ; and we have 30 TAESUS OF SPIDEE. the following results with this particular object, as shown in Plate XI. fig. 2, the arrow at the left-hand side indicating the direction of the light. When the markings are at right angles to the direction of the light (A), they are illuminated on the sides furthest off ; when they lie in the same direction as the light, with their narrow ends pointing to it (B), the broad ends appear like brilliant spots ; but when this direc- tion is reversed (C), the light from the points is so slight that the scales appear to have lost their markings altogether*. Now if the object were an opaque substance, this result would have been a convincing proof that the markings were depres- sions ; but as we know it to be transparent, it follows that these particular appearances can only be produced by eleva- tions. The continuity of the markings, which is a character- istic feature of the same object when the light is transmitted from below, is not so evident by this method, most probably for the reason that the quantity of light is much diminished when only reflected from the object ; there may, however, be other causes. Tarsus of Slider. After the two illustrations already given, the tarsus or last joint of the leg oiTegenaria atrica^ a large spider quite com- mon in outhouses and buildings (Plate XII. fig. 1), may be taken as a good medium object; for it is exceedingly beautiful, and a really good test. Under a power of about 50 linear, and with a Lieberkuhn, three or four different kinds of hairs may be detected ; whilst nearly all of these are again covered with the most minute corrugations or very short hairs, as shown in the surrounding figures, which are more highly magnified. This structure is more especially minute, and to * The markings are shown too distinctly in fig. C. FEATHEE OF PIGEON. 31 see it clearly and well defined requires the best performance of an object-glass and the nicest management of the light. The object itself wants no preparation whatever, but care must be taken that the hairs are not broken off by careless handling ; and although cast skins will often furnish suffi- ciently good specimens, these are generally so far injured or dirty as to make it preferable to secure a living specimen for the purpose. Feather of Pigeon. The illustrations on the right-hand side of Plate XII. show the structure of the barbs of a pigeon's feather, examined under illumination from above. The figures above and below give the upper and under surfaces of the vane of the feather, and the intermediate one is a section in the direction of the letters fig. 2. According to the late Professor Quekett*, there are "at least six elements entering into the composition of a single feather : viz., primarily, the quill (I) (see accompanying figure), the shaft (K), and the vane (L, L) ; and, secondarily, the barbs (M), with their barbules, and the barbu- lettes." Each barb consists of a central rib and two dis- similar sides (see Plate XI 1. figs. 2 and 4) ; on the under side, and in the part shown by the left-hand portion at c (fig. 3), there are a series of isolated 1 j hooks or barbules, which fasten on to the opposite portion of the adjoining barb, which will be the same as the structure at consisting of a number of continuous ribs with recurved edges (shown here in section), and not isolated hooks similar to the left-hand * Trans. Micr. Soc. 1849, vol. ii. p. 25. 32 AEACHNOIDISCUS JAPONICUS. portion (at c), as they have been described by the author already mentioned. The processes or barbulettes (e) on the top of one side of each barb are in some birds much more fully developed than in the Pigeon, and they are especially so in the feathers of the Owl, as described in the paper already alluded to ; but instead of holding the opinion given there, that such struc- ture is for the purpose of rendering the flight of the bird noiseless, it appears to us far more probable that these pro- cesses repel any moisture and prevent it soaking into the plumage — a provision v^hich the Ov^^l would more especially require as a night-flying bird, and constantly exposed to heavy dews. AracJinoidiscus Jaj^onicus. Plate XIII. illustrates the results that can be obtained by Lieberkuhn illumination with :^th-in. object-glass, and repre- sents the AracJinoidiscus Japonicus in three positions. This diatom, when complete, consists of two valves connected by a transparent annular membrane, shown in the edge view at the bottom of the plate. The inner and outer surfaces of each valve vary consider- ably in their appearance. For whilst externally only minute annular markings, somewhat varied at the centre, are to be detected over one general plane, as in the lower figure on the left; the structure internally, as shown by the large figure at the top, is much more striking and complicated, the material here being evidently distributed so as to furnish great strength to the valve, and yet to leave a considerable space and depth unoccupied. The following diagram (fig. 1) represents the section of a valve in which the curved upper line is the elevated portion of the inner surface ; it starts AEACHNOIDISCUS JAPONICUS. 33 from the circumference as an annular plate (r^, h)^ from which it proceeds in numerous radii or spokes, alternately dipping down to the lower surface, or continuing to and through a smaller central annulus (c?, d)^ which descends by a beautiful curve to the lowest surface of the valve ; the radii in some specimens proceed even beyond this point, as at and the appearances {g) near the circumference are most probably caused by other very short perpendicular radii beneath the plate [a^ h). The lower surface internally differs but little from that externally, and is shown in fig. 3 highly magnified : A, A, h represent the radii connected by somewhat rectangular lattice-work, in which the silex in the lines (^, i) is often of such considerable thickness as to be- come a distinct feature. These particulars of structure can be easily and quickly verified by a binocular microscope, excepting perhaps the appearance shown in fig. 3, a clear view of which is de- pendeat upon the part being quite clean and unconfused by very thick or very irregular ribs ; but, with such condition, the lattice-work structure is easily detected internally, exter- nally, or on the edge of the valve. In endeavouring to determine the structure of any of the siliceous valves of the Diatomaceae, it must be more particu- larly remembered that they consist of a transparent substance, D 34 " DAEK-FIELD ILLUMIXATION," and consequently it is only the refraction or the reflexion of the light at the various edges, or irregularities of the different parts, that makes the object visible at all; it is owing to this circumstance that the dark centre of the valve has often been taken for an aperture, whereas the silex is present in this and many other parts that appear black and structureless. " Dark-field Illumination'' — Wenham's Parabola. An illumination which gives an appearance to objects very similar to that produced by light coming from above is the " dark-field illumination." This method of examining ob- jects only came into general use when perfected by Mr. Wen- ham's invention of the parabolic reflector ; but the principle itself had long been known and practised, by throwing very oblique light with the mirror. In every kind of " dark-field illumination" the light comes upon the object from below, but at such an oblique angle as never to enter the object-glass direct ; when, however, a suit- able object intervenes, it disperses the light and appears in the microscope brilliantly illuminated, the field of view still remaining dark. The action of the parabolic reflector may be easily under- stood by reference to Plate VI. fig. 8, which represents it in section, and shows that the rays of light, r, r\ r", entering perpendicularly at its surface {a)^ are reflected by its parabolic surface {h) to a focus at and then diverge without entering the angle cde^ which may be supposed to represent the pen- cil of light admitted by an object-glass. To prevent any light passing through direct from the mirror, a stop {g\ attached to a wire (/i), is fitted in the centre, and when raised in the sliding fitting (Jc), it will cut off the rays which are reflected at the least angle, such as r, This adjustment is necessary in cases where the object-glass has a large angle of aperture, WENHAM'S PAKABOLIC EEFLECTOE. 35 the efficient use of the parabolic reflector being dependent upon a dark field of view. In the first-class instruments the parabolic reflector (PlateVI. fig. 15) slides by its tube into the cylindrical fitting under the stage; and the adjustment of its focus (which is attained when its apex almost touches the object) is made by rack and pinion connected with the milled heads (Plates II. & III., U). In the other instruments it (Plate VI. fig. 13) fits into the tube (Plate IV. fig. 2, P) under the stage ; and by giving it a spiral motion when in this position, that is, carefully push- ing it up or down at the same time that it is turned round by the milled edge (Plate VI. fig. 13, a), the focus may be adjusted with every nicety. As it is always necessary that the rays of light should be parallel when they enter the parabolic reflector, some care is required in the illumination. The flat mirror must always be used, and daylight has only to be reflected directly from it ; but the rays from any artificial source have to be made parallel by the aid of a condensing-lens. Either the bull's-eye (Plate X. fig. 7) or small condenser on stand (fig. 9) answers well ; but in using them for this purpose, whilst their dis- tance from the mirror is immaterial, some five or six inches being best, they will only refract the rays parallel when they are placed the exact distance of their respective foci from the lamp or other source of light. Objects for which any kind of "dark-field illumination" is available must be more or less transparent, and many which it is almost impossible to illuminate at all from above will be brilliantly shown by the parabolic reflector; the specimens will also exhibit their natural colours, which are generally quite obliterated when the light is transmitted through them in the ordinary v^ay. The objects we have chosen for the illustration of this sub- D 2 36 THE EEECTIIS-G-GLASS. ject are some of the Polycystina from the fossil Barbadoes earth (Plate XIV.), a deposit which is now universally known amongst microscopists. The drawings just alluded to, give somewhat the effect produced by illumination from above ; this has only been done to give some idea of the shape of the specimens, which would otherwise appear too flat. The Erecting-glass for reducing the magnifying ^ower^ and for Dissection. This piece of apparatus (Plate V. fig. 4) screws into the stop at the lower end of the draw-tube, and is used in com- bination with the frds-inch object-glass. There are two results obtained by it: first, the object, which is always in- verted by the ordinary compound microscope, is shown in its natural position, which helps considerably in dissection or when the object requires any manipulation ; and, secondly, it reduces the magnifying power, but not to any one definite amount, for a very considerable range is obtained by merely sliding the draw-tube in or out, as may be seen by the follow- ing Table : — lAnear Magnifying Power of Erecting-glass, when used with the ^rds-inch Object-glass and No. 1 Eyepiece. Inches and tenths. Mag. power. Draw-tube pulled out •5 5 •7 10 J> " •9 15 J> 7J 1-15 20 JJ J? 1-55 30 1-95 40 ?> 5' 2-35 50 » >5 2-8 60 » ?7 3-2 70 }f 7? 3-6 80 77 77 4- 90 77 7 4-45 100 POLARIZED LIGHT. 37 The New Halfyenny. To illustrate these facts we are at least successful in select- ing a most familiar object, for it can only be the very richest who are not thoroughly acquainted with the new halfpenny coin of the realm ; and yet, whilst this perfect knowledge of the object saves us from giving any very minute description, we venture to draw attention to one or two particulars. The coin is an exact inch in diameter (see Plate XV. figs. 2 & 3), but when magnified 5 times (about the lowest power the erecting-glass gives) it appears as seen in fig. 1, and may ex- plain to many, in a very familiar way, what linear magnifying power really is. With the power raised to 25, the object be- comes so much beyond our scope of illustration, that we have to confine ourselves to Britannia's foot alone ; and we must claim the discovery of a new locality for this ubiquitous mem- ber, if henceforth, through our instrumentality, it should find place and rest in quiet microscopic cabinets. For once we must decline a more minute microscopic examination of our object, and any further criticism we leave to those who are gifted with some knowledge of art-design or execution. On our own part we are content to point out with pride on this coin the Eddystone Lighthouse, de- signed and built by Smeaton, whom, originally a mathe- matical-instrument maker, we may honestly claim as a fellow- craftsman. Polarized LdgJit, as applied to the Microscope. The use of polarized light in the microscope always pro- duces, in suitable objects, the most beautiful effects, and it frequently assists in the accurate determination of structure when no other method is of any avail. 38 POLAEIZED LIGHT. NicoVs Prisms. To apply this kind of illumination to the microscope, two Nicol's prisms are generally used ; and it is necessary that one, the " polarizer," should be under the object, whilst the other, the " analyzer," should be somewhere above ; both prisms being mounted so that they can be turned round when in their proper positions. In all the microscopes alluded to in these pages, the pola- rizer (Plate XVI. fig. 2) will slide in the fitting (fig. 1) which generally receives the diaphragm, under the stage ; but in the first-class instruments it will also fit in the cylindrical fitting (as shown by fig. 22, A) : it must, how^ever, be remembered that, except when used with the achromatic condenser, as described hereafter, it is important to bring the polarizer as near as possible to the object. The best application of the " analyzer " (fig. 4) is over the No. 1 eyepiece, in the place of the eyepiece-cap: another position for it is immediately above the object-glass, and this may be attained by either of two adapters; the one (fig. 19) screws into the stop at the lower end of the draw-tube, the other (fig. 20) forms an intermediate piece between the nose- piece of the microscope and the object-glass. In the former the analyzer cannot be rotated without turning round the draw-tube ; in the latter the outside of the adapter has openings on opposite sides, so that an internal tube (fig. 20, B) which carries the prism may be easily reached by the tops of the fingers : but before the analyzer can be applied by either of these adapters, it is necessary to reduce its mountings (as shown in fig. 15), by removing the ordinary eyepiece-fitting (fig. 4, C) and the screw-cap (D). These two positions of the analyzer may require some ex- POLAEIZED LIGHT. 39 planation. When the prism is placed over the eyepiece, it necessarily, from its particular shape (although made espe- cially for the purpose), removes the eye some considerable distance from the top lens, and with all the eyepieces, except that of the lowest power, it cuts off considerable portions of the field of view : this is not the case when the analyzer is placed immediately above the object-glass, but then any de- fects in the workmanship of the prism (and there are sure to be some) are magnified by the eyepiece. The choice of position is therefore entirely dependent upon the character of the object ; if the best definition be required, the analyzer must be used above the eyepiece, whilst the second position is often quite satisfactory to an observer who looks more at the general display than at the minute details. The effect produced by the prisms alone may be observed by leaving one of them stationary whilst the other is turned round, and it will then be seen that twice in each revolution the light will be entirely stopped : this is, of course, sup- posing that an object-glass and an eyepiece are on the micro- scope, and that, without the prisms, there is an ordinary full illumination. If now a polarizing object, such, for instance, as that shown in Plate XVII. fig. 1 (crystals of sulphate of copper and magnesia), be placed under the microscope when the prisms stop the light, the object will present the appear- ance shown by the drawing, and the dark and light parts will change their relative positions when either prism is revolved: with this object, and under these conditions, no colour whatever is shown; but this deficiency may be sup- plied by a plate of selenite specially prepared for the pur- pose; for if this be put in the place of the object, the field of view will appear coloured, instead of being only black and white as with the prisms alone. 40 DAEKEE'S 8ELENITE PLATES. The Selenite Plate. The particular colour given by a selenite plate is de- pendent upon its thickness ; but each piece, during one half- revolution of either prism, will always show two distinct or, as they are termed, complementary tints, and the plates, as generally supplied, produce either red and green or blue and yellow. The colours of the selenite may be almost entirely neutralized in certain positions of the Nicol's prisms ; it is therefore necessary, for varying the tint or for obtaining the greatest intensity of colour, not only to revolve either prism separately, but also to change the relative positions of both of the prisms to the selenite plate ; or, what amounts to the same thing, where practicable, to rotate the selenite itself. Either selenite plate (Plate XVI. figs. 17 or 18, the former mounted in brass, and the latter between two pieces of glass) has to be placed under the object, and does not admit of rotation ; but we make provision in the first-class instruments for this movement in two ways. In the simpler form, a circular plate of selenite (fig. 6) drops into the brass cell (fig. 8), and is held in its place by the ring (fig. 7), which fits tightly over it ; the whole fitting (fig. 8) will either slide by its larger diameter (E) into the cylindrical fitting (fig. 22), or by its smaller diameter (F) it can be attached to the brass-work of the polarizer; but the milled ring (G) by which the selenite can be rotated must either project above the cylindrical fitting, or it must, as when attached to the prism, come opposite to the side opening where the finger can reach it. Barker s Eetarding-Plates of Selenite. TJiis other arrangement is specially contrived as the most DARKEK'S SELENITE PLATES. 41 convenient way of using Barker's series of retarding-plates of selenite; these consist of three plates (Plate XVI. figs. 9, 10, & 11), each of them engraved on the brass rim " P|A," together with a number, J, f , or f , which repre- sents a certain power of retarding a wave of polarized light. When the plates are superposed with their marks P|A in the same positions, the power they represent is the sum of their numbers ; but when placed at right angles (see figs. 12 & 13), they oppose each other, and then their differences will give the power : thus if \ and f are placed over each other with their marks P|A in the same direction, they will represent f ; but if either of them be turned round one quarter of a revolution, they will only give f , and conse- quently the three plates, with their various alternations, will give thirteen different colours, together with their com- plementary tints, as shown in the following list : — Prisms at right angles. Complementary tint. ^ by itself very light lavender straw-colour. 3 1 — 2. 4~~4 — 4 darker ditto light yellow. |- by itself deep blue light maize. 3 4_ 1 — 4 4i^4 — 4 very light blue orange. 9 3 1 — 5. 4 4 4 4 lake emerald green. 9 3 6. 4 4 — 4 deep blue bright yellow. 9 1 1 3._7. 4 "r4 4 4 light green light purple. 9._ 1 — 8. 4 4 — 4 light plum -colour pea-green. ■| by itself blue-green salmon. 9 1 1 — 10_ 4~r4 — 4 green-yellow mauve. 9 j_ 3 1 — XX 4:'T4: 4 — 4 pink light green. 9 1 3 12. 4 ~r 4 — 4 light pink deep green. 9 j_ 31 1 13. 41 4"r4 — 4 very light red stone-green. The brass-work mounting, by which the alternations just given may be made under the microscope, is shown in fig. 16 ; 42 OBJECTS UNDEE POLAEIZED LIGHT. the selenites are fitted into three cells, which can be rotated in the three separate arms (J, K, L) ; these arms adapt by a short dovetail (M) to the cylindrical fitting (fig. 22) under the stage ; when in that position, they may be turned either in or out by means of the three nibs (N, O, P), and the finger can reach the milled rings through the opening (fig. 22, H) for the purpose of rotation. By this method any change of the selenites can be made with quickness and facility, and with- out interference with the position of the object, or any other arrangement. LarJcers Selenite Stage. Barker's selenite stage (Plate XVI. fig. 14) is also a very complete piece of apparatus ; the three plates (figs. 9, 10, 11), already described, drop into a ring (fig. 14, P) which can be rotated in the plate (S) by turning the small milled head (T), and an arrow upon this may be used for registering any par- ticular amount of rotation, sixteen turns making one revolu- tion : the only objection to this arrangement is that the object which rests on the ledge (U) must be removed at every change of selenite ; but in many instances this is of no consequence. The tints produced by the selenites are again much varied by the object : thus in Plate XVII. fig. 2, the same object as in fig. 1 is represented, but with an infinite variety of colour imparted by the interposition of a plate of selenite, which by itself, and in that particular position, gives only the blue ground, as shown round the crystal. Then, again, there are many instances in which the use of selenite only detracts from the brilliancy and the variety of the colours of such objects as are represented by the other figures, whose appearance is entirely due to the use of the prisms only. Fig. 3 is an oblique section of rhinoceros TOUEMALINES. 43 horn ; fig. 4 is a section of dried tendon of the ostrich ; figs. 5 & 6 are crystallized salicine (an alkaloid from the bark of the willow), these last two drawings showing the change pro- duced by one-quarter of a revolution of one of the prisms. All polarized light considerably diminishes the intensity of any illumination ; and although this loss may not interfere with the appearance of an object under the lower object- glasses, yet, when the magnifying power is increased, some colours are quite lost, and all are much less brilliant. This deficiency of illumination may be obviated by employing the achromatic condenser to concentrate the polarized light ; and the arrangement will then be to have the polarizer at the lower and the achromatic condenser at the upper end of the cylindrical fitting (Plate XVI. fig. 22), — the selenite, if used, being placed between these two, or immediately under the object ; and the smaller apertures of the condenser, without the front lens, are generally quite sufficient. Tourmalines. Besides Nicol's prisms, there are many other means of polarizing light ; of these the most remarkable are tourma- lines (Plate XVI. fig. 5). Very thin slices of some of these crystals are sufficient for the purpose, and consequently as analyzers they have a great advantage over Nicol's prism in giving a full field when used above any of the eyepieces. Their only fault is that they are never free from some colour in themselves, and therefore they make material changes in the true appearance of an object. They are, moreover, when of a sufficiently light tint and still retaining their polarizing power, very scarce ; so that the small pieces even, which are quite large enough for the microscope, can only be purchased at high prices. 44 EXPEEIMENTS WITH DOUBLE-IMAaE PEISMS. Polarizers for large objects. Before the extra large polarizer (Plate XVI. fig. 3) was in- troduced, the illumination of the whole of an object under a low power was often found to be imperfect, and was remedied by the use of some other polarizer : either a piece of black glass (fig. 21) was placed over the mirror and then inclined at the proper angle, or a bundle of thin glass plates (fig. 23), properly mounted, was slid into the cylindrical fitting under the stage, so that the light would be polarized by either passing through or by refiexion from it ; but these methods are not much employed at the present time. Experiments with Double-image Prisms. The microscope may also be made to exhibit various results produced by polarized light, as the subjoined extract from a paper by Mr. Legg * may explain : — " The following experiments, if carefully performed, will illustrate the most striking phenomena of double refraction, and form a useful introduction to the practical application of this principle. " The apparatus necessary is — " A Nicol's prism (Plate XVI. figs. 2 or 3) to be adapted under the stage. " A selenite plate, figs. 17 or 18. " Two double-refracting prisms, adapting to each other and to the eyepieces, figs. 24 and 26. " A film of selenite adapted to the double-refracting prisms, fig. 25 ; and * " On the Application of Polarized Light in Microscopic Investigations." By M. S. Legg. Read before the Microscopical Society of London, Dec. 9, 1846. EXPERIMENTS WITH DOUBLE-IMAGE PRISMS. 45 A plate of brass, 3 inches by 1, perforated with a series of holes, fig. 27. " Exp. 1. — Place the piece of brass so as for the smallest hole to be in the centre of the stage of the instrument, employing a low-power object-glass, and adjust the focus as for an ordinary microscopic object ; place one double- refracting prism in the place of the cap of the eyepiece, and there will appear two distinct images (Plate XVIII. fig. l^a); then by revolving the prism the images will describe a circle, the circumference of which cuts the centre of the field of view ; the one is called the ordinary, and the other the extra- ordinary ray. By passing the slide along so as for the larger orifices to appear in the field, the images will not be com- pletely separated, but will overlap, as in fig. 1,^. ''Ex]). 2.— Place the polarizer (Plate XVI. figs. 2 or 3) into its place under the stage, still retaining the double- image prism over the eyepiece ; then by examining the object there will appear in some positions two, but in others only one image ; and it will be observed that at 90° from the latter position this ray will be cut off, and that which was first observed will become visible ; at 180°, or one-half of the circle, an alternate change will take place; at 270° another change ; and at 360°, or the completion of the circle, the original appearance (see Plate XVIII. fig. 3). " Before proceeding to the next experiment, it will be as well to observe the position of the Nicol's prism used as a polarizer, which should be adjusted with its acute angles parallel with the sides of the stage (see fig. 7), in order to secure the greatest brilliancy in the experiment : the proper relative position of the selenite may be determined by no- ticing the natural fractures or flaws in the film, which will be observed to run parallel to one another: these flaws 46 EXPERIMENTS WITH DOUBLE-IMAGE PEISMS. should be adjusted to about 45° from the sides of the stage, to obtain the greatest amount of depolarization (see fig. 8). " Exp. 3. — If we now take the plate of selenite thus pre- pared, and place it under the piece of brass on the stage, we shall see, instead of the alternate white and black images, two coloured images, as in fig. 2, 6?, and fig. 4, composed of the constituents of white light, which will alternately change (by revolving the double-image prism over the eyepiece) at every quarter of the circle; then by passing the plate of brass along, so as to bring the larger orifices in succession into the field, the images will overlap, and where they over- lap, white light will be produced (see fig. 2, d). If by accident the prism should be placed at 45° from the position just in- dicated (see fig. 9), no particular colour will be observed, and it will then illustrate the phenomenon of the neutral axis of selenite ; because when placed in that relative position, no depolarization takes place. " The phenomena of polarized light may be further illus- trated by the addition of the second double refractor (fig. 26, Plate XVI.) and the film of selenite (fig. 25) between the double refractors. " Exp. 4. — By placing the apparatus as described in the first experiment (that is, removing the Nicol's prism and plate of selenite, but retaining the brass plate), we shall ob- serve the two images as shown in fig. 3, Plate XVIII. ; then by placing the second double refractor over the first, so as for all the faces of the one to be parallel to all the faces of the other, as if they formed but one piece, the eye will perceive two distinct images, but at twice the original distance from each other (see fig. 5, e). If we now turn the prism nearest the eye from left to right, two faint images will appear ; con- tinuing the turn, at 45° the four images will be all equally CRYSTALS TO SHOW EINGS. 47 luminous (fig. 5, /) ; and when the prism has turned round 90°, there will be only two images of equal brightness (fig. 5,^) ; continuing the turn, two other faint images will appear; further on the four images will be equal ; still further they will be unequal; and at 180"^ of revolution they will all coalesce into one bright image (fig. 5, h). " Ex]p, 5. — The above results will be rendered more inter- esting by interposing between the double refractors the film of selenite. Instead of the two white images, as in the pre- ceding experiment, we shall see three, of which the two outer ones will be one colour (say green), and the middle, its complementary colour or red (fig. 6, i); by turning the prism nearest the eye, the middle image will gradually divide, until the completion of a quarter revolution, when four images will appear of equal brilliancy, two of each colour (fig. 6, revolve the prism until the completion of the half-circle, and the three images will reappear, but with diff'erent properties, the outer images being red and the middle green (fig. 6, ; at another quarter revolution, four images, but with opposite colours, will be observed (fig. 6, m), and at the completion of the revolution the original appear- ance (see fig. 6, i). " In this experiment the relative positions of the double- refracting prisms and the selenite must be carefully observed, as, if the neutral axis of the selenite be parallel or perpen- dicular to the plane of polarization, no depolarization takes place, and no colours will be produced, the results then appearing as if the selenite were not interposed." Crystals to show Bings. The systems of coloured rings, produced by crystals cut perpendicularly to their axes, can also be beautifully shown 48 WENHAM'S BINOCULAR MICEOSCOPE. in the microscope with polarized light ; they are best seen by placing the polarizer (Plate XVI. figs. 2 or 3) under the stage, and employing a low-power object-glass; it is usual to place the crystal over a No. 2 eyepiece, made without a stop ; and either a short prism or a tourmaline may be used as an analyzer over the crystal. Plate XVIII. fig. 10 shows the appearance of calc-spar under such circumstances. The following is a list of the most interesting specimens, each of which is generally mounted in a brass fitting, as shown in Plate XVI. fig. 28. List of Crystals. Quartz, right-handed. Nitre. Quartz, left-handed. Topaz. Calc-spar. Sugar. Borax. Arragonite. Wenliams Binocular Microscope. Wenham's binocular microscope is now so well known, that it may appear hardly necessary to occupy a portion of these pages with any explanation or defence of its principle ; but binocular vision itself, as well as this particular applica- tion of it, still meets with such strong opposition from many microscopists, that we venture to give with some minuteness a few facts connected with the subject, and, more especially, because we consider Wenham's binocular body to be the most valuable addition to the compound microscope since the perfecting of the object-glasses by Mr. Lister. That binocular vision is advantageous, if not necessary, is quite sufficiently proved by the fact of our having two eyes, and it is also known that the stereoscopic effect con- veyed to the mind increases as the object approaches the eyes; consequently, when the simple design of the WENHAM'S BINOCULAE MICEOSCOPE. 49 microscope is to enable the eyes to see an object, or the image of an object, at a shorter distance than the natural limit, under such circumstances stereoscopic vision must be of the greatest importance. In Mr. Wenham's contrivance, the binocular body is merely an addition; when adapted to an instrument, it does not interfere in any way with the use of the single body only, in its perfect condition. This is a most important feature ; for it also affords the opportunity of an immediate comparison between the appearances seen by single or double vision ; and thus not only can the accuracy of the binocular body be easily tested, but the observer may obtain in an instant a double analysis of the structure or condition of an object. / We believe most of the opponents of the binocular prin- ciple to be those observers who have accustomed themselves to the examination of objects as transparent ; and we venture to draw especial attention to this particular condition, under which so many judge of the value of the Binocular Micro- scope. This method of examination, peculiar to the micro- scope, and one to which the naked eye is quite unaccus- tomed, conveys to the mind a most imperfect idea of the form or vertical distance of the various parts of an object, whilst in very many instances the appearances bear no re- semblance even in shape to the true structure: this may be readily conjectured from the various shapes the markings on Pleurosigma formosum assume when illuminated in dif- ferent directions (see Plate IX. fig. 1) ; but most conclusive evidence is furnished by a careful examination of the scales of Lepisma saccharina. This insect may be found in most old houses, frequent- ing damp, warm cupboards, or as an associate of black beetles and cockroaches, and its scales have long been E 50 WENHAM'S BINOCULAE MICEOSCOPE. known to microscopists. The insect, which is very active, may be caught without injury in a clean pill-box, with a few pin-holes in the lid ; and a drop of chloroform over these holes will soon make the inmate insensible, when it may be turned out upon a piece of clean paper. The best way to remove the scales is to press gently one of the ordinary 3x1 glass slides upon the part from which the scales are required, and they readily adhere to the glass, appearing to the naked eye like a smear of dust ; under the microscope they present considerable variety, not only of size and shape, but also in the character of their markings. The scales that are most abundant resemble the one shown in Plate XIX. fig. 3, and upon it the more prominent mark- ings appear as a series of double lines which run parallel and at considerable intervals from end to end of the scale, whilst other lines, generally much fainter, radiate from the quill and take the same direction as the outline of the scale when near the fixed or quill end ; but there is in addition an interrupted appearance at the sides of the scale, which is very different from the mere union or " cross-hatching " of the two sets of lines. In the first place, the scales themselves are truly trans- parent objects ; for water instantly and almost entirely obli- terates their markings, but they reappear unaltered as the moisture leaves them; therefore the fact of their being visible at all is due to the refraction of light by superficial irregularities. The following experiment establishes the fact still more conclusively, and also determines the structure of each side of the scale, a matter which it is impossible to do from the appearance of the markings in their unaltered state. Having removed some scales from the insect to a glass WENHAM'S BINOCULAE MICllOSCOPE. 51 slide as already described, cover them with a piece of thin glass, which may be prevented from moving by a little paste at each corner. The subjoined drawing may be taken as an exaggerated section of the various parts. D E ^ ? ^ ^" ^ ^ " A, B, is the glass slide with scales, c, c, closely adherent to it, and D the thin glass cover secured to A, B, by a very little paste at the corners : in this state the whole should be placed under the microscope, — a high power, such as a |-th and No. 3 eyepiece with achromatic condenser illumination, answering well. If under these circumstances a small drop of water, E, be placed at the edge of the thin glass, it will run under by capillary attraction ; but when it reaches one of the scales, it will run first between it and the glass slip A, B, because the attraction there will be greater, and consequently the markings on that side of the scale which is in contact with the glass slip will be obliterated, whilst those on the other side will, for some time at least, remain unaltered; when such is the case, the strongly marked vertical lines disappear and the radiating ones become continuous (see Plate XIX. fig. 4, left-hand lower portion). To try the same experiment with the other, or inner, surface of the scales, it is only requisite to transfer them by pressing the first piece of glass, by which they are taken from the insect, upon another piece of glass, to which a few scales will adhere ; and then the same process of introducing fluid, as already de- scribed, may be repeated with them, when the radiating lines will disappear and the vertical ones will become con- tinuous (see fig. 4, right-hand side of scale). These results show, therefore, that the interrupted appearance is produced by two sets of uninterrupted lines on diflerent surfaces. E 2 52 CONSTEUCTION OF BINOCULAE MICROSCOPE. It may be interesting to many to try these experiments for themselves, whilst others may be satisfied with the appearance which some scales are almost sure to present in every slide that is mounted. Fig. 4, already alluded to, is a camera-lucida drawing of a scale which happens to have the opposite surfaces obliterated on either side : this is seldom the case, for it is generally only the outer surface of the scale that is in such a condition. Fig. 1 shows a small scale in a dry and natural state, the direction of the markings upon which is shown by the faint lines : at the upper part (a) the interrupted appearance is not much unlike that seen at the sides of the larger scales ; but lower down, at b, where the lines are of equal strength and cross nearly at right angles, they are entirely lost in a series of dots ; and exactly the same appearance is shown in fig. 2 to be produced by two scales at the part (c) where they over- lie each other, although by themselves they only show the parallel vertical lines. These kinds of contradictory results produced by the re- fraction of light, combined with an illumination to which the naked eye is unaccustomed, make the binocular micro- scope of little avail in the examination of true transparent objects; but with those specimens that are opaque, or nearly so, its assistance is most remarkable, and we do not know a single object of this class in which its use is not essential. Construction of Binocular Microscope. The only plan for a binocular microscope, as yet known to be practicable, is the equal division of the rays after they have passed through the object-glass, so that each eye may be furnished with an appropriate one-sided view of the ob- ject. The methods at first contrived to efiect this not only CONSTEUCTIOX OF BINOCULAR MICROSCOPE. 53 materially injured the definition of the object-glasses, but also required expensive alterations in their adaptation, or more frequently still a separate stand ; whereas the following arrangement, contrived by Mr. Wenham, forms no obstacle to the ordinary use of the instrument, and the definition even of the highest powers with the binocular body is scarcely im- paired. It consists of a small prism mounted in a brass box (Plate XX. fig. 3), which slides into an opening immediately above the object-glass (fig. 1, I), and reflects one half of the rays, which form an image of the object, into an additional tube (B) attached at an inclination to the ordinary body (C). One half of the rays take the usual course, with their con- ditions unaltered; and the remainder, although reflected twice, show no loss of light or definition worthy of notice, if the prism be well made. As the eyes of different persons are not the same distance apart, the first and most important point to observe in using the " binocular " is, that each eye has a full and clear view of the object; this is easily tried by closing each eye alter- nately without moving the head, when it may be found that some adjustment is necessary by racking out the draw-tubes (D, E) by the milled head (K), which will increase the distance of the centres; or when moved in the contrary direction, they will suit those eyes that are nearer together. If the prism be drawn back until stopped by its catch (fig. 3, F), the field of view in the inclined body is darkened, and the whole aperture of the object-glass passes into the main body as usual, neither the prism nor the additional body interfering in any way with the ordinary use of the microscope. By pressing back the spring-catch (fig. 3, F) of the prism, it can be withdrawn altogether for the purpose of being wiped ; this should be done frequently and very care- 54 CONSTRUCTION OF BINOCULAR MICROSCOPE. fully, on all four surfaces^ with a perfectly clean cambric or silk handkerchief or a piece of wash-leather; but no hard substance must be used. This construction of binocular body can be applied to any of the microscope-stands already described and drawn with the single body only. The first few plates of this work were engraved before Mr. Wenham's contrivance, or the illustra- tions would have included a binocular body in each instance, as it is now but seldom that we send out instruments with only the single body. The most suitable kind of illumination for the binocular microscope has been already alluded to, and includes all those methods in which the light is thrown upon the upper surface ; but for those objects that are semitransparent, as sections of bone or teeth, Diatomacese, living aquatic ani- malcules, &c., the dark-field illumination, by means of the parabolic reflector, will give a very good result. For the illumination of perfectly transparent objects, it is best to diffuse the light by placing various substances under the ob- ject, such as tissue-paper, ground glass, very thin porcelain, or a thin film of bees-wax run between two pieces of thin glass. When employing the polarizing apparatus with the " bin- ocular," the analyzer is fitted into an adapter (fig. 2), which applies immediately between the object-glass and the prism, with the means of revolving the prism by turning its tube round at opposite slots in the sides of the adapter, and the effects are exceedingly beautiful. Although the binocular body makes the various features of an object so distinct and so easy to distinguish, yet the representation of them in drawings is extremely difficult, be- cause the stereoscopic appearance can only be given by the LIVE-BOXES AND TEOUaH. 55 management of the shadows : this has been attempted in the following illustrations : — cast skin of silkworm, Plate IX. ; splinter of lucifer-match, Plate XI. ; tarsus of spider and structure of feather, Plate XII. ; Arachnoidiscus Japonicus^ Plate XIII. ; and Polycystina from Barbadoes earth, Plate XIV. To see these illustrations with the best result, they should be held so that the light falls on them from the top right-hand corner of the plate; only one eye should be used ; and if the margin round the drawing be cut off by looking through the hand when nearly closed, the elfect is considerably improved. Sundry Apparatus. — Live-boxes and Trough. To confine small living objects for examination under the microscope, different pieces of apparatus are used, according to the size or the nature of the object. Those that are dry and active may be secured in a live-box (Plate XXI. figs. 1 & 4). This consists of two parts : the lower piece (fig. 4, a) is a brass plate, with a short piece of tube (h) in the centre, carrying a circular piece of thick glass (c) at the top ; over this fits the upper piece or cap (d), carrying a thin glass. The object is held by the pressure of the two glasses, and the amount of separation may be varied at pleasure by sliding the cap more or less on. The thin glass is in a cell, and may be changed or replaced by unscrewing the top milled ring (e). A smaller live-box is shown in fig. 1. These pieces of apparatus answer well for many objects in fluid; but if employed in this way, the quantity of water, or whatever it may be, should, if possible, be limited, as shown by the accompanying figure, in which the small central ring represents the appearance of a dro] 56 LIVE-BOXES AND TROUGH. of water when held between the glasses of a live-box. The object, if small enough, may be confined thus, either with or without pressure, whereas, if the fluid be in excess, the objects will move about over too large a space, or fre- quently they reach the edge of the live-box and disappear altogether. When fluid objects are very small and cannot be injured by moderate pressure, a very simple and efficient plan is to use the plate-slip (fig. 5, a); the fluid is placed upon this, and then covered with a thin piece of glass (^), which is pre- vented sliding off" by the ledge (d). The glass trough (figs. 2 & 3) is intended for larger ob- jects in water ; it must be used with its thinner plate of glass (fig. 3, a) in front. The modes of confining the objects, and keeping them near the front surface, must vary according to circumstances. For many it is a good plan to place the piece of glass (h) diagonally in the trough, its lower edge being kept in its place by a strip (c) at the bottom ; then if the object introduced be heavier than water, it will sink till stopped by the sloping plate (b). Sometimes the whalebone- spring (d) may be applied behind this plate to advantage, with the wedge (e) in front to regulate the depth. The glass tubes (fig. 6) are employed to catch any animal- cule or other object that may be swimming about in a vessel of water. If a finger be pressed close upon the small opening at the rounded end (a), the other end of the tube may be dipped in the water to any extent without the water entering the tube; but immediately the finger is lifted off, the water rushes up to the same level as that in the vessel, and together with it any animalcules which were near the lower and of the tube ; the finger is placed again upon the small LEVEE COMPEESSOE. 57 opening at the top of the tube, which can then be removed, together with its contents, from the vessel. Compressors. In many cases, objects require careful and yet considerable pressure whilst under the microscope, and there are many contrivances for the purpose. Screw Live-box, In the screw live-box (Plate XXI. figs. 9 & 10) the pres- sure is produced by two small spiral springs (a, a) acting against the upper plate (b), on the top surface of which a piece of thin glass is held by two springs c) ; the lower plate holds a thick circular glass, and outside it is a milled ring (d), on which the upper plate is constantly pressed ; the distance be- tween the two glasses is regulated by the milled ring (d), which screws up or down, and two pins (e, e) prevent the plate turning round. Lever Compressor. The lever compressorium (figs. 13 & 14) has also a thick glass on the bottom plate ; but the thin glass is cemented in a ring at the extremity of an arm or lever [a)^ which is moved up or down by turning the small screw {b). In this instrument the amount of pressure is the force imparted by the screw (^), and it is very considerable ; it is equally distributed over the glasses by the ring [c) being swung in the centres [d^ d), and by the semicircle (e) having a revolving fitting at (/) ; the lever (a) can be turned on one side, so as to expose both glasses when they want cleaning, or when the object is to be changed. 58 EEVEESIBLE COMPEESSOES. Wenhams Compressor. Wenham's compressor (figs. 7 & 8) was designed especially for use with the parabolic reflector or achromatic condenser. The bottom plate {a) is very thin, and a circular thin glass is cemented in the middle ; the top plate (h) is a thin brass arm, also carrying a circular thin glass cemented to it; the pressure is imparted by a spring or set which is given to the arm {h\ and the two pieces of glass will approach or separate according to the direction in which the small milled head {c) is turned ; the arm will also turn aside, as in the lever compressor. The simple construction of Wenham's compressor makes it a very easy and convenient instrument to use ; it has, however, one or two disadvantages — the two pieces of glass do not move in parallel directions, and the amount of pressure is rather limited. Reversible Compressors, The next two compressors are our own contrivance, and both of them individually combine in one piece of apparatus the excellences of those already described, together with the following new qualities: viz., a parallel and equal compres- sion, with an immediate action up or down; the means of turning the compressor over, so as to see both sides of an object without disturbing it; the use of thin glass only either at top or bottom ; and lastly, such restrictions in the thickness of the brass-work as permit the use of the achro- matic condenser, or the parabolic reflector, on either side of the object. Mr. Slack suggested the basis of the construction in each case ; he proposed that two oblong pieces of thin glass (fig. 15) should each be secured to a separate brass plate by the heads REYEESIBLE COMPRESSORS. 59 of two screws ; spaces were then to be made for the heads of these screws in each opposing plate, and the two pieces of glass could be brought close together. This simple plan has great advantages : the pieces of glass are easily cut ; for no great* nicety of size is required, and they can be changed, or replaced, without difficulty and with little loss of time. The "parallel plate compressor" (figs. 11 & 12) consists of two brass plates, furnished with thin glass, as already described, and connected by four small rods (a) : this is in fact the commonest parallel-rule motion, and very nearly a ver- tical one ; for when the plates are near together, the position of the connecting rods is such as to cause no perceptible end- movement. The brass plates, when about Tb-th of an inch from each other, are kept apart by two springs, which supply the separating power, the compressing force being given by a small screw (b) with a conical end, attached to the one plate, working into a corresponding recess in the other plate ; the first hold the point of the screw gets is at the bottom of the recess, so that the plates are drawn together as the screw advances. When the inner surfaces of the thin glasses want cleaning, or when the object or the glasses have to be changed, the screw (b) must be brought quite back, and the plates will then separate to the extent of a full inch. In the "cell compressor" (figs. 16, 17, & 18), the thin glasses are secured to two circular plates of brass ; the one fits the ring (fig. 18), and the other the counter ring (fig. 16) of a brass cell (fig. 17, a); when these are screwed together, the plates approach each other, or when unscrewed, they sepa- rate, and some slight intermediate brass springs counteract any loss of time that there may be in the screws or in the fittings of the circular plates. Two upright pins in a flat 60 FROG PLATE. brass plate (fig. 17, h) pass through both the circular brass plates to prevent them turning round whilst the cell is screwed or unscrewed, and a small screw (c?), working by a slight taper against a push-piece (6?), holds the cell itself firmly in a sunken ring of the brass plate {h\ into wMch it drops. For cleaning the glasses, &c., the circular plates may be entirely separated by unscrewing the cell. The chief novelty in both of these compressors is the opportunity they afford of examining both sides of an object whilst under pressure. The "parallel plate compressor" maybe turned over altogether, and used from either side ; in the " cell com- pressor," after the push-piece is loosened by slightly un- screwing the small milled head the cell will lift out of the sunken ring and off the pins, to be placed on again with whichever side is wished uppermost. Prog Plate. The frog plate (fig. 19) supplies the means for viewing the circulation of the blood in the web of the frog's foot, and consists of a long thin brass plate [a^ a), with a square aperture (b) at one end covered with a piece of glass. A small bag is supplied, in which the whole of the frog is put, except one hind leg ; and to prevent this being drawn in, the neck of the bag should be pulled tight ; the frog, thus con- fined, is then secured to the unglazed end of the brass plate by ribbon wound over it and through the holes at the sides of the plate, the ends being held by a spring underneath. The foot is next drawn out over the glass (^), and the web extended by fastening to the extremity of the toes, pieces of fine silk which can be wound round the pins (c, c). The glazed end of the plate must be clamped firmly to the stage of the microscope, and the frog as well as its foot should be CAMEEA LUCIDA. 61 constantly moistened with cold water; if also a piece of thin glass with water underneath be placed over the part of the web that is under examination, the effect is much im- proved. Camera Lucida. Wollaston's camera lucida, when applied to the achro- matic microscope, is of the greatest use and importance ; by its aid the most intricate structure of objects can be drawn with perfect accuracy and to an exact scale. This piece of apparatus (Plate XXII. figs. 6, 7, & 8) slides on in the place of the cap of either eyepiece, with its flat side (fig. 7, a) uppermost, as shown also in fig. 8, which is a drawing to scale of the camera lucida when in use. The body of the microscope must be in a horizontal position, and a piece of paper laid upon the table should be exactly ten inches from the flat side of the prism. Then if the eye be placed so that its pupil is divided as it were by tlie edge of the prism (see accompanying figure, in which ~- a represents the pupil of the eye and h the top |^;;[ surface of the prism), the object will appear upon the paper, and can be traced on it by a pencil, the point of which will also be seen. Only one eye is to be used; and the light must be regulated so that no more than is really necessary is upon the object, whilst a full light is thrown upon the paper. Perfect steadiness of the eye is also necessary, and the eyebrow may be gently rested upon the prism-fitting as shown in fig. 8. Any one who cannot see to read distinctly at ten inches should use a lens in the position shown in figs. 6 & 8 ; it must be convex for long sight, and concave for short sight : in general the former only is supplied, but it is easily changed when necessary. It must not be supposed that any carefully finished draw- 62 CAMERA LUCIDA. ing can be made with the camera lucida; this is seldom possible; and when the object to be sketched is irregular on the surface, or larger than the field of view, it often requires no little care and patience to retain the relative position of the parts correctly ; but considerable facility is soon acquired, and when observers who are quite unable to draw from the eye alone succeed in producing a faithful representation of an object, the result is most gratifying and frequently of some value, more especially if the specimen be not permanent. It is well known amongst observers that generally no minute comparison of objects can be made without drawings, and it is almost impossible to obtain such without the aid of the camera lucida ; at the present time there are many illustra- tions of objects which are completely puzzling and compara- tively worthless because they are not drawn to scale, but merely represent the appearances presented to the eye of the artist. If there be substituted in the place of the object a piece of glass ruled into lOOths and lOOOths of an inch, termed a stage micrometer (fig. 3 or 4), its divisions can be marked on the same or another piece of paper, and by comparing them with the drawing of the object, the most accurate measure- ment can be made. The whole of Nobert's lines (Plate VIII.) and the markings on Navicula rhomboides (Plate VII. fig. 13) were measured in this way. In Plate XXII. fig. 11 is a simple sketch to illustrate the usefulness and capabilities of the camera lucida ; it represents the stellate tissue as occurring in the transverse section of a rush (Juncus conglomeratus), very commonly used in London for tying up bunches of watercresses. The left-hand portion of the sketch is the mere outline exactly as drawn by the aid of the camera lucida, the right-hand portion being touched THE MICROMETEES. 63 up more or less to show how it may be finished if necessary, and at the bottom are traced lOOths and lOOOths of an inch to serve as a scale for measurement. The magnifying power can be easily ascertained by com- paring the magnified stage-micrometer lines traced by aid of the camera lucida with, a rule divided into inches and tenths : thus, supposing to o^^ inch, when marked on the paper, to measure 1 inch and -njths, the magnifying power would be 130; but in such calculations particular care must be taken that the distance from the edge of the camera lucida to the paper is exactly 10 inches, as this is the standard distance of distinct vision with the naked eye. The Micrometers, The following is a description by the late Mr. George Jackson, who was the inventor of this method of using micrometers with the compound microscope : — " In ordinary observation, when no drawing is made, a micrometer in the eyepiece is the readiest method of mea- suring. But here it is obvious that we shall be comparing an enlarged image of the object with the divisions themselves, and not with their enlarged image. It is therefore necessary to ascertain the value of these divisions with each of the object-glasses of the microscope ; or, in other words, to deter- mine the relation which the micrometer in the eyepiece bears to the image of the one on the stage, subject to the same magnifying power that is to be applied to the object to be measured. " Insert the proper micrometer (Plate XXII. fig. 2) in the eyepiece (see fig. 1), and adjust the upper lens (a) by its screw, so as to see the lines clearly when the light comes through the body of the instrument. Place a micrometer 64 THE MICEOMETEES. (fig. 3 or 4), divided into lOOths and lOOOths of an inch, on the stage, adjust the focus, and make the two sets of lines parallel by turning the eyepiece ; then notice how many divisions in the latter correspond to one in the former. Suppose that nineteen and a half cover one-hundredth of an inch (fig. 5, a), by carefully adjusting the length of the draw- tube, the coincidence may be rendered exact at 20 divisions (fig. 5, h). Then, as twenty divisions cover one-hundredth of an inch, 2000 (20 X 100) will cover an inch, and each division will be equal to 1-2 000th of an inch. " In doing this with each object-glass, the draw-tube of the microscope should be so adjusted as to give a number that can be reduced to a decimal fraction by multiplying or di- viding by a single figure ; but if it be preferred to express the dimension by a simple vulgar fraction, we have merely to divide the number of divisions in an inch by the observed number. Thus, if the length of an object be eight divisions of the above scale (8.2000ths), it will be l-250th of an inch, or decimally '004. "A memorandum should be made, in a tabular form, of the value of the eyepiece micrometer with each object-glass, together with the length of the tube drawn out, so that the instrument may be readjusted for measuring without repeating the above operation : thus — Value of each division of Eyepiece Micrometer with the following Ohject-glasses. Amount of tube drawn out, Fraction of Decimal of J®^ "S ^ss. tenths of an inch. an inch. an inch. I 7 -0005 " When moving the lines to their coincidence, the action of the stage will be found rather too quick ; but the most correct adjustment can be made by the small screw (fig. 2, a) attached to the eyepiece micrometer." LEESON'S GONIOMETEE. 65 Indicator. Quekett's indicator (Plate XXII. figs. 9 & 10) is a fine pointer, fitted in the interior of the eyepiece, and capable of being turned in or out of the field of view by means of the small quadrant (fig. 9, «). It answers admirably for the very useful purpose of indicating some particular part of an ob- ject ; and any of the eyepieces can be furnished with it. Double Nose;piece, Brooke's double nosepiece facilitates the change from one object-glass to another, and avoids the loss of time incurred by screwing and unscrewing in the ordinary way. This piece of apparatus (Plate XXII. fig. 14) is attached to the microscope by the screw-piece («); two object-glasses are screwed to the extremities (^, ^), and, by merely rotating the arm [c^ c) on the centre {d)^ either object-glass may be brought into the position for use : a pin {e) in each instance forms a stop to ensure correct centering. Quadruple Nosepiece, We have extended the same principle as that of the foregoing to a quadruple nosepiece (Plate XXII. fig. 13); this is applied to the microscope by a screw-piece, as in the double one ; but the object-glasses are changed in position by drawing the plate (fig. 13, a)^ to which they are screwed, a little forward, to release it from a pin, when it may be turned round, and a slight spring, confined in the top (^), will press the plate home again, when the next object-glass will be only central with the body of the microscope. Leeson's Goniometer. This instrument (Plate XXII. fig. 12) is admirably adapted for measuring the angles of microscopic crystals. It con- 66 MALTWOOD'S EINDEE. sists of a circular divided plate, above which a Biot's double- refracting prism is mounted so as to admit of rotation by means of the arm (A), which also serves as an index-hand. The whole piece of apparatus fits on the eyepiece, to the flange of which it is secured by a pin, which drops into a corresponding hole. When a crystal, or any angle of a crystal, is viewed through the prism of the goniometer, there will appear two images, which may be made to occupy various relative posi- tions by revolving the prism, as shown in the annexed wood- cuts, figs. 1, 2, & 3. Fig. 1. Fig. 2. Fig. 3. ^ Z07 Let y, z be the angle to be measured : hold the arm (Plate XXII. fig. 12, A) at zero, and revolve the prism by the milled ring (B, B) until the lines forming one side of the angle to be measured coincide in both images, as, for instance, the lines ^, x\ 2/' (fig. 2), then move the arm over the graduated circle until the two lines forming the other side of the angle z, y, z' are made to coincide (fig. 3) ; the amount of rotation thus obtained is the measure of the angle, or its complement, according to the direction in which the arm is moved. In- stead of starting from zero, it is of course sufficient to take the difference of the readings in the two positions. Maltwood's Finder, A " finder," as applied to the microscope, is the means of registering the position of any particular object in a slide, so that it may be referred to at a future time, and by any microscopist who possesses the finder. MALTWOOD'S FINDEE. 67 The subject of the best form was very fully discussed in the pages of the ' Quarterly Journal of Microscopical Science amongst the various schemes we selected the fol- lowing, which was proposed by Mr. Maltwood, and it has now become a universal standard of reference. It consists of a glass slide, 8 X inches, with a scale {a) MALTWOOD'S FINDER STOP PHOTOGRAPHED BY 5MITH.BECK&BECK LONDON. True size. occupying one square inch, and consisting of 2500 squares, each of which is separately numbered with a longitude and latitude. The scale is in each instance at an exact distance from the bottom and left-hand end of the glass slide, which, when in use, should rest upon the ledge of the stage of the microscope, and be pushed against a stop at the end ; this stop, which is best as a simple pin, should be about one inch and a half from the centre of the stage, and at a point from the ledge indicated by an arrow upon the finder at h. The object-slide must be placed under the microscope with the same care as the finder ; and when the particular object is in the field of view, remove the object-slide, put the finder in its place, and read the numbers of the square that comes into view ; this may be recorded upon the object- slide ; and to refer to the same object at a future time, the process has only to be reversed, by first finding the particular square of the finder, and then by placing the object-slide in its place. F 2 68 MICEOSCOPE-LAMPS. There is an easy way of recording the numbers by which each square may be subdivided into 5 ; thus : — Supposing the following figure to represent one of the squares ; if the object should be out of the centre of the square, put two lines in addition to the figures, to. indicate the particular corner in a h 24 12 G d [24 , 24l Avhich it occurs ; thus, if it is a, write -|^2, if at ^, -|^2 '