CSfarttBU HMiucrattg ffiibtarg 3tiiaca. Nm IJoth THE CHARLES EDWARD VANCLEEF MEMORIAL LIBRARY BOUGHT WITH THE INCOME OF A FUND GIVEN FOR THE USE OF THE ITHACA DIVISION OF THE CORNELL UNIVERSITY MEDICAL COLLEGE MYNDERSE VANCLEEF CLASS OF 1874 1921 Cornell University Library QH 205.S76 Microscopy:the construction, theory, and 3 1924 003 076 225 Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924003076225 MICROSCOPY MICROSCOPY THE CONSTRUCTION, THEORY AND USE OF THE MICROSCOPE BY EDMUND J. SPITTA L.R.C.P. LoND., M.R.C.S. Enc, F.R.A.S., F.R.M.S. President of the Quekett Microscopical Club Author of Photomicrography, and Joint Author of nAn Jltlas of Bacteriology With 47 Half-tone Reproductions from Original Negati'ves and 241 Text Illustrations NEW YORK E. P. BUTTON AND COMPANY 1907 S7fe ^A^A ' x-3- \4- PRINTED BY HAZELL, WATSON AND VINEY, LD,, LONDON AND AYLESBURY, DEDICATED TO THE COUNCIL AND MEMBERS OF THE QUEKETT MICROSCOPICAL CLUB PREFACE This work, which I bring before the reader with con- siderable diffidence, is the outcome of a wish expressed by several friends that I should make the attempt to write a book upon the Construction, Theory, and Use of the Microscope expressed in the simple language employed in Photomicrography. Two things seemed to encourage me : one was the gratifying way in which the last-mentioned brochure was dealt with by the critic, whose kindness in overlooking its many faults and failings had greatly impressed me ; whilst the other was the fact — which gave me no small pleasure — that so many workers with camera and microscope had expressed themselves with such pronounced generosity as to the utility of its subject- matter. It was further pointed out, as an additional incentive to start upon the work, that a practical book on the Microscope, besides assisting the amateur, might meet a want much felt in the medical and other laboratories, where at present the lecturers and demonstrators have to waste much of their valuable time in teaching students the rudiments of the microscope by word of mouth. It is universally recognised that this knowledge could be acquired just as well from a book if a suitable one existed. Moreover, some went so far as to say that such a handbook might be of even greater service still to those who, in a later period of life, took to viii PREFACE the Microscope as a source of pleasure and profit, or became ; -engaged in original research, but had not received any previous ■training in the scientific use of the instrument ; such persons imight probably be desirous of availing themselves of any help or guidance that would lead them to use their microscope to the greatest possible advantage. To meet these requirements, then, has been the aim of Microscopy. ' As it is desired this work should deal with the subject from beginning to end, it was thought advisable to. devote a small space to explaining the general properties possessed by lenses in general, particularising their employment as hand- magnifiers or as hand-microscopes, whilst to aid more advanced students a full description of the method of testing objectives and condensers has been added. For this purpose special , attention has been paid to the use of the Abbe test-plate, which I believe is not dealt with in any text-book in the ' English language. But, to enable the reader to follow the subject from be- ginning to end intelligently, it has been found necessary to interpolate articles upon what might be called the more recondite problems connected with microscopy, such as the estimation of the magnifying powers of objectives and oculars by the "rational" method, as well as by the system devised by the late Prof. Abbe ; the explanation of what is really meant by the expression Numerical Aperture; upon the art of obtaining and using Oblique Light, with the theory in- volved in so doing ; the importance of the proper use of the Substage Diaphragm ; the selection and special adaptability of objectives of certain focus and numerical aperture for particular purposes, as well as an explanation of the real difference existing between the semi-apochromatic and apochromatic ■combinations. Further, as the Microscope is nowadays the handmaid of so many of the Arts and Sciences, it seemed absolutely imperative to devote a chapter to the assistance PREFACE IX of those about to embark upon particular branches of the subject, showing what are the special requirements attending each case ; for it is very obvious the kind of apparatus demanded, say, by the bacteriological student, would be of an entirely different character from that required by one whose aim was the investigation of the strain in metals, or the details of the molecular arrangements in various kinds of iron and steel ; let alone the special wants of the student of simple pond life or botany, in comparison with one whose aim was the discovery of the final structure of diatoms. Lastly, in consequence of the principles which underlie the formation of the highly magnified microscopical image, more especially when the instrument is dealing with minute objects of periodic structure so small as to be commensurate with the wave-lengths of light, I have thought it would be an omission on my part if no mention were made of so en- grossing and far-reaching a topic. Seeing, however, that the explanation of a difficult problem of this nature, to meet the requirements of the strictly philosophical student, necessarily involved its careful consideration from a purely theoretical standpoint, I have availed myself of the kind assistance of my friend Mr. A. E. Conrady, F.R.A.S., as I felt that his intimate acquaintance with the subject in all its mathematical intricacies would enable him to grapple with and explain it in a far more scientific and philosophical manner than I could hope to do myself I have to thank the opticians in many parts of the world, for having kindly lent me blocks of their manufactures, besides permitting me to examine critically their objectives ; as well as the Scientific Press — the proprietors of my book on Photomicrography — for their permission to use a few excerpts, blocks, or diagrams taken with this distinct acknowledgment from that work. Also I am greatly indebted to Mr. Alfred Dent, of the firm of Dent & Co., for the personal attention he has given to the manufacture of the extra blocks herein X PREFACE contained over and above the few kindly lent by the Scientific Press, to which reference has been naade ; to Messrs. Hazell, Watson & Viney and their executive for the care and trouble they have taken not only throughout the work, but especially in printing the Plates so as to obtain as much from the blocks as possible ; as well as to Mr. John Murray for sparing no expense incurred in this matter. Two debts of gratitude yet remain unacknowledged ; one is to my friend Mr. Conrady, not only for his chapters above mentioned, but also for the trouble he has taken in assisting me with numerous details, as well as for his kindness in reading through a considerable portion of the MS. before its final issue to the Press ; and, lastly, to the Council of the Quekett Microscopical Club in granting me their permission to dedicate this little effort to the "Club." In conclusion I have only to express the hope that, in reading MICROSCOPY, the critic will be kind enough to over- look its many failings, bearing in mind that it is not intended to compete with the highly classical and standard works already written upon the subject, but merely to represent " a special effort to meet a special end." EDMUND J. SPITTA. Hove, 1907. CONTENTS CHAPTER I The different kinds of Lenses enumerated and defined — Their Action upon Rays of Light explained — Snell's Law — The different kinds of Prisms and the Path of Light-rays through them explained — The Angle of Minimum Deviation — A Lens consists of a Series of Prisms — Conjugate Foci— Methods for ascertaining the Focus of a Lens . ... CHAPTER II ^JThe Simple Microscope : Methods of ascertaining the Magnitude of an Image and the Theory upon which such are founded — Varieties of Simple Microscopes by different Opticians 20 ^ CHAPTER III The Compound Microscope : the Mechanical Portion described — English and Continental Models discussed — The various Fine Adjustments, Stages, Auxiliary Stages, and Substage Arrange- ments adopted by different Opticians 32 CHAPTER IV Compound Microscope {continued) : the Optical Portion— Passage of Rays of Light through the same— Objectives and their Correc- tions ; Semi-apochromatic and Apochromatic Constructions dis- cussed, with a Description of the Difference between the " Dry " and " Homogeneous " Systems— The Care of Objectives . . 59 CHAPTER V Numerical Aperture described and fully discussed — How to ascertain the Numerical Aperture of an Objective by the Apertometer and by the Method suggested by Mr. Conrady — Depth of Focus defined and explained 81 Xll CONTENTS CHAPTER VI Eyepieces : Huyghenian & Ramsden : their Construction and the Path of the Light-rays through both the Simple and Compen- sating—The Ramsden Circle discussed and explained — How to ascertain the Diameter of the Emergent Beam issuing through an Eyepiece when employed with Objectives of different Aperture . 104 CHAPTER VII Magnification— The Evaluation of Objectives and Oculars by the Rational and Abbe Methods, and the limits of useful Magnification 1 19 CHAPTER VIII Substage Condensers, their Varieties and the Special Properties of each — Obtaining their Numerical Aperture — Conversion of Numerical Aperture into the " F ratio " — The Aplanatic Cone and how to ascertain its Diameter — The various Foci of Condensers and their suitability for different Objectives — The Substage Dia- phragm, its Abuse and Use 142 CHAPTER IX Methods of Illumination ; the Bull's-eye and Heliostat — Monochro- matic Light, its Uses and how obtained — Various Forms of Dark- ground lUumiriation — Mr. Rheinberg's " Differential Colour Illumi- nation" — Oblique Light, its Theory and Use — Illumination of Opaque Objects — Theory and Use of Polarised Light, its varieties and how they are employed 160 CHAPTER X On the Use of the Microscope — The relative Merits of the Long and Short Tube discussed — Illumination and the Adjustment of the Mirror — Fixing and Removing the Objective — Focussing : Safety Methods of doing the same with "Dry" and "Homogeneous" Systems— Centring the Condenser— Obtaining Critical Light — Making Correction for Thicknesses of Cover-glass — Finding the Specimen with "High" and "Low" Power Objectives — Objective- changers— Centring a Battery of Objectives— Centring a Circular Stage— Reading the Verniers— How to mark positions on Micro- scopical Slides 206 CONTENTS xiii CHAPTER XI PAGE. The Binocular Microscope and Stereoscopic Vision — Difference between Binocular, Stereoscopic, and Pseudoscopic Visions, and how the same are produced 237 CHAPTER XII Measuring Objects with the Microscope, and the Unit of Measurement adopted by the Microscopist— The Metrical and English Systems compared— How to change the One into the Other— Tables for Rapid Use . 245. CHAPTER XIII The Microscope and Objectives suitable for Different Purposes : Botany, Pharmacy, Brewing, Biology, Histology, Pathology, and Bacteriology — Special Forms of Microscopes for Petrology and Metallurgy — Portable Microscopes — Microscopes for Critical Work and the Employment of the Highest Power Objectives — The Distinguishing Uses of Semi-apochromats and Apochromats fully discussed — The Opinions of several "Experts" as to the most Desirable Objectives to purchase when entering upon Different Branches of Microscopy 255, CHAPTER XIV Testing Objectives — Abbe's Test-plate described and Directions how to use it — Test-objects : what to select, what to see in them, and how to obtain the finest results with different objectives . . 33a CHAPTER XV The Undulatory Theory of Light, with especial regard to its Appli- cation to the Theory of Microscopic Vision 382 CHAPTER XVI Theories of Microscopic Vision : Airy-Helmholtz, Abbe, Dr. Altmann : Recent Developments of the Abbe Theory . . . . 397 PAGE xiv CONTENTS CHAPTER XVII Microscopical Accessories, and how to use them . . ■ . 412 CHAPTER XVIII Hints upon correcting several common "Faults" met with in using the Microscope and its Accessories 434 Appendix . ..... ... 445 Index 449 PAGE 2 3 3 3 4 4 S LIST OF TEXT ILLUSTRATIONS For List of Plates see page 471. ■FIGURE 1. Different kinds of Lenses 2. The Centre and Radius of Curvature in a Bi-convex Lens 3- 1, ,, ,, Bi-concave Lens 4. Finding the Optical Centre in a Bi-convex Lens. .5- )> ,, ,, Bi-concave Lens 6- ,, ,, „ Meniscus Lens . 7- >> ,, ,, Crossed Lens 8. Snell's Law 9. Path of an Oblique Ray through a Glass with Parallel Sides 10. Various kinds of Prisms, showing Summit, Refractive Angle, and Base of each 11. Path of Rays through Prism and "Angle of Deviation 12. A Lens consists of a series of Superimposed Prisms 13. Collective Lens converging the Rays to form Focus 14. A Radiant placed at twice the Focus of a Lens forms an Image at twice the Focal Length on the opposite side . 15. Radiant moved further away, causes Focus to approach Lens on the opposite side j6. Parallel Rays forming True Focus of ^ Lens 1 7. C««vergent Light : how dealt with by a Convex Lens . 18. Different Points of Light from an Object not situated on the Axis : how dealt with by a Collective Lens 19. Ascertaining the True Focus of a Lens by making Image and Object the same size 20. Ascertaining the Focus, approximately, in an Apartment 21. „ Magnification of an Object with a Hand Magnifier -22. ,, ,, ,, ,, 123. Looking at the Aerial Image formed by a Convex Lens of an Object placed beyond the Focus 24. The Object within the Focus and the Eye placed in the Emergent Beam 25. Magnification of an Object to the Unaided Eye . 26. The Eye applied to a Lens used as a Simple Magnifier 27. The Case of Two Objects seen at the same distance ; the Ratio of their Apparent Diameter exactly similar to that of their Magnification 26 28. Concerning the best position to which the Eye should be placed with a Simple Microscope 26 13 13 14 16 17 18 21 21 22 23 24 24 XVI LIST OF TEXT ILLUSTRATIONS Dissecting Microscopes Zeiss's Hand Magnifier Mr. Nelson's Hand Magnifier English Model Microscope by Powell & Lealand Latest Continental Model by Zeiss Auxiliary Stages by different Opticians . Substage Arrangements by different Opticians 29. sc- 32- 33- 34- 35- 36- 37- 38- 39- 40. 41. 42. 43- 44- 45- 46. 47- 49- 50. 51- 52. Fine Adjustments by different Opticians 53- 54- 55- 56A&B , 57- 58- , 59A&B , 60. , 61. , 62. , 63. . 64A. Path of Light-rays through a Microscope having an Achromatic Objec tive, Huyghenian Ocular, and Achromatic Condenser 64B. The same through an Apochromatic Objective, Compensating Ocular and an Oil Condenser Spherical Aberration 65 66. „ Correction 67. i7«ai?>'-correction 68. Oz'er-correction 69. Sine-Law .... 70. Fulfilment of the Sine-LaW 71. Non-fulfilment of the Sine-Law 72. Un-achromatic Lens 73. Cfc«»--correction 74. Visual Correction . 75. Achromatising for Green ; a slightly un. corrected ordinary Achromatic PAGEl 28- 28: 29. 30- 31 31 33 34 39^ 39 40 40- 41 42 43 44 4+ 44- 45 45 45 47 48 50 51 52 52 53 54- 54 55 5& 5& 57 58 ♦ 6r 64 65 65 65 66 67 67 68 68 69 69 LIST OF TEXT ILLUSTRATIONS xvii FIGURE PAGE 76. Achromatising for Blue ; an ordinary Photographic Lens ... 70 77. Colour-part of Apochromatic System ; Three Colours united . 72 78A, B, c, D. Explanation of the cause of the Colours perceived when a High-power Semi-apochroraat is employed upon a minute object such as a Diatom, within and outside the Focus 74 79. Dry and Homogeneous Objectives 7S 80. Construction of the Front Lens of a i'30 and a 1*40 N.A. 2-mm. Objec- tive compared. After Zeiss 79 ■81. Mathematical Proof that N.A. of an Objective equals the Semi-Diameter of the Emerging Pencil divided by the equivalent Focus ... 84 .82A. Snell's Law 91 S2B. Passage of the Light in Dry and Homogeneous Objectives ; Use of Immersion Fluid 91 ■83. Abbe's Apertometer 96 ■84A & B. Depth of Focus 100 ■85. Ordinary Huyghenian Eye-piece ; Path of a Monochromatic Ray of Light IDS S6. Passage of Red and Blue Rays through Compensating Huyghenian and Holoscopic Oculars 106 ■87. Path of Monochromatic Ray through an ordinary Ramsden Ocular . 108 •87A. Passage of Red and Blue Rays through a Compensating Ramsden Eyepiece no 88. Colours at Edges of the Diaphragm explained in ordinary Un-achromatic Ocular _ U2 Sg. Colours at Edges of the Diaphragm explained in Achromatic Ocular. 113 90. Over-corrected Eye-lens 113 91. Ramsden Circle nS 92- .. "5 93- .. "6 94- .1 ., "6 •95. Magnification .... 119 96. „ 120 97. Abbe's Imaginary Lens added to the Microscope : Explanation . .132 98. Aplanatic Condenser 148 99. Over-corrected ditto 148 100. Uncorrected ditto 148 loi. Under-corrected ditto 148 102. Iris Frame • iS8 103A & B. Bull's-eye Illuminators 163 104. 16 J05. Bull's-eye Illuminator and Lamp combined 165 106. Dr. Johnstone Stoney's Heliostat 166 J07. The Author's Monochromatic Light Arrangement. After Baker . . 168 108. Wenham's Paraboloid I74 109. Passage of Rays of Light through a High-power Condenser when Oblique Light is used 178 no. Diagrammatic Representation of Direct and Spectral Beams as seen at the Back Lens of an N.A. I '40 Objective, with Pleurosigma angulatum on the Stage 180 III. Oblique Light 181 XVIU LIST OF TEXT ILLUSTRATIONS FIGURE 112. Oblique Light - 114- " -.' 115- ii6. „ 117. 118. 119. 120. 121. 122. Use of Vernier Binocular Microscope. After Swift Wenham's Prism .... Zeiss's New Form of Binocular Microscope Abbe's Stereoscopic Eyepiece Powell's Binocular Prism Spider-line Micrometer. After Walson . The Metre, Millimetre, Micron, Double Mu, and the their relative values graphically explained Botanical Microscope Plantation Microscope Microscope for Pharmacy and Histological purposes Swinging Substage, if required .... Microscope for Pharmacy and Histology Diagrammatic Representation of Oblique Light Arrangement (in plan) of One Method of Illuminating Opaque Objects „ „ Second „ ,, „ „ „ Third „ „ ,, Fourth „ , „ „ Beck's Vertical Illuminator 123A & B. Zeiss's Vertical Illuminator 124. Polarised Light ... 125. Nicol's Prism . . ... 126. Polarised Light; Parallel and Crossed Planes 127. Arrangement of Microscope for using Convergent Polarised Light to show " Rings " and " Brushes " . . ... 128. Zeiss's Objective-changers . . .... 129. "Facility" Changer by Watson & Sons .... 130. Eye-shade .... 131. Setting a Circular Stage in Alignment with the Optical Axis 132. ,, >, » » " 133' 134- 135- 136. 137- 138. 139- 140. 141. 142. 143- 144. 145. 146. 147. 148. 149. 150. 151- 152. 153- «54- 155- 156. 157- 158. 159- Tenth Metre Medical Microscope PAGE 181 l8^ 182: 183 184. 185 18^ 191 192 193- 193 194. 196- 197 200 204. 225 228 229> 231 231 232- 232 234 23s 238 239- 241 24Z 244 245- 251 255 256 257 25& 25^ 261 261 262 263 264. 268 269 270 271 272 275 LIST OF TEXT ILLUSTRATIONS XIX 1 60. 161. 162. 163. 164. 16S. 166. 167. 168. 169. 1 70 A 171. 172. 173- 174. 175- 176. 176A, 177. 177A. 178. 178A. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192A. 192B. 193- 194. I9S- 196. 197. 198. 199. 200. 201. 202. 203. 204- Medical Microscope Petrological Microscope »» n Metallurgical Microscope & B. „ Hand Microscope . Portable Microscope Microscope' for Critical Work Abbe's Test-plate Diagram to show Folding-over Points of Spectrum with Corrections .... Nature of Light-vibrations Combination of two Waves, nearly in the same Phase „ „ opposed to each other in Phases „ ,, of Different Wave-length Formation of Diffracted Light Illustrating Phase-reversal Airy's Limit of Resolution applied to the Microscope Isolation of the Direct Light passing through a Point A Metal Holder for the Metallurgist Dr. Detto's Modified Auxiliary Stage by Zeiss . Mr. Traviss's Expanding Central Stop . Stead's Illuminator Zeiss's "Verant" A New Vertical Illuminator by Leitz . „ Watson & Sons different 275 276 277 278 284 286 288 290 293 29s 298 299 301 302 303 304 305 306 307 308 309 310 313 314 31S 316 317 319 320 321 322 333 334 341 383 387 388 389 393 395 398 402 412 413 415 416 416 417 417 XX LIST OF TEXT ILLUSTRATIONS riGURE 205. Zeiss Stage Screw Micrometer 206. Kingsford's Troughs 207. Camera for Fixing on the Microscope 208. 209. 210. 211. 212. 213. 214. 215. Davis Diaphragm .... Cover-glass Marker .... Indicator Eyepiece .... Spectroscopic Ocular ,, ,, Interior of Drum Wright's Eikonometer Relations between Object and Image PAGE 41-8 420 421 421 423 424 425 426 427 432 446 THE MICROSCOPE 7 CHAPTER I INTRODUCTORY The word Microscope, derived from two Greek words fUKpo'i (small) and a-Koiria (to see), is the name of an instrument that magnifies an object. Microscopes are of two kinds — simple and compound. The former consists of one or more glass " lenses " fixed into a suitable wooden or other handle ; whilst the latter is composed of one " lens " or set of " lenses " called the Objective, sur- mounted by another set named the Ocular or Eyepiece. The two arrangements are mechanically held in association, although distinctly apart, by a tube which in its turn is attached to a conveniently designed metallic adjustable support called " the stand." The word " lens " above used calls for an immediate explana- tion, hence it will be advisable before proceeding further to explain the meaning of the term and to name and describe the several varieties. A lens is the name given to a piece of glass or other trans- parent medium — usually circular in form — having its two faces ground and polished in a specific manner, which imparts to it the property of causing rays of light after passing through to converge together or diverge apart. The curves on these faces may be spherical, cylindrical, or of a parabolic nature, but it is only with the first type that the microscopist has to deal. The combination of a spherical surface on one side with another on the other, or with a face that is plane, gives rise to eight different kinds of lenses. These are shown in Fig. i. The first is a double or bi-convex, because the convex curve on each side is similar ; the second is a plano-convex, one side I 2 DIFFERENT FORMS OF LENSES being plane and the other convex ; whilst the third, having a convex surface on one side and a concave on the other, the former of which is the more pronounced, is called a convexo-concave or converging meniscus. The fourth, with both sides concave, is termed a double or bi-concave ; the fifth a plano-concave ; the sixth a diverging meniscus or concavo-convex, because the ruling curve is a concave one ; the seventh a crossed convex, because although both surfaces are convex they are of different curvature ; and the eighth a crossed concave, as each surface is concave although of dissimilar curvature. It should be noticed that numbers i, 2, 3 and 7 are all thicker at their centres, whereas 4, 5, 6 and 8 are all thinner. The former are all termed in a general way convex, positive, or collective lenses. 5 Fig. I. 8 as they will be shown to gather and converge rays of light to form a real image of the object, i.e. one which can be received on a screen ; whereas the latter are collectively known as concave, negative, or diverging lenses, because rays falling upon them are diverged or dispersed and so do not form real images. In the description that follows the double convex and the double concave are only considered, as the properties possessed by these two types apply equally to the remainder, which differ from them |only by the degree and nature of certain defects called aberrations. The curves of a lens are described from given centres, each being called the " centre of curvature," and the radius of such circle, of which the curve is an arc, is called the " radius of curvature." The line joining such centres passing through the body of the lens is called its axis, or the " principal axis of the FINDING OPTICAL CENTRE lens." Moreover, every lens has what is termed its " optical centre," often simply termed the " centre of the lens." It is about these we now speak. In Figs. 2 and 3 let L be the lens, a bi-convex in the first case Axial '""'"'T,- -ee- Fig. 2. and a bi-concave in the second, and A A' the axis. CC is the centre of curvature for one curve and C'C for that of the other ; A CC V -ec — A Fig. 3- CC joined to C or C'C to C illustrates a radius of curvature in each case. A— £ To find the optical centre of a bi-convex lens, consider Fig. 4. AA' is the axis, and C.' and C" the centres of curvature for the two 4 FINDING OPTICAL CENTRE curves. Take any radius of curvature CD' and another C"D". They must be drawn parallel to each other. Join D' and D". Where this line cuts the axis AA', is the optical centre required. With a bi-concave lens, as in Fig. 5, the same proceeding furnishes the position required. In the case of either form of meniscus the optical centre lies outside the lens. Let Fig. 6 be considered. C and C" are the centres of curvature for the two surfaces. If such points as D' and D" be found and the line joining them produced, they meet the axis AA' at O, which is the optical centre sought after. With a crossed lens, Fig. 7, C and C" being again the centres of curvature and CD' and C"D" the radii of curvature, the line joining D' and D" cuts the axis within the lens, but in a different situation from that in the case of the double-convex. The optical centre, then, in crossed lenses, whether convex or INTRODUCTORY REMARKS ON LIGHT s concave, varies its situation very much according to the curves of the two faces. - Optical Centre Before explaining the passage of light-rays through different lenses, showing how in one case the beams are bent differently from those in another, it will be necessary for the context to be intelligibly followed to make a few introductory remarks upon the subject of light in general, and upon refraction in particular ; but the reader must not expect in what immediately follows to find the matter treated in a rigidly mathematical manner, for that is given in another part of this work, but rather in as simple a way as possible. The rays issuing from an illuminant, assumed to be of small size, naturally divtrge in all directions from that point ; but if we consider the light falling upon a comparatively small object from a very distant illuminant such as the sun, the divergence is so infinitesimal that we may safely regard such light as consisting of parallel rays. It may just be remarked here, that converging light does not exist in nature : it can only be obtained by refraction or reflection, and to some extent by diffraction, but this matter will be referred to later on. The path of any ray in a given medium is always straight until the beam or pencil meets with another medium more or less dense than itself, when, with one exception noted hereafter, it is bent aside, undergoing what is called refraction ; after such bending, however, it will again resume its rectilinear propagation along its new path, until it meets with a fresh medium, when on entrance it will be bent again if the density of such medium be 7n' 6 SHELL'S LAW different. Change of density, then, o/t/te medium is the cause of refraction, and this should be held in mind. It will be of advantage now to point out briefly the nature of this alteration of direction brought about by the change of medium, and for purposes of description to have resort to Fig. 8 Let ABCD be a vessel containing water and AC the water line ; BD, the Normal, is drawn at right angles to AC, cutting it at E. All angles are referred to this line. When the beam is incident along B and E perpendicularly into the new medium there is no refraction — the only instance referred to when it undergoes no bending — for it passes on into the water, uninterruptedly following the course of the line ED. But when it is incident at any other position — say at m along 7«E — there is refraction at E, for the beam will be found to strike the point n. Suppose it is incident at m' along w/E, then there is also re- fraction at E, for the ray will be found at n . Snell made a celebrated investigation concerning this bending of the rays, by which their path can always be predicted. Were it not for his discovery, about to be explained^ we should not have had the grand computation of lenses with which, in the present day, we are all so familiar. He first drew a line from m to meet BE at right angles at o, and another from n meeting ED at/. The lengths om and np were measured and divided, the greater by the less, and a quotient obtained. Now what he discovered was the fact that, wherever the angles were taken, whether from m or in\ the quotients — in all cases using air and water — came out the same, viz. i"333. This he called the refractive index of water. Other substances were substituted for the water, and each substance he found had its special refractive index. Flint glass, for example, was found to be about i'S4 to i'64, according to its manufacture, and so on with the other substances, complete lists being found in all books upon the subject. If the reader SNELL'S LAW 7 be mathematically inclined, he will at once see these lines, mo, np, really represent the sines of the angles BE»« and %E/ respectively, so that, continuing our precept, the sines bear a certain definite ratio one with the other wherever the incident light striking E may come from ; that is, the ratio between om and np, which is about as 4 is to 3, holds good, whether the ray starts from m or «'. It is quite evident now that we can calculate where the ray will strike the arc AD, after starting from any given point in BC. For example, let m strike E to make an angle tn^o, say, of 45°. It is required to find the angle ti^p, so that we can draw %E correctly. We take out of the oi;dinary tables the natural sine of 45°, and find, roughly speaking, it is 07, and multiplying that by 3 and dividing by 4 gives us 0-5. Resorting once more to our tables, we find 0-5 is the sine of 30°, so that 30° must be marked off from D to find the position of the line nY.. Although simply put, this is the idea that mainly pervades the computer's mind in con- structing new lenses. As a matter of fact, the details become exceedingly operose in real calculations, as different colours are refracted at different angles ; and so the problem, where many lenses are concerned, becomes intensely intricate. But the law underlying these calculations is the same from beginning to end. The same law — reversed, of course — holds good when rays pass from the water into air, and when passing from one kind of glass to another, although then with certain modifications which need not here be mentioned. One more remark. Seeing that n', passing to E, becomes refracted to m', what will happen to a ray starting, say, at x ? It will pass into the air and graze along EC. If this be true, what will take place if one starts still nearer A, say at ^■P This ray cannot get out of the water at all, and so is said to suffer " total reflexion " at E, for it appears again at Z'. There is one angle, then, it is very evident, which is the last, that allows a ray to get out ; this is called the '' critical " or " limiting angle," and is known for all kinds of glass. We have seen, then, the first point to notice is that the path of the ray is largely affected by the density of the glass employed in the manufacture of the lens.^ ' The substance of this paragraph and the diagram are taken from the author's Photomicrography, with the kind permission of the Scientific Press. 8 GLASS WITH PARALLEL SIDES If a ray passes in the direction of the normal upon the surface of a piece of glass having parallel sides, it continues its course uninterruptedly just as it did in the case of the water ; but if the ray be incident at any angle — say as in Fig. 9 — it is bent by the glass towards the normal NN, because it is entering a medium that is denser than air. The amount of bending of course varies with the refractive index of the vitreous compound. But the emerging beam on leaving the glass is bent this time away from the normal, because it is entering the air, a medium less dense. As it quits the glass then to re-enter the air, the same medium in which it started, so it is bent back again the same amount in the opposite direction as it was deviated in the glass ; hence the incident and emerging rays are parallel, although not in direct continuation one with the other in a straight line. If, instead of emerging into the air, it had entered another piece of glass, or other medium oi different density, its direction would have been changed directly in accordance with the change of index of refraction of the new medium. When, however, the glass has not parallel sides, but is in the form of what is called a prism, the conditions being modified, the results are not similar. A prism may be defined optically as a transparent medium contained between limiting surfaces which meet together at one end, forming what is called the summit of the prism, the separated ends below being joined together by a boundary called the base of the prism. The angle enclosed by the two sides that meet to form the summit is termed the refractive angle. EFFECT PRODUCED BY PRISMS 9 Fig. 10 shows three kinds of prisms, and the summit, base, and refractive angle of each. When the refractive index of the medium composing the prism is known, and the normal drawn, the path of the ray can be struck as previously shown. Let ABC in Fig. 11 be a prism, OD the incident beam, and the dotted lines at D and K normals to the respective surfaces with which they are in contact. The incident ray OD, on entering . SunniT A""~" — Summit >v A_ , .\- RiFRACTivE Angle-- /..\- -Refractive Amsle--/ "^..^'X i- ( i Base * i-- Base f • N Fig. 10. the glass, is bent towards the normal, because it is entering a denser medium, its path being shown as DK. On leaving the surface AC, it is bent away from the normal in the direction KH, because it is entering a medium of rarer density. If the eye be placed at H, the ray appears to come from O', so the object O appears in that situation. It should be noticed that in this case the ray has been twice bent in the same direction, so that it is turned towards the base of the prism ; hence it should A Summit a Normal \ , 1 Angle of Deviation ^ ■' Normal ^0 c bASC B Fig. II. be borne in mind that objects seen through a prism appear shifted towards its summit. The angle O'EO is called the angle of deviation. As a matter of fact, objects under these conditions are seen in all colours of the rainbow, constituting the phenomenon called the dispersion of light; but of this subject we speak no more at present, although its effect is discussed later, when the 10 PRISMATIC CONSTRUCTION OF LENS construction of objectives for the compound microscope is being dealt with. In discovering the path of the rays passing through different portions of a lens, it is legitimate to consider such as being made up of a series of superimposed prisms, as shown in Fig. 12, bearing in mind that, with a positive lens, the summit of each prism is directed towards the periphery of the lens ; but in the case of a dispersive or negative one, the summit is turned in the opposite direction : in other words, the base is turned towards the periphery. Further, it is legitimate, when computing the exact path of the ray, to consider the number of these prisms as infinite, and only consisting theoretically of the actual strip N "^'J f^ "^^ ^^~~~~^ --..^X;^^^^ n N / "^"^■X"""""^ V \"^>s III N r^ ^ZTTV" --4 / Axis Ax>T"~~"-"~^:<^, Centre ofCudvaturl Fig. 12. of glass occupied by the ray in question. Each little prism may also be said to possess its plane surface coinciding with » and constituting the lens surface itself — both being one and the same thing — so that the curved lens front may be analytically considered as consisting of an aggregation of an infinite number of plane surfaces of infinitely small size. A line drawn perpen- dicular to any of these theoretical planes is called its Normal. But little further consideration will suffice now to show that all or any of these normals, N', N", N,'" in Fig. 12, for example, when produced will take the path of the radius of curvature, and so arrive together to meet at the centre of curvature. Collective lenses, it has been stated, converge the rays falling upon one side to form an image of the object on the other THE FOCUS OF A LENS ii (Fig- 13)- This position, where the image is formed, is called the " plane of focus," the act of making the rays form the image on the suitably placed screen, " focussing the object," and the distance (when the incident rays are parallel) this plane is from the optical centre of the lens, the " focus of the lens.'' Negative lenses, we have already stated, are dispersive, and so cannot form a focus of an image ; hence it may seem very illogical to at once state they are differentiated one from the other and designated by the same nomenclature as positive lenses which do form an image. But the phrase focus of a negative lens has a conventional meaning, for it is meant to imply that such a lens — say we speak of a 2-in. negative — has the property of neutralising the collective power of a Fig- 13- 2-in. positive lens} If, therefore, a 2-in. negative and a 2-in. positive be placed in juxtaposition, and an object looked at through them, it is neither magnified nor diminished, for the two lenses act just the same as if they were one piece of glass with parallel sides. This fact is taken advantage of by the practical optician. If he has an unknown negative lens, and he desires to ascertain its focus, he keeps trying several positives with it until, when looking through both lenses at an object, such object ceases to " shake," as it is called, when he moves the lenses. When this result is obtained, he knows he has neutralised the negative, and the focus of the positive lens necessary for this purpose is called Xh.'S. focus of the negative. The same ' Really, the same definition covers foci of positive as well as negative lenses, if a " virtual " focus be accepted for the concave. The term " virtual" is explained hereafter. 12 OBJECT AND IMAGE DISTANCES can be done with an unknown positive by using a set of negatives of known foci. In describing the rays entering and leaving a lens it is con- venient to know which are being spoken of. Rays isXYmgupon a lens are called incident or affluent, while those quitting it are termed emergent or effluent. Rays that become closer and closer together as they advance are called "converging," and those which separate further and further apart are designated " diverging." Rays that run side by side without diverging or converging are called " parallel." With respect to a convex lens, when incident rays from a pencil further away than its focus have traversed it, they emerge convergent. But when rays have passed through a concave Fig. 14. lens they leave it divergent, or — in the case of light entering strongly convergent — with diminished convergence. The emerging rays from a convex lens converge, in most instances, it has been said, to form an image at the focus, but as the distance from the optical centre of the lens at which this image is formed varies with the position of the object — or radiant or luminant, as it is sometimes called — it will be well to explain in detail the relation which exists between the object and its image. If a radiant R be placed at a given distance — for convenience of description let it be said in the first instance now under consideration to be equal to twice the focal length of the lens — an image will be formed on the other side of the lens at twice its focal length. This is shown in Fig. 14, where the distance of R to the optical centre equals that from I to the centre. The distance, then, from R to I is equal to four times the focal length TRUE FOCUS OF A LENS 13 of the lens. If R be now moved further away from the lens C, as in Fig. 15, I becomes proportionately nearer to it. If R be moved still further away, I draws nearer still to C than before, and so on until R be placed so far away that the rays coming from it are parallel as in Fig. 16. The position now occupied by I under these conditions is said to be that of iying in the true focus of the lens. Because it is hardly possible to place R at a sufficient distance for the rays to be truly parallel, so the sun or the moon or the stars are usually selected, as their rays may be called sensibly parallel : hence the true focus of a lens is often spoken of as " the solar focus." Seeing the positions of R and I are theoretically interchangeable, if the radiant be placed at the focus I the rays issue parallel on Parallel Rays True Focus Fig. 16. the other side. Hence a rule may be stated, " That if a radiant be placed in the 'principal focus ' of a lens, parallel rays issue from it on the other side!' But in the preceding diagrams. Figs. 14 and 15, where neither rays are parallel, and seeing that the radiant and image are interchangeable, the foci on each side bear a certain relation one to the other, for as one increases 14 TRUE FOCUS OF A LENS the other diminishes, and vice versa ; hence they are spoken of as the conjugate foci of the lens.^ We have now discussed how a convex lens deals with rays that are ^/verging, and also the effect it produces on those from a radiant placed at so great a distance that the individual beams are parallel, as in the case of sunlight. It remains yet to be shown what effect it has upon beams that are "• ""om the It should be mentioned that when U is greater than / V is negative EFFECT OF CONVERGENT RAYS 15 had the rays been parallel that fell upon it, for they would of course have focussed somewhere near F. This change, it should be understood, is entirely brought about by the convergency of the beams in question. Hence as a rule to recollect, " When converging rays fall upon a convex lens itfocusses them at a plane which lies within its true focus!' We may further just remind the reader, if a radiant were placed at I (within the true focus) the rays issuing from C would be a^/vergent instead of parallel, as would obtain had it been placed at F, the true focus. It can readily be inferred from what has been said how great changes can be effected in the path of rays by combina- tions of lenses associated in this manner, and moreover how such can be additionally modified by the distance the com- ponents are apart. It is on this account, in the manufacturing of lens-systems, the optician has to be so careful all the components shall occupy precisely their exact relative position one with the other that are set forth in the computer's formula. The following five principles may now be tabulated : 1. When parallel rays enter a collective lens they are united in a focus at a certain distance from it on the other side, such distance being called "the true focus" of the lens. 2. Conversely, if a radiant be placed at the true focus of a lens, parallel light issues on the other side. 3. Rays falling upon a collective lens in a ^zVerging manner, within certain limits leave it in a converging manner to form a focus of the radiant. 4. Rays falling in convergency leave it with greater conver- gency still, to form a focus which lies within the true focus. 5. If a radiant be placed within the true focus of a lens the rays leave it in a diverging manner, although to a less degree than those incident upon it. So far the radiant has been mostly depicted as a point of light and usually situated on the axis of the lens ; it remains now to be shown what happens when the object is one of (as in this case), so the image is said to lie on the opposite side of the lens to that of the object ; when, however, V is less than/, V is positive, so the image is on the same side as the object (to be hereafter explained). The magnification, it may be stated, of the image to that of the object is as V is to U — hence in the above case the amplification is 50 diameters. i6 SECONDARY AXES sensible area. Not much difficulty should be here experienced when it is recollected that a self-luminous object of sensible size is nothing but an aggregation of self-luminous points. There is this which is new, however : these points in this case are not all situated on the axis of the lens, hence their paths should be indicated to clear the reader's mind. Let Fig. i8 be considered, the arrow BC being an object of sensible diameter and AA' the axis of the lens L. The rays from B of course radiate in all directions as from any other point, and those that fall upon and are collected by L pass through it, being bent to focus and form an image at b as indicated in the figure. Those from C focus at c to form that part of the arrow, whilst the rays issuing from other points of BC are cast (although not shown in the diagram for clearness of rendering) Fig. i8. in their respective positions to fill up the gap between b and c. It is obvious now that the image becomes inverted to that of the object. Were the image and object changed— the one for the other— the same explanation would hold good and the object would be inverted just the same. If the object be further from the lens than its image, the latter is smaller than the object, whilst if the former be nearer than its image, the latter is greater. This is easily understood as the natural results of the working of the conjugates. It should be noted for convenience of future reference thaj: the entire system of rays issuing from, say, B or C, or both, are not always shown in a diagram because of complicating it, so that it is not uncommon to represent the whole mass of rays by simply drawing their axes, such as B^ or Qc, which materially lessens the number of lines in a figure and yet furnishes all that is really required. Such axes are called "the secondary axes ASCERTAINING FOCUS OF A LENS 17 of the lens." The matter is merely referred to here as such figures have often been known to puzzle considerably the beginner unacquainted with the subject. To ascertain the true focus of a lens, it is only necessary to throw the image of the sun (which means the use of parallel rays) upon a screen suitably placed, and to measure the distance of such image plane from the optical centre of the lens. As, however, it is not easy at all times to locate, for the purpose of such measurement, this centre, it may be necessary to adopt another method which does not necessitate knowing its position at all. It is based on the fact already mentioned that if an object be focussed on a screen by the lens in question so that the image shall have exactly the same size as the original, the distance between object and image is exactly four times that of the focus, so that dividing the distance by four furnishes the exact focus without having anything to do with the optical centre of the lens at all.^ See Fig. 19. Imacc /\ Objut True Focua for I I True Focus for Parallel Rays \ / Parallel Ravk Fig. 19. AB, BL, LC, and CD are all equal, and BL and LC the true foci of lens, therefore each is one-quarter length AD, so AD divided by 4 equals the true focus of lens. This can only be accomplished if the image A is exactly the size of the object D. Occasions, however, may occur when it is desired to learn hastily, approximately anyhow, the focus of a convex lens, the sun or moon perhaps being absent, and the means for carrying out the equalisation of image and object not at hand. The following is then useful. A radiant is placed at the end of the apartment and its image cast on a piece of paper pinned to ' Although we have stated this positively, still it should be borne in mind that the distance between object and image is tiot mathematically four times the focus ; it differs from that by the distance between the two cardinal points. For further information the reader is referred to text-books upon Optics, as it would seem beyond the scope of this work to enter into the subject at greater length. See Appendix. 2 i8 ASCERTAINING FOCUS OF A LENS the wall at the other and opposite end, as in Fig. 20. The exact distance between paper and lens centre is taken, and between radiant and centre also. Let L equal to ^2 in.. be the Rasiaht at CHD or Been Fig. 20. latter, and / equal to 3 in. the former. The true focus / then can be found by solving the simple formula following : /■= / - ^ = 3 - A = 3 - J = 2j in. It is obvious why this reduction of / is necessary, when it is recollected that as one conjugate lessens, the other increases ; hence as the rays coming from the end of the room cannot be parallel (because they are not far distant enough), so the conju- gate on the other side must necessarily be a little longer than the true focus ; this the formula rectifies by showing how much it has to be reduced.^ Sometimes, however, it is not easy to ascertain the distance of the object from the lens centre. In this case the differences in magnification of image and object are utilised in the following manner. An illuminated glass scale is placed just beyond the focus F of the lens on one side, and a screen on the other, in such a position as to receive a portion of the scale greatly magnified. Let / be the length of a given part of the scale, L the length of the same portion as seen on the screen in the magnified image, and d the distance of the screen from the lens centre. Thenthe true focus is found by solving the following : I f = d / + L' ' This formula is very closely accurate if the focus is short compared to the available distance ; if however it be long, then the absolutely rigorous expression /= = — ;— had better be substituted. The difference in the above example, however, is only '005 in. ASCERTAINING FOCUS OF A LENS 19 There is yet another method of obtaining the true focus, and that is by the use of a collimator. This is an instrument constructed to produce parallel rays artificially. An object glass is fixed at one end of a tube, and a piece of ground glass at the other, in such a position that the sun is sharply focussed upon it. The ground glass removed, its position is occupied by a slit of very small dimensions in a piece of brass, which otherwise covers up this end of the tube. If, now, a light be placed immediately behind the slit, parallel rays will issue from the lens, as the radiant has been placed at the focus on the other side. With these rays the true focus of the lens can be found just in the same manner as if the radiant had been the sun, and the actual focus thus obtained is the real one. The focus of a negative lens is often obtained by finding what positive it will neutralise ; the focus of the positive that fulfils this condition is said to be that of the negative. Another method, especially convenient when positive lenses are not at hand, is to let sunlight fall on the negative, and ascertain at what distance it must be placed from the screen for the circle of diffused light to be twice the diameter of the lens in question. This distance is the equivalent focus. A convenient plan to carry out this method is to measure first the diameter of the negative, and then draw a circle on a piece of white paper with a diameter twice as large. Now hold the negative at different distances until the diffused light exactly fills this circle : the distance fulfilling this condition is the focus required. CHAPTER II THE SIMPLE MICROSCOPE The simple microscope is of two kinds, the common magnifying glass and the hand magnifier. The former usually consists of a single bi-convex, a crossed convex, or a plano-convex lens ; but in its best form it is composed of two glasses adjusted to correct certain aberrations inherent in all single lenses. The hand magnifier is of higher amplifying power, and has been brought to great perfection in recent years both by English and Foreign opticians. In its best form it always consists of two, and very often of three lenses of suitably chosen glasses to secure the finest results. Its magnifying power usually varies from five to twenty diameters. With this class of microscope it often happens that its mag- nification is required to be known. Although such information is usually afforded by the optician, still it may be desirable for the user of the lens to be able to verify the same for himself. This may easily be done in the following manner : A small piece of a foot-rule — a mere fragment will do — is fixed on a suitable support, and the magnifier placed in the position that yields the best focus of this fragment when the eye is placed as near the lens as possible.^ A complete foot- rule is then examined with the naked eye, and the distance at which it is best seen carefully noted. This distance is tech- nically known as the observer's " distance of distinct vision." It may vary from S in. with a short-sighted person to 20 in. or more with a long-sighted one. The distance for the so-called normal eye is usually said to be that of lo in. or 250 mm. The complete rule is then fixed up so that when one eye is looking through the magnifier at the fragment, the ' How to ascertain the best position theoretically at which to place the eye is given later on. 20 ASCERTAINING MAGNIFYING POWER 21 other eye sees the complete rule. Each object then may be said to be at the distance of distinct vision, one for one eye and one for the other. This is rudely shown in plan in Fig. 21. A rule: Left Eye = FRAGMEriT 5HARR.Y Fbcusseo BY ^^ Lems to be Tested O^f-^ WITH THE RiotiT Eye Fig. 21. little practice is here necessary, for the mind must accustom itself to recognise both images superimposed one on the other at the same moment. As an example, let half an inch of the fragment be the chosen unit of measurement, using, say, the right eye, whilst the left is locking at the complete rule. The I I'l I I I I I I E I I I I I I 1I I I I I I I 1 *1 I I T <;«'• The complete pule mot cmtibelt €| i snewn as viewed BY LEfT EYE TMCrRAOMCTfT FOcuiSEP BY THE Ltrl& U VIEWED 6Y RIOMT Ere. /i INCH OF rffAGMcnT E4)u*LLma 2^ rMcrtes of emtirc itule Fig. 22. eyes and images must now be so regulated that the magnified fragment lies on the complete rule, as it is attempted to show in Fig. 22. There it will be seen that haJI" an inch of the rule 22 THE SIMPLE MICROSCOPE fragment is so magnified as to apparently cover from i|^ to 4 of the scale of the complete rule, which means a magnification of 5 diameters as the half inch appears to cover 5 half inches. We say, then, that the magnifier amplifies 5 diameters. This method has only one drawback, that different results are obtained according to the observer's " distance of distinct vision"; for it is obvious, if this be at 5 instead of at 10 in., the result will be dissimilar from that of the long-sighted with a 20-in. distance of distinct vision. From this it is evident, in the evaluation of different lenses, no end of confusion would arise according to the distance of distinct vision of each observer ! To avoid this, the magnifying power of all lenses is estimated by using a normal distance of distinct vision of 10 in., the short-sighted recollecting the lens will magnify less to him, and the long-sighted bearing in mind it will magnify more for him. How the difference is easily ascertained and Fig. 23. corrected will be given later on, for it will be convenient first to show and explain how magnification is produced in the simple microscope. No mention hitherto has been made as to what the eye perceives if it be placed in the path of the emergent beam ' coming from a convex lens. First let a lens focus the image of an object OO, Fig. 23, placed at a point beyond its focus F, as at SS. If the eye were placed there, nothing would be seen but a confused mass of light ; but if the head were withdrawn to S'S' — provided the distance S'S' to SS were equal to the observer's distance of distinct vision — the eye would at once see the inverted imao-e of the object, the arrow, much reduced in size, being suspended, as it were, in the air. If, however, the object be placed within the focus of the lens instead of without it, and the eye be placed in the emerging beam, the observer will very readily find a position close to the lens where an image of the object VIRTUAL IMAGE 23 appears to his eye erect and magnified, and which seems to He on the same side of the lens as the object, although at a certain distance beyond it. In Fig. 24, let 00 be the object placed within the focus F of L the lens ; ^ the rays coming from O and O are shown passing through the lens and re-issuing the other side to fall on the pupil of the observer's eye. Tracing these backwards through the lens, as shown by the dotted lines, they reach O' and O', forming the image O'O' as if in that situation which is obviously magnified and erect. The distance from the eye at which this image is apparently formed is that of the distance of distinct vision of the observer. The image, however, is not a real one and cannot be received on a screen, but is mental, and so would not form an image on a photographic plate or upon a screen placed in the position O'O' as indicated. For this reason -*f^ O' Fig. 24. the image is called a virtual one, and the distance from the lens at which it appears is called the virtual focus. From what has been said the following deductions may be enunciated : 1. When an object is placed before a convex lens, at a point without the focus, an inverted image is formed on the other side of the lens by the emerging rays. Such image is real, and can be photographed or seen when cast upon a screen. 2. When the object is placed within the focus no real image is formed at all — that is to say, no image is formed that can be shown on a screen ; but if the eye be placed in the emerging beams, an image which is erect and magnified can be seen as if on the same side of the lens as the object, projected, as it were, at the distance of distinct vision of the observer, but which, being mental and not actual, is called virtual, and can only be ' For clearness of rendering F is placed farther away from 00 than it should be. 24 THE SIMPLE MICROSCOPE photographed by the use of auxiliary lenses, a matter which, for the present purpose in hand, need not be considered. These remarks have been made in as simple a form as possible, but to those who desire to enter more fully still into the subject, the following may be welcome, which is explained in somewhat different manner : It should be first stated that the apparent magnification of an object to the unaided eye depends upon the angle it subtends to the observer. Thus in Fig. 25 let AB be the object and O the observer's eye; the apparent magnification, then, of the object is the angle AOB contained by the two visual rays drawn from the centre of the pupil to the extreme ends of the object. But if the same object be now placed at ab, the angle aOb is evidently greater, and so the object is said to be larger. To the eye which is applied to a lens, as in a form, say, of the simple microscope, the apparent magnification of the object Fig. 26, is the ratio of the diameter of the virtual image to that of the real object, both being at the distance of distinct vision as already explained. To make this quite intelligible, let Fig. 26 be considered. AB is again the object, and A'B' the virtual image As A«' and B<5' are drawn parallel to the axis A"A", so a'b' is equal to AB. The magnification, then, is evidently equal to the angle A'OB' divided by the angle a'Ob\ or the length of A'B' divided THE SIMPLE MICROSCOPE 25 by that of a'b', or A'B' divided by AB. As the angle A'OB' evidently equals AOB, so A'B' bears the same relation to AB as DO does to CO. But DO is very approximately the distance of distinct vision and CO nearly equals FO, the focus of the lens ; therefore the magnification practically equals the ratio of the distance of distinct vision to the focal length of the lens. Of course the magnification becomes greater as the focal length of the lens becomes smaller, and at the same time becomes greater as the distance of distinct vision becomes increased.^ From the foregoing, two more enunciations may be made : 1. That when the same object is seen at unequal distances the apparent diameters vary inversely as the distances, so that the same object at twice the distance is seen at half the size. 2. That in the case of two objects seen at the same distance the ratio of their apparent diameter is exactly similar to that of their magnifications.^ It has been previously mentioned, in seeking the measure of the magnification of a simple microscope, that the object should be situated within the focus in a position that furnishes the best vision to the eye when placed as near as possible to the lens. It was then stated that the actual position furnishing the best results could be computed. The following is the method, when desired, of so doing : ' A word about the angles subtended by objects might not here be out of place, for the want of a better situation for mentioning the same. It is that in using optical instruments, the angles met with and dealt with are usually so small the arcs which measure such angles do not differ very sensibly from their tangents, hence the ratio of two such angles may be said to be the same as their tangents. ^ To those who require a further proof of these two assertions the following may be acceptable : 1. In Fig. 25 let AB be the object in one position and ab the other. For convenience these are shown in such positions that the line OC passes at right angles through their central points C and c. It is sufficient, however, that ab and AB should be the bases of isoceles triangles having a common vertex at O. AB is virtually an arc of a circle described from O with radius OC. Likewise ab is an arc of a circle whose centre is O with radius Oc. Therefore — . ^„ ^, AB ab I I AOB: «0^ = oc = 0^=OC'o7' hence AOB varies inversely as OC. 2. Two objects are placed at the same perpendicular distance OC from 26 THE SIMPLE MICROSCOPE Let X represent this distance, / the focal length of the lens C — Fig. 28 being considered — and d the distance of distinct vision of the observer figured as that between C and K. Then the pencils of rays proceeding from the object AB at the distance x must, after passing the lens C to form the virtual image, have the same divergence as though they proceeded Fig. 28. from A'B' at the distance x. The condition may be expressed, then, by the following formula : jr = T—-> (derived from the well-known optical formula -j = ^V If the object AB were viewed by the unaided eye — that is, without the lens C — it would have to be placed at ab, because that is the plane of best vision for the observer, and so would be seen under the angle aQb ; but with the lens in situ, it is the eye O of the observer as in Fig. 27, AB and A'B' respectively. They Fig. 27. may be called arcs of a circle whose centre is at O with radius OC • therefore — AOB ; A'OB = M . ^' = aB : A'B', which explains the situation sufificiently. THE SIMPLE MICROSCOPE 27 seen under the angle ACB, being mentally referred to the dis- tance of distinct vision. It consequently appears of the same magnitude as though it really occupied the space A'B', the virtual image. The ratio A'B' to AB, then, is the measure of magnification as before explained, and that is the same as A'B' to ab, or CK to CH, and finally as d vs, \.o x expressed as — . It has just been shown, however, that — df ^ d d+f ^ = ,^^7, hence - = ^, ■which expresses the magnification of an object for the distance of distinct vision d. It follows, then, with normal vision the magnifying power may 10+/ be properly represented by the fraction — j — , bearing in mind, if a long-sighted person of 20 in. distance of distinct vision, that the 20 has to be placed in the numerator instead of 10 ; and if a short-sighted one of 5 in. distance of distinct vision, then that 5 be substituted for that figure.^ Before quitting the subject of magnification, the following remarks may be read with interest to the microscopist : As the actual magnification of an object is directly proportional to the angle subtended by it to the pupil of the eye, so it is said to be in the inverse proportion to the distance of such oh]QCt from the eye. The observer, then, that is short-sighted, say at 5 in., may be said to have a vision four times as strong (for want of a better word) as one whose distance of distinct vision is 20 in. ; for with an extremely small object, which the short-sighted individual might be just able to see with his naked eye at 5 in., the long-sighted cannot see at all unless he uses a lens of 6| in. ' For lenses of short focus the expression is often written as -?, which is practically correct ; but owing to this statement having gained admission into several books as true for all lenses, it has been inferred as correct for lenses even of long focus, which evidently is an error ; for if such were true, say with a lens of 10 in. focus, the result would be no magnification at all but worse still if the focus were longer, for then it would seem as if a diminution rather than an enlargement took place. The simple magnifi- cation formula, however, is rigorously correct for positive lenses of any focus if the eye be placed at the posterior focal plane . 28 THE SIMPLE MICROSCOPE Fig. 29. — Dissecting Stage. focus, which means he has to use a lens to magnify four times before he can examine it as well as the short-sighted observer at S in. does with his naked eye. As an illustration, supposing we Fig. 30. — Large Dissecting Microscope. THE SIMPLE MICROSCOPE 29 have a lens of half an inch focus ; taking the formula ^ d ■\- f we find the place of the object, to be viewed distinctly, should be iV in- from the lens for the short-sighted observer, with d = t^, and 1^ in. for the long-sighted individual at 20. Consequently with the lens in question the object then would have approxi- mately the same angular measurement with both individuals. By this we see that with lenses of high powers all observers, I^'ig- 31- — Dissecting Microscope with Erected Image. whether short, normal, or long-sighted, see objects with nearly, if not quite the same facility and distinctness. The simple microscope is used in two forms, the one known as a dissecting microscope, of which there is an endless variety by different makers, and the other as a hand microscope. The dissecting microscope is used more especially for the purpose of preparing specimens for the microscope ; and as both hands are needed for this purpose, the actual optical portion of the instrument is held by a suitable support. F'igs. 29 and 30 show different varieties of arrangement. The next two illus- trations, Figs. 3 1 and 32, are added among this type of microscope THE SIMPLE MICROSCOPE 31 3 V? because they are used for the same purpose as the preceding, but optically speaking they are in reality compound instruments with erecting eyepieces. The hand microscopes are intended, as their name implies, to be used by the hand only, and are con- venient for use by medical men in examining skin diseases, and for other purposes which readily suggest themselves to the reader. The highest class of microscopes of this description are the "loups" of Zeiss, fixed in a handle, as shown in Fig.' 33. They are made of different magnifying powers from 6 to 30 times, all dropping into the same handle. Mr. Nelson has designed a special form of hand magnifier fitted with an extended lens silvered on the back, which causes the magnifier to reflect light upon the object under examination and so to illuminate it. At times this may be a most useful arrangement. It is illustrated in Fig. 34. Another very handy form of variable magnifier has been brought out by Messrs. Watson & Sons very much after the fashion of the " Brucke " type, much used on the Continent. It ntiagnifies from 5 to 10 diameters. The working- distance is quite excep- tional, being, it is said, 2 in. with the minimum magnification. Its size, 3 in. X if in., renders it inconvenient for pocket use, but it is a most useful adjunct to the consulting room or the laboratory. La.stly, Koristka of Milan has designed a compound hand magnifier giving a very great range of ampli- fication (30 to 90), a large '/rontal distance and an extensive field of view. \^' Fig- 34- Fig- 33- CHAPTER III THE COMPOUND MICROSCOPE The compound microscope is far more intricate than the simple, both in construction and use, and indeed is the microscope meant when the term is used in ordinary speaking. There are two models, which in their primitive forms are very dissimilar in appearance, although, of course, they are both designed for a common purpose ; but in recent years so many compromises have been made by different opticians embracing the usefulness of both types and avoiding the in- conveniences peculiar to each, that many are now sold which save for the length of the tubes — to be hereafter explained — it would be difficult to say belong distinctly to either model. The long-tube class are usually called the English models, a classical pattern being that shown in Fig. 35, by Messrs. Powell & Lealand, whilst the typical Continental short-tube pattern may be represented by that made by one of the oldest firms of manufacturers abroad — viz. Carl Zeiss, illustrated in Fig. 36. In each case, for the assistance of beginners, the names are affixed to the different parts of the instruments. It is convenient for the sake of description that a microscope be divided into two portions : the Mechanical and the Optical. The Mechanical Portion. — This division includes the entire metal portion of the instrument, which may be said to consist of the following parts : 1. The foot and upright support, with joint for inclination. 2. The tube carrying one or more draw-tubes, with its nosepiece. 3. The body and the coarse adjustment. 4. The stage — simple, mechanical, and auxiliary. 32 THE ENGLISH MODEL OF MICROSCOPE. By Powell & Lealand. Capped Eyepiece. Draw-tube Fig. 35- THE CONTINENTAL MODEL OF MICROSCOPE (NEW MODEL). By Carl Zeiss, Eyepiece or Ocular. Di I lube. Objective Changer. Revolving Staple : lifts off when not required, to be replaced by vul- canite slab. One handle of Mechanical Stage. Abbe Condenser and Iris Dia- phragm. These swing out upon the joint J. The rack beneath is to put the iris out of centrality with Ihe optic axis when required for oblique light. Fig. 36. THE COMPOUND MICROSCOPE 35 5. The substage, including the diaphragm and mirror. 6. The fine adjustment. 1. The Foot may be three-legged, as shown in Fig. 35, or the horse-shoe shape, as in Fig. 36. Other forms are made, but are not now so much in favour as the two mentioned. In the English pattern the union of the two front legs, it will be .seen, is so arranged that a joint is made between them at which the in- strument can be inclined or placed completely horizontal ; whilst in the Continental model, two supports usually rise up vertically from the horse-shoe which end in a pivot arranged for the same purpose. A handle on the pivot, or some other simple arrangement, is usually provided to tighten the joint when through use it becomes loose. 2. The Tube is seen to be longer in the English form than in the Continental ; but in each model a supplemental one — called the draw-tube — is contained within it, by which means the entire " draw " ^ can be lessened or increased. The extreme draw of the English, or long-tubed instrument, is usually about 12 in., whilst that of the short tube, or Continental model, is limited to about 8 in. It is rapidly becoming the fashion, by the use of a third tube, usually articulating by means of a special rack and pinion with the drawAuhe, to make the instrument capable of being extended to 12 or 13 in., but closed to 5 in., a very great convenience, as will hereafter be seen. The end of the tube that does not receive the draw-tube is provided with a fitting called the nosepiece, which is a casting turned out a specific diameter, and threaded with a screw thirty-six threads to the inch.^ This combination of diameter and thread is called the " universal fitting," and all objectives, both English and Continental, are now made to fit the same. A similar nosepiece, but of a very much lighter kind, is attached to the end of a draw-tube that is contained within the tube. Its use will be described later on. The Draw-tube, usually divided into millimetre divisions, should slide in its fitting within the tube easily and smoothly, but the cloth fitting, which Messrs. Bausch & Lomb provide, is ' The " draw " of a microscope is usually measured from the upper end of the draw-tube to the end of the nosepiece. * The diameter is usually 7969 in., in the Continental microscope as well as the English one. 36 THE COMPOUND MICROSCOPE a very great addition, for it seems it does not get dry and stiff like the plain spring-brass one usually supplied.^ The diameter of the tube and draw-tube are greater in the English pattern (and, of course, the oculars too) than in the Continental make; but the American manufacturers, Messrs. Bausch 8i Lomb, seem to have adopted an intermediate size, which may have its advantages.'' The Royal Microscopical Society has laid down certain measurements for different-sized draw-tubes, which in future years will probably be of much service. At present the arrange- ment does not facilitate the interchange of oculars ; hence purchasers of eyepieces and other fittings that are dropped into the draw-tube should be careful in stating its exact diameter when sending orders by post, Messrs. Zeiss recommending an impression in wax being taken to prevent mistakes. 3. T/ie Body articulates with the tube of the instrument by means of the coarse adjustment, which consists of a rack and slide fixed to the tube that fit into a corresponding slide con- taining a pinion, forming part of the body. Several different forms of construction are adopted by different opticians in the details of this arrangement, but all are built and manu- factured to obtain a smooth movement from one end of the rack to the other, and an absence of what is called " back-lash" a name given to a loss of way that used to be present in the old forms of manufacture, when the raising of the tube was changed to a lowering movement. This is largely brought about by the use of a diagonally cut rack and spiral pinion. At both ends of the pinion are two large milled heads seen in both Figs. 35 and 36. Coarse adjustment is made by turn- ing these milled heads. It should be remarked the exact and accurate movement of the coarse adjustment constitutes one of the points to be carefully looked into in purchasing a microscope. In the common forms of the instrument the coarse adjustment is done away with, the tube drawing through a sleeve which is attached to the body instead. This type of microscope does not lend itself to the use of high powers. Whatever the type ' How to ease this fitting when becoming stiff, is found in the chapter upon " Hints for Faults " at the end of this book. ^ A full discussion of the relative merits of the Long- and Short-tube instrument, taken as a whole, is furnished later on. THE STAGE OF THE MICROSCOPE 37 of instrument possessing a coarse rack motion, such should be of the best description and accurately fitted. It is well, if any doubt exists upon the point, to rack the tube completely out and see if the slides (and rack) are filled with a heavy grease — if this be so it is a bad sign, for it is probably there to cover up a bad and loose fitting. 4. The Stage may be simple or compound (sometimes called mechanical). The former merely consists of a solid piece of thick brass fixed at right angles to the body, in such a position beneath the end of the tube that takes the objective, that it affords a convenient support to the specimen. It is perforated in the middle by a large hole for the passage of the light from the mirror. Two little springs are supplied with this form of stage for clipping and holding the specimens firmly to it. Some manufacturers make a broad slit completely through the stage on the side furthest from the body of the instrument,- converting the circular hole mentioned into a U-shaped opening. It serves the purpose of permitting the microscopist, when focussing with a high power, to lay hold of the slip containing the speci- men, between his thumb and finger, so that by lifting it up and down very gently from the stage he can mentally estimate the distance it lies from the front of the objective in use. Under- neath this simple form of stage may often be seen a sleeve which is to hold a substage condenser or a diaphragm. In the best form of instruments, however, the stage ismore complicated and is arranged so that, by turning two screws furnished with milled heads, two motions shall be available. These movements, to an observer looking through the instru- ment, are up and down at right angles to the optical axis and from side to side. In the English model this compound stage, with its mechanical superstructure of slides and screws, is usually square-shaped, but in the Continental it is more often round. In either form, with instruments of the highest grade, the move- ments to and fro and from side to side are all capable of being noted by verniers with graduations reading to either portions of a millimetre or of fractions of an inch. These afford a means of registering some particular part of a specimen' for future reference. Besides these two motions, however, in the very best ' How to do this is explained later in a chapter devoted to the purpose and to the discussion of the units of measurement used by microscopists. 38 THE COMPOUND STAGE of instruments it is usual nowadays for the entire superstructure to revolve on the optical axis of the instrument, so that a specimen may be turned round in any direction desired, a vernier being again added to register the amount of circular movement. To make a microscope turn about its axis truly is no small matter, and in some imperfectly made instruments the act of turning causes the specimen to quit entirely the field of view ; it is usual, therefore, in the finest constructed apparatus, to add centring screws to adjust the stage to optical centrality when necessary. In the English stands we regret to say this adjust- ment is often conspicuous by its absence, whilst in the best Continental it is nearly always present. Very little reflection will enable the reader to understand that if the stage becomes eccentric through use, it upsets the values previously obtained by the verniers, and notes on different slides to indicate places of special interest become valueless in consequence ; hence the microscopist has to hunt again over the specimen to find the desired position, which practically does away with one of the objects of the mechanical stage. If, however, the stage can be always kept central — especially before noting a new position, or can be immediately reset to absolute centrality by means of the screws in question, the present readings taken, as well as all the old ones on other slides, will always be correct and correspondingly useful.^ Whether the stage is better in its round form or as a square or of a rectangular shape is a matter of opinion. The round form facilitates the recording of circular motion about the optical axis, although in the best English stands, even with their square stages, some means is usually provided which answers the purpose. The size of the stage varies somewhat according to what special use the microscope is to be applied ; for instance, in bacteriology it should be exceedingly large, but this matter is discussed later on when considering the class of microscope best suited for special purposes. In many instruments arrangements are provided to take up the wear and tear in the different slides of the mechanical stage and also the loss of way in the screws which produce the different movements. If not abused, these are very useful, ' How to set the stage "central" is fully explained later on, AUXILIARY STAGES By Chakles Baker. 39 w o Both rectangular movements are effected by rack and pinion, the vertical one of which carries a bar (fixed as to horizontal movement) against which the slide is pressed by a spring clip, and upon which is mounted the rack and pinion for the horizontal movement ; the points which press upon the slip are tipped with cork in order to grip the slide, and move it along the fixed bar, when the milled head is rotated ; the slide actually rests on two small raised surfaces at either end of the bar to minimise friction. Fig. 37- but many manufacturers have found adjustments of this nature to have been so unfairly or ignorantly employed, that injury By Bausch & Lome. The rectangular movements are both 6y rack and pinion, as it is impossible to make a worm screw movement that will not wear loose in time. The object slide rests upon the surface of the microscope stage, and may be used in immersion contact with the condenser if desired. The stop against which the slide rests is adjustable, permitting the use of slides of various sizes. The object carrier has extra long range, the movements being 35 and 60 mm. respectively. The stage is held in place on the micro- scope by a solid metal clamp. Fig. 38- to the slides of almost a permanent nature has resulted ; con- sequently they now no longer add them to their instruments. 40 AUXILIARY STAGES By Otto Himmlee, Berlin. In this arrange- ment one movement is by an endless screw, whilst the other is by rack and pinion. It can be clamped to the microscope quite easily. Fig. 39. All stages hitherto considered have been built into the stand, in other words are fixtures forming part of the instru- By LErTZ. This arrangement and the preceding are very closely allied ; the different shape of the milled heads is pre- ferred by some micro- scopists. Fig. 40. ment itself; but Carl Zeiss and many Continental firms, how- ever, in their circular stage, make the top plate to lift off to AUXILIARY STAGES 41 be replaced by a vulcanite one when using corrosive fluids. This has been found of great service, for if such should run on to the metal, they injure it very sensibly. With microscopes iitted with plain stages, the loss of a mechanical one is very much felt at times— such as when making a blood-count, for example, or hunting very syste- matically through a specimen ; hence opticians meet this want Bv Swift & Son. This engraving sliows the peculiarity of Ihe Qpnstruction and the best method of raising the lever, carrying the roller A, which, when released, presses the slide under examination against the friction rollers D, D. The milled head B works the friction roller D, D, and gives 2 in. traversing motion to the slide under examination. The milled head C allows of a vertical movement to the same extent. by supplying an attachable device which used to be called after the inventor Mr. Mayall, junior, although he is now rarely credited with the originality. We do not recommend any of these arrangements in preference to the previously mentioned substantial form for regul,fir use, but as a go-between they are decidedly useful. Illustrations are shown by different makers in Figs. 37 to 43. 5. The Substage. — The substage assumes a variety of forms according to the individuality of the manufacturer. Primarily 42 THE COMPOUND MICROSCOPE we may divide all kinds into two grand classes — the English and the Continental. In the cheap make of either type the substage proper is really not in evidence at all, its only representative being a sleeve (made of the correct diameter to receive an Abbe or other condenser with or without an iris diaphragm) and attached to the undersurface of the stage instead. " Up and down " motion, as it is called, by which is meant bringing By Messrs. Watson & Sons. This stage can be fitted to any ordinary microscope, ttie method of attachment being by means of a thumb- screw only, and as the mechanism is entirely on the side of the stage and not behind it, none of the working parts are interfered with by the instru- ment. This stage, which is quite new in construction, is controlled by a frictional wheel and one milled head only. At first sight it would appear that some difficulty might occur in moving this milled head from the vertical to the horizontal position, but experience entirely overrides this ob- jection. A steel spring is fitted at the top to give the necessary pressure, and directly the stem of the milled head arrives at the horizontal position, a check pin indicates it, and the same occurs when it is turned round to the vertical direction. It should be noted that if it is used at any point between the vertical and horizontal positions, the slide will be carried diagonally. This stage cannot fail to work, is entirely free from all chance of backlash , and is beautifully sensitive and accurate, even with high powers. It will be found superior to many of the ordinary expensive attachable stages. It gives about i^ in. of traverse. Fig. 42. — Watson's "Argus" Attach- able Mechanical Stage. up the condenser nearer to the slip containing the specimen placed on the stage of the microscope, or carrying it away further from it, is performed by pushing the condenser further into the sleeve, or by pulling it out again by hand, unassisted by any mechanism whatever. The whole arrangement is crude, but is sufficient to be in accordance with the general scope and design of what may be called a somewhat primitive form of instrument.^ ' The reader who is commencing the subject, must not confuse the " up and down'' motions of the stage with those of the substage. The former by convention always means in a direction ^t right angle? to the optical axis, the latter parallel with it. THE SUBSTAGE 43 In a rather better class of microscope, however, the sleeve of which wc have just spoken is not itself attached to the stage beneath, but is contained in a fitting of its own of simple design, furnished with a kind of thumbscrew by By Carl Zeiss. thnnt )SC l9llllllllllllllllill!iil|il''!^®!'ii!!!'!H!li!!l!i!l!f!'^'''' " "H ' |i'lill\CHROMATIC Fig- 74- Fig- 7S- shall quickly notice that the focus of the preferred colour is always the shortest ; so the spectrum may justly be said to be folded over at that point, for should the selected colour be yellow-green — which is, in fact, that usually taken for visual objectives — yellow-green will be seen to have the shortest focus ; orange and blue are folded together, and further on red and violet.^ Achromatisation for green — what has been termed a slightly under-corrected ordinary achromatic — we see depicted in Fig. 75. Here the preferred colour has again the shortest focus, a blending of yellow and blue coming next, whilst red and violet are seen still further on. A lens corrected for the ' gee chapter on " Testing Objectives," ^o ACHROMATISM blue ray — an ordinary photographic objective — is drawn in Fig. 76. Blue is seen to have the shortest focus, because it is the preferred colour ; green and violet are joined up next ; yellow and ultra-violet follow, whilst red, outstanding, has the longest focus of all. We shall find that in the ■ 'V'O'-C'--^ best work, by making the com- «Hi«,«T,seo^BLUE *' ""* ' ponents very thin, or else by ;^^ C.Zeiss , ^^y^ Jena Apertometer. Fig. 83. can be shifted around the outer edge of the glass shown at bb, are square one side and pointed on the other (see b in the side view). To use this apparatus, the glass is placed with the" graduated surface uppermost upon the stage of the microscope (fixed vertically) in such a manner that the circular portion is forwards, and the chord or bevelled piece backwards, towards the stem of the instrument. The edges of the little hole are now focussed with the objective to be measured, an eyepiece being used, and the length of the draw-tube the same as when the objective is ordinarily in use. The two indices, as bb are called, are then placed on the edge of the glass, as shown in the plate, but close to the middle of the semicircle. Their sharp points should lie along the vertical edge of the disc, and their flat sides upon its upper graduated surface. It is best to direct the points away from each other to the outer side, if the power ABBE'S APERTOMETER 97 to be examined is comparatively high (N.A. above 0'6 or 07), but towards each other to the inner side if a low objective is employed. With each apertometer an auxiliary objective is supplied which screws, or must be made to screw, into the end of the draw-tube, after which both are returned to the microscope, with the auxiliary lens passing down the main tube. The same eyepiece is then placed in the draw-tube as before, and the auxiliary microscope then obtained is focussed to the image of the indices by sliding the draw-tube in the main tube. Care must be taken both in pulling out and pushing in the draw-tube, not to alter the adjustment of the objective under examination by accidentally shifting the main tube. The indices are now adjusted, taking care they lie close to the glass plate until their sharp points just touch the periphery of the luminous circle seen on looking down the eyepiece. Their position found, the readings of the upper edges, which lie in the same vertical plane as the points, are read from one of the two scales on the plate. The half of the sum of the two readings on the outermost scale — that nearest the edge — will give the measured value of the N.A. of the objective under examination. Likewise the sum of the two readings on the inner scale will give the value of the angular aperture in air. The illumination must be shifted from right to left, or up and down, so that the light falls horizontally upon the edge of the glass. It should be noted that if the apertometer be used on low- power objectives, such as an inch, with high^N.A., owing to the size of the back lens having to be so large, the auxiliary com- bination may not be of sufficient diameter to give the maximum N.A. of the objective under examination. Also, and this is commoner still, with medium powers, say \, \, or \, it is not at all improbable the ordinary eyepiece, whether achromatic or compensating, may not command sufficient field of view ; so between the two troubles a false N.A. may be obtained. This actually happened in our case when testing an inch N.A. -3, an apochromatic quarter-inch, and an achromatic sixth, the mistake being only discovered when applying the next means about to be described for ascertaining the N.A. of an objective 7 98 CONRADY'S METHOD FOR DRY POWERS which gave us different results. To remedy the first fault with low powers, let the observer look down the microscope after the first focussing, and regulate the indices without the auxiliary lens, using no eyepiece at all ; whilst to avoid the latter trouble it is best by far to employ an ocular having no diaphragm on all occasions. Special instructions are given with each instrument, but lengthy as the description must necessarily appear, the apparatus is not difficult to use ; the only fault is its expense. Still, it is the only plan with immersion objectives. With dry powers, however, a simpler method of obtaining the approximate N.A. may be employed.^ Lay upon the table two pieces of white paper, using a black background, with their straight inner edges parallel to one another and a definite distance (say 20 cm. for lenses of N.A. over o"SO, less for low-angled ones) apart, then hold a rule vertically upon the table about midway between the two pieces of paper. Next hold the objective to be tested vertically against the rule and look down at the back lens. Images of the two pieces of paper will be seen there : now slide the objective downwards along the edge of the rule, always watching these images. They will separate farther and farther apart until at last a point is reached where only a slight bluish flicker remains visible on either side in the extreme margin of the lens, which, of course, indicates that the inner edges of the pieces of paper are in the direction of the most oblique rays which the objective is capable of receiving, or that the angle enclosed between these directions, which directions intersect in the principal focus of the objective, is the angle of aperture. To determine this angle, read off the distance from the table to the front of the objective, and subtract the working distance of the lens, so as to get the distance from table to focus. Then this distance divided by half the distance between the two pieces of paper is the cotangent of the semi-angle of aperture ; the latter may, therefore, be obtained from a table of trigono- metrical ratios, and the sine of the same angle is the N.A. of the objective. ' This was originated by Mr. Conrady, and was first brought into notice in the author's Photomicrography, from which this paragraph is abstracted. DEPTH OF FOCUS 99 Example : Distance between the two pieces of paper, 200 mm. Distance of front lens of objective from paper, 33"o mm. Working distance of objective, o'2 mm. ; .-. 33'o-o"2 ^ 32-8^ . g_ 200/2 100 o"328 = cotan, of angle 71° 49', as we find from the trigonometrical tables, the sine of which = o'95 = N.A. With great care this method will give results accurate to one or two units of the second decimal. In looking at the back of the objective the eye should be at a distance about equal to the tube-length for which the objective is designed, but the error caused by even considerable deviations from this theoreti- cally required distance is very small.^ Depth of Focus. Before concluding this chapter, seeing that the amount of " depth of focus '' (sometimes called " penetrating power ") possessed by an objective is largely though by no means entirely associated with its numerical aperture at the time of use, the following remarks may be read with interest. First, what is meant by the term ? It is this. When the superficial part of an object is in focus, how much of its third dimension— that of depth — is sharp and well defined at the same moment? The subject is a somewhat difficult one, and not very easy to explain, for it was wrapped in obscurity until Professor Abbe took the question in hand, being up to that time thought to be an inherent and distinctly mysterious property possessed by certain objectives over and above that 'to be found in other combinations. As we have just said, to explain the whole subject intelligibly is not at all easy, and we feel a pleasure in acknowledging very considerable assistance from Mr. A. E. Conrady, who has given very much attention to the matter. To simplify what follows let us consider Fig. 84A, where an objective OO is focussed on a plane containing F. Supposing the aperture of the objective to be reduced to AB, then it is obvious that light from all points loo DEPTH OF FOCUS of a lower part of the object between A' and B' would pass through this point F and would be mixed with the image of this point ; hence the confusion owing to the lower portion of the object being out of focus will be equal to the distance from A' to B'. Suppose we now increase the aperture of our objective to CD, then by the same reasoning we find that portions of the lower part of the object extending from C to D' will now be confused ; and it is easy to see that for a given distance between the sharply focussed plane and some other plane, the diffusion of focu-s for the latter must be directly Fig. 84A. Fig. 84B. proportional to the diameter of the object glass and with suf- ficient approximation to the numerical aperture employed. But the above figure also makes it clear that with the larger aperture CD there is a plane GH much nearer the sharp focus F where the diffusion CD", corresponding to the large aperture, is the same as that (A'B') produced by the small aperture at a greater distance from F. Hence we may also say that for a given allowance of diffusion the depth of focus is inversely propor- tional to the N.A., and in this form the influence of the N.A. will enter into our formula. The effect of magnification is obvious. The dimensions of A'B', CD', etc., are seen magnified by the microscope ; hence DEPTH OF FOCUS loi the greater the magnification, the less the size of the diffusion A'B' in the object which can* be tolerated in the magnified image ; the depth of focus must therefore be inversely propor- tional to the magnification M. Finally, the effect of the mounting medium arises from the same cause as the greater N.A. possible in dense media — i.e. from the refraction of cones of rays when entering the dense medium. Thus, if the objective OO in Fig. 84B had its focus in air at F, the introduction of a denser medium at MM would lengthen the cone so as to have its apex at F'. The entering surface MM being flat {i.e. the underside of the cover-glass), the reasoning applied in determining the value of a given angle in a dense medium as compared with the value of the same angle in air, applies, with the result that the cone to F' is very approximately n times in being the refractive index of the medium ^) as high as that corresponding to air which has its apex at F. The distances from F and F' respectively at which these cones attain a certain diameter (= a given diffusion) are evidently in the same proportion ; consequently the depth of focus is proportional to the refractive index of the mounting medium. From what has been said we may now state that the depth of focus can be expressed by the formula — D = a Constant x M X N.A. The Constant depends on the diffusion allowed. If this be assumed to be the fixed and usual quantity 1^ in., then with the aid of our first figure we reason as follows : Let the N.A, be yV ; then the diameter of the object-glass will be one-fifth its focus ; in other words the cone, having its apex at F, will con- verge at the rate of i in 5. It will, therefore, attain a diameter of j^(y in. at a distance of tI^t from F) but on either side of F ; hence the total range within which the cone is below j^^ in.- in diameter will be W in- This, therefore, is the depth of focus with an objective of N.A. yV on an object in air {n = i) provided there is no magnification (as otherwise we should have had to allow less diffusion in the object in order to keep within our limit in the image), which mathematically ' The Refractive Index is conventionally expressed by n. I02 DEPTH OF FOCUS means M = i. Introducing into our formula D = yVi n= i, M = I and N.A. = xb-, we obtain — = Constant lO I X iV whence we obtain the value of our constant — Constant = tV '^ iV = ilis, which gives us the depth of focus in inches when a diffusion of Y^o of an inch is allowed in the image, as — D= ^ . 100 X N.A. X M So far we have assumed the point F in sharp focus to be absolutely fixed, which implies that the image is formed at a fixed distance from the eyepiece, as, for instance, on a photo- graphic plate or on the retina of an eye devoid of accommoda- tion. When the observer uses his accommodation a further visual term must be added to the formula. As accommodation stands for the ability of seeing sharply at various distances, it therefore involves the formation of the final visual image at Various distances below the eyepoint, which in turn implies shifting of the conjugate points in the object. By differentiating the usual magnification formula (y = ^ + ^ )^ '^ '^ found that the magnification in depth is the square of the magnification in diameter ; hence the visual term Dy in the depth of focus formula must be inversely proportional to the square of the magnification, or— . a constant Dv = M^ One concrete example will enable us to determine this constant, provided we assume a definite range of accommoda- tion. Let us take it then that the normal range is from lo in. to infinity. Assume a magnification of loo ; this would mean an equivalent focus of the entire microscope of one-tenth of an inch ; a lens of xV-in. focus produces the image of an infinitely distant object at its principal focus, that of an object at lo in. distance at one-hundredth of its focus, or one-thousandth of an inch from the principal focus. With magnification x loo the ' Where L = long conjugate F = focus and / = short conjugate. DEPTH OF FOCUS 103 accommodation depth of focus is therefore = i^nrir in- Intro- ducing as above we again determine the constant, viz. : Dy = y^Vcr and M = 100, vsrhich introduced into the formula for Dy gives— I constant . . „ ^ ^ = . . Constant =10. 1000 I 0000 Hence, for the above assumption of a range of accommodation from 10 in. to infinity, Dv = — . Visually we therefore find the total depth of focus — ^ + "^ " 100 X N.A. X M + M^- For N.A. '3, magnification x 100 and an object in oil or balsam taken as n = rs ; this gives — D+Dv= '-^ h-^ 100 X '3 X 100 loooo 3000 I 0000 I I I • = = —r- in. 2000 1000 667 It is here instructive to point out that in this case two-thirds of the total depth is due to the accommodation of the eye, and is therefore lost in photomicrography. This is, indeed, a well- known fact to photomicrographers, as we can very truly and painfully acknowledge, particularly noticeable in low-power work, although it is almost if not quite negligible with the highest powers, because, owing to the square of the magnification in the visual term, the latter becomes evanescent with very high magnifications. If we introduce n = r5, N.A. i"4, and M = 1000, such as obtains when using a xs^-in. objective upon an object mounted in balsam and a magnification of 1000 diameters, we find the depth of focus is only zsttt of an inch ! CHAPTER VI EYEPIECES Eyepieces, or Oculars, as they are often called, are really of several kinds, but only two — the Huyghenian and Ramsden— will here be mentioned, as special forms are explained in the chapter on the auxiliary apparatus for the microscope. The Huyghenian may be of two varieties, the Ordinary and the Compensating. The Ordinary, which is the form more commonly met with, may be readily distinguished from the Ramsden by the fact that it is composed of two single lenses (the one nearer the eye being called the ej/e-lens, whilst the' other is termed the^«/^-lens), the convexity of each being turned towards the object in use on the microscope. The invention of this com- bination is usually ascribed to Huyghens, the celebrated astronomer whose name it bears, but there seems good ground for believing that Campani also devised an ocular much of the same type. From what can be gathered from the literature of the subject, it would seem the actual invention was of the nature of a happy inspiration rather than the result of any strict philosophical inquiry, but anyhow, be that as it may, the eyepiece, in some form or other, seems to be one of the best, both for the telescope as well as the microscope. In the high--povitr combination for the microscope, the con- dition of achromatism is best fulfilled when the field-lens has a focus three times that of the eye-lens, the two being separated by a distance (d') equal to half the sum of their focal lengths — ^ 2 ' but for /ow-power magnification there is usually a change of both these foci, i to i'5 being found about the right propor- tion, whereas for medium power about i to 2. 104 ORDINARY HUYGHENIAN OCULAR los The passage of the rays through the lenses should now be explained b)' consulting Fig. 85, where O is the objective, F the field-lens, and E the eye-lens. Dealing with those rays which emanate from a point about the arrow-head, and pre- suming for the moment they are monochromatic, they would focu/j at A if left undisturbed, but the interposition of the field- lens F refracts them to A', where the image is formed. Seeing, however, that this image plane is in the focus of the eye-lens, once again the rays are refracted, being bent towards the axis at P, where the eye is placed. But they are at the same time rendered parallel, which is the condition best suited for the eye to see with. It should be mentioned here that a mistake HUYCHE.NIAN EYEPIECE r -A^-J' ftismoN OF ReIl Imaqc from Object QLAU between Field 8c E.rEai.A6» A-q Lyepiece Fig. 85. js often made concerning the expression " that the rays leave this lens E parallel." It is not meant that they issue parallel to the axis, as often erroneously understood, but that they issue parallel with one another. This is obvious with a little con- sideration, for if they were parallel with the axis, the eye could never get the entire beam into it through the pupil, and incomplete vision would inevitably result, as will hereafter be evident.^ This then is the path of the rays for a mono- chromatic beam ; but light from an object is not monochromatic in the ordinary way, hence we must now show how the eye- piece causes such perfect achromatism. In Fig. 86, upper part— which is upon a necessarily much larger scale than the pre- ceding diagram— the passage of the red and blue rays is alone shown, the condition depicted being exaggerated very exten- sively but serving to illustrate the point at issue. The incoming beams if left alone would focus at A as before, but meeting ''■ How to ascertain the diameter of this pencil, see later page 114. c^ ■■/ ■I // // w \\ ft B K •a 3 ORDINARY HUYGHENIAN OCULAR 107 with the field-lens F are refracted to focus again at A'. If there were no eye-lens, and F were used by the eye as a single lens, it would produce a virtual image with colour fringes in the outer part of the field, for owing to the dispersive power of the glass the red rays sent out by the object would be bent to a less extent than the blue ones, and each point of the virtual ima;ge would be drawn into a spectrum with the I'ed end towards the optical axis (see Fig. 86, lower part). But in the Huyghenian combination, where an eye-lens is used, the rays— shown in Fig. 86, upper part — cross and become still further separated as they fall upon E. It is seen now that the blue ray meets the "eye-lens sensibly nearer the optical axis than the red one. As any lens may be regarded as a prism with a refracting angle increasing from the optical axis, it further becomes apparent with but little consideration that the red ray meets a prism of a greater refracting angle than its companion of blue, and is for this reason bent more than its fellow. It is true some of this advantage is counteracted by the difference of the refractive indices for the two colours (about as rSi is to i"S2), but with a sufificient separation between eye- and field-lens, the first effect greatly predominates, and to such an extent as to cause the red and blue rays to emerge from the eye-lens to P sensibly parallel one with the other. It is this that pro- duces the achromatic image. A diaphragm is placed at the focus of the eye-lens. The Compensating Huyghenian ocular is only an extension of ideas — the wish of the computer being in this instance to further accentuate the condition of things to such an extent that by a crossing of these rays in the formation of the virtual image as seen by the eye, the red image shall be made larger than its blue companion, and to just the right extent to com- pensate the opposite error of the apochromatic or other high- power objective. This is effected either by using denser glass and greater separation (as in the holoscopic eyepiece of Watson or a similar one by Swift) or by substituting an over-corrected achromatic lens for the simple eye-lens of the eyepiece. On looking at the lower half of Fig. 86 this is well seen, although again in exaggeration. It shows the condition that obtains with the holoscopic eyepiece. The rays of the two colours io8 COMPENSATING HUYGHENIAN OCULAR are seen well separated now as they arrive at the crown lens by a sensibly greater interval than in the former simple achromatic ocular. This increase of separation causes the red rays to issue forth to form the virtual image — if we may so speak — as seen by the eye, not parallel with the blue, but diverging and crossing in such a manner that the red virtual image becomes larger than that formed by the companion colour, for the purpose which we have already stated. The same explanation practically holds good if the compensation is effected by over-correcting the compound eye-lens ; and it is this state of things that gives rise to the red edge of the diaphragm — placed in the focus of the eye-lens — which furnishes- a ready method for rapidly distinguishing in Huyghenian oculars (and usually in the Ramsden too) the compensating from the ordinary. From what has been said, it is evident that as the Huyghenian eyepiece has its focus inside between the lenses, it cannot be used as a hand-magnifier like the Ramsden, or for micrometer work where the threads have to be focussed simultaneously with the object.^ The Ramsden Ocular may be at once distinguished from the former type of eyepiece as it consists of two lenses, the convex surfaces being turned towards each other. The general path Ramsden Eyepiece. /-Real Lower Focal i| Plane of tYEPiLce.. Real Eocus or InACE rROM OBJtcT Glass LrE& ouTaiDE THE Ocular Fig. 87. of monochromatic rays is shown in Fig. 87. The best form theoretically is where ./ = /' = d, that is to say where the focus of each lens is equal, and the distance apart equal to the focus of either. But as this condition would throw the lower focal plane of the eye-lens into the field-lens and the upper focal plane of the field-lens into the substance of the eye- ' This is the case ordinarily speaking, but if the field-lens in the Huyghenian be entirely removed, and the eye-lens made to focus the threads, it can then be used. See later. RAMSDEN OCULAR 109 lens, the arrangement cannot be strictly fulfilled. To avoid this, which would cause all imperfections in the glass of the field-lens, or any dust upon it to be annoyingly visible to the ■eye when the ocular was in use, the two foci are usually made slightly different and the separation less than that theoretically demanded. The consequence of this arrangement is to deprive the eyepiece of its freedom of colour, for chromatic under- corrections (taken in the sense of a single lens) become painfully apparent, whilst the focal planes still remain incon- veniently close to the lenses. These drawbacks can only be overcome by the use of achromatic combinations of crown and flint glass ; hence, although the lenses in the best form of Ramsden eyepieces look the same as in the cheaper type, they are really different, for in point of fact each lens is compound, the components being cemented together. Cheap Ramsden eyepieces may therefore be regarded with suspicion. In the compensating form the same idea of manufacture is carried out, but to a higher order, by introducing a sufficiently strong concave flint element to produce a chromatically over- corrected combination. The Zeiss form of arrangement is shown in Fig. 87A. Here again the whole appearance of the rays is greatly exaggerated, but it suffices to show how the extremely dense flint glass separates the blue and red rays so much that in the virtual image the red component is larger than the blue which is required to correct the opposite condition in the objective. On the other hand the figure serves to show that if the flint were not so dense a combination of this particu- lar form might be computed where the virtual image would be purely achromatic, for the ocular to be used as an ordinary Ramsden eyepiece. As a matter of fact, with the compensating eyepieces manufactured by Zeiss the Huyghenian type is in being for those up to the nominal x 6, after which the Ramsden form takes their place. This selection is found to be the most convenient because of arranging a suitably distanced eye-point and for enabling the adjustment to be such that the lower focal planes of the entire series shall lie in the same position when the oculars are inserted into the draw-tube; a change of eyepieces therefore necessitates scarcely any change of focus simply from the fact that the distance between the upper focal plane of the objective and the lower focal plane , OCULARS III of the ocular remains constant ; but to this we shall refer later on. In the holoscopic eyepiece the over-correction for the compensating effect is simply produced by separating the lenses — one of which is flint — sufficiently to make the red image larger than the blue. High-power eyepieces constructed on this principle have an unpleasantly near eye-point, and for general use we cannot recommend them ; but they are con- venient for, certain purposes connected with the testing of apochromats to be related hereafter. If the inherent nearness of the eye-point could be overcome they would be useful as avoiding the necessity for a double battery, Huyghenian and Compensating, for pushing the lenses together makes them ready for use with achromats, whilst drawing the lenses, apart renders them of service for apochromats or very high-power semi-apochromats. As with all classes of Ramsden eyepieces the focus is without the ocular, so they can all be used as hand-magnifiers, and in consequence are mostly employed for micrometers where mea- suring-threads are employed ; the webs being first set in the focus of the eyepiece, the eyepiece as a whole — i.e. webs and all — being moved nearer to or farther from the object when focussing it. By this means the webs and the object are simultaneously in adjustment at one and the same time and the different dimensions of the object can be taken. To this we shall refer again when speaking of measuring objects when we also point out how the Huyghenian form of ocular, simple or compensated, can be employed for much the same , purpose, although in a different manner. In the usual form of Huyghenian oculars a change of focus is necessary with each power, but Messrs. Bausch & Lomb have devised and made a series now that are all par-focal, as it is called, in which these eyepieces, like the compensating, have their lower focal planes in a constant position so that no change of focus (beyond the merest trifle) is necessary. Most oculars (for the short-length microscopes) fit the Conti- nental tube, but recently a change has taken place which to our mind has seemed a pity. Messrs. Bausch & Lomb, however, have risen to the occasion, and make most if not all their oculars of the new diameter. 112 COMPENSATING OCULARS , Compensating oculars, both Huyghenian and Ramsden, may usually be distinguished from ordinary eyepieces by looking through them when held up to the light : the former showing a yellowish red margin to the diaphragm, whereas the latter produces a blue fringe to the field. It has been often asked how the difference in colour is to be explained, and the writer is not able to point to any text-book wherein any scientific information upon this point is to be found ; hence the few following remarks may be of interest. Speaking of the Huy- ghenian form of either compensating or ordinary ocular, the first point to bear in mind is that the coloured rays in question are not due to the eyepiece taken as a whole ; by which is meant they are not due to a conjoint action of the two com- ponent lenses, the field and the eye-lens, but to the action of the latter entirely. Indeed the former may be considered merely as a condenser, for it may be removed and the effect is unaltered ! If Fig. 88 be consulted, the red and blue rays (only two colours < B Blue ray Red .. {Diaphragm Ordinary UN/tcffftoMAric Eyelens Blue Ray outside mence. Blue Margin to Field Fig. 88. are taken) from the edge of the diaphragm to the lens will be seen split up and separated at A. But the eye sees them as if in the direction B, where the blue ray lies outside the red — hence the blue margin to the field. In Fig. 89, which represents COMPENSATING OCULARS "3 the case of the achromatic eye-lens, the blue and red keep together, and so a colourless margin would be furnished to the Blue ray Red .f -=*-"** Side of -ttie Eye J ACHROMAT/C EYELELNS Blue » Red Rats remain together Hence Colourless Margin to Field Fig. 89. edge of the diaphragm. But in Fig. 90, of the over-coxr&cXsd. eye-lens (as in all Zeiss compensating Huyghenian oculars), the red is bent so much more than the blue that in the virtual Blue ray Red « k OvERCOffRECTED EyELENS RED OUTSIDE, Blue inside, hence Red 'or RATHER, OWING TO IT5 GREATER BRIULIANCT Yellow) Margin to Field Fig. 90. image, as seen by the eye, it lies outside at the arrow-points A thus explaining the reddish yellow fringe to the field. Curiously these distinguishing characteristics of colour-ren- 114 DIAMETER OF PUPIL dering do not obtain with the holoscopic ocular when adjusted to become either an ordinary or a compensating ocular. This is explained by consulting the lower part of Fig. 86, when it is observable how the rays do not take up their final position in the virtual image until at least some sensible distance from the eye; hence a blue margin is seen in either case, that is to say, when the eyepiece is adjusted for the ordinauy or compensating effects. The cause of the red edge to the diaphragm in the case of the Ramsden compensating ocular needs no further comment, as the matter explains itself by the study of the previous figures. Before leaving the subject of eyepieces, seeing the importance that the emerging beam should always be the required diameter to enter and pass the pupil of the eye, it would be an omission not to show how to ascertain such diameter and to point out the philosophy by which such computation is arrived at, for little reference is made to the subject in most handbooks on the microscope. Of course the normal diameter of the pupil varies with difi"erent individuals, but it should also be borne in mind that any pupil varies from its normal diameter at different times according to the direction and the intensity of the light impinging on the eye. To fix the actual diameter of the pupil, or its variation from the normal, under different circumstances has been a desideratum under consideration by many physiologists and others. Taking a mass of evidence it may be presumed that, under the circumstances which hold with the microscopist, the usual working diameter is not far from one-tenth of an inch ; but whilst stating this somewhat empirically it mmst be understood with the formulae that are given and the discussion that follows, any diameter can be interpolated. Before actually commencing to point out how to ascertain the diameter of the emerging beam from the eyepiece, it should be stated that such diameter is affected by two factors : (i) the magnification of the eye- piece, and (2) the N.A. of the objective, (i) In Fig. 91 let OL be a lens of the same focal length as the objective and EL another simple lens of the same equivalent focus as the ocular. These simple forms are taken for simplicity's sake and in no way affect the general reasoning. Rays from the objective OL DIAMETER OF PUPIL "5 focus at Fj and oblique pencils at P'2, all other rays being excluded for purposes of description. Half the inverted arrow A would be formed at this situation. The rays at Fj, the focus, pass on to the eye-lens EL and issue parallel, one on one side Fig. 91. and one on the other of the axis ad . Those focussing at F2 pass on to the periphery of EL, are rendered parallel one with the other, and are bent towards the axis ad, meeting those from Fj as the diagram shows. This point of union is called the Ramsden circle. In Fig. 92 the same argument holds, but as OL l?AMSDEIlClRCUe / CL Fig. 92. the eye-lens is of shorter focus (a higher magnifying power) a smaller Ramsden circle is formed. It is obvious then that the higher magnification, with its smaller Ramsden circle, needs a smaller pupil than the larger circle shown in Fig. 91, where the magnification was less. Hence the greater the magnification the smaller may the pupil be. (2) In Fig. 93 let OL be an objective and EL the ^^/ispiece lens as before. Let the rays AA be alone considered. This repre- sents a lens of low numerical aperture, and the beam to enter the pupil is small as indicated by A'A'. Now let the full ii6 DIAMETER OF PUPIL aperture BB be considered — a lens of larger numerical aperture ; the corresponding pupil B'B' is larger : hence the higher the N.A. of the objective the larger the pupil required. Fig. 93- As, however, the N.A. remains constant with a given objective whilst the magnification is raised or lowered, so it is only with the first statement we have principally to deal. This, for con- venience of description and to clear the mind so as to under- stand better what follows, may be put another way. The diameter of the issuing beam becomes larger and larger as the magnifica- tion is lessened. The problem then is to show how to ascertain the lowest magnification with a given objective that is permissible to allow the beam from the eyepiece completely to enter the pupil of the eye, say of yV in. diameter. This magnification we state for convenience at once to be equal to 200 times the N.A . The argument for proof may be taken as follows : It must first be borne in mind that the compound microscopa^ apart from the inversion of the image, produces the same effect f r\ Eye I- Fig. 94. as would be shown by an optically perfect lens of the same N.A. and magnification. In Fig. 94 let f be the focus of the lens L, which has a clear diameter P. RAMSDEN CIRCLE n; From what has been said in the chapter upon numerical aperture, the general rule will be understood that follows : 1 p N.A. = —F~ or half the aperture divided by the focus. Transposing this — (I) N.A. = |,. The magnification (at loin.) of any lens / is m = —?. Trans- posed this becomes /= — , ni being the magnification under consideration. Introducing this latter into (i) we get — («) N.A. = ^— or N.A. = l^^J^. 2 X 15 111 In this formula we get the N.A. required to fill a pupil of given diameter at a given magnification. Example : What N.A. is necessary to fill, say, \ in. pupil at a magnification of 200 ? Then by a we find — i X 200 N.A. = L^ = 1-25, so N.A. r2S is required. If, however, we desire to know the diameter of the emerging pencil with a given N.A. and a given magnification, we have — „ 20 X N.A. {b) m Example : An objective with N.A. -65 and a magnification of, say, 650 ; what is the diameter of the emerging pencil ? „ 20 X '65 Again, on the other hand, presuming a given N.A. and a given diameter of pupil, what is the magnification required so that the pencil may pass the pupil ? Then — 20 X N.A. {c) - - M = p . Example : Let the pupil be fixed at tV '"•> ^"d the N.A., say, •65 ; then — ,7" 20 X -65 M = — -J- — = 130 diameters. ii8 RAMSDEN CIRCLE If now we put this another way, then — 20 X N.A. M = ; = 200 X N.A., which shows and furnishes the proof that the assertion made at the commencement of this discussion is correct. This formula also shows that the emerging pendil is only -^ in. in diameter, when the limit of useful magnification (viz. looo times the N.A.) is employed.^ ^ This subject may be put a different way which appeals better, perhaps, to the direct question. What is the Ramsden circle ? The Ramsden circle is really the ftnage formed by the eyepiece, of the full aperture of the objective, measured in. the upper focal plane. This image depends on the N.A. and on the focus of the objective in the well-known manner : Semi-diameter of the full aperture Equivalent focus of the objective ~ ' ' ' whence we obtain the diameter of the emerging cone of any objective, measured in its upper focal plane — = 2 X N.A. X Focus of the Objective. The eyepiece forms a diinmished image of this ; the diminution equalling the power of the eyepiece (according to Abbe nomenclature), i.e. equal to the number engraved on a compensating ocular. CaUing this number M, we have therefore the diameter of the Ramsden circle — 2 X N.A. X Focus of Objective ' = M • (i) This may be modified by introducing the initial magnification of the , . . 2SO mm. , , . , objective = '^^^.^^ ; whence we obtam by transposmg — ^ - , . . 250 mm. Focus of objective = , — ;^-j ^ — -. — ; ' Initial magnification and introducing this in (i) we get — 500 mm. X N.A. Diameter of Ramsden circle ; Initial magnification x Eyepiece number' The denominator is, obviously, the total magnification ; hence the simple rule — The diameter of the Ramsden circle = ~ — , '^^ — '-^^— . Total magnification The position of the Ramsden circle is where the eyepiece forms the image of the aperture of the objective, slightly above the upper focal plane of the eyepiece. Its distance from the top lens depends entirely on the construc- tion of the ocular, and cannot be foretold anyhow without a somewhat detailed computation. CHAPTER VII MAGNIFICATION The Evaluation of Objectives and Oculars and THE Limits of Useful Magnification To know how much an object is magnified is always a desidera- tum with the microscopist, but the importance of very great exactitude is often over-estimated by the student, who in addition is apt to think that amplification, taken as such, is everything, and who quite often forgets that unless it is accom- panied by sufficient " aperture " of the objective — which means by a sufficient inherent power of resolution — is useless and unprofitable. Concerning this important detail, we may mention the subject has been dealt with in the section devoted to the explanation of Numerical Aperture (Chapter V.), and that it is referred to again later on. Before explaining the methods that can be adopted for the evaluation of objectives and oculars, however, a few words should be said in defining the terminology used, which in recent years has undergone a certain amount of alteration. With the older microscopists two terms were in familiar use. An object was said to be magnified so many " times " (or " areas "), or so many diameters. Let Fig. 95 be con- sidered. An enlarged image of the object ABCD, we will say, is cast upon a screen at a Fig. 95. given distance, and shown as EFGH. If now a pair of compasses be taken, it will be found that EG is twice AB, GH twice BC, FH twice DC 119 I20 MAGNIFICATION and EF twice AD. It is not difficult to understand the dotted lines ; LKM and OKP are drawn equally, dividing EG and FH and EF and GH respectively. Then EL and LG are each equal to AB ; GP and PH each equal BC, and so on with the other sides. A little more attention and it is evident that there are four squares, each equalling ABCD ; so this object is said to be magnified four " times " or four " areas." But it is equally obvious that ABCD is only enlarged twice in each direction — twice from above downwards, and twice from side to side. Hence, when speaking in what is called linear measure, the object is said to be amplified two " diameters!' This holds good for any magnification, and in Fig. 96 the little square A is magnified five diameters in the enlarged picture by its side ; but as the larger diagram has twenty-five little squares in it, so it can be said to be twenty-five "times" as large in area. This is a simple explana- tion of the two different cc Fig. 96. terms that used to be in vogue. But the scientist never spoke in terms of areas at all, for his magnifications were always expressed in diameters ; hence, as time passed along, this expression of " times " simply died out of use. In comparatively recent years, however, it has become the fashion in daily use to speak of the magnifying powers of oculars in a manner that has led to a little confusion in the minds of some which we had better at once set straight. We refer to the expression that an eyepiece magnifies " times so much " ; for example, we read " that a times eight ocular (written X 8) was used in conjunction with a quarter-inch objective." Now what is universally under- stood in the present day is that the eyepiece in question had an initial magnifying power of eight diameters; but the mistake that has been made in the minds of some was, that " times eight " meant not diameters, but areas instead. Of course this has arisen simply from the unfortunate mean- ing which used to be attached to the word " times " as MAGNIFICATION 121 synonymous with areas, whereas now it is meant to be the same as diameters} Previous to the introduction by Professor Abbe of his system of apochromatics, he very rigorously reviewed the methods in vogue at the time for evaluating objectives and oculars. The difficulties and inconveniences in obtaining the real magnification of an object at the eye end of the microscope, which were thus made apparent to this careful observer, led him to reconsider the whole subject from quite a different standpoint, with the result that he originated and gave to the scientific and manu- facturing world what has been called his " new idea " upon evaluation ; and his method, which requires some little attention to follow, has been slowly but surely adopted by all, or nearly all, the leading opticians both in England and on the Continent. Before proceeding to explain " the Abbe evaluation method," however, we must first show the older methods which obtained up to the time in question, and which even now are employed by microscopists when dealing with objectives and oculars not arranged upon his special system of nomenclature. To obtain the magnification of an object as seen at the eye end of the microscope in the easiest way, is by the use of what has been called the " rational system." It is based upon direct experiment, which, although tedious to carry out, is easily made by any intelligent observer in the following manner : Place any objective — say an inch — on the microscope, and use first what is called an " A " or No. i eyepiece. Having procured a stage micrometer (which is only the name for a cover-glass ruled with lines of some definite distance apart and fixed on an ordinary 3 x i slip), and having focussed any two lines which are separated by an interval thought to be of con- venient dimensions, a piece of ground glass is placed at a distance of 10 in. from the eyepoint of the ocular — which will be found 5 to 10 mm. above its eye-lens. A pair of compasses are now used to measure the interval of the lines as seen on the ground ' glass, which interval (having been converted into terms of the 1 It has been thought advisable to interpolate this short explanation more especially as the original distinction between "number of times" and " diameters " is still held somewhat sturdily in the minds of certain laymen : indeed we have known a positive contention arise upon the expression " times eight" or "times twelve" as applied to an ocular in its modern sense. 122 ASCERTAINING MAGNIFICATION same order as those on the micrometer — that is to say, "so much of an inch, or so many millimetres") is then divided by the distance known to exist between those on the stage micro- meter. The quotient thus obtained is the linear magnification required very approximately.^ This process must be repeated for every eyepiece and with each objective in succession, and a table of reference made. Although this constitutes, perhaps, the simplest method of obtaining the existing magnification afforded by a given combination of objective and ocular, still it is obvious that fresh measurements must be made with every change in length of draw-tube. The consequence of this is, that when an observer draws out his tube to correct the aberra- tion of an extra thin cover-glass, all his magnification values are immediately upset, and he has again to recalculate them for the special " draw " in question if he desires any approach to accuracy. To meet this difficulty, opticians frequently not only give a table of magnifications for the combination of certain of their own objectives with their different oculars, but also add an appendix to show how much increase of amplification is caused by additional lengths of the draw-tube. For approxima- tions this tabular system amply suffices, but it is not sufficiently accurate to please some minds. Practically and theoretically it is really much better for the microscopist to ascertain, once and for all, the actual values for each objective and eyepiece separately, so that magnification at normal tube-lengths is immediately found by muFtiplying together these two factors, any increase in the tube-length proportion- ately increasing the magnification of the objective. By this is ' meant, that if such value at a normal tube-length of any given objective be, say, 60, and the tube has been additionally drawn out one-sixth the entire distance from objective to eyepiece, its initial value is increased thereby approximately to the same extent : we say approximately because hereafter a slight modifi- cation, it will be shown, is necessary if great accuracy be required. Having ascertained this new quantity, the amount has only to be multiplied by the magnifying power of the eye- piece in the usual manner to complete the operation. 1 To make this quite plain, suppose the lines were known to be ruled ^■^ in. apart in the micrometer, and they appeared on the ground glass to be separated by A in. instead, the magnification would be times ten, written x 10. RATIONAL METHOD : IMAGE PLANE 123 How to ascertain these separate values, however, involves some little thought and explanation, and seeing that such very fittingly forms an introduction to and explains the reason why Professor Abbe introduced his elegant and original modification of the entire subject from beginning to end, we will at once proceed to put the reader in possession of the whole matter from its very commencement. Theoretically, the process of obtaining the power of an objective consists in measuring the amount of amplification of the object in that particular plane within the draw-tube where the computer has elected his focussed image shall always lie. But it is here that difficulties at once arise. If the optician were asked to furnish the position of the " image plane," as it is some- times called, he would not describe its situation as being at such and such distance up or down the draw-tube, which without certain qualifications and explanations might be cumbersome and unscientific, but as so many millimetres distant above the upper focal plane of his objective (see Appendix). But where is this upper focal plane of an objective to be found ? How can it be located ? And what is the distance above it that is usually selected for the image plane to lie in ? None of these details are ever given with objectives,, even though manufactured by the best of opticians, and we cannot recollect having met with an English text-book that even mentions the question. When Professor Abbe took the matter into his consideration all these positions were in a chaotic state of confusion, for one computer chose one set of data whilst a second chose another. The conse- quence of this was that much had to be presumed, and the secondary consequence was that many objectives were thought to magnify more or less than others, although of the same focus ! To this confusion was added yet another, which arose from the fact that opticians insisted on calling their oculars by either letters of the alphabet A, B, C, D, or by numerals I, 2, 3, 4, without giving any hint whatever of their relative magnifications. It is usually now adopted by convention — owing largely to the masterful influence of Professor Abbe's writings and teachings — that the distance of the image plane of focus from the upper focal plane of the objective, called "the optical tube-length," shall be 180 mm. for the short or Conti- nental form of microscope, and 270 mm. for the long or English 124 OPTICAL AND MECHANICAL TUBE-LENGTHS form. But no such definite position has been decided, we believe, for the position of the upper focal plane of the objective.^ It will be shown hereafter that that is one of Professor Abbe's " proposals," and that such proposal is getting more and more accepted by all English and Continental manufacturers. Seeing that the real magnification of any objective can be at once calculated by dividing its optical tube-length by its real focus, without the trouble of actually measuring the amplification on a ground glass or other screen at the image plane of focus, so it is evident that it is of more than academic interest for the student to be able accurately to determine and locate the exact situation of this plane with any given objective under examination. From what has been said, the practical microscopist will readily admit that the magnification at the image plane will largely depend upon the length of this optical tube ; but it may not be immediately apparent how it is also largely affected by the true focus of the combination. This will be better under- stood by the following explanation dealing with, say, a 2-mm. objective. If it were possible to place a piece of ground glass at its upper focal plane, it would be found that there was no magnification at all. If the screen were removed 4 mm. from the same starting point, then the amplification would be found to be 2 ; if removed 180 mm., then 90 ; if 270 mm., 135, and so on. Hence the rule is simply this, that the real magnification of any given objective is always to be found by dividing the length of the adopted optical tube (that is to say, the distance of image plane from upper focal plane) by \h& focus. It is obvious then that the focus of the objective may be said to be a kind of yard measure — so to speak — of the amplification. Before proceeding to describe the method for discovering the position of this upper focal plane of any objective, no confusion must be allowed to remain in the reader's mind with respect to the two tube-lengths, of which we shall speak and of which we have spoken. The mechanical or standard tube-length is the name given to the interval that is included between the shoulder of the objective (when in situ on the microscope) and the eyepiece end of the draw-tube ; such distance being now by common consent fixed at 160 mm. or 170 mm. for the short or ' It varies, as a matter of actual fact, very sensibly in some cases. LOCATING UPPER FOCAL PLANE 125 Continental instrument, and 250 mm., or 10 in., for the English model. But when the expression optical tube-length is employed, it should be understood to mean the distance in millimetres \ between the upper focal plane of the objective and the image plane where the image of the object would be found in the draw-tube were the eyepiece removed after focussing and adjusting the mechanical tube-length to its proper amount. This length, we have just stated, is 180 mm. for the short or Continental instrument, and 270 mm. for the long or English form. It will be seen then that the optical tube-length is usually 20 mm. more than the mechanical — at least, that is the suggestion of Professor Abbe — in the case of each type of instrument. In locating the position of the upper focal plane the first step is to ascertain the actual focus of the combination. To do this two measurements of magnification m^ and m^ are taken with two tube-lengths Lg and Lj. The distance between the upper focal plane and a micrometer placed in the eyepiece will then differ from the mechanical tube-length by a constant quantity x ; therefore we should have, theoretically — ^" ^ ='«« and ' ^ =-.mu focus focus From this we see — L, + ;ir - (L„ + x) or — L. + X - ha - X focus =«.-'«o, reducing which we obtain — (i) - Focus =^^'^ _J, which being interpreted means that the _ difference of tube-lengths employed OCUS - jji|5fgrg„(;e of magnification experimentally found" In actual practice to carry this out, two rulings on cover-glasses are obtained, one with divisions -oi mm. apart mounted on a slip to place on the stage of the microscope, and the other with divisions separated by intervals of "i mm. This latter " ruling " should be mounted on a disc of glass , of such diameter that it can be slipped into a Ramsden eyepiece, which must be arranged so as to permit the rulings being inde- pendently focussed before the ocular is placed in the microscope. a 126 FINDING THE FOCUS ACCURATELY A Huyghenian form may be used for this purpose by removing the field-lens and using the eye-lens only, but here, too, arrange- ments must be made for focussing the rulings before using on the microscope.^ The exact distance between the eyepiece micrometer (remembering that the cover-glass ruling in these eyepiece micrometers is in most cases balsamed beneath the disc of supporting glass) and the end of the draw-tube must be very accurately ascertained with the eyepiece in situ. In an example which follows, this distance was found to be I3'5 mm. Having placed the objective to be tested on the microscope, several measurements must now be made (say four as in the example that follows) and their mean taken, so as to ascertain how many divisions of the eyepiece micrometer equal, say, five divisions of the stage micrometer. Let us say these are as follows : mm, mm, ■05 (say) is found to be contained in •05 Ditto ■05 Ditto •05 Ditto •20 = 2I'I2 Therefore i mm, = io5'6 mm. The observations repeated on another part of the scale we will say furnish the figures i mm, = 1047 mm., hence the final mean shows that the adopted magnification is io5'iS diameters. The draw-tube is now pulled out, say, 60 mm. (making, as it happens, an entire length of 260 mm. from the shoulder of the objective to the end of the draw-tube) and five observations for magnification are again made. In this case we will suppose — 52-8 divisions of the eyepiece micrometer, which equals 5*28 53-1 Ditto .... 5"3i 52-5 Ditto .... 5-25 52-8 Ditto .... 5-28 •04 is found to be contained in 54-0 divisions of the eyepiece of the micrometer, which equals . S'40 •04 Ditto .... 54-3 Ditto . 5-43 •04 Ditto 54'i Ditto • 5'4i •04 Ditto . , , , 54-0 .Ditto 5'4o ■04 Ditto . , , . 54-0 Ditto . 5-40 ■20 = 27'04 ' If any difficulty arises in the reader's mind concerning this arrange- ment he is referred to the section on ascertaining the size of given objects, Chapter XII. FINDING THE FOCUS ACCURATELY 127 Therefore i mm. = I3S"2 mm. and we will suppose a second series gives i mm. as equal to I3S'4 mm. Hence the mean shows that the adopted magnification is x I3S'3. Continuing the precept contained in (i) to obtain the true focus, the differ- ence in the tube-lengths (60 mm.) has to be divided by the difference in the magnification experimentally ascertained ; hence — 60 = I ■QQ mm. 135-3 - 105-15 which is the focus required. To ascertain the position of the upper focal plane all that is now required is simply to multiply the magnification obtained either with the tube in or with the tube out (we will say with the tube out) by the true focus experimentally ascertained. Thus 135-3 X i'99 = 269-2 mm. The position then of the upper focal plane will be found to be 269-2 mm. from the image plane focus, which was, at the position the micrometer rulings had been placed, 13-5 mm. below the upper end of the draw- tube. Adding this amount to the 269-2 mm. makes 282-7 mm., which becomes the distance of the upper focal plane from the end of the draw-tube when extended in these experiments. It has been shown that this extension of the microscope from the shoulder of the objective to the end of the draw-tube happened to amount to 260 mm. exactly, so deducting this amount from 282-7 leaves 22-7 mm., which is the position of the upper focal plane below tlu shoulder of the objective. In another set of experiments with another objective this position was found to be 23-3 mm. below the shoulder. With respect to the evaluation of the ocular we must again point out and protest that eyepieces, whether of the Huyghenian or the Ramsden type, are usually numbered with the numerals I, 2, 3, etc., or by the letters of the alphabet A, B,, C, D, lettering that conveys no possible information whatever as to their magnifying power. All that the microscopist knows is that No. I or No. A magnifies least and that No. 4 or D amplifies most. Some few opticians, it is true, give more information, calling their oculars by their real focal lengths, so that we hear of a 2-in., i-in., |-in., and so on. If these assigned foci be really correct we know at once their real magnification by dividing the conventional distance of distinct 128 MAGNIFICATION OF OCULAR vision, viz. lo in., by the focus— hence a 2-in. magnifies five diameters, an inch ten, and so forth. If we are dealing with the simply "lettered" oculars, their magnifying power may be found by using them upon any objective (of which the magnification value has been previously accurately determined) and projecting the image of the stage micrometer on to a screen lo in. away from the eyepoint (about S to lo mm. above the eye-lens) and measuring how much the final magnification amounts to. Knowing the initial of the objective we divide the final sum as shown on the ground glass by the amount, and the quotient gives the magnifying power of the ocular. If for example the magnification power of the objective has been ascertained to be 60, and the final amplification on the screen amounts to 300, we know at once that the eyepiece is responsible for a magnifying power of 5, because 300 divided by 60 = S. This method of testing the magnifying power of oculars furnishes true results provided the eyepieces are constructed by the optician who made the objectives ; for it is presumed he would have arranged them so that they all fall in the draw- tube the correct distance so that their lower focal planes shall coincide with the image plane of the objective. Unfortunately until Professor Abbe strongly urged a uniform position for all manufacturers to abopt, this was not, and is not even now, always the case ; and the consequence of the lack of uniformity is that an eyepiece by one maker may apparently magnify more than that of another (although of the same designation), or that an objective with a certain ocular may appear to ' magnify more or less than another objective although of the same focus ; obviously because the two manufacturers have not arranged for their oculars to drop in the tube a similar distance. If one were to have dropped too far, the final magnification would of course be too small, because really the optical tube was thus being unconsciously shortened, whereas if the ocular did not drop in far enough, the optical tube being thus lengthened by the error, the magnification would be imme- diately increased. It is scarcely necessary to add that all manner of confusion was frequently being introduced in this way, and makers were sometimes blamed for sending out an objective which did not apparently magnify enough, or perhaps LOCATING LOWER FOCAL PLANE OF OCULAR 129 one that amplified more than it theoretically should. Once again we stop to point out how these discrepancies urged upon Professor Abbe once and for all to set matters on a distinct footing by introducing a system quite different for his new apochromatic series of objectives and their compensating eye- pieces, with which no such fault can be found. Should the microscopist wish to ascertain the position of the lower focal plane of any eyepiece (see Appendix) he must proceed as follows : Lay across the end of the draw-tube any sort of glass scale with the divisions downwards, that is towards the objective, and place on the stage some well-defined object of any kind. Aided by some sort of hand-magnifier let him now focus the object on the stage in such a manner that when he sees the lines of the divisions correctly he sees the object on the stage equally well focussed. This means that the image projected by the objective lies on the same plane as the upper end of the draw-tube upon which the ruled lines have been resting. Having removed the latter rulings the Huyghenian ocular to be tested is gently slid into the draw-tube and a position found (without disturbing either the focus or the draw-tube) where the eyepiece shows the object in the stage distinctly focussed. The tube of the ocular must now be marked level with the top of the draw-tube, for that is the position of the lower focal plane of the eyepiece in question. If the ocular be a Ramsden, owing to its focus being outside the lenses in contradistinction to between them as obtains with the Huyghenian, a piece of tubing must be employed which, while holding the eyepiece ' at one end, will slip into the draw-tube at the pther. After ' obtaining the position of best focus (as before) a line must 1 be drawn on the auxiliary tube corresponding with the end \ of the draw-tube. This marks the position of the lower focal ' plane of the eyepiece in use. Strictly speaking, all these matters should have been gone into before measurements were made by projecting the image on the ground glass to obtain the final magnification, due regard being paid to such observations: then the final amplification on the ground glass divided by the magnifying power of the .objective gives the true and not approximate magnification of the eyepiece. When these magnifying powers have been obtained for objectives and eyepieces, any of the eyepieces 9 I30 ABBE NOMENCLATURE (tested) can be used upon any of the objectives (tested), and multiplying the values together will give the true magnification values required. Increase of the mechanical tube-length simply alters the length of the optical tube and so proportionately increases the magnification of the objective. The results of an increase of the draw-tube are now really true and not approximations as we before stated, when we considered the matter in the earlier stages of the argument and before the difference of optical and mechanical tube-lengths was pointed out. This concludes the explanation and discussion of the leading points concerning the methods of ascertaining the real magni- fication values of objectives and oculars under the old methods adopted before Professor Abbe came upon the scene with his new nomenclature. In consequence of his researches in the subject of microscopy in general, and his great and many investigations in all things optical in particular, a revolution has been slowly but steadily brought about in the minds of most computers, more especially evident since the introduction of his apochromatic series with the accompanying compensating eyepieces. The ingenuity of the suggestions embodied in the conception and carrying out of this apochromatic system and the practical utility found to exist in the general everyday use of his methods of evaluation both of objectives and eye- pieces, have induced most up-to-date manufacturing opticians to adopt his lines of thought and the leading features of his nomenclature. To an explanation of this we will now turn. The Abbe Nomenclature We have already stated that Professor Abbe proposed the length of the optical tube for the Continental microscope of i6o mm. mechanical tube-length should be i8o mm. and 270 mm. for the English model ; but we did not mention he decided to fix the position of the image plane for both models at 12 mm. within their draw-tubes. It is obvious this involved the construction of his compensating oculars for both models to be such that their lower focal planes should lie 1 2 mm. from the end of the draw-tube when slipped into their working position. This was an excellent idea, for interchange of oculars ABBE NOMENCLATURE 131 involved practically no change of focus.' Further, he elected to call the initial value of every objective — whether for the short tube or the long — what it would be if treated as a single simple magnifier held close to the eye : hence a 2-mm. would be said by him to have an initial magnification of 125 diameters (2 50 -=-2) whether used on the short or the long tube. It is at once seen that here he made a pronounced departure from all convention, for it was obvious that if a 2-mm. magnified 125 on the long optical tube of 270 mm., it could not possibly magnify the same amount on a tube 180 mm., two-thirds the length. To correct this apparent anomaly he gave to his oculars ficti- tious values, in other words not magnification values such as would be obtained by the hitherto orthodox method of dividing 250 by their focus. He consequently called his fictitious figures by a new name, that of "angular magnifications," the actual quantities being obtained by employing the following ingenious though absolutely arbitrary method. He considered, as we have already said, that the objective was nothing but a simple magnifier, of a power corresponding to its focus, producing a large and distant image of the object. Thus the " initial " magnifying power of all his objectives comes really to depend upon their focus only, and quite independent of the length of the draw-tube. In accordance with the conven- tional distance of distinct vision the value, as we have said, was based on a lo-in. or 2SO-mm. vision distance. Dividing this by the focus gives the initial power of the objective according to his system. The distant image produced by the objective can, like any other distinct object, be made to subtend a larger angle by looking at it through a telescope, and according to the power of such we should naturally get more or less " angular magnifi- cation." Of course, microscopes are not made up of a magnifier plus an astronomical telescope ; but Professor Abbe got over that difficulty by imagining a compound lens placed at the upper focal plane of the objective, such lens being composed of a concave portion just the right power to weaken the objective so as to turn the real projected image into a distant virtual one, in contact with an exactly compensating convex lens ' We have noted elsewhere that Messrs. Bausch & Lomb have adopted the same for their ordinary Huyghenian eyepieces. 132 ABBE'S IMAGINARY OBJECTIVE which formed the imaginary objective for his imaginary telescope. The numbers then on the compensating oculars mean the angular magnifying power of the imaginary telescope, with its imaginary but otherwise perfect objective in the upper focal plane of the microscopical objective. Obviously this telescope gets longer when the tube-length is increased, as on a real telescope, hence the same eyepiece magnifies according to the length of such telescope. Professor Abbe ideally pictures two of these telescopes, one with an imaginary object glass i8o mm. focus and the other with one of 270 mm. in length. It now becomes evident that the ocular must apparently magnify I'S times as much on the 270-mm. telescope as on the 180 instrument, and that explains the reason why he tells the microscopist if he uses the short-tube eyepieces on the long-tube microscope their values must be considered i'5 times greater.^ ' As the above paragraph may be difficult to understand, perhaps the following may make it more clear. Let Fig. 97 be considered : a micro- scope consisting of an objective O, field lens F, and eye lens E is turned on an object I. The objective alone would form the real image II. This is intercepted by the field lens F and changed into the smaller, but sharper, real image III, which latter is magnified by the eye-lens E into the virtual image IV seen by the eye. Abbe's imaginary compound lens is placed at A, in the upper focal plane of the objective— ze/^^ri? any lens may be placed without altering the equivalent focus of 0— and is supposed to be composed ABBE NOMENCLATURE 133 It will be readily seen in Abbe's nomenclature the initial values of the objectives are not powers of magnification at all in the strict and ordinary sense of the word, for they will not be found correct if experimentally tested on a i6o-mm. or on a 2So-mm. mechanical \.\ihe. instrument in the manner previously explained, neither are the eyepieces figured with their real magnifying powers obtained in the ordinary fashion, as we have already shown. But, strange as it at first sight may appear, when these two (if we may so speak) fictitious values in question are multiplied together the result is nevertheless the true magnification required. On consideration, however, such is not to be wondered at, if the subject be looked at in a different way. There are four factors employed. The first, which we may call F, is the focus of the objective ; the second, which we may term E, the focus of the eyepiece ; the third, T, the optical tube-length ; and the fourth and last, V, the conventional distance of distinct vision. In the old method of evaluation to obtain the final magnification we have Mag°- = — x 51 whereas V T in the Abbe method we have Mag"- = |r x ^. By this it is at once seen that, after all, the factors are multiplied together in the same fashion, which explains the apparent anomaly. For example, let a 2-mm. short-tube objective be dealt with. Its Abbe value is 125. If tested on a short-tube microscope (by the methods already described) of 160 mm. mechanical tube- length, its magnifying power is not 125 but 90; and if on a 250-mm. mechanical tube-length it will be 135. Still, if we use on the short-tube instrument, say, an 8-times compensating ocular, the result — obtained in the usual manner 125 x 8 — is 1000 ; a quite correct estimate, because really on the 180 optical of a concave and a convex component neutralising each other. By reckoning the concave of suitable focus (equal to the optical tube-length) with the objective, the latter becomes a magnifier producing a very distant image of the object. The convex part of A, taken with the eyepiece, forms an astronomical telescope by which further "angular " magnification is obtained — i.e. whilst the eye placed behind the imaginaiy concave lens would see the object under the angle a, it sees it through the imaginary telescope — under the larger angle ^. Tangent a divided by tangent /3 is the proper figure to engrave on the eyepiece, according to Abbe's nomenclature, as its power. _ 134 ABBE NOMENCLATURE tube the magnification of the objective has been shown to be actually go (180-^-2), and the 8 eyepiece having a focus of 22-5 mm. (which means in old-fashioned language a true magnifying power of irii) produces a net magnification of 999-9. A little further thought will show that the figures for the " angular magnification " of any of the compensating oculars can always be correctly obtained by dividing 180 mm. by the real focus in millimetres for the short tube, or by dividing 270 mm. for those adopted upon the long. Further, it will be now understood that as the initial values of the objectives (under this style) are recognised not to be really the true values either with the 160 or 250 mm. mechanical tube-lengths, and that as the figures for the oculars are not the real magnification quantities in diameters, why the term fictitious nomenclature has been by some writers applied to Abbe's elegant method, to distinguish it from what has been designated as the rational system already explained. But in justification for its general acceptance, it will be seen to be an arrangement of great convenience for the ordinary micro- scopist to calculate the final magnification at the eye end for the two ordinary models of microscope — simply by multiplying the two values, that of the objective and the ocular, together ; always provided the optical tube-lengths are either 180 or 270 mm. But it is just here at this point where the system may be said to break down in convenience. If when using, say, a 4-mm., without cover-glass adjustment, an additional draw of the tube is necessary to correct an extra thin cover-* glass, the optical tube-length is at once altered and the validity of the initial power at once flies to the winds. To obtain the real final magnifications under these circumstances, it is first necessary to find out the new length of the optical tube by measuring the distance from the upper focal plane of the objective to the lower focal plane of the ocular, which we have stated is fixed by Professor Abbe to be 12 mm. below the mouth of the draw-tube (let us say for argument this tube- length was found to be 200 mm.), and then, to ascertain the new values of the ocular, work a proportion sum. Seeing that the normal optical tube is 1 80, we say : 180 : 200 as the angular value of the eyepiece is to the required figure. ABBE NOMENCLATURE 135 Working this out, and presuming the eyepiece we were using was, say, an 18 on the short tube, we find the new fictitious value of the ocular is 20, and therefore the final value of the total magnification at the eye end will now be 60 x 20 = 1 200 instead of 60 x 18 = 1080, which it would have been with the normal optical tube-length. Owing to this little diiificulty, disciples of the old school dispute somewhat warmly the advantages " presumed to exist " in the new nomenclature ; but, notwithstanding, as we have before pointed out, the method has " taken " so with nearly all up-to-date manufacturing opticians, that it will be rare in the near future to find any who do not adopt it. With reference to its adaptation to objectives, when constructing a "series," it is not at all times easy to regulate the computations and the manufacture in such a manner as to conform strictly with the " new method." Constructively speaking, Abbe's fixed position for the upper focal plane is 32 mm. below the shoulder of the objective, because the optical tube-length of 180 mm. + 12 mm. (the position of the image plane below the end of the draw- tube) makes 192 mm., and 192 less the mechanical tube-length of 160 leaves 32 mm. as the limit. The computations, therefore, have then to be performed with such an accuracy and in such a manner that these figures shall be correct to within a possible error not exceeding 5 per cent. Looking back to the experimental examination of the 2-mm. short-tube apochromatic, we found the position of its upper focal plane to be 227 instead of 32 mm. from the shoulder, which is an error of 9 mm. in 180, just equal to 5 per cent. But, slightly to compensate this, and so reduce the error to about 4I per cent, we found the focus i'99 instead of 2'00. The idea of Professor Abbe to make all his apochromatics to one standard (save with a possible error not exceeding 5 per cent.) was doubtless a very good one ; but, as we have just said, at the same time it taxes very often the powers of the computer. In most cases this can be done with a fair amount of accuracy ; but in some instances, when the position of the upper focal plane is unavoidably wrong to a greater extent than would seem allowable, the careful computer will intentionally give to his objective a focus different from that engraved upon it, so that the final magnifications figured out according to Abbe's 136 LIMITS OF USEFUL MAGNIFICATION convention shall work correct for obtaining the final magnifica- tion values.^ On the Magnification of Objects in general, and on THE Limit of Useful Magnification in particular WITH Various Objectives There is no doubt that to the lay mind the most attractive feature of the microscope lies principally in its wonderful power of magnification : it naturally seems marvellous that an instru- ment can be constructed that will show anything enlarged a thousand diameters. But to the intelligent microscopist mag- nification pure and simple is quickly found to be of very little value unless the objective with which it is obtained is accom- panied with sufficient numerical aperture to render the details evident. Professor Abbe, in one of his laconic observations, went so far as to say, " Empty magnification is of no service whatever." It will be well to explain what he meant. To do so let us, by way of a popular illustration, presume for a moment we have a picture of a house with windows, front door, and chimneys complete ; and let it be further understood such a picture was formed upon some stretchable support, such as a piece of sheet india-rubber, and that its size was 4I x 3J. It is not difficult to understand that if this be stretched, say, to whole-plate size, 8| x 6\, the picture is enlarged ; in other words, it is magnified two diameters. If this now be examined, we shall see no further details whatever. It is true the chimneys are larger, and so are the windows ; but nothing more is shown about them with respect to detail in their structure or appear- ance. This is Abbe's " empty magnification." But if we had imparted to the objective magnifying the object that inherent property of adding detail at the same time that it magnifies — which is the same as saying if we had added to its numerical aperture — we should then have found the whole plate picture would have been furnished with distinctly fresh particulars. ^ We should mention that a little instrument called the Eikonometer has been devised by Professor Wright to enable the microscopist to obtain experimentally the exact value of any magnification with any objective, any ocular, and any length of draw-tube. It is described, with the method of use, in the chapter devoted to accessory apparatus. "EMPTY" AND "FULL" MAGNIFICATION 137 The windows would have been seen to contain curtains, the door a knocker, and the chimneys would have shown cracks in them. Further, if we repeated the process and increased the magnifica- tion and the numerical aperture, we should find the picture provided with more details still, for now the window curtains would be seen to be of lace, for the pattern is visible, the knocker on the door would appear distinctly as a serpent coiled up into the requisite shape, whilst the chimney-pots are evi- dently very old ones, as they show holes and minute cracks we could never see before. This illustrates in a popular manner what we may call " full '' amplification in contradistinction to Abbe's " empty magnification." With respect to the microscope, the relative peculiarities of the different kinds of amplification are perhaps best seen by examining the two reproductions shown in Figs. 3A and 3B, Plate I. The first illustrates " empty magnification," the ob- jective used being of insufficient numerical aperture to resolve the diatom into dots ; whilst in the second, on the contrary, the objective having a higher numerical aperture their pre- sence is seen quite distinctly, although, be it understood, the magnification in each case is similar. It is evident then a certain relation should exist between amplification and numerical aperture, so that empty magnification may never result, unless from some special cause such may be desired.^ This has been fully discussed in the chapter devoted to the N.A. of objectives ; but an outcome of the subject, although at first sight it may not be immediately apparent, is what may be called the converse of the problem, viz., seeing that the N.A. given to an objective is necessarily limited, to what extent is magnification justifiable by eyepiecing, so that fuzziness may not occur ; in other words, what is the limit of useful magnifica- tion ? (and upon what theoretical grounds is such obtained) in contradistinction to " what is the limit of useful numerical aperture." Theory shows indisputably that, owing to the finite wave-length of light, the image of a point cannot possibly be ' When dealing with objects such as tissues and the like, simple '' empty " magnification may be required to render the object more distinctly visible, so that the relation of one part to the whole may be better recognised ; hence pathological objectives used to be made of specially low numerical aperture. 138 DISC OF CONFUSION rendered by any lens or combination of lenses as another point, but must be represented by a disc of more or less sensible diameter. It is notorious, by way of illustration, that in the case of a telescope a star — which may for this purpose be regarded as a point of light— is not seen by the eye or shown on the photographic plate as a point, but as a disc. Moreover, it is known in the microscope that the size of this spurious disc is not necessarily a fixed quantity, as its diameter depends upon three factors: (i) the numerical aperture of the objective; (2) the wave-length of the light used (or perhaps it may be more convenient to say the number of waves to the inch of the light employed) ; and (3) the final magnification of the image. Seeing that twice the number of waves to the inch of the light employed ^ multiplied by the numerical aperture of the objective furnishes what is called its " resolving power," we may at once state, if the " resolution " of the objective be divided by the final magnification of the object, the reciprocal of the quotient is the diameter of the disc required. Take, for example, light having 47,500 waves to the inch and an objective N.A. v\o, and a final magnification of a thousand diameters. Simple arithmetic shows at once a circle of confusion of -^^ of an inch in diameter. We need scarcely add what we have said as applying to a point of light and its image produced by a lens also applies to a line, for that may always be considered as nothing but a sequential aggregation of juxtaposed points. It is very readily understood that by a suitable manipulation of the factors we have just mentioned as regulating the size of a spurious disc, its diameter may be kept within almost any prescribed limit. Hence the question very naturally arises. What is the smallest permissible disc {i.e. what is the least ^ Although mentioned in detail later on, it may be convenient to remind the reader here — seeing that wave-lengths are usually spoken of in the text- books in terms of tenth-metres — how to convert such measures into terms of the inch. This is easily effected by dividing the number 254,000,000 by the wave-length in tenth-metres, the result being that required. Vtce-versd, measures in inches can be at once changed into tenth-metres by dividing the same " nine-figured expression " when the quotient is the amount sought after. If, however, the wave-lengths be expressed in terms of what is called lifi (double mu), the nine-figured expression must be deprived of one of its ciphers and then treated as before. Visual light then of 47,500 waves in one inch is equal to about 5347 tenth-metres, or 5347 in terms of double mu. DISC OF CONFUSION 139 amount of fuzziness that can be tolerated) so that the eye may see the object distinctly defined ? Convention has agreed that the diameter of this disc shall not exceed ys-tt of an inch, con- sequently the care of the conscientious and practical microscopist should always be exercised, when adding oculars of increasing power, that this limit of disc-diameter is not exceeded. To assist him then in carrying out this extremely important detail, as well as two other cognate problems, the three following formulae are given : I. The first shows the method of ascertaining the diameter D of the spurious disc with a known magnification m ; an objective of a given numerical aperture N.A. ; and light of a number of waves to the inch equal to L. D 2(L) X N.A/ For example with an objective of numerical aperture, I'o; L 47,500 waves to the inch and magnification x looo, then — „ 1000 , . . , D = = 5V of an inch. 95000 X I 2. This formula furnishes the means of ascertaining the mag- nification m that will produce a disc of given diameter D with a light (L) of specified number of waves to the inch, and an objective of given N.A. — m = 2(L) X N.A. X D. Example : L = 47500, N.A. "65 and D = -005 in.. Then — m = 95000 x '65 x '005 = 30875 diameters. 3. If it be required to find the N.A that must be employed to obtain a given circle of confusion D, with light of L waves to the inch and a magnification m, then we employ — ^^•"- "-2(L) X D- Example : If D = ^ in., L = 47500 and m = 500, Then— N-A- - 95000 X -004 - ' 3^ """^''y- The table following is arranged to show at a glance the limit to be placed on magnification with different numerical apertures I40 LIMITS OF USEFUL MAGNIFICATION so as to ensure a disc of y^ of an inch not being exceeded, light 47,500 to the inch being employed : This is chosen because white light is usually considered as averaging about this number of waves to the inch. ^ . Approximate ^ '"■' magnification limit. •3 285 •5 ■ 450 I'o 950 I"20 . . . , . . . . 1 140 I'So • • 1235 i"3S 1282 I '4° 1330 If this table be carefully studied it will soon be seen to reveal a law, by the recollection of which such an array of figures need not be borne in mind. It is this. T/te magnification must never exceed lOOO times the numerical aperture or thereabouts. The utility of employing blue violet light for the most delicate work is very obvious from what has been said, and this was the reason the writer spent so much time in perfecting and arranging an apparatus for obtaining this monochromatic illumination with ordinary limelight, more especially for photo- micrography. Seeing that N.A. may be said to have practically reached its limit, further advance then in resolving power can only be expected by the use of light beyond the violet end of the spectrum, which is usually called by the name of ultra-violet light. Unfortunately, however, till lately two difficulties have seemed insuperable : one was the manufacture of a glass that would transmit these rays in question, and another was how to focus an image formed by light of this description, seeing that such is practically invisible to the human eye. The great ingenuity of the firm of Carl Zeiss has however, quite recently, overcome both these difficulties. The objectives are formed of molten quartz, and are corrected for a wave-length of 275 /u,/i, oculars being specially constructed from quartz crystals ; whilst to enable a focus to be made, a screen is temporarily employed — we believe of a character much like that used for X-ray work — by the use of which the rays are for the moment increased in length sufficiently for the eye to see the image, and hence for USING SHORT WAVE-LENGTH SCREENS 141 this operation to be effected ; but which of course is removed whilst a photograph is being taken.' It is obvious from what has been said that as the circle of confusion becomes smaller the shorter the wave-lengths of the light employed, the aim of the microscopist is to be able to command the use of light with a greater number of waves to the inch than 47,500. Monochromatic screens are used for this purpose, and they are explained and described later on together with an arrangement by the author for obtaining blue- violet light ; and mention is made also of a very nearly perfect blue glass by Zeiss recently introduced by the firm. ' The special features of this new type of objective are a very perfect union of rays (spherical correction) for the special light selected, the lack of a correction of chromatic aberration, and the composition of the system from uncemented single lenses all being formed out of the same material. It is needless to point out as there is no chromatic correction at all (because such is not needed) objectives of this make can only be employed with mono- chromatic illumination of the special wave-length for which the computation is designed. CHAPTER VIII THE SUBSTAGE CONDENSER AND THE DIFFERENT CONES OF LIGHT; AND THE SUBSTAGE DIA- PHRAGM: ITS ABUSE AND ITS USE; A SUBSTAGE condenser consists of a system of lenses which collect the light from the illuminant and concentrate it upon the object. The apex of the illuminating cone impinging upon the specimen without the intervention of any stop or diaphragm is said to form a "solid cone of light." If an iris or other diaphragm contracts the aperture of the lenses, the base of the cone being thereby reduced in diameter, the cone is spoken of as " a narrow one." If a stop be placed at the base of the cone, so as to prevent all rays passing through the centre of the back lens of the combination, the object has then a hollow cone of light impinging upon it, and is said to be illuminated by •' annular light." These condensers, or illuminators as they are sometimes called, vary in focus as well as numerical aperture, and are chromatic and achromatic in their corrections, a third class being erroneously called apochromatic. Several different forms of chromatic condensers have been made from time to time, but many of them are inferior to that devised by the late Professor Abbe and made by Carl Zeiss which has gradually supplanted them ; hence we confine our remarks to this special form of substage condenser. In its simple low-power form it is composed of a collecting lens and a hemispherical front which forms the focus of the light upon the specimen, the system having an aperture of not more than N.A. I'o. If this be well made it answers its purpose, but unfortunately, as supplied by some other makers, it often leaves a great deal to be desired. It is this fact that has led many 142 ABBE CONDENSER 143 microscopists (unfortunately including ourselves) to speak disparagingly of the performance of this combination ; but of course, as its name implies, it does not profess to be achromatic, and hence when used in its high-power form next to be described, shows colour to an objectionable amount when em- ployed with oblique light. The high-power form, N.A. 1-30, has an additional lens, and requires oiling to the slip in the same manner and for the same reason as an objective, of the immersion type, requires oiling to the cover-glass. Each of these chromatic condensers is mounted in a cell which drops into some sort of sleeve forming part of the substage. It is then capable of being racked up and down as necessity demands. In many Continental forms of stands this sleeve forms part of an independent fitting which is fixed— though not permanently so — to the substage, and h capable of being turned aside out of the way when not required. The achromatic variety, even for visual purposes, especially when oblique light- is being used, is in our way of thinking far superior, and we always recommend it. In photomicrography, too, unless monochromatic light be used, achromatic condensers are to our mind of greater service than the less complicated variety. It is perfectly true, however, that Mr. Poser, the manager of the English branch of Carl Zeiss in London, who is so well known both as a scientific expert of the highest order and as a highly practical mechanician, has taken photomicro- graphs with the chromatic condenser in use, which are pictures beautiful to behold ; still we have heard the critic say, " Would they not have been even better (if possible) had an achromatic form of illuminator been employed ? " Be this as it may, bearing in mind how differently an expert uses a piece of apparatus to one who is merely a tyro, we think the general tendency amongst all microscopists is to prefer the more highly ^ corrected condenser, even for visual purposes. This statement seems more or less evidenced by the fact that all the modern condensers are of the achromatic variety, such as those by Beck, Swift, Watson and others ; but it must in fairness also be stated that but few Continental firms advance their claims. The apochromatic condenser is a name unfortunately adopted by some opticians for an otherwise good combination. It is evident, however, that such is a misnomer, seeing that an 144 CONDENSERS apochromatic combination must before all things be absolutely free from spherical aberration and spherical zones, whilst all these condensers are not even capable of giving a full aplanatic cone ! Notwithstanding this we readily admit the type is of a useful kind (although not better than the first-class achromatic), as we ourselves can testify, having employed one in photo- micrography in many instances with considerable satisfaction.^ The leading points to be considered in a condenser are : the focus, numerical aperture, size of the aplanatic cone, and the definition. With respect to the length of focus of any given condenser, this is usually furnished by the maker as a result of his com- putations, and it is difficult to obtain experimentally save but by the same method as we have already given when dealing with a similar inquiry in connection with ordinary microscopic objectives. In the case of condensers made in England, seeing they are small and mostly mounted in the " universal fitting," this is easily performed by screwing them on to the nosepiece, and proceeding in the ordinary way ; but this cannot be carried out with those made by Zeiss and other Continental firms on account of their great size. The only method we know is to measure the size of the illuminant (taking care such shall be small by interposing a diaphragm in front of the same), and focussing and measuring it carefully. This measurement should be compared with the size of the same aperture as indicated by other condensers of known focus under similar conditions ; but the method is not a satisfactory one, and requires carrying out exceedingly carefully, or false results may be obtained. ' One point we ought perhaps to mention, seeing it has been brought forward as a further argument why the so-called apochromatic condensers cannot be truly apochromatic, is the entire absence of any compensating ocular or its equivalent. This at first sight appears a very formidable and convincing reproach. On consideration, however, it is not so because the important part played by the compensating ocular is mostly effective in the outer areas of the field of view, and least so at the centre ; hence it would only be with extreme oblique light such might be appreciable. But even here the matter is of no consequence in the case of condensers, as the loss of refinement in detail brought about by the non-adjustment for chromatic differences of magnification (the function of the compensating eyepiece) is not appreciable to the slightest degree ; hence the entire objection falls to the ground. FOCUS OF CONDENSERS 145 With regard to the most suitable length of focus for con- densers to have so as to suit objectives of different powers, a limit is placed thereon which may not be immediately apparent. For that reason we will enter into the matter somewhat fully, more especially as the subject has escaped the attention of most writers in the text-books published. It will be noticed by looking through the list given on page 152, that the foci of illuminators made by different opticians become less and less within somewhat defined limits the higher their numerical aperture. To explain this involves a little close attention. Consider a highly apertured condenser, say one of N.A. 1-35. It has to fulfil two conditions: to furnish plenty of light, and to have a high numerical aperture. Now the amount of light — which is another way of saying the brilliancy of the image of the illuminant — in any lens is augmented by decreasing the ratio of focal length to aperture. Readers who F are familiar with photography will recollect that -g- supplies four times the amount of light to the sensitive plate that is afforded by -p, no matter what is the focus of the system in use. This arises, as the reader also full well knows, because the avail- able diameter of the lens is twice as great, and as the area is the square of the diameter so the quantity is four times as much. Now to obtain the value of any numerical aperture expressed in terms of what we may call the F ratio, for reasons set forth in the footnote,^ we must divide -5 by the numerical aperture in ' (i) N.A. always = \, where rfis the diameter of the back lens and/the focus ; for example :— if i in. be the diameter of back lens and 4 in. the focus, we have NvA. = 7 = -8 = -^^S- F _ 4 ,1 J ^ (2) Rapidity or F ratio = -j, in our example - ^ = ^y called -■ To establish a ratio between the two quantities, multiply both sides of (i) by F and divide both sides by d. Then we obtain— ^xN.A. = i; and further dividing by N.A. we find— ■^ = F ratio = sta: "' W.\. ' 10 146 F RATIO OF CONDENSER question, the quotient being the denominator required; thus N.A.i-40 = :|-^. For convenience of reference the following table is set out : — F F 1-35 voo ■■ ■95 = •65: ■30^ •24 ■■ F •5 F •52 F 77 F 1-6 F 2-o8 By this it is seen that the i'3S condenser really works, as the F photographer would say, at — ; in other words a very brilliant image of the illuminant is rendered, one exceedingly so in comparison to that formed by a lens, the aperture of which is F restricted to -q, which only reaches '0625 in terms of numerical aperture. In the manufacture of any condenser for the micro- scope, however, a limit is placed upon the diameter of its back lens, because otherwise the combination would not fit into the " universal thread," which is the standard size mostly adopted by English opticians ; and if larger than this, complications are found to arise with the working of the centring arrangements. This actual limiting diameter is about yV of an inch. But to obtain these high numerical apertures large back lenses to the combination are absolutely necessary, far larger indeed than it might be supposed, because it is the ratio of the semi-diameter of the back lens to the focus that constitutes the numerical equivalent. Hence, as a limit is imposed on the computer in this direction, he must necessarily lower the focal length accord- ingly, and consequently we find the actual focus of these high- apertured combinations must be somewhere about |- or ^ of an F RATIO OF CONDENSER 147 inch to fulfil all the conditions of which we have spoken. The microscopist then has not much scope for selection. It can be readily understood that the light issuing through the I '3 5 condenser of so short a focus (seeing that the shorter it is, the smaller the image of the illuminant) is exceedingly intense, which can be better appreciated by the photographer when we remind him the F ratio is so remarkably small. It will be further seen that the 13 5 combination passes about 18^ times the light transmitted by a , low-power condenser, say one of N.A. "3, by which we mean the actual image in the one case is about 18^ times brighter than in the other. A question may here be asked which is often met with. If this theoretical statement be true, how is it that when using the "3 condenser and an inch objective N.A. -3, say with an ocular x 4, the light of the lamp is almost unendurable ; whereas with the I "3 5 condenser, and, say, a ^^th of corresponding aperture with ocular X 8, the field is sometimes too dull to be useful ? How can this be when the higher apertured condenser, we say, passes V through 18J times more light? It is due to the difference in the relative final magnifications used. In the first case this amounts to only 40 (10 x 4), whereas in the latter it is 1000 (125 X 8). The direct consequence is that the light from the lamp is really, although not apparently, spread over a very much larger area of field (only a small piece of which is utilised), and hence is fainter to the eye than in the previous case, where, owing to the amplification being so much smaller, the image, though primarily of much less brilliancy, is so much less spread out that to the eye it actually appears very much more intense. It is evident then that the choice of foci for condensers to be used with objectives of different numerical aperture is neces- sarily limited by the demands of optical construction. Without pressing the matter further, these conditions limit the focus of the illuminators for high aperture to about f to J of an inch ; for those about N.A. I'o to f to f, whereas with quite low powers the focus may stretch between f of an inch to even 2 in. From what has been said, the image of the illuminant in high- apertured systems is necessarily small. Usually the diameter afforded is sufficient, but at times it is often felt that a larger flame image would be very useful. This can be effected by use of the bull's-eye, as we have already stated, but its use is not always 148 APLANATIC CONE OF CONDENSER attended with desirable results as respects definition ; hence, to meet this end, Mr. Conrady has computed and Messrs. Watson & Sons have made a condenser of N.A. I'O with aplanatic cone of '95 that is a trifle longer in focus and hence furnishes an image about | times greater. Of course this demands a large back lens, but its diameter just enables it to be used with a special centring fitting in the ordinary substage. It is a very excellent combination, and by removing the top lens the remainder can be employed for objectives of lower numerical aperture. There are several makers of good condensers, but of course many microscopists have their favourites ; before selection, how- ever, it would be well for the student to test the performance of the combination in the manner about to be explained. First, as respects its numerical aperture. This can be often obtained by the use of the apertometer, but not if it be a condenser with a large back lens. It is best then to use the method described on page 98, originated by Mr. Conrady. But condensers are now more usually classified according to the N.A. of what is called their " aplanatic cone," a term which we at once proceed to explain. This is one often used but rarely explained on account of the somewhat involved nature Fig. 98. — Aplanatic. Fig. 100. — Uncorrected Lens. Fig. 99. — Over-corrected. Fig. 101. — Under-corrected. of the reply. The word itself, derived from the Greek, means, in point of fact, " free from wandering," by which the optician understands (as he uses the word) that all rays, whether from the periphery of the lens or nearer its axis, shall meet in one ASCERTAINING SIZE OF APLANATIC CONE 149 point in a given plane, as shown in Fig. 98. This is the ideal perfeetion of the optician's art. As an ordinary uncorrected lens always suffers from what is called "spherical aberration" (by which is meant the marginal rays come to a focus at a point on the axis closer to the lens than those situated nearer to its axis or centre, as seen exaggerated in Fig. 100), so the art of the optician referred to is to try to unite these planes of focus by combining glasses having different properties. If he overdoes it, producing what is technically called " t^z^^r-correction," he brings the peripheral rays too far along the axis, as shown in Fig. 99 ; and if he does not correct enough—" under-co^icc\S.ox\" as it is termed — he leaves the combination with the same error outstanding, although in a less degree, as that possessed by an uncorrected lens, as shown (greatly exaggerated) in Fig. lOi. Aplanatic Cone. — To ascertain the size of the largest aplanatic cone of a given condenser, say one of N.A. I'O, we proceed as follows : Fix it in the usual position on the substage, and place on the nosepiece of the microscope first an objective of N.A. •6, and on the stage a diatom. Focus it with the objective, using as an illuminant the edge of the flame, and rack the condenser up and down until this image of the flame is seen across the field with the diatom lying in its centre. This is obtaining what is technically called critical light, and the resulting image is called " the critical image'' Shift the diatom just out of the field of view, still leaving a portion of the slip and its cover-glass in situ. Remove now the eyepiece, and look down the tube of the microscope. One ought to see the back lens of the objective full of light, because the aplanatic cone of the condenser should be greater than that of an objective 06, such as we are supposed to be here using. Return now the eyepiece and remove the objective, substituting one of 0-95 N.A. ; again focus the diatom, and again obtain critical light by focussing the condenser on the diatom until the edge of the flame is seen across the field. Once more shift the diatom out of the field, and look down the tube as before. The back lens should be quite evenly filled if the aplanatic cone equals the numerical aperture. Then close the iris diaphragm until its edge is just seen, and carefully note the exact size of the opening with a pair of compasses. Now remove the 0-95, and place in its stead an immersion objective ISO ASCERTAINING SIZE OF APLANATIC CONE of 1-40 N.A. Treat as before, with respect to focussing and obtaining critical liglit, and look down the draw-tube. Only the centre two-thirds of the back lens is now seen full of light, and the slightest touch of the condenser upwards, so as to try- to fill the lens to a greater amount, will cause two dots of black to appear on each side of the lamp flame, which then becomes immediately recognisable. The last point before the appearance of these black dots (really due to spherical aberra- tion) indicates the largest aplanatic cone of the condenser. Slowly and cautiously close the iris diaphragm until it is just visible, and measure the size of the aperture with compasses, as before. If the diameter is slightly greater than the previous measure for the 0-95 lens, the aplanatic cone is, of course, just above o'95. A little experience and thought will soon render these operations quite easy, and the microscopist will be able readily to compare the largest aplanatic cone of the condenser he is testing with its advertised N.A., and the performance of one condenser with another. The difference which so often exists in these two measures is very striking, and is said to be mostly due to errors in spherical aberration, most condensers being more or less under-corrected (Fig. 100), and consequently focussing their central rays at a greater distance than their peripheral ones. If a condenser be well corrected, the lamp-flame image, as seen on looking down the microscope with the eyepiece in situ, should be, when accurately focussed, intensely bright, whilst the field is commensurately dark ; but very frequently this darkness is conspicuous by its absence. * It may be here asked, What does it matter even if the condenser should be badly corrected and possess a small apla- natic cone ? It is this. The object of a condenser is to bring as much of the light of the illuminant as possible to a focus on the object. If now all the rays do not come to the same focus all of those which come to another are so many lost, and only serve to scatter light into the field ; and besides this, when using a broad illuminant (such as is produced after obtaining critical light with the edge of the flame, by turning the lamp-flame broad side on), not only is there an unequal illumination of the field which is immediately apparent, but no critical light is obtainable; at the margins of the field without losing it in the. DEFINITION OF CONDENSER 151 centre, and vice versd. Hence one of the uses of having a large aplanatic cone is to obtain uniform lighting.^ As now the best of definition will only be over the area where critical light exists, so a critical image cannot be obtained over the zvkole field at one and the same time, and appearances may thus be produced in that part where it is absent, which to say the least are objectionable. The Definition afforded by a condenser is important, but only up to a certain extent. If a good sound image of the flame edge is not well shown it is very obvious it is more difficult to obtain critical light with the same ease as if it was good, but condensers never give so fine images as objectives — it would make them too- costly. To test for definition the condenser may be placed on the microscope, and its performance com- pared with that of an objective of the same N.A., always remembering that the slide should be turned round the opposite way, i.e. with the cover-glass towards the mirror and the plane glass of the slip towards the condenser when fixed on the nosepiece. This, of course, is necessary because the correction has been made, or should have been made, by the optician with respect to the thickness of the slip just as he makes the correction for the objective with respect to the thickness of the cover-glass.^ Another point corhes into notice here. Slips unfortunately vary very greatly in thickness, some being much thinner than others, hence when the condenser, if it be over N.A. I'O, is made for a thick slip and used on a thin one, one or more cover-glasses, oiled together and to the slip and condenser, must be used to fill up the gap, or else the oil will leave the slip should the condenser have to be lowered to obtain critical hght. If the oil-condenser be made for a thin slip, it cannot be used for a thick one, and must have its top lens removed and replaced by another constructed for the purpose. We have ' This is the object of looking down the tube of the microscope to see if the condenser be properly adjusted before commencing to make an observa- tion — a method we always recommend, especially when employing high- power objectives — because, if the field be not uniformly illuminated, the best results of definition are not to be obtained. * The substance of these last few pages has been taken, by permission of the publishers, from the author's book on Photomicrography. 152 FOCI OF CONDENSERS three top lenses to one of the high-angled condensers we use. With dry condensers, a plan adopted by Mr. Conrady in his N.A. i"0 type is highly commendable, the top lens being ad- justable by means of a correction collar in the same way as dry-power objectives of high power are fashioned. By this means different thicknesses of slip are provided for. The following table, extracted from Carpenter on the micro- scope, of the performance of different condensers will be of interest : Total Aplanatic Condenser. aperture aperture Power. N.A. N.A. I. Powell & Lealand's dry achromatic (1857) ■99 •8 i 2. „ „ top lens removed . •5 i 3. „ „ bottom lens only . — ■24 f 4. Swift's achromatic ■92 ■5 A 5. „ „ top lens removed . •22 I 6. Abbe's chromatic (3 lenses) (1873) . 136 ■5 i 7. „ „ top lens removed . ■3 f 8. Powell & Lealand's chromatic (Abbe's formula) 1-3 7 i 9. Powell & Lealand's oil achromatic (1886) 1-4 I'l i 10. „ „ used dry . 10 •8 i II. „ „ top lens removed — ■4 A 12. Abbe's achromatic (1888) .... .98 •65 i 13. „ „ top lens removed — •28 I 14. Powell & Lealand's low-power achro- matic (1889) ■83 ■5 f 15. Powell & Lealand's apochromatic (1891) . "95 •9 A 16. Zeiss's " aplanatische Lupen" large field (Steinheil formula) .... — •32 I 17. Beck's achromatic dry (1883) . 10 ■9 i„ 18. „ oil achromatic (1900) 1-4 I "3 i 19. Swift's apochromatic dry (1892) ■95 •92 i 20. „ panaplanatic dry (1897) . I'O •93 i 21. „ „ oil (1898) . 14 1-30 i 22. Watson's parachromatic dry (1898) 10 •95 f 23. Watson Conrady oil . I '33 r2S i 24. Zeiss oil achromatic . 1-30 — — 25. Baker's semi-apochromatic 10 •95 i •'The values of the first sixteen and of Nos. 22,23, and 25 THE SUBSTAGE DIAPHRAGM 153 have been obtained from actual measurements ; the others are from the estimates of the makers. " The limit given in the table is for the edge of the flame as a source of light. When, however, a single point of light in the axis is the source, the condenser will be much more sensitive, and a lower value for the aplanatic aperture than that given in the table will be obtained. But as a single point of light is seldom, if ever, practically used in microscopy, it was deemed better to place in the table a practical, rather than a theoretical, and probably truer result." The actual construction of the different condensers sold by the numerous opticians of the present day is so various that it would occupy too much space to illustrate them ; but the main feature in the English-made combinations is that they are of so much smaller diameter than the Continental, which are in our way of thinking uselessly large. The convenience of having them so much smaller is very great, as quite a small substage is all that is necessary ; whereas with the Continental design everything beneath the stage has to be specially arranged. It is a great pity that the size of the two different types of condensers — the English and Continental — cannot be made similar, for then interchange of condensers could be much easier effected than it is at present. The Substage Diaphragm : its Abuse and its Use. The substage diaphragm in olden days used to be nothing else than a metal wheel perforated by many different-sized holes ; nowadays it is nearly always of the iris or self-closing pattern. The diameter to which this arrangement is closed has a very far-reaching effect, and indeed is of such importance that some little attention must be given to the matter. The first point to be mentioned is its limiting powers upon the working aperture of the condenser with which it is used. To understand this it is only necessary to remind the reader that the numerical aperture of any lens is practically the ratio of the available semi-diameter of its back lens to the focus. Hence it is easy to infer that curtailing the back lens — that is, the one nearest the mirror — promptly lowers the numerical aperture of the system. But, from what has been said elsewhere, 1 54 AFFECTS N.A. OF OBJECTIVE this is obviously a serious matter, for curtailing the N.A. of the condenser involves a curtailment of that of the objective in use with it also. Here an error has crept in to which we must at once refer. One often hears it stated that, if the iris be shut so as to produce a given numerical aperture to the condenser, the objective is always ixduced to a similar amount ; so that, if the illuminator in question were cut down to, say, N.A. "65, no matter the aperture for which the objective was designed, it would be cut down to the same extent. This, however, is not exactly true, though so frequently stated, and we call attention particularly to the fact because it explains certain little matters without any difficulty which otherwise are not ea.sy to under- stand. Owing to a certain portion of the light coming from the condenser upon an object being diffracted by it and scat- tered, a small quantity of this scattered light falls upon the front lens of the objective. If now the objective system to which this belongs be one of higher aperture than that of the condenser in use, the extra amount falling upon the front lens is caught up by it and transmitted through the entire com- bination, filling the back lens to a greater degree than would be at first sight anticipated, and so makes the working aperture of the objective higher than that of the condenser itself at the moment. Although this increase in illumination, it is true, is somewhat feeble in comparison with the direct beam, still the point to bear in mind is that the back lens is filled with rays of a wider cone, which give to the combination a higher working aperture than is furnished by the illuminator itself In order to ascertain the amount an objective is thus increased from this • cause, in other words to be always able to estimate the working aperture of any lens of high aperture when used with a condenser of a lower numerical equivalent, it is only necessary to add together the two apertures and take the mean. This mean is the estimate required. Take, for example, a lens of i'40 with an illuminator of ro. The sum is 2-40, and the mean i'20. This is the working aperture of the i'40 objective when used in conjunction with a i"o condenser. It is this increase we wish to call attention to, for it immediately explains why, when using a I -40 lens, say, with a 1-30 condenser cut down to N.A. I'O, better resolution is obtained than when employing an objective of the same reduced numerical aperture — a fact well known for FALSE EFFECTS PRODUCED BY SMALL CONE 155 years to the practical microscopist. These additional rays to the I '40 objective we speak of can be easily seen by looking at its back lens when in use with the condenser reduced to N.A. i"o in question. A ring of faint light surrounds the brilliant direct beam, which is entirely lost when the objectives are changed and the N.A. i"0 substituted, the brass mount of the latter and the different shape of the lens-front preventing its admission. It is scarcely necessary to add, the object must be focussed and the objective oiled to the cover-glass in making the experiment. So far we have only pointed out how the diameter of the iris affects the numerical aperture of the condenser, and so indirectly that of the objective in use at the time. We must now explain what the general effect of lowering the aperture of the condenser has upon the actual image of the object. This means, of course, the effect produced by using a small solid cone of light in contradistinction to a wide one, for example between using a wide solid cone of N.A. v^o (with a suitable objective) and a reduced one of, say, N.A. ro whilst still employing the same magnification. The evil of this is nothing actually new, for Mr. Nelson has in his practical manner called attention to the danger of using small cones times without number, but what follows puts the matter in perhaps a somewhat different light. One of the effects of reducing the aperture of any lens whilst employing the same magnification is to increase very sensibly what is called " the circle of confusion.'' We have elsewhere pointed out that owing to the finite wave-length of light, the image of a mathematical point cannot possibly be another mathematical point, but must be a diffused disc of more or less sensible size. We have shown, too, that the usually accepted limit to the diameter of this unavoidable disc is x^tt of an inch — that is to say, aJ^ of an inch on each side of the object — which, for argument's sake, we may speak of as a point. The question now before the reader is to show how lowering the diameter of the iris increases the diameter of the disc if the same magnifica- tion be maintained. To ascertain how to calculate the diameter of the disc, only two things are necessary : (i) to find the resolution, and (2) to multiply such by the magnification. Take the first. This is obtained by Abbe's well-known law, " Multiply twice the number IS6 DIAMETER AFFECTS SIZE OF SPURIOUS DISC of waves to the inch of the light employed by the numerical aperture of the objective." As an example, let us say the light used has 47,500 waves to the inch ;i twice that is 95,000 ; and so, if the N.A. be 1-40, the resolution is 133,000, which means any two lines at this distance apart can theoretically be separated if oblique light be used. Presuming now that the magnification is 1000 diameters, then the circle of confusion — TtjI^ot X i°oo = ih of an inch. Should the diaphragm be further closed to N.A. ro the circle is increased, whereas if finally closed to N.A. -50 the circle is enlarged still more. The consequence of this is immediately apparent, for the object is distinctly fuzzy. Of course this circle of confusion about the point of light is really produced by diffraction phenomena ; hence as the diaphragm is more and more closed with objects of sensible area the image becomes crowded with all manner of diffraction effects, so much so, indeed, one scarcely knows what is real and what is false. White lines may appear around bacteria to " make believe " they have discreet capsules ; hairs may appear double-tipped, divisional markings between portions of a diatom may grow to such an extent as to appear several times thicker than they should, actually encroaching upon the true structure of the valve. To explain why this is so, why such different appear- ances are produced by the same cause, is very difficult to say, but it must here suffice to add that all diffraction effects (more especially, perhaps, of this type) are caused by interference phenomena between the rays coming from the sajne source of light, one with the other. Those that come in contact in the same phase — in other words, those of simple multiples of the same wave-length- — are additive, and seem to strengthen one another, causing increased brightness ; whilst those not in the same phase, being perhaps half, or any portion, of a wave-length ahead or behind the others, serve to quench each other, causing; darkness. ' The ordinary wave-lengths of different coloured light are usually given in tenth-metres. To convert these into terms of the inch, divide 254,000,000- by the number in tenth-metres— z/z« versd, if in inches, divide the same 9-figured quantity by the number in inches. For example, say, 5500 tenth- metres = 46,182 waves in one inch. UTILITY OF CLOSING IRIS DIAPHRAGM 157 Diffraction phenomena then, taken as a whole, are charac- terised by what are termed " bands of brightness '' and " bands of darkness," which can be understood from what has been stated ; but they may also be described as being arranged in maxima and minima. These can be readily seen around the so-called point of light witnessed in the telescope when focussed on a star. It is surrounded with rings of brightness and rings of darkness, first one and then the other.^ Now the same arrange- ment of phenomena, it may very justly be assumed, takes place about the image of an object other than a star or point of light, such as one would meet with in the microscope ; hence it has been thought that the reason these phenomena appear to vary in appearance— sometimes a white line around an object, whilst on another occasion an increase of darkness in the dark places already known to be existent — is because from some cause hitherto unexplained — possibly a remote effect of contrast — the eye in one case recognises a maximum, and in the other a mini- mum effect ; in other words, at one time sees a bright band, and at another a dark one. It is, hov/ever, quite possible the change of effect may only be due to a slight alteration of focal adjustment. We have now pointed out the dangers of closing the iris, and what care must be exercised in so doing ; it remains now, on the other hand, to be explained, strange as it may appear, how this closing effect under certain circumstances becomes of the very greatest possible service. We refer to the use of the diaphragm in cutting off stray light from entering the tube when employing a condenser of higher aperture than the lens with which it is in use — say, for example, a '65 objective and a N.A. I'O illuminator. Let both be placed on the microscope. Having focussed a specimen — say an Abbe test-plate — let the ocular be removed, and whilst looking down the tube the iris be shut until its leaves just appear at the periphery of the back lens of the objective. The ocular being returned, the plate should be carefully watched whilst the iris is suddenly opened : a rush of light will be seen flooding the whole field, spoiling very sensibly the general definition of the lines. From its submerging effect on the image, this used always to be called " flooding the specimen with light." Repeating the process, ' In making the experiment it is well to use a monochromatic screen, placed between the eye and the eyepiece. IS8 LIMIT OF USEFUL CLOSING but on this occasion watching what happens in the back lens when it is looked at, instead of the specimen through the ocular, we shall see, when the iris is opened, that quite a quantity of stray light enters the tube — coming in edgeways through the lens — which is reflected off its edges into the ocular, causing the flooding in question. If now the iris be shut, so as to prevent this, the objective performs under fair conditions. Attention is especially called to this fact, as otherwise a com- bination may be blamed for a bad performance which was sim.ply due to this irregular addition of stray light, which might not have occurred if the condenser had been of exactly the same aperture as the objective. No microscopist then can handle his substage diaphragm carelessly, for if he does so he may produce effects that may lead him quite astray in forming an opinion upon the true structure of an object. It is not an easy matter to furnish the student with any distinct limit to this closing of the iris that is justifiable, one that will not introduce these irregular diffraction phenomena ; but taken as a general rule for daily practice, Fig. 102. however, it may be asserted, with a moderate amount of cer- tainty, that no objective should ever be cut down more than by, say, its outer third, by which we mean the outer third of the back lens of the combination as seen by looking down the tube of the instrument, the eyepiece being removed. If it requires more cutting down than this before a good image is MARKING FRAME OF IRIS 159 obtained — save perhaps under some peculiar circumstances — the objective is probably a valueless one, and the sooner it is got rid of the better. Before quitting the subject of the iris diaphragm, it may be mentioned the frame in which the leaves work is often divided as shown in Fig. 102. This is for the convenience of noting the different apertures that correspond with definite amounts of numerical aperture. These quantities are readily ascertained by using objectives of known values of N.A., the leaves of the diaphragm being shutdown so that they just touch the periphery of the back lens of each objective (as seen when looking down the tube the ocular being removed) when in turn it is placed upon the nosepiece. The exact reading of the figures being noted in each case, when in future the diaphragm is shut down to the same figures, it at once indicates the amount of N.A. in operation at the moment, no matter what objective is in use at the time. CHAPTER IX METHODS OF ILLUMINATION Most objects are examined by transmitted light, the rays of the illuminant being reflected by the mirror through the con- denser, object, objective, and eyepiece to the eye of the observer. Occasionally, however, it is desirable to do away with the mirror altogether, and, setting the instrument horizontal and raising the illuminant a convenient height, to employ the light straight away from the lamp. There is little to be said in our opinion in favour of such method (which of course cannot be employed if fluids are used on the stage as media for objects) save but for one purpose, and that is to do away with the double reflection of the light from the mirror, owing to the glass of which it is made being too thick.^ Some microscopists think better definition is always obtained by the use of this " direct " light, as it is called, than by employing the ordinary '' reflected " beams off" the mirror ; but as to this there does not seem a universal agreement of opinion. When using the lamp and mirror in the ordinary fashion, it has been already stated the light should be placed and the condenser so adjusted that the flame image is seen in the field of view of the ocular stretching across it. When condensers were first used, however, before any theory explained their use, they were racked up and down, that is to say within and without the focus, so that the flame image was avoided. The " Carpenter " school declared the better effect was always obtained by racking without the focus ; the " Quekett " student maintained it was just the reverse ; whilst Sir David Brewster thought the source of light should be focussed on the object, the same opinion in fact that has been held of later years. ' Dr. Dallinger, whose great experience always demands a corresponding consideration, is said to be in favour of using a right-angled prism instead of a mirror, the total reflection doing away with the possibility of all double images. 1 60 FOCUS OF ILLUMINANT: CRITICAL LIGHT i6i Recently, however, owing to the researches of several mathe- maticians and others, a good deal of controversy has re-arisen upon this subject ; but a long series of considerations by Mr. Conrady, although arousing some opposition at first, seems to be " taking hold " with the savants, for it would appear, upon mature consideration, his arguments are indisputable. These lead us to believe that the actual focus of the illuminant is not per se really an actual necessity, so long as the back lens of the objective is filled with light. Mr. Poser (Carl Zeiss) — whose name and knowledge connected with the theoretical and practical details of the microscope command very great respect — has we believe arrived at the conclusion that, whilst agreeing with Mr. Conrady in the importance of filling the back lens of the objective, the best practical position for the condenser to focus in is just above the front lens of the objective in use. We have ourselves recently been much engaged in numerous experiments, photographic and other- wise, in connection with this subject, and have come to the conclusion (i) that filling the back lens is the important factor to obtain the best definition, and for that reason the microscopist should always look at the back lens of the objective (to see such condition is fulfilled) before even examining his specimen ; (ii) that seeing the ground glass of the Nernst lamp, or the edge of the flame actually in focus, is often objectionable, more especially the former, no injurious effect is produced in the definition by either raising or lowering the condenser a small amount provided that the back lens is not emptied in the slightest degree by so doing, and that (iii) we think Mr. Poser is correct when he states more light is obtained by raising the condenser jV^j^ above, rather than by lowering \t just beneath the position where it forms the image of the illuminant, although theoretically there should really be no difference. If it be desired to pursue the matter further, let the doubting mind consider the following : When the edge of the flame is focussed, is it in reality the actual edge that is in use?. Presuming it is so, does it make any difference — and if so, what— should the centre portion of the wick be focussed instead whilst the edge is still presented to the mirror ? Likewise what change in definition follows should the light corresponding to the very furthermost edge of the wick be II i62 CRITICAL LIGHT employed instead of either of the preceding? It must be allowed there is no change. Seeing this is so, it is obvious a range of focus exists from the front to the back of the wick, which, being granted, shows the truth of what we have said, viz. that a certain "play" of 'the condenser is admissible — it being always- provided the back lens of the objective is equably filled with light.^ It must not be thought in saying this we are backing out of the necessity, so often stated, for always obtaining critical light : we mean nothing of the sort, but merely that recent researches have broadened out the definition of what is actually meant by the term " critical illumination " and its method of production. With respect to the selection of illuminators to suit objectives of different focus we have already spoken when dealing with condensers as a whole, but it remains to explain the special object of having different foci at all. Putting aside the utility, which is obvious, of having them of the same N.A. as the objective, or anyhow not less, the use of different foci is to regulate the size of the image of the illuminant or of the illuminated area of the field of view, as well as the intensity of the light. This is of course obvious, for the larger the image of the illuminant the feebler the intensity of the light. Should, however, the image of the jlluminant be too small at any time, the aperture of the condenser being correct, it can be readily broadened by using the auxiliary or bull's-eye condenser between the mirror and the source of light. In doing so it had better be fidgeted about so that its position does not spoil definition, which it may do if incorrectly placed. Care should' be taken in doing this that the back lens of the objective is filled equably with light ; for unless this be the case, the critical state of illumination will be lost, and the consequent array of troubles ensue, just as obtains when an ordinary substage condenser is badly placed. Most if not all of the ordinary bull's-eye condensers are poor examples of the optician's art, even the best being not superior to the finest lantern condenser. To remedy this defect, and supply a much-felt want, Mr. Conrady has recently computed, ^ This bears out what Mr. Nelson has maintained so stoutly for many years, viz. that the back lens must not show any portion of its area unequally illuminated by dark spots ; if these exist the adjustment is not correct. BULL'S-EYE CONDENSERS 163 and Messrs. Watson & Sons have made, an achromatised aplanat of the very highest quality. We have enjoyed the use of one for some little time. It can be employed not only as a very perfect bull's-eye, utilising all the light possible from the illuminant, but the optical parts in our arrangement are made to lift out and be placed in the substage, where the aplanat makes a very magnificent low-power condenser of great utility with objectives of suitable focus. There are one or two mountings for these auxiliary condensers which have proved very useful over and above those ordinarily i'"' \ ^fflf Fig. 103A. Fig. 103B. met with. One is by Leitz — a firm whose fame has justly increased by leaps and bounds in recent years — which we give in Fig. 103 A. The lens is large, the mount very steady 164 BULL'S-EYE CONDENSERS and not likely to get out of adjustment, and the price exceed- ingly moderate. Messrs. Watson & Sons, another firm whose ambition is to turn out articles for the microscopist of all sorts, lenticular and otherwise, as much up-to-date as possible, have more or less recently introduced a very portable and convenient ball-and-socket stand of much service. It is illustrated in Fig. 103B. We have had one in use some little time as the mounting to the Conrady condenser, and are quite satisfied with its performance. Messrs. Bausch & Lomb have lately introduced a novelty which, we think, simple as it is, of [a serviceable nature. It Fig. 104. consists in fitting a counterpoise to the mirror, at the other end of the arm which supports it. This is to prevent any dropping of the mirror by its own weight, and does away with the necessity of clamping-screws to hold it in position. It is shown in Fig. 104. C. Baker has also a pattern with lamp complete ; a rack to raise it up and down, and one to move it side to side with the bull's-eye, itself capable of being turned aside when not required, completing a most useful combination. This is indeed a very serviceable arrangement, for the bull's-eye is very quickly brought into use, and equally quickly turned aside when not required. BULL'S-EYE CONDENSERS I6S Like this firm's characteristic attribute, everything has been carefully thought out in the details — although perhaps the idea originated from without — and perfected by the experienced and exceedingly skilful manipulator, both as microscopist and photo-micrographer, Mr. Lees Curteis, who is the leading spirit in this department of the firm. It is illustrated in Fig. 105. Space will not allow us to illustrate any more of these bull's-eye conden- " sers, but we should men- tion that other equally good arrangements are made by Messrs. R. & J. Beck, Powell & Lea- land, Ross, Swift, and others ; although none of them, we believe, are optically equal to the Watson-Conrady apla- nat of which we have just spoken. The selection of a suitable illuminant de- pends very much upon the individuality and requirements of the microscopist. For every- day ordinary routine we suppose the usual micro- scopist's lamp — which is too well known to need description — is that form most commonly met with. There are several varieties even of this, some being more expensive than others. The Nernst electric (Sj.) lamp is in favour where electric current is available, but is not powerful enough when oblique light is used, as hereafter explained, in conjunction with different monochromatic screens. For this purpose even the Welsbach gas mantle, otherwise a useful form of illuminant, is not equal to the occasion, so resort must be had to another type of the 1 66 HELIOSTAT Nernst make/ a lamp requiring half an ampere to make it burn properly. It has a great advantage over all other semi-powerful electric lamps inasmuch as it does not need any specially thick " lead " wires for its use : it can, in fact, be placed on the ordinary house supply, although such may require a stronger fuse being used on the circuit. In focussing either of these electric lights or the Welsbach mantle with the condenser to obtain critical illumination, the ground glass of the chimney is usually employed as the object to focus. Daylight is not desirable as a luminant for the microscope, owing to its diffuse nature ; but sunlight, if utilised in the proper manner, leaves no- thing to be desired save the little that it is seen in winter in this country. A difficulty, however, which pre- vents its more frequent use is that owing to the earth's rotation there is great trouble — in fact, it is impossible with ordinary means — to keep the image of the sun always on the mirror of the microscope. To do this effectually so that it will not shift, even upon different parts of the mirror, an instrument has to be used called a Heliostat. This is a very expensive apparatus, and . unless it be really a good one is of no use at all. We know of several ; but we believe one of the best, if not actually so, is that manufactured by Messrs. Watson- & Co., according to the instructions of Dr. Johnson Stoney (Fig. io6). This is only to be expected when designed by a man of such eminence, » Owing to the delicacy of the Nernst lamp it is extremely likely to break down, at an inopportune moment perhaps : hence it may be useful to know of a convenient substitute. This is afforded by the employment of a 32-candle power electric incandescent hght by Steam, which, unlike most other manufactures, is composed oi parallel filaments. It should be used edgeways, with a piece of ground glass placed between it and the mirror, as near to the lamp as possible. JSA Fig. 106. MONOCHROMATIC LIGHT 167 one whose ingenuity as a mechanician is only equalled by his mathematical knowledge in all the subtle theories connected with the optics of the microscope. Full instructions are issued with the instrument, so we need not wait to explain how the arrangement is used ; it must suffice, therefore, to say that when once set upon the sun it projects its image upon the mirror of the microscope, where it remains apparently quite stationary. Those using the sun's light for the first time are especially warned not to place their eye to the ocular at all without using a protective monochromatic screen — and a deeply stained one too — intervening between the mirror of the heliostat and the mirror of the microscope. Arrangements for producing Monochromatic Light The object of using light of one colour is of a twofold nature : (i) the first being to aid resolution, and the second (ii) to assist in providing greater contrast between different parts of a specimen. (i) Ordinary so-called white light may be said to consist of all varieties of wave-lengths, say, from ^^is^ in. (red) to ^^y^utr i"- (violet) ; its mean wave-length, however, being usually spoken of as TTTTnr of an inch. Seeing that Abbe's Law for ascertaining the theoretical power of resolution with any objective is to multiply twice the number of waves to the inch of the light used by the N.A. of the objective, it is very obvious that twice the resolution, roughly speaking, is obtained by employing violet light rather than by using red. To be able, then, to use blue or blue-violet light has long been the desideratum of the microscopist. To employ blue glass is of no use, as none that is made passes blue rays only,i and to use true spectral colours with an ordinary spec- troscope is most troublesome and difficult. The firm of Zeiss make an arrangement — a sort of spectroscope attachable to the microscope, which we have heard well spoken of, but have never tried ; and Mr. Nelson has arranged another, in the using of which we have not met with the success we expected. Blue ' Whilst going to press Carl Zeiss have sent for our inspection a new blue glass which is very nearly perfection. It certainly does pass a minute quantity of red, but the amount is so small as to be negligible. The firm make to order the thickness necessary for any illurainant that is to be used with it, whether oil, incandescent gas, electric light, or limelight. i68 AUTHOR'S APPARATUS fluid filters have been employed, more especially ammonio- sulphate of copper, in cells measuring about 3 in. in length, 2 in. in breadth, and ^ in. in thickness ; but the great difficulty of using any of these fluid arrangements is the large amount of light absorbed thereby. If the special 'i^ernst J-ampere lamp already spoken of be employed, and the solution be not too concentrated, a fairly favourable light-filter is formed with the ammonio-cupric-sulphate or with the acetate of copper solu- tions ; but neither can be called truly monochromatic, for they nearly always pass red rays. The only means we know Fig. 107. of to obtain absolutely blue light is by the employment of the special arrangement devised by the author, and exhibited at the Royal Microscopical Society some few years ago (Fig. 107). Besides details of an ordinary nature — which can be seen in the figure — the machine is constructed to furnish prismatic light of any colour by employing one of Thorpe's replicas, which is attached to a glass prism specially designed to keep the blue and green rays parallel on leaving the prism, to the incident beam projected on the replica. By this arrangement, which in its final form is very convenient and handy to use, limelight or an ordinary low-power Nernst lamp can be employed, although the more powerful form is preferable when deep violet light is MONOCHROMATIC SCREENS 169 desired (see Journal Roy. Mic. Soc, December, 1902, part vi., p. 727). The filter next in importance is the F.-line screen of Gifford. For practical everyday use we know none of such excellence and usefulness. It is a trough made by the Leybold's sealing process, which contains a thin slab of signal-green glass immersed in a solution of malachite- or, in some cases, methyl- green. As sold, it is usually provided with a suitable stand. A very useful green glass of the " pot " variety may be employed with great advantage.^ It transmits light of about the same maximum effect — viz. about 5550 wave-length — as the malachite-green variety of the Gifford's screen, but differs somewhat with that passed by the methyl-green type occasionally met with. The former two screens are more perfect in their action than the latter. (ii) The second use of screens is to create a greater contrast in different parts of a specimen. Such use is, we are ready to admit, more of service in photomicrography ; but it is of much comfort especially when employed during a hurried examination through several specimens, for it prevents very materially the exhaustion of the eye. We recommend this detail not only for this purpose, but because using a suitable green screen causes objects stained red, for example, to appear black ; hence they are easily distinguishable, although the general illumination is so much softened. The green glass above mentioned may be used for this purpose with specimens stained other colours ; but more especial directions and details are given in the chapter devoted to the use of the microscope in Bacteriology.^ Dark-ground Illumination Dark-ground illumination is used by the microscopist with low powers to show up the details of an object in a somewhat remarkable and at the same time somewhat beautiful manner. ' This particular glass, which is very cheap, is sold by Charles Baker, 244, High Holborn, E.G., and by Messrs. Watson & Sons, and is often called after the author's name. It has an advantage over the fluid screen, namely, that it does not fade with age ; moreover it is exceedingly tough, and will not readily break. Different thicknesses are sold. * Mr. Rheinberg, by the use of his original method of arranging dif- ferential coloured illumination, described a little later, thinks contrast effects can be produced almost equal, if not quite so, to that by the ordinary method. I70 DARK-GROUND ILLUMINATION The idea entertained in the method is that the object shall be lit up by extremely oblique rays only, and by no direct ones at all. All manner of curious silvery-looking effects are thereby introduced, which in popular demonstrations of the instrument are often greatly admired, although as a source of investigation, however, not so much is gained thereby as might be expected, save perhaps in learning the general contour of the object and the relation of one part to another. The usual method adopted is twofold, either by employing the Spot Lens (or its equivalent, a " wheel stop," placed beneath the ordinary substage condenser) or by the Paraboloid. The Spot Lens is merely a condenser with a piece of black paper more or less permanently attached to its lower lens in the centre. In some cases, instead of using paper, the glass is itself ground rough and painted black in the same situation. The disadvantage of this method is that the diameter of the black disc only really suits the individual objective for which it was made, and it is expensive to have several condensers, each being ground and painted to suit a battery of objectives ; and it is equally inconvenient to have to cut individual pieces of black paper to affix to the condenser for every combination used in the microscope. To meet this trouble stops are often used that are made like " wheels " with only three very thin spokes. The rim is also thin, but the " box " of the wheel is made in different sizes. By having several "wheels" to suit the numerical aperture of different objectives, one can usually be found that, placed in the carrier beneath the condenser, prevents all the direct light from passing through it, whilst still allowing the oblique rays to pass. The peculiarity of this illumination depends upon this very fact, namely that the only light falling upon the object is that provided by rays of great obliquity (see Fig. 109) — for the central direct beam is cut off, or should be cut off, by the stop in the centre of the wheel in the manner already described — and the characteristic effect produced by this arrangement is that, whilst the object is itself brilliantly illuminated, the background remains perfectly dark. A certain amount of raising or lowering of the condenser and wheel is necessary, and the iris may have to be closed' a little before these conditions ' If a " Davis Diaphragm '' be used instead of the substage iris, see Accessory Apparatus for directions how to use. RHEINBERG'S DIFFERENTIAL ILLUMINATION 171 are fulfilled ; but it is equally of importance, if the best effect be desired, that the " box-of-the-vvheel" stop should be made of exactly correct dimensions which vary according to the numerical aperture of the objective. Carl Zeiss makes additional diaphragms to assist in perfecting the image, which drop over the back lens of the objective to limit its numerical aperture a definite amount instead of closing the iris. These wheel-stops, we have said, are used with an ordinary condenser of suitable aperture placed beneath it ; but the spot lens proper that we have described drops into the sleeve of the ordinary illuminator, which is temporarily removed.^ It would appear as if we were guilty of a decided omission if, before we concluded our remarks upon this kind of illumination, we neglected to mention a curious and beautiful modification discovered and elaborated by Mr. Julius Rheinberg, F.R.M.S., and called by him '' multiple or differential colour illumination," more especially as it seems to have escaped the attention of so many microscopists. It appears to have suggested itself to him quite by accident after placing a piece of coloured glass between the illuminant and the mirror on one particular occasion when using dark-ground illumination. He noticed then that " the object was illuminated with the colour of the glass much more so than the background." Following up this little discovery, much time was spent in devising and perfecting methods whereby colour differentiation between an object and its back- ground, or between parts of the same object, could be attained by optical means, resulting in three quite different methods ' In Photomicrography will be found a modification of the above- mentioned wheel, which may be called an economical one. It was devised by the author of this work to save the expense of having a quantity of wheels with different-sized " boxes." An ordinary wheel is taken, and the central stop cut away until nothing remains of the metal save enough to keep the three little "spokes" in contact. At their juncture a pin is attached, over which different-sized discs can be dropped, their diameter being experimentally determined by first using little cuttings of needle- paper. The exact diameter being found that is suitable for a given objective, a metal disc can then be made, perforated by a little hole the diameter of the pin, and dropped over the wheel to form the box, when the microscopist has the special wheel for that particular objective ready at hand. These are made by Mr. Mason, optician. Park Road, London, S.W. Whilst going to press Mr. Traviss has introduced an "Expanding Spot" for suiting objectives of differing numerical apertures (see Accessory Apparatus). 172 RHEINBERG'S DIFFERENTIAL ILLUMINATION being found : one of them — named the refraction method — applicable chiefly to low-power work ; the other two — named the diffraction and composition methods respectively — being chiefly for high-power work. As the refraction method, suitable for use with objectives like an inch, is the easiest to apply, and shows what results may be attained perhaps even better than by either of the others, we shall confine our subsequent remarks to this one; but the reader who is anxious to further follow up this interesting subject will do well to consult the original papers given in the footnote.' The principle involved in the refractive method is nothing but a modification of ordinary dark-ground illumination, and consists in using, as a central stop to the condenser, a pro- nounced, clear and transparent colour, say blue, whilst the remaining portion of the illuminator is covered with some other colour, as, say, a well-marked red. For example, a disc of red gelatine (such as that used with crackers) is cut to fit the ring usually found in some form beneath the substage condenser of most modern microscopes. A hole is punched in the centre of this equal to about one-third of its diameter, in which is fitted a blue interior of the same material. The " fit " need not be so exact as it might be imagined is necessary, for what may be called a loose one does perfectly well. This bi-coloured disc is then dropped into the ring beneath the con- denser, and the adjustments made similar to those that obtain when ordinary dark-ground illumination is employed. Presuming an inch objective is in use, the result of this method of illumination is very astonishing, especially when ' " On an Addition to the Methods of Microscopical Research, by a New Way of Optically Producing Colour Contrast between an Object and its Background, or between Definite Parts of the Object itself," Journal Royal Microscopical Society, 1896, pp. 373-88. " Note on Coloured Illumination," Journal Quekett Microscopical Club, 1897, pp. 346-7. " Note on a New Modification of Double Colour Illumination," Journal Quekett Microscopical Club, 1897, p. 438. " Notes on Colour Illumination, with Special Reference to the Choice of Suitable CoXown" Journal Royal Microscopical Society, .1899, pp. 142-6. "Multiple Colour Illumination," Illustrated Annual oj Microscopy, 1899, pp. 44-50. Percy Lund, Humphries & Co., London. " On the Choice of Colours for Obtaining the Best Effects with Multiple Colour Illumination," Illustrated Annual of Microscopy, 1900, pp. 13-16. RHEINBERG'S DIFFERENTIAL ILLUMINATION 173 objects such as Polycystina, Diatoms, or even living organisms like Rotifers are placed on the stage, for the background is blue, whilst the little objects are coloured brilliantly red. Combinations of colours having a marked contrast produce the best discs, but it should always be recollected the colour of the central portion must be less bright than that of the peripheral, a point often overlooked in the discs sold by opticians for this process of illumination ; an unfortunate circumstance, for the best results cannot be obtained under these circumstances. Very beautiful effects also result with certain specimens by using a coloured centre only, leaving the rest of the disc white ; but a positively remarkable arrangement is one where the coloured pieces are shaped in such a manner that when the disc is used with a piece of silk muslin on the stage, the transverse fibres are illuminated by one colour, and the vertical ones by another! Mr. Rheinberg, in his papers in the Illustrated Annual of Microscopy, describes how this particular disc is made, and those interested should not overlook its description, as well as several others of equal interest. It is scarcely necessary to offer an explanation of these different phenomena, for any one who has mastered the simple philosophy of dark-ground illumination will understand them quite readily. It is obvious in the case mentioned, red outside and blue inside, that the blue central disc, taking the place of the usual black one, furnishes the colour of the background ; whilst the oblique rays that usually illuminate the object with white light are coloured red (in this instance) by their trans- mission through the outlying red portion of the gelatinous disc. The extension of the application of this method of illumination in the many directions explained in the original articles by Mr. Rheinberg is entirely due to his painstaking and carefully conducted experiments, and we must say we do not think he has received the credit due to him for the amount of patient work necessarily involved in such a class of research. We ought to mention that it has been argued by some microscopists that this method of illumination merely furnishes spectacular effects, and does not offer additional information as to the formation of structures or organisms examined by its means over and above those obtained by the use of ordinary dark-ground illumination ; but we must say the direct contrast 174 THE PARABOLOID presented to the eye by the object in one colour lying on a background of another furnishes a means of differentiating that is of great service when examining the general contour of an object, and it is hardly questionable that the transition in hue from one colour to a strongly contrasting one assists in a more vivid realisation of the disposition and relative thickness of different parts of an object than results from examining the " studies in black and white " as obtained with ordinary dark- ground illumination. We might mention incidentally, and in conclusion, Mr. Rheinberg considers he gets in many cases, by the use of this method of illumination, the same benefits, or what appear to be the same, as those arising from the use of " monochromatic " screens. (ii) The Paraboloid. This seems to have been something of a mixed invention of Messrs. Shadbolt and Wenham, although each worked on EVEL OF 5PECIMCN Wenhams Paraboloid Shqwinq Path of Rays 8( approximate FbsmoN of Specimen Fig. io8. somewhat separate lines at first. It consists, as shown in Fig. 1 08, which is drawn in section, of a piece of glass shaped as a paraboloid, but flat at its larger or lower end, and deeply curved at its upper extremity. In the centre of this is placed MR. GORDON'S SUGGESTION 175 a piece of metal, curved or flat, but anyhow so as to obstruct the direct rays from the illuminant. It needs no explanation to follow the path of the rays, which on consulting the figure are seen to be reflected off the parabolic surface into the glass again, to quit it at the deeply curved upper extremity. The object of this deep cutting away is that the rays may leave " normal to the surface," and so not be broken up into coloured ones. They impinge, as will be seen, upon the object placed in the focus F, and scatter afterwards somewhat irregularly. A certain few, caught up by the low-power objective, are carried to the eyepiece. For convenience in use, the little central piece of metal is iixed to a stem, which although not shown in the illustration really passes right through the axis of the paraboloid, ending in a little knob beneath. An up-and-down movement can by this means be applied to the metal disc so as to arrange the darkened portion of the field in accordance with the numerical aperture of the objective, and the diameter of the object, and the general requirements of the case. It is obvious in the employment of this arrangement the ordinary condenser is removed, for the paraboloid is usually made to be placed in the sleeve in its stead. Reference should here be made to a method for obtaining dark-ground illumination which has been recently suggested by Mr. J. W. Gordon, His idea is, so far as we understand it, that the object should be lighted by a condenser in the ordinary way and that the direct light should be stopped out by a central stop either behind the objective or, preferably, above the eyepiece in the so-called Ramsden circle.^ Whilst there can be no doubt that the appearance connected with dark-ground illumination, viz. that of the object standing out bright against a dark ground, could be perfectly realised in this manner, the proceed- ing would seem to be one dangerously inviting the formation of false images. Dark-ground illumination at its best is apt to yield deceptive images, as has been repeatedly proved at the Royal Microscopical Society by instructive and con- vincing experiments, shown both by Mr. A. E. Conrady and ' The Ramsden circle is fully explained in the article on Eyepieces, where it is shown the diameter is equal to — 500 mm. X N.A Total Magnification* 1/6 OBLIQUE LIGHT by Mr. J. Rheinberg. It is highly probable then the possibilities in this direction must be enormously multiplied when part of the full aperture of the objective is blocked out by a stop in the Ramsden circle ; but it is quite certain that such placed behind the objective itself is a most fruitful source of false effects. Microscopists cannot be too often reminded that the most startling " nightmares '' included in the famous experiment with Abbe's diffraction-plate were obtained by the use of such stops, and that images so utterly false cannot, as a strict matter of fact, be obtained by any means whatever if the normal round aperture of the objective be left undisturbed. The extraordinary appear- ance of blood corpuscles having " sculptured surfaces," recorded by Mr. Gordon by his method, it would seem belong undoubtedly to this order of "invited phenomena." It is obvious then, with but little further consideration, that the arrangement he suggests must be used with the greatest possible caution as a means of research, and no result obtained should be depended upon unless amply confirmed by more legitimate methods of observation. Illumination in General and Oblique Light in Particular Experiments and mathematical considerations have gradually led microscopists in recent years — notably Mr. Nelson amongst the number — to point out very forcibly the dangers that may occur in using narrow illuminating cones ; false and true ghosts, « intercostal markings in the image of a fly's eye (!), and many complex and false images with the coarser diatoms become visible, all of which are impossible to be obtained with a wide one. These have been actually photographed in many instances. Yet we are at once, for the sake of pure justice in dealing with the question, bound to add, on the other hand, that Professor Abbe, who has but recently passed away from our midst, dis- credited the whole matter. Indeed, he actually recommended the use of small cones, saying that " the resulting image produced by means of a broad illuminating beam is always a mixture of a multitude of partial images which are more or less different and dissimilar from the object itself," and moreover that he did NARROW VERSUS LARGE CONES 177 not see there was any ground for believing " that the mixture should come nearer to a strictly correct projection of the object . . . than the image which is projected by a narrow axial illuminating pencil." The situation then is exceedingly difficult to deal with ; for, when the result of direct experiment, conducted with all the refinement and skill of a master hand like that of Mr. Nelson, coupled with a full scientific appreciation of the situation, seems to point absolutely and directly in the opposite direction to the teaching of a mathematical expert and philosopher such as the late Professor Abbe undoubtedly was, one who has never been surpassed, if ever equalled, in acuteness of thought coupled with resourcefulness of investigation in all matters concerning the microscope — we repeat, when these opinions are positively at variance, the onlooker is compelled, from sheer inability, to wait and consider. We are bound to confess, however, after several years of attention to this difficult and far-reaching problem, the weight of evidence in our opinion, taken for what it is worth, certainly rests in favour of Mr. Nelson's view, and we venture to suggest that, perhaps, the data upon which the learned Professor built his theoretical considerations may not have included a sufficient " weight " to the teachings of actual experiment ; and hence that, although the theory deduced was undoubtedly correct, the data from which it was made were insufficiently extensive. For example, bacteriologists seem mostly agreed that the bacillus tuberculosis is probably not an organism likely to have a capsule under ordinary conditions, and yet with a narrow cone, whether the specimen be stained or unstained, a very pronounced encircling capsule, as bright and clear as possible to the eye, appears in every case ; yet, as the cone is steadily and slowly increased, so does this mysterious capsule disappear! Other illustrations might be given, but we refrain from mentioning many, though we feel obliged to furnish one more peculiar effect of using too small a cone. This is with the common object, the proboscis of the blow-fly. So treated, the exceed- ingly small hairs which lie upon the space intervening between the two lobes actually appear double, especially at their tips; whereas with a cone even of moderate angle such indication is entirely absent. The question then arises. How far can we reduce the aperture of the substage diaphragm without the 12 178 OBLIQUE LIGHT risk of introducing false images ? To tiiis we reply that, speaking in general, it must not be curtailed to a greater extent than a cutting off of the outer third of the back lens of any ob- jective as seen by looking down the tube of the instrument, the ocular having been removed. From what has just been said, it may seem exceedingly strange that we should now advance to the improvement effected by the use of oblique light in the definition and resolution of an object, especially so, seeing that such is produced by a very large curtailment of the back lens of the condenser by the iris diaphragm ! It will be necessary, therefore, to show the differ- ence between a narrow cone per se, and the narrow beam necessary to produce oblique light. Before actually proceeding to consider this interesting subject, it is necessary to qualify first what is meant by the actual term " oblique light." A mistaken notion has often been entertained that by the use of this class of illumination was meant the employment of a beam of light sent by some means into the full aperture of the condenser obliquely. This is not exactly true. Whilst allowing that the mirror if obliquely placed does affect the image — we refer to this when dealing with the testing of high-power objectives in conjunction with the use of the Abbe test-plate — to a certain degree, still this is not what is technically meant when we speak of oblique light. When using the term in its restrictive sense, we mean the stopping out of the greater portion of the con- denser by a diaphragm of* say a quarter or eighth moon-shaped design, placed in such a manner beneath the illuminator that the light reflected by the mirror passes into the condenser at one edge only, and so impinges very obliquely upon the such a diaphragm be so If specimen as shown in Fig. 109 placed (in the foreign models of microscopes this is readily effected by shifting the partially or nearly closed iris diaphragm OBLIQUE LIGHT 179 away from the centre of the field to its periphery) and the eyepiece is removed, the observer will perceive, on looking down the tube at the back lens of the combination, a small illuminated elliptical or oval-shaped portion of the field to be the only illuminated area, all the rest being in darkness (see Figs, in and 112, showing the illuminated areas in different parts of the field of the back lens of the objective). Now Prof. Abbe has explained in his theory of microscopical vision, which seems, notwithstanding some recent doubts that have been thrown upon its truth, to hold its own as well — perhaps better — than ever, that the final image of a small object is formed by the union of two or more differently formed beams — the directly transmitted one from the illuminant on the one hand, and on the other by those varying in number according to the arrangement of the minute structure of the object caused by diffraction (interference phenomena).^ The union of these differently formed beams brings out the definition of the minute structure of the object. The importance of such blending or union is shown by the fact that if the diffraction effects are artificially stopped out, so that the ocular deals only with the central or dioptric beam, the minute details of the object are immediately lost, and the objective seems all of a sudden to have lost its power. It should be borne in mind, we should mention in passing, that with coarse objects, however, such is not so evidently the case, or anyhow may not be so apparent; but of this we' have hardly time to speak in this place, for the details of the formation of the microscopic image are fully gone into elsewhere in this book. To put, however, our assertion to the proof that these diffraction images do enter into the formation of the image with such a potent effect, let the following experiment be performed : Place on the stage a specimen of Pleurosigma angulatum, use a twelfth homogeneous objective, focus and adjust for critical light, centrality of condenser and so forth. Remove now the eyepiece, having closed the iris to a sensible amount, and look at the back lens of the objective. A central brilliant dioptrically formed white image of the iris will be seen surrounded by six diffraction spectra coloured red outside and blue nearest the centre of the field, ■ These are also called the diffraction spectra. i8o OBLIQUE LIGHT as in Fig. iio.^ If now we change the slide, and use in its stead a grating — ruled lines of different distances apart — one being especially sold by Carl Zeiss for this particular experi- _ ment, we shall soon discover that the spectra always lie at right angles to the objects forming them, and that the nearer the lines are ruled together the further away from the centre do the diffraction spectra become. Further, if we used different-coloured lights — say violet — we should find this distance in question less than if we used red ; in other words, the '^' ' shorter the wave-length the less the distance. More as a convenience for future reference than any other purpose these three observations are here set forth. (i) The two diffraction spectra lie at right angles to the objects forming them, one on each side of the dioptric beam. (ii) The nearer the fine structures lie together (such as dots or striae in diatoms), the further the diffraction spectra are placed from the centre of the back lens where the dioptric beam is seen. (iii) The shorter the wave-length of the light used, the shorter the distance of the diffracted spectra from the dioptric beam. In the case of Pleurosigma angulatum, inasmuch as the dots or hexagons happen to be separated by just the correct distance for the purpose, both the direct light and the spectra can be seen in the field of the back lens at one and the same moment (Fig. 5, Plate I.), hence it follows all are blended together to form the image as seen in the ocular. For the purpose of again experimentally proving the utility of such fusion, let a diaphragm be made of the correct dimensions and placed over the back lens of the twelfth, so as, in fact, only to permit the passage of the central or direct beam ; on looking through the ocular the minute structure of the diatom will now be found to have disappeared. A little further consideration is sufficient to render it evident, if the back lens were too small in diameter — which is only another way of saying if the N.A. ' In Fig. 5, Plate I., a photograph of the back lens of a N.A. Vd,o objective is shown. OBLIQUE LIGHT i8i were insufficient ' — to transmit tliese diffraction spectra, then of course the combination would be unable to show the minute structure of the diatom. For the purpose of explaining the exact nature and use of oblique light, it will be convenient, before proceeding further, to make an additional experiment. Let the specimen be changed to one of Amphipleura pellucida, and for future convenience let it be placed with its greater length from above downwards in the field of view. It is to be understood we continue using the same objective, but add to the existing details an oiled f35 condenser (achromatic). If the N.A. of the objective be i'40 and the lens a good one, more especially in the correction of its outer zone, it will be possible with a low-power x 6 ocular to see just faintly visible the transverse lines — as we have pointed out later on when considering test-objects for an objective of the focus in question. Place now an eighth moon-shaped diaphragm, such as repre- sented in Fig. Ill, under the illuminator (or if using a Zeiss or other Continental stand, close partially the iris diaphragm and shift it across the field to produce the same effect), and the lines Fig. III. Fig. 112. should now start out into great distinctness (Fig. 3, Plate II.), provided that the specimen be a well-marked one and that the eighth moon-shaped diaphragm lies at the lower portion of the field, as shown in Fig. in, which represents the appearance presented by the back lens of the objective.^ ' Numerical aperture may be said practically to be the ratio of the semi- diameter of the back lens of an objective to its focus ; hence the smaller the diameter of this lens, the less the N.A. of the combination if the focus remains constant. 3 Of course this means that the crescent-moon opening is at the top or opposite side of the condenser, its lower portion being covered up. i82 OBLIQUE LIGHT Rotate the diaphragm a quarter of a turn to make it change ts position similar to that shown in Fig. 1 12, and then, returning the eyepiece, the longitudinal lines as they are called — which run along the diatom lengthwise — should be easily seen. It must be borne in mind, however, that these lines are always more difficult to separate than the transverse ones, because they are in most cases just a trifle nearer together. Lastly, change now the position of the diaphragm once again, so that it occupies a position midway between those shown in Figs, ill and 112 ; and if pure green or, better still, pure blue light be employed, the dots should be visible, provided the specimen be a good one for the purpose. Presuming the reader has followed these remarks by trying the actual experiments, he is in a position now to understand the explanation that follows. If, whilst the transverse lines of the amphipleura are faintly seen when using the lower power eyepiece and employing a solid cone (without any oblique light), the ocular be removed and the substage diaphragm be the veriest trifle closed, the appearance seen in Fig. 113 will with some difficulty be recognised.^ If one of the diffraction spectra (here, as above stated, we refer only to the blue portion) on either side of the central could have DirrRACTion Cem-RAL BEAM, THE IRIS BEina SHUT DOWN Fig- 113- Fig. 114. been entirely got into the field of the back lens of the objective, then the lines of the specimen would have been well defined ; but inasmuch as it is absolutely impossible to bring more than ' The edge of the lower dififraction spectrum is extremely difficult to see, and the eye must be shifted about before it will see the upper one. OBLIQUE LIGHT 183 a small portion of it into view, this accounts for the faintness and imperfection of definition to which reference has been made. Now what happens when oblique light is used ? Practically it is simply this, it means a shift of the central dioptrically formed beam, in company .with the diffraction spectra, further across the field, as shown in Fig. 114, which permits in con- sequence, when the iris is more closed, both central beam and diffraction spectra to be taken up by the' eyepiece completely and entirely at one and the same moment. By doing this the definition is rendered as perfect as the construction of the zones of the objective will admit, constituting another proof of the correctness of the Abbe theory of the formation of the microscopic image. The same explanation applies when the observer looks at the longitudinal lines; but because such lie (it is usually found) some- what nearer together in most specimens, so by proposition (\\) their spectra should lie nearer the edge of the field when the dioptric beam is centrally placed, in the back lens, Big. 115. Putting this in other language, as they lie further from the dioptric beam than those which come from the transverse markings, so they are more difficult to see unless the microscopist uses a little more oblique light — that is to say, fT^TiT employs a little furt/ter " shifting-" across — the field — to get them within its limitations (Fig. 115). Now as to what happens when the dots become visible.' If the reader has experimented he will have found it is not easy to locate the exact position for the direct beam to occupy in the area of the back lens, so that the diffraction spectra from both longitudinal and transvese lines shall be present at one and the same moment in the field.^ To facilitate this operation it is ' The student should compare Fig. 115 with the preceding. Whilst recognising both are somewhat diagrammatic, the dioptric beam is readily- seen to have been sensibly shifted a further distance from centrality in this than in the other figure. ^ If the microscopist be using an instrument that is provided with a circular stage that can be turned around the optical axis, it is easier to move the specimen than interfere with the substage arrangements, as by this means the illumination of the field is not interfered with. i84 OBLIQUE LIGHT mostly necessary to employ blue light, because by employing the shorter wave-length it lessens the distance of the diffraction spectra from the central beam by proposition (iii), and hence gives a better opportunity of squeezing, so to speak, all three beams into the limit of the back lens (see Fig. ii6). The real use then of employing oblique light to show the dots is simply this : to enable the microscopist to get the two spectra required, and also the central or direct beam, into the back lens of the objective at the same ^noment, so as to p-j jjg be utilised by the ocular for the final building up of the image as seen by the eye.^ From what has been said, the necessity of having a large aperture to the back lens, in other words of having a great aperture to the lens in use, is very apparent, an addition of even "05 N.A. being possibly of a little service in perfecting the image. It further shows, with low-power objectives (seeing the addition of the diffraction spectra with them is not of such paramount importance, owing to the details of a specimen used' with such a lens being much larger and further apart), the advantage of using oblique light is not so readily felt. The explanation of this difficult subject — the formation of images and their improvement in detail effected by the use of oblique light — has been written in a manner, it is hoped, that will suit the taste of and be understood by the lay reader ; but to those who prefer an explanation expressed in perhaps a more philosophical way, and certainly in more technical language, the following rendering may more directly appeal. The law governing diffraction by regular periodic structures is such that, after the direct and diffracted pencils have passed through an aplanatic objective, the distances and angles be- tween the several pencils remain constant, no matter how the direction of the dioptrically formed beam is changed. So true is this that the distribution of light seen on looking down the tube could be reproduced exactly if we were to cut out the ' In Fig. 6, Plate I., a photograph of the appearance presented by the back lens of a N.A. i'40 combination is shown when the " venue " is changed, a Pleurosigma angulatum being used. OBLIQUE LIGHT 185 complete diffraction spectrum of the structure in a piece of cardboard (provided the proper scale to suit the focus of the objective were maintained) and shift it about over the back lens of the objective. Any combination of openings which can be got that way corresponds to a combination of diffraction spectra obtainable by using appropriate oblique light. To understand this more fully, Fig. 117 may be consulted. The Theory of Oblique Light diagrammatically represented. Amphipleura pellucida on the stage and a i"40 N.A. objective in use. X represents the central or diop- trically formed beam, whilst the black circles are supposed to be the diffraction spectra, the blue end being turned in all cases towards the central beam X (see Fig. no). Circle A. — The appearance presented at the back lens of the objective when green light is used. Circle B. — Oblique light when used to show the transverse lines. Circle C. — Qblique light when arranged to show the longitudinal lines. Circle D. — Oblique light when set to show the dots : two spectra (the blue ends) being in the field at one and the same time. Fig. 117. B^ Here we have represented the image seen in the back lens of an objective with unlimited numerical aperture. The numerous spectra (although even all are not shown which theoretically exist) are set out in diagrammatical arrangement, as if the Amphipleura pellucida Were under examination ; but it must be distinctly understood, of course, that such an ideal light-grasp is impossible. The circle A may be taken to re- present (rudely) the area of the back lens of an objective with a N.A. I -40, X showing the central beam. The position of this circle shows that, with the central beam centrally placed in the field, a portion of each diffraction spectrum of the transverse lines is all that is contained within the prescribed limits. This accounts, as we have before indicated, for the lines being very imperfectly or faintly shown when using the low-power eyepiece. They may not have been seen at all if the outer zone of the objective were too small or not well i86 OBLIQUE LIGHT corrected. This explains, too, with a poor specimen of the optician's art, or one with a low numerical aperture, why it is the observer has such difficulty in persuading himself there are any markings at all, the diatom appearing without structure. Position B shows the " venue " changed and oblique light in use. One diffraction beam is now noticed to be entering in the field at the same time as the central, so the transverse lines should be well shown when the eyepiece is in use. Position C explains the situation when the arrangement is changed and the " venue " made for the purpose of showing the longitudinal lines, and it further explains why it is always more difficult to see them also ; because the spectral beams, it will be noticed, being considerably further away from the central one,' entails the use of so much more oblique light (or so much more shifting of the ''venue"). Position D indicates the position chosen for displaying both lines, which means displaying " the dots." For this purpose both spectral beams, or as much as possible of each, with the central beam must be in the field at one and the same moment of the back lens. As seen in the diagram, it will be noticed this has not quite been accomplished, because the light supposed to be in use at the time has too long a wave-length ; hence blue or blue-violet must be employed to shorten the distance between dioptric and diffi'action beams (iii), thereby allowing their more complete passage through the limited area of the back lens of the i'40 objective. When this takes place, but not until, can the "dots" be seen. The study of the circle shown at D is very important, and one that must be borne in mind by the microscopist. This concludes the explanation of the theory involved by the use of oblique light. In practice some little care must be employed, lest by too rapidly changing the position of the semi-lunar diaphragm the exact position may be lost for the complete fulfilment of the necessary conditions. It is an open question whether it is better to have the half-moon diaphragm a large arc of a small circle, or a small arc of a large one. In the latter case a portion of the outer part of the intermediate zone of the back lens of the objective is usually included with the outer ; whereas in the former the outer zone is for the most ' On account of the lines being closer than the transverse. ZEISS OBJECTIVE N.A. i-6 187 part alone employed. It is evident from this that the advantage between these two cases depends to a large extent upon the relative merits of the outer and middle zones. As a practical guide to the student, what has seemed to us the best method of dealing with the subject is to put both conditions to the actual test of direct experiment. It is not a little curious also that objects of different types often appear to require slightly different treatment ; but whatever the amount of oblique light demanded (which, of course, largely depends upon the closeness of the details), it should not be allowed to produce " effects " in the field of view actually outside the object, lying in space ! Further, it is our opinion, seeing that the introduction of false (diffraction) phenomena are very easily introduced into the final image, no details should be admitted as rea/ unless they can be seen, although perhaps imperfectly, with direct light, or at any rate with but a small amount of oblique illumination. The reader may now very naturally ask if it be possible to obtain greater resolution by any means than that of oblique light used as we have described. To answer this question, we must remind him that increase of resolution can only be obtained in two ways — either by making the N.A. greater, or by making the wave-length smaller ; hence the improve- ment so much desired can only be effected by employing one or both of these two expedients. Up to the present the first is that which has been mostly adopted ; but it is well known by the veriest tyro that a limit has been reached for practical purposes by lenses of N.A. 1-40. Here we do not forget the N.A. 1-6 objectives made by Zeiss with this laudable object in view ; but as , these lenses require the whole system, immer- sion fluid, condenser, slip, cover-glass, and mounting medium to be at least of the same high index of refraction, a restriction is placed upon the active employment of such a combination for all practical purposes, if for no other reason, upon the ground of expense, for we have been informed the cover- glasses— usually made of flint— cannot be prepared in the ordinary commercial manner, but have to be ground and polished by hand. Consequently the only improvement that seems to be within the range of practical microscopy is to adopt the second expedient mentioned — namely, the use of light of shorter wave-length than the ordinary green. For this i88 ILLUMINATION OF OPAQUE OBJECTS purpose the author strove for some time to perfect the apparatus already described for giving blue-violet light, and it is undoubtedly of service. But even to this expedient there is unfortunately a limit, perhaps to the reader, of an unexpected nature. It is this. The human eye has not the power of perceiving images produced by light of much shorter wave-length than blue- violet ; hence, were it possible easily to utilise light of this nature the eye would be unable to see the object when looking down the microscope. Further, ordinary glass is very imper- vious to these ultra-violet waves, although quite recently some has been manufactured by a special process which transmits rays never before thought possible ; hence special objectives must be made for their utilisation. These are now commercial, halving been, introduced by Carl Zeiss ; but, in accordance with what we have said, the eye cannot see the object, hence resort has to be made to photography. To enable the object to be focussed, of course, was the difficulty ; but this has been over- come by the use of a screen, much after that employed for X-ray work, which enables the operator to see the object (by lengthening the rays into those visible by the eye) which is removed before the photograph is taken. The resulting photo- graphs are very fine. But the whole process is still somewhat in the experimental stage. The Illumination of Opaque Objects Most objects prepared for the microscope are examined by transmitted light ; this, however, is not possible in certain instances, on which account their illumination must be effectecf by some other means. Of these there are several. The first is by the simple method of casting the light of the lamp or other illuminant upon them, as shown in Fig. ii8, which in plan indicates the portion of the lamp and specimen with a bull's-eye^ condenser interposed. There is some differ- ence of opinion which side of the plano-convex condenser should be turned towards the specimen, for theoretical considerations point to different positions according to different circumstances.^ ' A reference to the different kinds of bull's-eye is given in a previous chapter. ^ Theoretically, the piano side should be turned towards the shorter conjugate to obtain the best results. ILLUMINATION OF OPAQUE OBJECTS 189 We have frequently tried both positions of the condenser, and have found that in actual practice it is far better (although this statement may shock some readers) to try by direct experiment which gives the better result. It should be mentioned, however, what dissimilar effects may often be produced by using different angles for the situation of the illuminant, a point which we have never seen noticed before. It is well known that the mountains of the moon show up much better at the first and third quarters, Slip Arrangement in Plan or ohe METHOD OF ILLUMINATING OPAQUL 0BJECT5 Fig. 118. when the light from the sun falls obliquely upon them, than when they are illuminated by beams falling almost, if not exactly, at right angles upon the surface of the moon. A little shadow effect then seems to help to delineate and bring out the mountains very considerably. So it is with certain low- power objects under the microscope. When the light is placed so that its beams fall upon the object in a direction almost parallel with the stage, the effects appear to be very different from when it falls upon it almost vertically. Hence we make it a rule always to try to see whereabouts is the position that gives the best effects by the simple means of direct I90 ILLUMINATION OF OPAQUE OBJECTS experiment.^ The position, however, in this particular type of illumination is necessarily very often limited to a great degree by the mounting of the low-power objective in use at the moment, for some of the older make are so blunt-ended, and of so great a size, that the light can get to the object only when the lamp is in one position. This can be avoided by using objectives of the more modern manufacture that are not so constructed, having their brass mount tapering off to the front lens. On this account we are fond of employing, for the purpose in question, the Holos objectives sold by Messrs. Watson & Sons, or combinations made after the same fashion, as their formation is such that the front lens is itself carried downwards away from the brasswork in a conical fashion, and to such a sensible distance as to permit the light being thrown on the specimen with much greater ease than with many an objective otherwise mounted. Sometimes the illuminant is so hot that the rays focussed by the bull's-eye upon the object will actually burn or injure the specimen when the examination is a protracted one. It is best then under these circumstances to interpose a water-bath of some description. An exceedingly handy, cheap, and small arrangement is that designed by Mr. Kingsford and shown at the Quekett Club. It consists of two plates of glass separated by rubber stops and surrounded to a greater part of their circumference by a rubber ring, supported by a strip of brass capable of being tightened by screws. Easy to fill, easy to empty, and easy to clean are very great recommendations. They can be fitted to the ordinary bull's-eye stand, or supplied on stands of their own. These are more fully explained in the chapter devoted to " Filters." Not too large a one serves the purpose in hand, for, if the water gets too hot, it can be easily emptied out and fresh put in, remembering that it is always best to use water that has been boiled and subsequently cooled, because of its containing so much less air. This bath had better be placed between the illuminant and the condenser, rather than between the condenser and the specimen, as there is usually too little room to spare in the last-mentioned situation. The above-mentioned arrangement usually answers very well ' This will determine very often which type of illumination is the best to select out of the four mentioned in this chapter. ILLUMINATION OF OPAQUE OBJECTS 191 with low powers ; but when using a magnification of between 200 to 300 diameters, there is great difficulty in illuminating the object at all. A plan suggested by Mr. James to get over the difficulty is worthy of a trial. It is that of placing the light low down, and the bull's-eye condenser so obliquely that it casts a wedge-shaped beam along the surface (or very nearly) of the stage, just passing between the front lens of the objective and the specimen. A second method is a modification of what we have called the first. The lamp is placed so that its rays, after leaving the condenser, pass in a more or less parallel beam ^ along the CONDLNOCR Arrangement in Plan of a second method of illuminating ofaque object5 Fig. 119. surface of the stage. On the opposite side of the specimen these are received by a silver parabolic reflector of curious shape which, placed in the correct position found by experiment, returns them on to the object (Fig. 119). Theoretical instruc- tions are often given as to the best position for the mirror ; but we have said before that experiment is better than theory under these circumstances because the conditions vary so much — whether a thick or thin object, whether the light requires coming more or less down upon the specimen, or whether it is better from side to side, and so on. 1 How to obtain parallel beams from a lens is fully described in Chapters I. and II. of this book. 192 ILLUMINATION OF OPAQUE OBJECTS Another modification constitutes a third method of illumi- nating an opaque object. This time it is to have a parabolic mirror, with a hole in its centre, through which the front lens of the objective just protrudes (see Fig. 120). The light passing upwards through the slip around the specimen — which implies that the object must be mounted as if for use with transmitted light — falls directly upon this mirror, which returns it to focus W Arrangement in Plan of a third method of illuminating opaque objects by mean5 of the lllberkuhn Fig. 120. on the object, an adjustment being provided to assist it in so doing. The above arrangement furnishes most excellent results, but unfortunately can only be used for the special objective for which it is constructed, as a longer or shorter focus lens will need a longer or shorter focus mirror, without which the object will not be properly illuminated. The mirror is called a Lieberkijhn, after its inventor. A fourth method of illumination, effected in two different ways, is by what is called " vertical illumination." The principle involved is the same with both arrangements, and consists in utilising the objective as its own illuminator. A beam of light enters either device through a little hole guarded by a diaphragm ILLUMINATION OF OPAQUE OBJECTS 193 at its side, the perforated brass mount serving to hold the objective at one end whilst it is attached to the nosepiece by n Condenser Lamp Fig. 121. the other (Fig. 121). In the case of one arrangement the light then falls upon a cover-glass placed at an angle of 45° (Fig. 122) I'll JMp'li Fig. 122. — Beck's Vertical Illuminator. to the optical axis of the microscope (suitable adjustments being provided), by which it is reflected into the objective and from 13 194 ILLUMINATION OF OPAQUE OBJECTS thence on to the object ; whilst in the other (Fig. 123) it falls on the hypotenuse surface of a prism designed to cover only- half of the objective, passing from there by total reflection into the objective, and from thence, as before, on to the speci- men. The first variety offers but little difficulty in use, but the latter needs special' objectives arranged with very short mounts, whilst with both types it is needful to employ speci- mens devoid of cover-glasses. Unfortunately with dry powers this implies their special correction for the purpose, which means A, view (partly sectional) at- t:.rhed to the lower tube and the i.ljective C, the latter in short nnjunt ; f, reflecting prism ; B, Ii'.ivn view ; K, milled knob for revolving the prism. B A Fig. i23.^Zeiss Vertical Illuminator (Full Size). expense ; but with oil immersions a cover-glass can be used with both forms of arrangement. The use of either of these illuminators requires particular care in adjusting the details. It is very obvious that the light has to be directed into the little aperture in the side of the mount with the greatest exactitude. To perfect the illumina- tion and to furnish enough light, the rays from the illuminant are gathered by a bull's-eye condenser and cast directly through the aperture on to the little glass reflector, or on to the prism, as the case may be.' When all is adjusted, no subsequent movement of the tube for focussing purposes is obviously permissible, and only the fine adjustment can be used to a limited amount. This constitutes a very great objection to ' See " Accessory Apparatus " concerning a new form of illuminator recently brought out by Leitz and Messrs. Watson & Sons. POLARISED LIGHT 195 the use of the vertical illuminator with the ordinary micro- scopical stand, and is impossible to be conveniently got over. In metallurgical instruments, described hereafter, the difficulty is met by making the stage to move up and down; hence coarse adjustment (and also fine adjustment as well) can be effected to any amount after the illuminating arrangements are complete. Polarised Light One of the first questions asked by the amateur when he sees the beautiful rendering of objects by this peculiar method of illumination is. What is meant by the term Polarised Light ? The answer to this is not at all easy, and it is very remarkable how most text-books on the subject of the microscope shirk any explanation. This very probably arises from the fact that to reply to it briefly is so difficult, and to do so thoroughly involves too much space. Perhaps no more concise description and explanation of what is meant by the term exist than that given by Mr. Spottiswoode in his fascinating little volume de- voted entirely to the subject in the Nature Series, from which we quote the following in the celebrated author's own words : — It is considered as established that light is due to the vibration of an elastic medium, which, in the absence of any better name, is called the ether. The ether is understood to pervade all space and all matter, although its motions are affected in different ways by the molecules of the various media which it permeates. The vibrations producing the sensation of light take place in planes perpendicular to the direction of the ray. The paths or orbits of the various vibrating ethereal molecules may be of any form consistent with the mechanical constitution of the ether ; but on the suppositions usually made — and none simpler have been suggested — the only forms possible are the straight line, the circle, and the ellipse. But in ordinary light the orbits at different points of the ray are not all similarly situated ; and although there is reason to believe that in general the orbits of a considerable number of consecutive molecules may be similarly situated, yet in a finite portion of the ray there are a sufficient number of variations of situation to prevent any preponderance of average direction. This being assumed, the process of polarisation is understood to be the bringing of all orbits throughout the entire ray into similar positions. Even this elegant description, however, may not thoroughly explain the matter to the lay mind, for it requires, anyhow, a certain, though very elementary, knowledge of the subject 196 PLANE POLARISED LIGHT of light in general, not perhaps possessed by a reader whose attention has been previously directed entirely to other matters. To him, then, the following remarks, though perhaps not so scientifically accurate, may more directly appeal. It may be reasonably presumed that ordinary white light consists of vibrations of the ether in all azimuths — that is to say in paths in all directions, each and every one of which are directly at right angles to the path of the ray itself. This is shown in Fig. 124 A, which rudely represents the section of a B ^^ Fig. 124. ray of light coming to the eye. Plane polarisation consists in the arrangement of all these azimuths, or paths of vibrations, into one plane only, as in B or C in the same figure. An object viewed by light of this description would only appear as if illuminated rather more feebly than usual ; but if examined in a particular manner to be hereafter explained, and with the special ap- paratus about to be described, certain beautiful and curious results, phenomena most gorgeous to behold, would be ex- hibited, and a specimen so illuminated and examined is said to be viewed by plane polarised light. If, however, a still further alteration is made in the apparatus employed, as fully explained later on, the object may be viewed by polarised light of a different character, because in this instance the vibrations, instead of being reduced to oscillate in one plane, are made to move in 2.' circular orbit. An object seen in this manner is said to be viewed by circular polarised light. It is not desirable to complicate the description of the subject any further, but we should not omit to mention that certain PLANE POLARISED LIGHT 197 crystals possess the peculiar property of reducing all the azimuths of common light into two planes, each at right angles to the other, as, for example, a crystal of Iceland spar. As will be seen in the footnote furnishing a description of what is called a Nicol's prism, ^ the aim of this arrangement is to eliminate one of these, and so to permit the passage of rays polarised in one plane only. The subject scientifically treated, though extremely interest- ing, is too deeply complicated to be thoroughly explained in a book of this description, and indeed requires much mathe- matical and philosophical reasoning ; but the use of these special forms of illumination, and how they are best arranged and produced for the purpose of the microscopist, forms the subject-matter of what follows. To produce the first effect — viz. the formation of light polarised in one plane — a Nicol's prism is mostly employed, for it is more ' A Nicol's prism (Fig. 125) is constructed from a rhombohedron of Iceland spar thrice as long as its diameter; one of its faces, which naturally makes an angle of 70° with the blunt edges, is cut off obliquely so as to give the new face an inclination of 68° instead. The whole block MlCOLS Ppism Extra- ordinapy Ordinary Ray is then divided in a special manner with relation to the axis, the two portions being afterwards united by Canada balsam. A ray entering the new prism is divided by it into two, each in a different plane of polarisa- tion, the ordinary and the extraordinary. But the refractive index of Canada balsam is 1-54, intermediate between that of the ordinary (1-65) and the extraordinary (1-48) rays respectively. Hence the most refracted ray finds in the layer of balsam a less refracting medium, and is totally reflected to one side, and so for most purposes practically got rid of ; whilst the other finds in the balsam a denser medium, and therefore passes through. This is the ray used. igS PLANE POLARISED LIGHT convenient than any other method.^ This prism, called the polariser, is placed and held in position beneath the condenser between it and the mirror by various means, according to the ingenuity of the optician. In some forms the arrangement is constructed to revolve within its mount or fitting an entire revolution about the optical axis of the instrument, such being effected by the use of a milled collar band placed outside ; whilst in other cases it is fixed. In any case, the apparatus is so made as to drop into a sleeve or such-like device so loosely that it permits of a slight amount of rotation sufficient for the purpose of adjustment. The polariser should not be unduly small in diameter, for if it be so it will cut oiY too much of the light issuing through the condenser ; hence if high powers be employed the consequent loss of aperture and illumination will be distinctly felt. Still, however, it should not be too large, for it will then be cumbersome and inconvenient, and should rotation be employed the fingers will keep knocking against the mirror, causing thereby considerable annoyance. The light issuing from the prism (the polariser) is, we have already said, what is called " plane " polarised, but for the observer to be able to witness the peculiar phenomena spoken of, it must traverse yet another nicol before reaching the eye. This is called the analyser. Although the principle involved in the action of this second prism is similar to that of the polariser, still its actual shape is somewhat different, according to which position it occupies, viz. — (i) In the microscope tube directly above the objective, (ii) as a rotating cap over the ocular, (iii) or as a combination with lenses to form what is called Abbe's analysing eyepiece, which is used instead of an ocular. (i) When arranged to fit into a cell to work above the objective ' A bundle of glass plates made of very thin glass also produces light polarised in one plane, but to obtain good results so many layers are required that the arrangement is too cumbersome to be used with the microscope. A modification, however, has been suggested by Mr. Michael, a former President of the Quekett Microscopical Club, which is worthy of notice. It consists in using a piece of opal glass instead of the ordinary mirror. If set at the best angle for furnishing polarised beams — technically called " the polarising angle " — and the instrument arranged in accordance, this gives very good results as a polariser where a powerful light is not required. PLANE POLARISED LIGHT 199 it is short, and the mount is attached to the nosepiece at one end and receives the objective at the other, a milled collar serving to rotate the prism around the optical axis. (ii) When constructed to be used over the ocular as a cap (Prazmowski prism), the spar is shorter still and cut somewhat differently ; rotation being effected by revolving the whole cap and prism about the top of the ocular. With this kind and with the previous one, almost any ocular of any power, whether Huyghenian or compensating, can be used. (iii) Abbe's analysing eyepiece consists of a very long specially devised prism of the Nicol type, with a lens at each end. It may be described as a special ^r'lsm placed within a special ocular. It is a delightful device to use, and is made loose enough to rotate quite easily within the draw-tube. It is almost needless to state, only being of one power, no change of magnification can be employed. Should this be required, the objective must be altered. These eyepieces are made as Huyghenian or compensating. It will be noticed from what has been said, that either polariser or analyser can be made to revolve with equal effect ; in fact, it is quite optional which movement is chosen. Should this be the polariser, the fingers in turning it are rather apt to knock against the mirror and so put it out of position ; if the analyser, eye-cap form, or the Abbe eyepiece arrangement, the eyelashes may get in the way of the fingers or thumb whilst rotating, whereas if the form that is placed above the objective be employed, all these difficulties are removed. There are objections, however, to this type which do not arise in the use of the other two, for the object may appear to shake as the prism is rotated, unless the fitting be very nicely made so that it revolves in its jacket very smoothly and evenly ; or to travel about the field, if the inside fitting be at all eccentric to the optical axis or the prism badly made. After having placed the concave surface of the mirror in a suitable position, and attached an inch objective to the nose- piece of the microscope, on moving the polariser or the analyser around the optical axis it will be immediately found that alternate intervals of light and darkness will be produced. This is caused by the single " planes " of polarisation being parallel or crossed 200 PLANE POLARISED LIGHT one with the other (see Figs. 126A and b). If now a "polari- scopic object"^ be placed on the stage, given portions of it may present beautiful variegated colours (if such portions be of the correct thickness for the purpose), whilst the whole object will always show extremely elegant and attractive, not to say at times very pronounced and beautiful, changes of black and white effects, varying from almost blackness to a most pearly, silvery white. All manner of details are brought into evidence by this means and certain conditions are revealed which in many instances are not to be seen by any other method of illumina- tion. For example, badly annealed glass may be detected, A B PARALLEL CROSSCP DIAGRAMMATIC REPRCSCNTATION OF THE PLANES "PARALLEL AND CROSSEo" Fig. 126. and also glass lenses under strain. Certain effects, too, in the growing of seeds may be witnessed by this simple means that are not visible by other methods. Should, however, a thin slice of mineral called Selenite^ be placed on the stage between the analyser and the polariser, colour changes take the place- of the black and white effects just described. As this plate is revolved about its axis, there will be found to be two positions in an entire revolution where a maximum effect is produced. These should be noted by some ' This is the name given to objects, or to crystals or such like, that are " suitable " to exhibit good effects in polarised light. ^ Selenite is a mineral consisting of hydrated sulphate of lime in obhque prismatic crystals. It requires much practice to cut perfectly even slabs of uniform thickness. We have been able to split circles of about half-a-crown in diameter by using a very flat knife and keeping the material under water. We believe the finest specimens are ground and polished ; but the method adopted by the trade is kept a close secret. THE USE OF SELENITE 201 sort of mark corresponding to one placed on the polariser, so that by putting mark to mark the position of maximum effect can in the future be at once secured without any direct experi- ment.* What colour effects are actually produced depend upon the thickness of the selenite. Plates are commercially sold of two thicknesses — one yielding blue and yellow colours, the other red and green. In the previous experiment, we said it was possible that certain parts of the specimen showed variations in black and white effects ; when the same object is placed on the stage with the selenite beneath it, these black and white phenomena are now changed into modifications and blendings of blue and yellow, or red and green, according to the thickness of selenite employed. It is obvious then a set of suitable specimens, called " polariscope objects," reveal different colour phenomena with each selenite, hence by this simple means many an enjoyable hour may be spent by those fond of gorgeous scenic effects. But there is yet another form of polarised light which, when correctly used, gives results so beautiful and entrancing that it puts the phenomena just described quite into the shade. We refer to the use of what we have already called attention to, and which is termed circular polarisation, in contradistinction to plane polarisation, which we have lately been explaining. The curious feature of this class of polarised light is that, instead of variations in blue and yellow, or red and green, the colours of the whole spectrum are utilised. As the analyser (or the polariser) is revolved, one end of the spectrum seems joined up with the other, hence when one nicol is revolved in one direc- tion, blue merges into green, green turns into yellow, yellow into orange, and then red, whilst the union of red with blue, to complete the circle we mentioned, forms a curious plum colour of a most magnificent hue. Reversing the nicol reverses the order of colours. All these changes are brought about by placing above or below the selenite, but beneath the specimen, ' Lest any confusion should arise in the reader's mind by saying the selenite is revolved about its axis, vi^ might explain that if held between the thumb and finger, one on the front surface and the other on the back, revo- lution around these fixed points is the movement about the axis we speak of. It is convenient to have the slab circular ; its " best position " then can be marked so that the mark can always lie upon the top of the polariser in the same place. 202 CIRCULAR POLARISED LIGHT what is called a quarter-wave or quarter-undulation plate. This is really nothing but a piece of mica, exceedingly thin and mounted in Canada balsam between two thin pieces of glass.^ A position of maximum effect has to be found for the mica when rotated above the selenite, and when such is ascertained, some means of restoring the quarter-wave plate to the same position with respect to the selenite should be made, so that in the future it can quickly be placed correctly in situ without the trouble of experiment. The best plum-coloured effect, we think, is always obtained by using the quarter-wave plate with a red-and-green selenite, rather than with a blue-and-yellow one ; but there are very possibly those who do not agree with us in this opinion. Suit- able specimens used with circular polarised light thus obtained give the most gorgeous and magnificent aggregation of different colour renderings imaginable as the analyser is turned. No artist can depict, or eye picture, such a mixture of shades and changes of colour as may be witnessed by this simple means.^ If the light be not equally distributed over the whole field of view — the condenser having been suited to the objective — the other side of the mirror may be tried. High powers do not seem to yield such brilliantly coloured effects, and altogether are not so suitable as low ones. We always think the Nernst electric lamp furnishes the best illuminant for the polariscope, as lamplight, being yellow, does not give rise to the excellent possibilities easily obtained with the white electrically formed light. A very great amusement is furnished to the microscopist in making his own specimens by the simple method of forming concentrated solutions of different soluble salts, and allowing ' A quarter-wave plate may be made with a little practice by splitting a thin slab of mica (a form of which is commonly called " talc ") into extremely thin slices with a fine needle. Several should be made, and one will usually be found which, when placed between two nicols, shows no change of colour on the revolution of either prism, save the changing of a delicate bluish grey to a rathery^zw^z-coloured one : this is (approximately) a quarter-wave plate. ^ To prevent complication, it has not been mentioned before that the actual thickness of different parts of the specimen also produces modifications of colour effect as the nicol is revolved, so that the mixture of phenomena, some due to the selenite and quarter-wave plate alone, whilst others are due to alterations dependent upon the thickness of the specimen, renders an exhibition which baffles all description. CONVERGENT POLARISED LIGHT 203 drops of them to crystallise out on slips or on cover-glasses, finally protecting them by suitable means. Convergent Polarised Light So far we have only spoken of the use of plane polarised light writh and without the interposition of a slab of selenite between the nicols, concluding with an account of a third form of this peculiar illumination called circular polarisation, where, in addition to the selenite, a quarter-wave plate of mica is added : there yet remains, however, to be described a fourth method of employing this interesting means of investigation, one restricted to the viewing of what is called the " rings " and " brushes," which certain crystals exhibit when viewed with the special device we are about to describe. To understand the object of the special arrangenient in its component details, it should be mentioned that hitherto we have been explaining the effect produced by the employment of plane polarised parallel beams of light, showing what marvellous information they unfold of the inner constitution of bodies whether as a revealer of unequal tension — as in the case of unequally cooled glass, for example — or of the different interference phenomena exhibited when layers of unequal thickness of certain substances are successively viewed. Now, however, we wish our apparatus to be so arranged as to show the curious effect that sections of certain crystals exhibit when plane polarised rays of distinctly convergent light are brought to bear upon them. These effects are collectively called the rings and brushes. They vary very much in uni-axial and bi-axial crystals,^ but in either case are very curious, and their interpretation and thorough comprehension offer a considerable intellectual enjoyment. The great object, then, now of the microscopist is to arrange the microscope to obtain these con- ' In the uni-axial crystals, such as calcite, quartz, borax, sugar, nitrate of soda, ferro-cyanide of potassium, etc., only one ray performs in the " ordinary " manner : the other is what is called the '' extraordinary," which means it does not follow the usual well-known laws. But in the bi-axial crystal discovered by Sir David Brewster neither follows the usually well- known laws ; both are therefore " extraordinary," the index of refraction varying with the direction of the ray, the refracted ray being not always in the plane of incidence. Such crystals then exhibit a double set of rings and brushes, which, while complicating the phenomena, add very much to the magnificence of the final effect. Some crystals are particularly fine in 204 CONVERGENT POLARISED LIGHT vergent beams in such a manner that they shall fall on the crystals in question, and be viewed in the proper manner. For this purpose the microscope has practically to be turned into a telescope of such a nature that it will deal with wide-angled beams. The first thing necessary is a wide-angled condenser, and we believe in the usefulness of the achromatic variety, although, be it understood, it is not an absolute necessity. The objective should not be of very high power, for we are not dealing with the very minute ; but the important point to recollect is that it should have enough and no more numerical aperture than required, about '65 to 70 being sufficient.^ If the objective be of too low a power, although it be of the stipulated N.A., the back lens may be too large to be entirely viewed through the nicol ; hence, generally speaking, the best for most purposes is a |^ or a ^-in. The upper nicol may be above the eyepiece, or in the more usual position above the objective. To complete the conversion of the microscope into the ideal telescope, a 2-in. objective^ (such as the one used with the apertometer will suffice in most cases) should be screwed on to the nosepiece attached to the draw-tuhe, thus constituting one of the uses for this detail referred to when describing this part of the microscope in the earlier part of this work. For convenience of those using this arrangement for the purpose in question, a diagram (Fig. 127) explaining details is " n n " " b fe^ Fig. 127. the phenomena displayed by them. Of these may be selected nitre, native crystals of carbonate of lead, glauborite, and some of the varieties of felspar called adularia. ' Strictly, the combination should have its N.A. equal to or exceeding the ang'h of the crystal. ^ The form most suitable is a plano-convex or achromatic combination especially made for the purpose and called a " Bertrand's Lens." CONVERGENT POLARISED LIGHT 205 given, being followed by the order of procedure to get the best results, which we believe is directly or indirectly due to Mr. Nelson. 1. Fix objective on the nosepiece of the tube; centre con- denser and light, and open iris wide. 2. Set the nicols so that a white field is obtained. 3. Add auxiliary 2-in. objective (Bertrand's lens) to the nose- piece of the draw-tube, and replace it in the tube in much about its usual position. 4. Place specimen on the stage. 5. Drop the tube (and, of course, with it the draw-tube) by means of the coarse adjustment until the objective (say the j-in.) all but touches the cover-glass or the crystal.^ 6. Focus with the draw-tube, leaving the coarse adjustment entirely alone. 7. It may be necessary to change the position of the substage condenser to obtain plenty of light. It will mostly be found to require raising. If the analyser or polariser be now revolved on the optical axis in the ordinary manner, the " rings and brushes '' will be well seen. Sometimes magnificent and curious effects are produced. ■ We append the following notes, which may assist the student when commencing to use convergent polarised light : i. If the microscope in use be one with objective-changers and the analyser placed, over the objective in a fitting, and it is found the auxiliary lens will not focus the brushes properly,— it arises from such being of too short a focus. Use one of longer focus or remove the changers. ii. If the circle of hght as seen through the ocular appears "cut off" in one part which revolves as the analyser is turned, the condenser requires lowering. iii. If the object be too much magnified, use a lower ocular ; a lower power objective is not very successful. If requiring magnification, use a higher ocular. iv. If the brushes are not shown well, or do not cross the field completely, it is probable the " best position " of the polariser has not been found with respect to the specimen. Turn the former one-eighth of a revolution. V. A selenite with or without a quarter-wave plate may be used if desired. 1 Usually the absence of the cover-glass produces the best results ; indeed in some instances it is compulsory* In cases where the crystal is mounted dry beneath a cover, the attempt may be made first with it in situ, removing the cover subsequently if it be found necessary. CHAPTER X ON THE USE OF THE MICROSCOPE Every microscopist should endeavour to become master ot the instrument in all its uses and in all its details. There are, no doubt, many objectives that have been purchased and thought to be " splendid " at first, which have subsequently been found faulty simply owing to the purchaser not having had adequate experience in the art of testing them at the time of purchase ; but there are far more specimens that have been laid aside or rejected as poor and badly marked, because the microscopist has been ignorant of the proper way of centring his condenser or using his objective to obtain the finest possible seeing. As this work is intended to start the actual beginner on. his way, as much as indeed it is hoped it may be of service to others more advanced, so the method of using the instrument will be explained in detail even from the very first. I The question often asked by those about to commence the i subject, especially those that intend entering the medical pro- fession, is. Which tube-length shall I buy, which is the better, and what is the difference? This is a long matter to discuss, and after all is much a matter of individual opinion. As regards the origin of the two instruments, there is no doubt the long- tube model originated in England, whilst the short-tube instru- ment had its birth abroad ; but it seems doubtful who was the actual originator of either system, although the latter is usually ascribed to Oberhauser. ' When first introduced into England the Continental instru- ment was not at all well received by the majority of microscopists. I This arose from the fact that it was then held as an unwritten i law that all, or very nearly all, of the magnification of an object ' should be performed by the objective, and as little as possible i by the eyepiece. Hence, as it was obvious to obtain an equal magnification with the objective placed on the short tube as 206 ON THE USE OF THE MICROSCOPE 207 could and would be obtained if it were attached to the long, it necessitated the use of a higher power ocular ; " an instrument, therefore, demanding such a condition of things could not be recommended or tolerated for a moment." This dictum, however, rested on an entire misapprehension. [ It is, of course, true that with the same tube-length a higher eyepiece puts the objective to a severer test ; but the fact was lost sight of that the higher eyepiece, when applied to a short tube, received a smaller, and therefore sharper, image of the object, and that, if the resulting magnification was the same, the quality of the image was also identically similar. Hence this ( objection entirely falls to the ground. Optically speaking, there is no difference between the per- 1 formance, say, of a good xVin- on either form of model, 1 provided, of course, the actual specimens of the optician's art | are of equal merit. The advantages and the disadvantages of the difference in the size of the oculars in the case of the two instruments is also a question that has often been discussed, without much profit in the end. The increase of field in the long-tube eyepiece (because of its diameter being larger) is of questionable advantage, seeing that such increase is usually more or less fuzzy, the reasons having been explained already when dis- cussing objectives and eyepieces generally. But the principal point of a dissimilarity in the instrument to lay hold of, we think, is the great difference in portability in the one case over the other, and this is especially to the front when instruments have to be carried about, especially by medical men in the i tropics, where the distance travelled is often very great. Further, ; when observations have to be made with the stage liorizontal, the ; long-tube instrument often involves the use of a stool rather than j a chair, which is of sufficient height with a Continental instrument. : It has been stated also that one point connected with the Continental model has been often overlooked. It is that a smaller difference of tube-length produces a greater effect in the adjustment of objectives than obtains with the longer tube. Although classified as a defect, it is open to consideration as to whether this is not an advantage, as a smaller amount of shift brings about the adjustment required ; but it may be argued, on the other hand, that greater care is needed. 2o8 SHORT AND LONG TUBE-LENGTHS Mr. Nelson has additionally pointed out what he considers as yet another disadvantage with a Continental tube-length, and that is, the eye does not see the stage in focus (unless the vision is a short-sighted one) without drawing back the head a sensible distance. As a matter of fact, we personally hold this to be an advantage, for the " off-duty " eye, which should be always kept open, not seeing objects in a good focus, is not so likely to cause a mixing-up effect with what the other eye is seeing as it looks down the tube. It should not be forgotten, in the comparison between these two stands, that to obtain the highest magnification the English model must be employed because of the greater length of the optical tube (and consequently the great magnifying power pro- duced thereby) ; whilst as a set-off against this it should be borne in mind that to employ the lowest amplification possible the use of the Continental model is imperative, because of the shorter optical tube-length.'' ' This may not be immediately apparent, but it will rapidly be understood by the following argument : All oculars on the short tube apparently magnify i^ times more when transferred to the long, because .the optical tube-length of the objective is ij times greater when adjusted for that mechanical tube-length. Hence when a given magnification is obtained with the most powerful objective and the highest ocular on the Continental instrument, the same ocular and objective (the correction of the latter for the change of tube-length being neglected for the moment) when trans- ferred to the long tube furnish \\ times the magnification previously obtained on the short one. Vice versa when the lowest magnification is obtained that is possible on the long tube, this is immediately proportionately reduced by transferring the ocular and objective to the short one. The change in each case, we have said, is not really due to the ocular, but to the alteration of optical tube-length of the two objectives when differently corrected for the Continental and English mechanical tube-lengths. It might be mentioned here that Dr. van Heurck, instead of changing the actual objectives, uses what he invented and called a " transformer." This was either a negative or a positive achromatic combination, which, added at the back of the objective, either corrected the long to the short tube- length, or vice versd, the short to the long. This avoided the actual change of the individual objective, but we have never tried the arrangement. He says that it corrects in either case so perfectly that a double set of the expensive apochromats, those corrected z;z ikeir manufacture for the long and for the short, is not required, " you merely have to add the transformer in either case." He adds, too, that the definition is in no way impaired even with " the highest power objectives." ILLUMINATION 209 It is evident then, taking all things into consideration, there | are advantages and disadvantages with each type of stand, hence we think that the happy mean is struck by employing a stand which, by the use of two draw-tubes, can be employed for both purposes. This can, as a matter of fact, be done with an in- strument of Continental length by having a short length of tube made to drop into the draw-tube when required ; whilst in the case of the English model any method of shortening it is, of course, impossible. Microscopes are now manufactured with a double draw-tube, which enables them to be closed sufficiently for using objectives corrected for the short tube, whilst at the same time they can be extended to suit the correction of those made for the long tube. This then would seem the ideal instrument to select if required for the double purpose mentioned. Illumination The ordinary lamp ^ used by microscopists being trimmed and lighted, it is placed with the flame edgeways towards the observer, about six or seven inches from the mirror,^ the concave surface of which is turned uppermost. The instrument should be inclined at an angle suitable to the observer, so that he can look into the eyepiece without straining his neck. It is a good plan for the actual beginner, in learning how to adjust the mirror, to commence — after removing both the ocular and objective — by looking down the empty tube towards its lower end. There will be seen the mirror. On examination, it will always be found to move very easily in two directions. To learn what these are in the simplest manner, it is best to affix a short length of pencil — say an inch and a half long — by means of a little piece of common candle-wax to its very centre, at right angles to the surface, and with the point directed vertically upwards. The microscope being placed in front of the observer in the usual position, the mounting of the mirror will be found to provide two sets of movement, one of which is termed " the side ^ The electric Nernst lamp, now so much in vogue, will be referred to again later. ^ The distance away of the illuminant is an important matter when dealing with high-power condensers (see p. 223). 14 2IO SETTING THE MIRROR to side '' motion, in which the pointer moves in an arc stretching from right to left, or from left to right, as the case may be; whereas the other, called the " to and fro " direction, makes it travel exactly at right angles to the former line of motion. The object of these movements to and fro, and from side to side, is obviously, by their combined use, to find a position that ensures the mirror reflecting the light of the lamp into the instrument in such a manner, after traversing the lenticular portions, it shall reach the eye of the observer. To perform these movements quickly and yet with precision, it is best to place the right arm on the table around the corresponding side of the instrument, the left passing likewise around it on the other side. The iirst finger and thumb of each hand should grasp the corresponding edges of the metal cell containing the mirror, and then with a little practice the operator will find he can make the light reflect up into the centre of the tube, and so to his eye with great facility. Most beginners find considerable difficulty in " getting the mirror right," as they call it, and often have to waste much time in so doing ; but we venture to suggest, if they will only learn to adjust its position in the simple and primitive fashion above described, before attempting to do so with the lens and ocular in situ, their subsequent difficulties will rapidly vanish when they get a little more experienced. Having attained proficiency in adjusting the mirror so that the operation can be speedily accomplished, the tyro had better now place an inch on the nosepiece and a low-power ocular in the draw-tube — say a No. I of some opticians, or an A eyepiece or a 2-in. of other, manufacturers. In screwing on an objective to the nosepiece, and in taking it off, many a one has been dropped and perhaps seriously injured. It is well then for the beginner at once to learn the proper way of doing this, so as to avoid the above-mentioned accident. Let the objective' be held as far away from its screw end as possible — that is to say, as near as convenient to the end next the small front lens — between the first and second fingers of the right hand, much in the same fashion as a cigar is held between these two fingers, the screw end of the mount repre- senting the portion of the cigar that goes into the mouth. Having previously raised the tube of the microscope by the SCREWING THE OBJECTIVE ON AND OFF 211 coarse adjustment, the screw end of the objective is placed against the nosepiece— screw to screw — being gently held there by the two fingers of the right hand, as already explained, whilst the thumb of the same hand serves to balance and steady it in position. In the interval between the two fingers and the screw end of the objective, the thumb and first finger of the left hand are now slid in such a manner as to grasp somewhat firmly the milled edge of the mount always present. This must be turned in the opposite direction to the movement of the hands of a watch, the microscopist throughout the operation being supposed to be sitting or standing behind the microscope — that is to say, with the instrument in front of him. The right hand should now gently press the objective upwards, towards the instrument, so as to assist in making the screw of the objective engage into the thread of the nosepiece. If this will not " take in " easily, it is a good plan to draw back in the opposite direction for about half a turn or so, until the thread of the one gives a click as it drops into that of the other. A few turns, and the objective is " home " and in its final position. In removal, the same method may be adopted, but the order of everything is necessarily reversed. Gripping the lens with the left thumb and forefinger around its milled edge, and turning in the direction the hands of a watch move, the combination begins to leave the nosepiece. Before allowing it to advance too far, the first two fingers of the right hand should be quickly placed over the free end to hold it cigar-fashion as they did before, which position allows them to prevent the combination falling on to the table or floor should the screw disengage itself from the nosepiece before it was anticipated. This simple expedient to save accidents should be very freely practised over and over again, until, in fact, the operation can be performed almost unconsciously ; for, be it understood, dropping an expensive apochromat, for example, often turns out to be a far more costly trouble than at first thought it might appear, on account of the jar being so apt to loosen or displace (if not actually to break) one or more of its numerous little component lenses ; an accident that may quite spoil the performance of the combination and necessitate its being sent to the optician to overhaul and repair. The inch being safely attached to the nosepiece, a specimen — say the proboscis of the blow-fly — should be placed on the 212 FIXING THE SLIP ON THE STAGE stage in the reverse position to that in which it is desired to be seen/ and duly fastened there. If the stage be a mechanical one, the-adjustment of the specimen into its proper position beneath the objective is made by turning the screws provided for the purpose ; but if it is only a plane one having but a couple of clips, a word or two of advice may be given as to how to shift the slide from side to side, or from above downwards, in the most con- venient manner. The thumbs of both hands should be employed upon the slip, one at one end of it and one at the other, the fingers being placed beneath the stage so as to get a firm hold. When, on looking into the ocular, the position is found to be correct — the thumbs moving the slide until it is so — the left thumb should press the specimen gently but firmly on to the stage, so as to hold it there, while the right hand adjusts the clip, after which the right thumb does the holding, whilst the left hand completes the fixing by manipulating the second clip. Pressing either of these clips " home " causes them to hold much tighter in case they " work loose." To find the correct position of the specimen, however, or even to find it at all, is often a great trouble to the beginner, or even at times to the advanced student, and sometimes to the experienced worker. The follow- ing " dodge " we have often found of great convenience, with dry powers especially. Having placed the inch — for example — as near in focus as can be judged — a little too far off is better than the reverse — the ocular is removed and the head drawn back a few inches, whilst the eye glances down the tube of the instrument. Most frequently the object can be very readily seen, as the thumbs move it about in all directions ; it can then be quickly slipped into an approximately central position, to be finally adjusted later on. It is difficult to use this method, however, with high powers. Whilst focussing a specimen, a method equally well to remember is always to lower the objective as near as possible to the cover-glass before attempting to look into the instrument, and then, whilst the eye is at the ocular, to ■ This is often spoken of as "upside down." It is not however a strictly accurate method of speech, for it might be taken as meaning that the " slip " was to be turned next to the objective, and the cover-glass to face the condenser ! What is meant is, that if the cover-glass represented a watch dial, the xii should be turned round, so that it occupied the usual position of the vi and the iii that of the ix. CARE ON REMOVING THE SLIP 213 obtain a sharp focus by raising up the objective, rather than by lowering it down — the more frequent method. With all micro- scopists, save those that are frequently at work, this simple expedient saves many a crushed cover-glass or broken front lens. It should be mentioned, however, the method is only of use with dry objectives ; with immersion ones another safety plan will be given when their use is under discussion. Fine focussing of the specimen may now be performed by using the fine adjustment screw, but before ever attempting to use it the learner should satisfy himself which way the screw turns to lower the objective, and which serves to raise it up. All microscopes are not quite alike in this respect, although in far the majority, by turning the milled head in the direction that the hands of a watch move, the objective is lowered, and on screwing in the opposite direction it is consequently raised. Before leaving this part of the subject, we should like to answer a question that may be very naturally asked by, or anyhow arise in the mind of a reader, and that is why all these precautions should be taken with an inch objective, seeing that it focusses such a long way off the specimen ? We reply, in answer to this question, that it is because of the great expediency of getting the beginner into habits of care and caution ; for if such be established while commencing to learn the use of the instrument — as indeed was the case when we began ourselves — when the student later on employs higher powers, consequently of shorter focus, he will follow on in the same lines, having from the commencement learnt that with delicate tools a delicate handling is necessary. There is yet another piece of advice which may be mentioned here, in want of a more suitable place. It is always to recollect to raise the tube, and consequently the objective, before ever attempting to remove a specimen off the stage, whether it be to replace it by another or simply to put it away. If the latter, it is to prevent the "ringing" of varnish so often present catching against and very possibly scratching the delicate front lens of the combination ; ^ whereas if for the former purpose it is, in addition, to save jamming the next slide between the objective and the stage — an accident possibly occurring when the second slip happens to be a thicker one than the first. If now the ' Especially the case with high powers, as their working distance is so much less. 214 ZEISS "LOUP" AS A LOW-POWER CONDENSER tube has been previously raised in either of these cases, a nasty accident is thereby avoided. To resume, the delicate focussing can be done by tlie fine adjustment which may be necessary when a high ocular is in use even with an inch, although of not so much service with a low-power one. It is quite likely now that, even with the A ocular, directly the student looks at the proboscis he will recognise that the mirror does not reflect the light equably over the whole field, and hence that it requires a little further ad- justment. This should be done with the arms resting on the table as before explained. But perhaps with all this the image is poor ; this may arise from the concave mirror requiring a little raising up or down. If the high-power ocular now replace the low one, it will soon be found, especially as the student's eye learns to see and appreciate fine definition, that the very minute hairs of the proboscis do not look quite sharp and clear. They may appear, no matter what the focus, fluffy and with double tips. This is very likely because a substage condenser is required. There are several very good ones in the market, but few seem to know that the "loups" used as hand-magnifiers made by Zeiss and others can be employed as excellent condensers for an inch objective. We repeat that very excellent low-power condensers are made by most manufacturers, but we must admit to having a great liking for the very lowest one made by Messrs. Watson & Sons after the formula of Mr. Conrady. Its lenses are about i^ in. in diameter, and its focus is 2 in., and when mounted it just drops into the substage. When not in use there, it makes the best bull's-eye with which we are acquainted. Having placed the condenser into the substage, or in the sleeve which takes its place, between the specimen and the iris diaphragm or its representative, the whole is racked up or down, or pushed by the fingers, until a very perfect illumination is efi"ected. On focussing, the finest hairs should now appear in excellent definition, looking as if they grew upon the stage and were rising up to the eye ! Should the light be found too powerful, the condenser may be lowered (permissible with this long-focus objective) just a little, or the iris may be closed a trifle; but it should not be forgotten that both operations, especially with a high-power objective, are apt to spoil definition and reduce the resolving power of the combination. If, however, the light CENTRING THE CONDENSER 215 be still too bright, a thin opal glass may be interposed between the mirror and the lamp, or a. thin piece of black glass or some ground glass placed there instead. When using a f-in., which has usually about the same N.A. as that of the inch, no difference need be made in any of the operations, only it should be recollected that it focusses much nearer the specimen. Whilst stating this, it is well to recollect, however, that owing to the variety of computations adopted by different opticians, the exact position occupied by a particular inch or a f-in. may not be that required by others of similar focus made by different firms. We know, for example, an inch that works almost as near as a \-in. by another maker. The beginner then should have a care in this matter. When using a |-in., which has usually a N.A. varying from '65 (Zeiss's apochromatic) to, say, '40, a different condenser must be employed. It is best to use it with an aperture as near as possible to vo} for it will then be of service with objectives of shorter focus than the ^-in., and which have usually a higher aperture still. Centring the Condenser. — In using a condenser of this descrip- tion a fresh operation has to be conducted before attempting to look at a specimen ; it is called " centring the condenser." This means that the optical axis of the illuminator shall be placed in -adjustment or in line with that of the objective. To do this properly must be the aim of the microscopist on all occasions, for without so doing the objective never performs properly, especially if it be of high power. It is effected in the following manner, by employing the adjusting-screws provided either in the condenser mount itself or in the substage fitting. To learn the art, anyhow at first, it is best to use no specimen at all, but to rack the condenser up to the level of the stage and to lower the objective down until it nearly touches it. ' It is sometimes a convenience, however, because of the larger image of the illuminant, to use a condenser of longer focus and of N.A. -45 for objectives not above this numerical aperture. We often employ with great advantage an illuminator by the same makers as just mentioned, of exactly this aperture, but condensers of excellent performance are sold by most of the leading opticians. The special care necessary when using a condenser of larger aperture than the objective, lest the image should be " flooded," is discussed in the chapter devoted to the Use and Abuse of the Substage Diaphragm. 2i6 CENTRING THE CONDENSER The correct position is found when the image of the illuminant is in focus. The iris diaphragm should now be closed to a large pin-hole (with the highest powers it must be shut as dose as possible) and the eye placed at the ocular, a low-power ob- jective, such as the inch in this instance, being selected. Raising the objective, unless the condenser is • greatly out of centring, should quickly reveal the small opening of the iris brilliantly illuminated, provided the mirror has been " set " before com- mencing operations.^ Sometimes, however, after closing the iris all is dark, and no matter how much the objective is raised or lowered the little opening of the iris fails to be visible. This means that the condenser is wildly out of centrality. Let the objective be returned at once till it nearly touches the front lens of the condenser, and then be very slowly re-raised with one hand, whilst the other slowly opens the iris. A time will come when the lens will focus an edge of the iris at some part or other as it appears stretched across the field of view. At that moment let the objective be left alone and attention be directed to watching the iris as it opens across the field. It will very soon be seen the way it is moving, which serves to indicate the adjusting-screws that must be employed to bring it apparently in the centre. Working slowly and circumspectly, the little opening can be gradually brought nearer and nearer the centre of the field until at last it is centrally placed, when the adjusting-screws should be left. The iris should now open concentrically with the area of the back lens of the objective as seen down the tube when the ocular is removed, but if not it requires a little re-adjustment until the desired effect is produced. The process should be repeated over and over again, the illuminator being purposely shifted eccentrically for the purpose of putting it into the centre again, simply for the sake of practice. At length the student will attain such a familiarity with the process and find it so easy that the adjustment will become as easy as focussing and can be carried out at once with a high power, doing away with the use of the low power altogether. Having learnt then to centre the condenser, it should be racked up and down until the image of the edge of the lamp- flame be seen stretching from the top to the bottom of the field, the flat surface of the mirror being the best now to employ. ' See Chapter XVIII., "Difficulty in Focussing the Iris." OBTAINING "CRITICAL LIGHT" 217 The specimen should then be placed on the stage and focussed. If the image of the edge of the flame be not quite sharp now, a little further adjustment of the substage, up or down, will rapidly make it so.^ This process is called obtaining " critical light." It really consists in using light that is focussed upon the specimen, as witnessed by the image of the iiame, at the same time that the objective focusses the object to the eye. If the flame image be considered objectionable, just a touch of the substage screw puts the condenser a shade lower or a shade higher, which spreads out the flame a little more evenly over the entire field ; this does not with low powers affect the definition. If it does so seriously as to be noticeable, critical light must be re-obtained and a bull's-eye placed between the mirror and the illuminant. Great care is here necessary, that in doing this the very thing wished to be avoided is not unexpectedly introduced — we mean a spoiling of the definition. Adjustments, however, of both condensers will usually rectify the fault.^ We confess at times to have found the bull's-eye more trouble than it was worth, save with quite low powers and a very dense object that re- quired all the light possible. When using a Nernst electric light or a Welsbach gas lamp the ground glass is used for focussing and obtaining critical light in the same manner as the edge of the lamp-flame is with the ordinary lamp, or a pencil held against the glass serves equally well as the object to focus. Some prefer this plan to any other. When using a \-\w. or a ^-in., having a N.A. of about "9 or less, no different treatment is required, save that all the care in ' To do this with greater ease, some substages are provided with a fine motion to the condenser. We used to hold this a most useful addition. Of later years, however, especially since it has been shown that there is a certain freedom in focussing the light of the illuminant, and that the ad- vantages of critical light are not restricted to so very refined a position of the condenser as hitherto believed, we have ceased to recommend this somewhat expensive addition. ^ It should be noted that with quite low powers, if definition be not quite as good as expected, it is a good plan, notwithstanding the use of a condenser, to try the effect of changing the mirror from the " flat " to the " curved " side, or vice versd. For reasons not immediately apparent, but really depending upon nothing else than the alteration in the angle the rays impinge on the condenser, a great improvement is sometimes effected by this change 2i8 THICKNESS OF COVER-GLASS IMPORTANT making the adjustments must be increased, because of their greater magnifying power and because both objectives work so much nearer the cover-glass. Even with these lenses they can with a little patience be lowered so as almost to touch the cover, and focussed afterwards by being raised rather than lowered until the student gets accustomed to their use. So, too, with the dry -^-in. or xj^-in., but the last lens is one somewhat difficult to use as a dry lens, for it usually works so exceedingly near the cover-glass. This brings the microscopist face to face with another difficulty not hitherto mentioned ; it is that, when dealing with these high powers from J-in. upwards, to obtain perfect definition the actual thickness of the cover-glass itself has to be taken into consideration. It is for two reasons. First, because if very thick indeed there may not be room enough to bring the front lens sufficiently near to focus the specimen, which of course puts a stop to everything ; and the second, because the varying thickness of the actual glass introduces errors in the adjustment of the components of the lens system. Opticians usually correct their lenses to work with a special thickness of cover ; that mostly chosen is 'i/ mm. or thereabouts, the variation being between, say, '16 to "iS mm.^ If now a cover be employed of, say, "22, a source of error becomes present which has to be dealt with if the best results are desired. There are two means ; one, which we personally prefer — although it adds sensibly to the cost of the objective — is for the combination to have what is called "a correction collar," by the turning of which the required adjustment of the lens to suit the special cover can be effected ; whilst the other is to push in or pull out the draw- tube containing the ocular by different little increments until the best effect is produced — remembering, if the cover be too thick, pushing in is the remedy ; whilst if too thin (rarely the case), pulling out obtains the correct adjustment. Both of these methods of correction require practice, because the proof of having correctly adjusted for any special cover, after all, only lies in the eye being sufficiently trained to recognise when the finest definition is obtained, and of its ability to judge whether a pull out or a push in, or a turn of the collar in one direction ' Zeiss marks each dry high-power lens with the thickness that is most suitable for the objective in question. It is in very small figures on the mount. CORRECTING FOR THICKNESS OF COVER 219 or another^ improves the image or makes it worse ! The Abbe test-plate is the best thing to practise on, and over and over again must it be done until a real proficiency be gained ; this, however, has been referred to before. But we have said that the thickness of the cover may be so great as to prevent the objective being lowered sufficiently to focus when the combina- tion is of a very short length. For this reason, and to guard against an accident, the student, after having lowered his objective by means of the coarse adjustment as far as he dares, should never finally focus with it when using these high powers, but always employ the fine adjustment instead. It is obvious that by doing this the objective is lowered very gently and gradually indeed ; hence, should it touch the cover — as it certainly will if it be a high power and the cover-glass abnormally thick, as frequently found in slides made many years ago — it will do so with such softness and gentleness, provided the screw be turned slowly and steadily, as to injure neither the specimen nor the front lens of the combination. The microscopist can tell when contact between cover and front is made, because he will find somewhat suddenly that the fine-adjustment screw has become quite " slack," as if indeed it had in a moment lost all its power. Directly this occurs, without a moment's hesitation, the screw should be reversed, lest the weight of the tube and objective on the cover causes injury. As we have already pointed out, directly the focus is obtained the correction collar should be used to get the finest definition with the cover-glass in question ; but a word of caution yet remains to be stated when adjustment for cover-glass thickness is arrived at by pushing in the draw-tube instead. It is simply this, to see that the inner tube — the draw-tube, as it is called — works smoothly and easily in the outer one, and that the rack- work of the latter runs stiffly ; for if it be loose, the downward pressure applied to the draw-tube may become communicated to the tube itself, and crash comes the objective upon the cover- glass with, perhaps, most disastrous results. The moral of this is either to see that the outer tube is sufficiently tightly held in its rack and that the rack is sufficiently stiff in itself, or to hold the milled head of the coarse adjustment with the left hand, so that it shall not turn whilst pushing in the draw-tube is carried on with the right. 220 FINDING THE SPECIMEN Finding the Specimen is always more difficult with high powers than with low ones/ so much so that it is better by far for the beginner to use a ^-in. to find the specimen and to centre the condenser with, and then to obtain critical light, changing to the higher power when all the adjustments are perfectly complete. But the learner will very soon find — perhaps to his sorrow — that yet another trouble will begin to appear with which he has to deal. Changing the objectives is quickly performed, but he may be very disappointed to find that, in so doing, the part of the specimen he has placed so carefully into the field with the low power — say the J-in — utterly refuses to appear in that of the high one. This arises because the centring of the two objectives may not be quite similar. It is especially found to be the case when using what is called a "revolving nosepiece." Further, in addition, from the same cause, the arrangement of his mirror, the centring of his condenser, and the adjustment for obtaining critical light are all apparently upset and of considerably less use. If this be so when using a ^-in. or ^-in. what will it be when the change is made to yVin. ? Especially, as we have just said, are these troubles found when using a revolving nosepiece, for it never is, and never can be, made to work truly, for if true with one objective it will not necessarily be so with another. For this reason the firm of Zeiss, with their charac- ' In some cases, when the object is single and small as a diatom, very- considerable difficulty may be experienced in finding it if anything like a high power be in use. The following method is exceedingly useful and quite simple to employ, and may very frequently save the trouble of changing the objective for one of longer focus : Most of these little objects have a ring of varnish around the cover-glass, cementing it on to the slip, the material being attenuated and thin at the edge abutting the specimen, and this forms a suitable object to primarily focus upon. The entire ring of varnish, how- ever, is too large in diameter to be entirely contained in the field of view at one and the same moment, so a portion only is usually visible. This takes the form of an arc of a circle, and should be shifted about by moving the slip on the stage until it is so placed as to be accurately bisected by an imaginary horizontal diameter of the field of view. When this bisection is accurately effected, it is evident — seeing that the object is usually placed in the centre of the area enclosed by the ring of varnish — that if the slide be now simply moved horizontally, the object will fall into the field of view- without further trouble. If the object be not surrounded by a ring of varnish, the same process can be carried out to find it, by employing the edge of the cover instead of that of the varnish. Finding a specimen by means of the verniers is described later on in the chapter upon Verniers and their Uses. USING "DRY" HIGH POWERS 221 teristic desire of perfecting all details, have designed their arrangement of " objective-changers " upon a novel system, and very effective they are we can testify after using them for many years. Their use is described a little later. All the high powers— say the |-in. and yVi"- — to be of much real service for resolving purposes, must possess a higher aper- ture than it is possible for them to be made with as dry lenses, and for this reason are mostly constructed as immersion systems. In the article on numerical aperture the subject of the immersion lens has been fully gone into and explained, and the object of the construction discussed in all its bearings, so nothing further upon that score need be here said. But there is one point to which no reference was made, as it was left to consideration in this chapter. Seeing the design of immersion systems is for the purpose of admitting more light, or rather light occupying a cone of greater angle, it can be easily understood that the power of such an objective cannot be completely utilised unless the condenser employed with it be a combination equally well constructed to transmit a cone of similar dimensions. In other words, the condenser must have approximately, anyhow, the same numerical aperture as the objective — that is, if the latter is to work to the best advantage. Not only is this true, but the condenser so constructed must be oiled to the slip with objectives over N.A. ro for the same reason as the front lens of the objective is oiled to the cover-glass, viz. to have what is called " optical continuity." Then too, as a matter of fact, the specimen itself must be prepared in a fluid or medium at least of the same refractive index as the numerical aperture of the objective, although experience has taught and very fully shown that better definition still, and greater contrast and depth of focus too, is brought about by employing a medium of a much higher index of refraction than the one named. It will be gathered then that the microscopical student has yet something more to learn, namely how to use the immersion system of lenses. As this is nowadays such a matter of consequence, the subject must be fully dealt with in all its bearings. The centring of the N.A. vio substage condenser can be pri- marily obtained with the inch, or better for this purpose with the ^-in., objective in the ordinary manner already explained, remembering to raise it up to the level of the stage before 222 CENTRING HIGH-POWER CONDENSER commencing operations, and the mirror subsequently set to its approximately correct angle, the xVi"- not being substituted until these two adjustments are complete. When the change is made, and it is required to see that the condenser is quite central, no oiling of the objective to the front lens of the condenser is required. Even with this high power, for the purpose in view, it can usually be lowered sufficiently near the condenser, so that focussing of the closed iris can be carried out by raising the tube rather than by lowering it. If this raising method for any reason be objected to, the fine adjustment should be used lest the coarse should do the work too hurriedly, or bring the front lens of the objective in contact with that of the condenser. When the closed iris is seen, final perfection in the adjustments can be carried out. Everything so far complete the tube is raised, and the specimen, previously oiled, is laid on to the stage in such a manner that the oil makes optical continuity between it and the condenser. To " perfect the getting " of critical light with the oiled con- denser, we strongly advise the beginner first to employ the ^-in. This we urge because on raising the condenser should it be necessary, if it be overdone and the top lens strike the slip, this in its turn will cause the cover to strike the front lens of the x^-in., which is an accident to be strenuously avoided. It is needless to point out, if the over-raising of the condenser accidentally occurred when using the ^-in., no such accident would take place, because its front lens would be too far away. Fortunately, for those who do not or will not adopt precau- tionary measures, when the arrangements have been carried out in the order and manner suggested, seeing that the condenser was raised to the level of the stage to commence with, it in general only requires lowering instead of any attempt at raising. In executing this downward motion, however, yet another trouble may unexpectedly confront the beginner. It is this. The con- denser may have been computed to be used with a rather thick slip, and perhaps the slide in use may just happen to be an exceptionally thin one, in which case it will be found that as the flame image appears focussed by racking down the con- denser {the specimen being in the focus of the objective) the oil quits the under-surface of the slip entirely, leaving only a vacuity instead. USING AN OIL-IMMERSION CONDENSER 223 To remedy this annoying difficulty one, two, or more cover- glasses oiled together should be placed on the top of the condenser, oil being further used to make a complete optical continuity between the covers, the slip, and the condenser. Occasionally a trouble of quite an opposite character presents itself. The condenser cannot be racked up high enough to make a focus of the flame at all. Even when it actually touches the under-surface of the slip, owing to the latter being abnormally thick, the condenser requires lifting up even higher. The microscopist should now try the expedient of bringing the lamp as near as possible to the mirror. If this does not succeed, there is no other alternative we know of save that of his having a new front to his condenser that is especially designed to work through a thicker slip. We have three of such to work with different-sized slips, and have often found them of the greatest service. Care should be taken of these little " top lenses " that they are not scratched when put away out of use. To proceed, let it now be presumed the flame image has been focussed in the field of view by lowering or raising the condenser, then critical light is said to have been obtained. The J-in. is now removed and the iVi"- substituted. This lens has now to be oiled to the cover-glass, an operation which is performed by one or two methods in the following manner : — ■ Either a drop of cedar-oil is placed on to the front lens of the combination (care being taken not to scratch it) before affixing it to the instrument, or a drop placed on the cover instead, where it is known the objective will come in contact with it. In lowering the tube great precaution and some little practice are necessary. The coarse adjustment can be employed until the oil makes contact between the front lens and the cover-glass — a fact that will be easily recognised by a little flash of light quite visible when looking sideways at the specimen ; but further lowering to obtain the focus must be entirely effected by the use of the fine adjustment only, and very gently and very slowly indeed. If the cover be known to be over-thick, still further caution should be taken, the eye watching through the ocular the first dawn of any signs of the object coming into view, and the screw being instantly stopped the moment it seems to become slack, which 224 CARE IN USING IMMERSION OBJECTIVES indicates tlie front is resting on the cover. Instant reversal then of the screw is necessary, as before explained, to save a crash. Objectives of N.A. i'4, having fronts that are hyper-hemi- spherical, are much more delicate than those with N.A. i'3 ; hence the judicious beginner will commence first with the latter combination rather than the former, because the fronts, being not so hyper-hemispherical, bear rough usage (comparatively speaking, of course) much better than those working at a higher aperture. Final adjustments must then be carried out to obtain critical light, the object and the flame being both required to be simultaneously in focus. In shifting the specimen about, to examine different portions of it, focussing should be re-made at every short increment of movement, in case the cover-glass is much thicker (or even in some cases slightly bent) in some parts than in others. The microscopist who lets his slide " run " without re-adjusting the focus may break the cover almost before he is conscious of any jamming of the specimen. From what has been said it will be seen that the whole process of using the T2--in. or other high-power immersion system is one not to be learnt in a minute, neither is it one that can be undertaken without a certain amount of care until continued familiarity renders it comparatively easy ; but it should always be recollected familiarity must never lead to contempt. Further it will be readily understood that when using a J-in. (for example) to primarily focus with, to set the mirror with, and so on, the ■j2-in. should have the same alignment of axis as the \-in., for otherwise the object may not be in the field when the high power is substituted for the low one. This often constitutes a sensible difficulty in carrying out all the details we have suggested, but to attain to it, and in fact to remove this source of trouble, we have already mentioned Carl Zeiss have invented their sliding objective-changer — a simple arrangement which answers the purpose most excellently (see Fig. 128). To prepare a battery of objectives requires a little consideration. Before commencing to do so we should mention that the slides consist of two portions — the tube-sXxtle. and the objective-%X\di^ — the former {a. Fig. 128) being permanently screwed to the nose- piece, and one of the latter {b. Fig. 128) permanently attached to each objective. ZEISS " OBJECTIVE-CHANGERS ' 225 As we have said, a little care is needed so that all the battery shall be in perfect alignment. To do this effectively the fol- lowing plan is easily learnt and is thoroughly effective. A low- power ocular being placed in the draw-tube, the highest-power lens of the battery — say an immersion x?-in- — is first screwed on to the nosepiece of the instrument in the ordinary way — that is, without the intervention of an adapter or fitting of any kind. A large and well-defined circular diatom, such as the one we Fig. 128. — Sliding Objective-changer {full size). ri, tube-slide ; b, objective-slide with objective attached ; c, in section. usually use ourselves for the purpose — the Aulocodiscus Brunii — is then placed on the stage, and fidgeted about until it is in the centre of the field and roughly in focus. No oil need be used between the objective and cover, or between the condenser and slip, as the best definition is not required just to place the diatom as nearly central as possible. The lens is now unscrewed and laid aside, care being taken in doing this not to touch either' the specimen or the stage. The tube-sY\6.& of the apparatus — that which, as its- name implies, is for the purpose of affixing to the tube — is attached thereto in such a manner that the opening to IS 226 HOW TO "ALIGN " A BATTERY OF OBJECTIVES receive the objective-aXiAe is in the most convenient position. The objeciive-sMdG is now screwed on to the objective itself, and the two slides united by slipping one into the other. When the diatom is focussed once more, it will probably be found to be no longer occupying the centre of the field. To make it do so the little watch-key supplied with the apparatus is applied to one or both of the little screws shown in b. Fig. 128, forming part of the objective-slide, and a few turns or portions of a turn are made until the desired effect is produced. The objective should be slid off and on again several times until it is made quite certain that the object always appears in the desired situation. It is well now just to understand the rationale of what has taken place. The idea of putting the objective on to the instrument without adapter of any kind was to place the diatom actually in the optical axis of the objective. After the sliders were united the subsequent adjustments with the little screws and watch-key were merely carried out to restore the lens to its original position. This ensures its best possible performance. The lower powers (each in their own adapters) should now be centred one after the other on the diatom, which is easily effected by screwing an objective slide on to each and adjusting with the watch-key in succession. It is needless to observe the diatom must not be touched, or the stage interfered with in any manner during the entire operations. It is very evident now that any object placed centrally in the field with the low power will be central when it is changed to the higher one, hence it can be understood all the previous directions of different kinds we have given are much more easily carried out and with far greater precision than if no changers were in use. Moreover, in the every-day use of the instrument it is a great saving of time to find that in changing from one objective to another all centring of the condenser and adjustment of the mirror suitable for the first combination, shall not be immediately upset and require readjustment when employing the second ! The convenience afforded by the accuracy of these objective- changers is manifest in more ways than one. If supposing two or three objectives of the same focus have to be compared, it is essential, to do the thing fairly, that the same part of the specimen (and consequently the same refinement of the illumi- nation) should be employed with each. Now this can only be GREAT USE OF ALIGNMENT 227 done expeditiously in the manner just related, taking one as the standard and setting the others in alignment with it. If it here be said they can be as well tried, one against the other, by first screwing one on to the nosepiece and then the other, we shall admit that the argument is true, but only if the centring of each lens is exactly similar. But this is sometimes not the case, and the consequence is that the same, exactly the same, portion of the specimen is not in the field of view on each occasion. The secondary consequence of this is that when this original position is obtained, the light will now be found not to be exactly central, and all the adjustments have to be made over again to compare one combination fairly with the others. This trouble is prevented by first aligning the different objectives to the same centre as we have suggested. Of course, if one par- ticular combination requires a very large change of position to be effected by the little adjusting-screws before it is centred to the same alignment as the rest, it is possibly best to examine that one separately, by placing it directly on- to the nosepiece ; but this does not often happen. ^ Then the great comfort afforded by the use of these changers is manifest in another way, namely by the ease with which a specimen may be run over with a low power, any spot requiring the aid of the more powerful combination being readily examined simply by the interchange of objectives, no adjustments of any kind being further required save that of altering the focus. Similar ease of examination can rarely be obtained with the revolving nosepiece, as no means is provided for setting objec- tives in one and the same alignment. We are aware that some opticians assure us that their nosepieces are perfect in this way, asserting that they are made so exactly that one objective will follow on the other quite truly ; but surely they forget that the fault mostly occurs in the actual mounting of the combination itself rather than in the nosepiece, which no amount of accurate manufacture can possibly correct unless some special means of adjustment is provided. When there are only low powers in the battery, as obtains with many amateurs, this exact centring of each objective is not of such primary importance ; indeed, the refinement is almost uncalled for in most cases. Under these conditions the objective-changers of Zeiss may be found a trifle cumbersome, 228 WATSON'S CHANGERS FOR LOW POWERS and perhaps too costly, although lately reduced in price. To offer a better means of rapidly changing the different powers other than by the rotating nosepiece, which although commonly in use has the disadvantage of weighing heavily on the tube, especially when filled with three, if not four objectives, Messrs. Watson & Sons have introduced an exceedingly eiificacious changer made in magnalium. This is fixed to the nosepiece, and is so constructed as to grip the screw end of the objective — protected by a little ring, sold for a few pence, to attach to each combination — so firmly and so truly that it would seem to leave nothing to be desired. It is called the "Facility" Objective- changer, and is shown in Fig. 129. We have used one for some time on a low-power instrument, and it has given us every satis- faction. Its size, however, is not suitable to the Continental model of microscope, as it interferes with the movement of the tube in its slides. To use it is very simple. The turning of the handle Fig. 129. A causes the inversion downwards of a pair of jaws having a screw-thread cut upon them. The objective is placed in the aperture, and directly the handle A is released the jaws are carried back to their natural position by the action of a boxed- spring, in doing which their threads engage the threads of the objective and carry it up to the shoulder. In consequence of the varieties of sizes, within very small limits, that still prevail with objective threads, it has been found desirable to supply the rings mentioned to screw to the objectives, these having threads of an absolute gauge which will be gripped by the jaws of the nosepiece with certainty. Before quitting this part of our subject a few words may be said with respect to the way of using the eyes. Of course, only one can be employed with the ordinary instrument at a time, and what follows refers more especially as to what to do with, the other. This should never be closed up tightly by its own WHAT TO DO WITH THE EYE NOT IN USE 229 muscles, as the strain thereby effected is very apt to spoil the perceptive faculty of the eye in use. Neither should the hand be used to shut it. It is best to learn to keep it open ; but if this cannot be acquired, the hand should only shade, and not touch or close the eye off duty, so that, although it is prevented seeing anything, it is not kept shut. It is best, as we have said, to keep it open ; but when doing so the observer, in addition, should try to make it turn as if it were looking at the object seen by the eye in use. By this means an unconscious similarity in the focussing is brought about at one and the same moment. If, however, the observer lets his " off-duty " eye simply become a blank, then this focussing is not effected, and it may be that a certain kind of diplopia (double sight) may be brought about by this means, which is very unpleasant ; for the effect is that the observer, after leaving the microscope, apparently sees double, even, perhaps, for an hour afterwards. Fig. 130. For those unable to learn to do what we have said, a neat little arrangement is made to fix on to the draw-tube that holds a small shield, effectually cutting off "the seeing" of the eye not in use. Some users of the microscope regularly employ this ingenious little piece of apparatus. It consists of two parts, as shown in Fig. 130, jointed in the middle ; one part has in it a circular aperture, which slides over the draw-tube of the microscope, and the other shuts out light from the disengaged eye. It is usually made in vulcanite, in two sizes, one for the Continental, and the other for the English size draw-tube. The Position the Verniers should Occupy and the Method of Centring a Circular Stage If a 3 X I -in. ordinary glass slip be taken and its centre marked with a dot of ink, this dot should be exactly i^ in. from either end and \ in. from either side. This may be called the centre of the slip. If a cover-glass be taken with a circular diatom, 230 VERNIERS: CENTRING CIRCULAR STAGE such as an Aulocodiscus Brunii burnt on to it, and the diatom placed so as to cover the dot, then the diatom will show the centre of the slip in a more convenient fashion. All these measures need only be approximately correct. Placing this "centring slip" upon a square-shaped movable stage and by the use of the ordinary milled-headed screws in such a position that the diatom occupies the centre of the field of view when using a J-in. (or other low power) and a x 4 ocular, it will be found, if the verniers are fairly well located, their readings will be about midway of their length. For example, if one be 60 mm. long and the other 40 mm., then the readings should be approximately . If they differ very much from these figures, supposing they were —, for example, the instrument should be returned to the makers, because when used with a slip having (wo covers upon it, in all probability the verniers will not be able to be used, as one of the covers, if not both, will be beyond the reach of the graduations. By this we mean the scale readings will be at an end before the stage is shifted far enough. Providing the verniers are reason- ably well placed, a high power should now be used instead of the low one and the exact readings of both verniers taken when the diatom is exactly in the centre of the field, a note being made on the centring slide, with some additional indication as to which way it is in the future to be placed on the stage. A capital letter R on the top right-hand corner is the method we employ ourselves. If now at any time in the future, after having set the vernier to the previously recorded position marked on any particular slide, the special position of interest desired to be seen fails to appear in the field of view — provided, of course, such positions were correctly recorded — it must arise from the centrality of the stage having by some means been upset, or, what is the same thing, the verniers must have accidentally slipped. To enquire into the fault the " centring slide " should be placed on the stage in its proper position as recorded upon it. If no accident has occurred to the stage of course the aulocodiscus should appear in the centre of the field, in which case the previous " failing to appear " evidently has arisen from some mistake in CENTRING CIRCULAR STAGE 231 the notation upon the slide in question ; but if, on the contrary, the centring diatom does not come into the centre of the field, it proves most unmistakably that some accident or other has upset the bearings of the stage. To set matters right, the aulo- codiscus should first be made central in the field, according to its recorded figures, by means of the ordinary stage screws, after which the verniers themselves should be released from their bearings by undoing the minute screws that retain them in situ. A slight enlargement of the little holes through which the minute screws pass will enable the graduations to be set correct again, so that the verniers once more read according to the figures noted on the " centring slide." This done, the recorded positions of interest on slides containirig specimens will now once again be correct. With a circular revolving stage, however, an additional motion has to be taken into consideration ; it is that whilst revolving around the optical axis the specimen shall remain in the centre of CRESCEMT SHAPED MOVEMEMT DESCRIBED ON REVOLVING THE STAGE Fig. 131. ARC COMVERTED inTO AH ARROWHCAP 6MCWIN0» tOQE or FIELD TOWARDS WHICH THE DIATOW HAS TO BE MOVED Fig. 132. the field. Hence with a stand of this description, directly it comes from the maker the centring slide should be placed on the stage and adjusted to the centre of the field by the ordinary milled-headed screws, first with the low power and then with the highest of the battery, taking care there is no changer or revolving nosepiece used at all. Revolution about the axis is ther 232 CENTRING CIRCULAR STAGE made and the diatom watched. If no " travel " of the diatom' can be noticed about the field — merely its own revolution on its axis — then the axis of revolution of the stage is concentric with the optical axis ; but if, on the contrary, it appears to describe a crescent-shaped path, as shown in Fig. 131, it proves that the axis of the stage is not in alignment with that of the objective. To make it so, one or more of the little screws usually provided for the purpose in all well-made stands have to be turned, but the question of difficulty always is to decide which. To dis- cover a solution of the difficulty is quite easy if the following plan be adopted : The eye must watch the arc described by the diatom before referred to, and this should be mentally compressed into an arrow-head, the apex of which will point directly to the edge of the field to which the diatom requires moving, as indicated in Fig. 132. Each screw can be now gently tried in succession until the right one be found, or it may even be discovered that the AMOUMT or SHIFT TO DIATOM PLACED AGAIN BE TRIED AT FlSar BY "^ CENTRE OF FIELD BV MEANS OF THE SPECIAL "''"^ OgPinARY STAGE SCREWS ADJOSTinCi SCREWS Fig- 133- Fig- 134- direction requires the use of two. The diatom need not be moved far at first, but left in the position shown in Fig. 133. It is now recentred in the field, as in Fig. 134, by the ordinary stage screws and the stage revolved again. If it still " travels," then another shift must be made, and so on, again and again, until at length no movement is detected, save of course its own revolution on its axis. It should be recollected in securing CENTRING CIRCULAR STAGES 233 the adjustment, through one screw being not turned enough, or one of the two, if two were used, being more turned than the other, the situation of the arc in the field may frequently change its position, but this requires no alteration in the method of treatment. The arrow-head must be mentally pictured each time and a fresh adjustment made. When as perfect as can be, a higher power should be used, and finally the highest of the battery. It should be mentioned that with a great magnification the motion will not appear smooth and regular except in the finest instruments, and a certain allowance must even then be made for the unexpected presence of exceedingly small pieces of foreign matter — thickened grease — or the like making it apparently jump a little until they are removed. In numbering the slides for the cabinet, room should always be made for the vernier readings, and, as we have suggested, the letter R should always be placed on the top right-hand corner of each slip to indicate its position on the stage ; and it is convenient, we have pointed out before, always to put the reading of one vernier at the top and that of the other under- neath, so as to be able to differentiate the verniers to which they apply. Thus means the vernier moving the stage up and down must be placed at 30'45, whilst that recording horizontal motion is to be set at 25'io. We have repeated this suggestion because many microscopists in using their verniers in an irregular manner — one reading of the vernier being upper- most in one case and just the reverse in another — have led them to think mechanical recording stages to be of no service. So too with placing the R always at the top right-hand corner : if this be not always done, it is impossible to know at some future date which way the slide has to be placed on the stage. Reading the Verniers. — The ingenious arrangement known by the name of a Vernier was the invention of a French mathe- matician, Peter Vernier, who flourished somewhere about 1630. In the microscope stage there are usually two, one being to record the motion up and down as seen in the field of view, the other to indicate a movement from side to side.' Each consists ' Sometimes a third is added to indicate the amount of revolution of the stage about the optical axis. 234 VERNIER READINGS of two scales, a long one attached to some immovable portion of the framework, and a short one affixed on the contrary to some part that is movable — in point of fact to one of the frames that hold the specimen. The smaller is so arranged that it slides along the edge of the greater scale, and both should be within easy sight of the microscopist. The longer scale, usually about 50 mm. in length, is graduated throughout its entire length, more commonly nowadays in millimetres, whilst the smaller or movable portion has divisions engraved upon it only for a distance equal to 9 mm. ; but this space is divided into ten equal divisions. It is obvious then that each division of the smaller scale (which is mostly called by the simple name of the vernier) is exactly one-tenth less than each division of the long one. In this lies the principle of the arrangement. In order to read a given position of the vernier, we ascertain Fixed Scale T" I I 10 1 ■ I ■ I ■ 1 : r==i 15 \ I J A Movable. Rdrtion, usuau-Y CALLED 3>iE Vernier VERNIER SHOWING THE S^h DIVISION COINCIDENT WITH I2TH AND SO READING 48. Fig. 135- for certain the scale of 9 mm. is divided into ten equal parts, and that the first line of the divisions is marked o. This is called "the zero" of the vernier. In "taking a position" we first note the position of this zero ; let for example it lie as in Fig. 13s, between 4 and 5 on the greater scale. We write down 4, because it is evident the position, although greater than 4, is less than 5. We next proceed to find out how much greater this position taken up by the zero really is, and consequently how much more we must add to the 4 to make the reading correct. To do this the eye is run along " the vernier " scale until it VERNIER READINGS 235 reaches a division that will correspond in alignment exactly with one on the fixed scale. This we see in Fig. 135 occurs at the eighth division of the scale in question ; for there the line appears to be exactly continuous with the twelfth division of the greater scale of millimetres. As this distance at the eighth division of the small vernier is equal to eight-tenths of a millimetre (because we have already shown each of the divisions of the smaller scale was one-tenth less than each of the greater), so we learn the amount to be added to the prime figure 4 is simply '8, which makes the correct reading 4'8. If the reading happened to have shown the third division of the vernier scale, instead of the eighth, was in alignment with some other division of the fixed scale, then we should have only added '3 to the 4 : whereas if the alignment had been at the sixth, then the correct reading would have been 4'6 and so on. Should the zero in the figure have been resting between o and i of the free millimetre scale instead of between 4 and 5, then the figure o would have been written in the place of 4 ; and if the subsequent alignment had been found to have occurred at the first division of one scale with that of the other, making as it were one continuous line, we should have only added 'i, the reading appearing as o*i. So far it is easy to understand ; but the case may arise — |o 5l iol 'is| \ 3: « 10 ^Sl 1= VERNIER SHOWING THE S^h DIVISION ABOUT EQUAL DISTANCE BEYOND THE 12th. AS THE Qth DIVISION IS BEHIND . I3TH READS A'SS. Fig. 136. indeed it often does when using the stage verniers of the micro- scope — that having noted the prime figure, as for example the 4 in the previous argument, we cannot subsequently find any two divisions that are really actually in alignment between the scales as represented in Fig. 136. The vernier reading 8 is there seen to be just as much in advance of the twelfth divisional marking on the fixed scale as the ninth of the movable is behind the thirteenth of the fixed one. Seeing then the advance in 236 VERNIER READINGS question really means half a tenth or -^V' °^ °o millimetre, so we get over the difficulty by adding that amount to the reading, making it finally 4-85. The scales will not readily admit of finer differentiating, although the practised eye may distinguish between '025, -05, and '075 ; but in reality such refinement is never required with the microscope. It should be understood, however, in passing, that of course verniers, when so desired, can be made to read quite conveniently to the third place of decimals of inches, as for example we usually find obtains in such instruments as the standard barometer. It now remains to be explained how to set the verniers to take up a given reading. For simplicity let it be desired to set them at 4'00. We slide along the vernier until its zero rests at the required figure on the fixed scale, and the thing required is done. Should, however, the numerals be 4'8, it is evident the zero must be passed along beyond the 4, nearer to the S, because 4'8 is T^ of a millimetre more than 4'00. Accordingly we count eight divisions on the vernier scale (that is to say the smaller one), and, fixing the eye upon the graduation, move the whole stage, which causes the vernier to shift in the required direction until this line meets with the first graduation on the great scale, to which we set it in alignment. This is the line 12 as indicated in Fig. 135. Supposing, however, that the figures we wish the vernier set to are 4'8s, we recognise that the vernier scale yet requires more movement still, so that the zero shall be shifted 05 further. To do this we gently turn the stage screw a trifle, just enough in fact to make the 8 advance over the twelfth division about as much — that is to say about the same distance — as the ninth division is behind the thirteenth. The object for which the readings are taken should now be in the centre of the field of view in the ocular, provided the figures furnished were correctly given.^ ' We should again mention that for the object to appear in the centre of the field of view another thing is necessary. It is that the stage itself shall not have shifted out of centre since the record upon the slide was made. This is the reason that stages of first-class make are provided with centring screws, so that, should the upper plate become eccentric through wear and tear, it can always be r^-set in alignment with the optic axis. When this is so the readings on the specimen will once more be of service, provided of course the stage was truly central at the time they were taken. It has already been explained how this is effected. CHAPTER XI THE BINOCULAR MICROSCOPE AND STEREOSCOPIC VISION The ordinary form of this instrument is illustrated in Fig. 137, where by mere inspection it will be seen the leading difference between the Binocular and the Monocular microscope is that the former is provided with two tubes (and two oculars) — one for each eye — whilst the latter is only provided with one. By this arrangement it is possible to produce — in the manner about to be described — the effect known as "stereoscopic vision," which, explained briefly and simply, according to the theory propounded by Wheatstone, is as follows : Let a thin book, say about an inch in thickness and five in width, be placed upon a table, standing upright thereon as it does in fact upon an ordinary book-shelf The back of the volume where the title is usually printed must face the observer, and be in an exact line with his nose at a distance of, say, 18 in. therefrom. Each eye will now just be able to see a different side of the book, the right eye the right side, and the left eye the left one. When both .eyes are simultaneously employed, the book looks to be very solid and to have a decided depth, no confusion arising in the mind of the observer by the blending of theise two images in •question, although taken from two different standpoints. The same effect of depth is produced in the stereoscope, where two photographs, each from a different point of vantage, are simul- taneously viewed through the instrument. Here, in point of fact, the union we speak of produces such a strong and pro- nounced mental impression and suggestion as to the depth dimension that details — say in the photograph of a landscape — that lie one behind the other appear to do so in such a marked and vivid, distinct and unequivocal manner that no possibility 237 / Fig. 137. Swift's Binocular. WENHAM'S PRISM 239 of doubt can rest for a moment in the mind of the observer as to which are really in front and which are behind. It is the aim then in the Binocular Microscope to imitate this effect — this increase in the recognition of the depth dimension — so that the details of the object on the stage shall show up their relative positions one to the other in the same unequivocal way, those in front being made to '' stand out " apparently well above or in front of those that are behind. To bring about this effect a prism is supplied of peculiar construction, named after its WENHAM6 Pr16M Fig. 138. inventor, Mr. Wenham, which, when mounted in a suitably con- structed carrier, slips into the body of the tube just above the nosepiece and below the point of union of the two tubes (see Fig- '^n)- It is so arranged that it can be withdrawn wherl not required, and then the right tube being alone in use the microscope becomes once more a simple monocular instrument. This prism (Fig. 138) divides the cone of rays proceeding upwards from the objective by intercepting the right half, 240 ZEISS BINOCULAR which passes, as shown in the figure as a, b, c, d, after two reflections into the body and thence through the left tube, of the instrument to the corresponding eye of the observer. The left- hand half of the cone, however, is not deviated or interfered with in any way, but passes uninterruptedly into the right tube and so to the right eye of the observer. But little consideration is sufficient to show that the right-hand half of the cone of rays — those beams proceeding to ^.\\q left eye of the observer— travel a much longer distance than those of the opposite side ; hence it is obvious the image formed by them is the more magnified of the two. To correct this inequality of amplification in the images, the magnifying power of the left eyepiece is purposely made to be less than that of the right. It is usually found that however well made the prism may be, the images are not comparable as regards perfection of definition, that presented to the right eye being always (so far as we have ever seen) far superior to that seen by the left. When the images are united together by the use of both eyes, however, this inequality in perfection is prac- tically of no moment and does not materially interfere with the elegance of the final result. The Wenham prism is not suitable in its ordinary form for objectives of shorter focus than about a half inch, unless specially made for the purpose ; but we are informed even then the images leave something to be desired. Neither can the prism be used on the short or Continental form of instrument. To meet this latter defect the firm of Carl Zeiss have recently introduced quite a new form of binocular built upon entirely different lines. In this arrangement it will be seen by consulting Fig. 139 stereoscopic vision is obtained, not by a division of the pencils of light (one going to the right eye and the other to the left) passing through a single objective, but by an ingenious com- bination of two juxta-positioned microscopes which are complete in themselves, each Jiaving its own objective. Instead of oculars capable of being raised or lowered to suit the different inter- pupilary distance of different observers as obtains in the usual form (Fig. 137), each microscope has an erecting Porro prism fixed to it, made after the same style as that supplied in the firm's ordinary prismatic binoculars for field purposes now so well known. By rotating these the change for inter-pupilary ZEISS BINOCULAR 241 distance is readily effected. The microscopes are simultaneously raised or lowered by the use of a single coarse rackwork, a fine adjustment being not required. The magnification by this arrangement cannot be raised more than about 70 diameters, which in our opinion is quite sufficient for all stereoscopic effects. We should mention certain dia- Fig- 139- phragms are also supplied beneath the stage which assist in perfecting the results. Seeing that Wenham's prism, as we have already said, is stated not to be suitable for high powers in its usual form, and that some observers are not content with the performance of that form made for objectives of short focus. Professor Abbe designed a special kind of stereoscopic eyepiece which drops into the draw-tube of the monocular microscope, which is itself lowered sufficiently to make the tube-length the correct amount for which the objective is computed. 16 242 ZEISS STEREOSCOPIC EYEPIECE The eyepiece is shown in Fig. 140. It will be seen in the illustration that the division of the pencil of rays emerging from the objective— for the purpose of producing two separate images — is effected at the upper end of the tube by partial reflection at a thin stratum of air between the two opposed glass prisms. This air space is now made •01 mm. thick. One set of rays passes straight through the Fig. 140. Abbe's Stereoscopic Eyepiece {two-thiyds full size), prisms b and a to form an image in the A ocular, whilst the other reflected on the hypotenuse of the rectangular prism b' passes into the ocular B, which is inclined at an angle of 13° to the axis of the microscope. To adjust the eyepieces for inter- ocular distance, the screw D is provided. In order to obtain perfect vision the two oculars must be constructed to give equal definition and magnification, so to fulfil these conditions are made ZEISS STEREOSCOPIC EYEPIECE 243 differently, ocular A being an ordinary Huyghenian of a focus of 45 mm., whilst ocular B is of the Ramsden form of similar focus.' It is necessary to carry out Professor Abbe's views ^ to cover up portions of each ocular, hence two half-moon dia- phragms are provided. These must be arranged so that the inner portion of each beam is occulted, consequently for stereoscopic projection the observer only uses the outer halves of the rays of each ocular ; whilst for pseudoscopic vision ^ the diaphragms are placed in exactly the opposite position, the inner halves of the beams being alone employed. The arrangement when first brought out was not at all well received on account of an objectionable double image in the eyepiece B, which arose from the stratum of air above mentioned being too thick. In the recent instruments, however, by reducing this in thickness, the objection has been entirely removed, and we much regret that recent works upon the microscope have failed to notice this great advance — the entire removal of the objection above stated — as it leads the reader of the present day to have nothing to do with one of the most ingenious and convenient of modern appliances. Through the kindness of the firm we have had one to examine for a sensible time, and struggled to see the faintest ghost of a second image, but entirely failed to do so, probably because it was not there ! The eyepiece can be used for high powers, but achromats only, as compensating oculars are not provided. ' A little thought will show this is an ingenious way of equalising the magnifying power of the eyepieces, as the Ramsden focusses outside the combination, whereas the focus is within in the case of the Huyghenian. ' Professor Abbe's theory of stereoscopic projection in the microscope (for which the reader should consult his original papers, scattered, it is true, and somewhat difficult to find upon the subject) is not the " view " here referred to at all. This only relates to his method of obtaining stereoscopic vision with the microscope, and his departure is merely that, instead of dividing the light at the back of the objective itself, he divides it in a very similar manner in the image at the back of the eyepiece instead, i.e. at the Ramsden circle. Optically speaking the effect is absolutely the same as in the usual binocular microscope, where the Wenham prism is used, ^ If an object like " a jelly," as it ordinarily appears on the table, were under observation, the stereoscopic projection gives to it depth, and it is seen to stand up on the dish ; pseudoscopic vision is the reverse, when it appears to the eye sunken and receding, as if indeed the jelly mould were being looked at instead. 244 POWELL & LEALAND'S BINOCULAR PRISM We should mention, before concluding, that the comfort expe- rienced by certain observers — although not recognised by all — in using both eyes instead of only one, led Messrs. Powell & Lealand to construct a special form of prism which, placed in the Wenham carrier and used in the same manner, converts the binocular microscope into what may be called a " double- visioned " instrument. The peculiarity of this arrangement is that no stereoscopic effect is present we are informed, and that it can be employed with any objective whether of short or long focus. The prism is shown in Fig. 141, and its action is simply this. Part of the light that falls upon the parallel-sided plate of glass passes through it to one eye, whilst the portion reflected off it passes into the right-angled prism adjacent, being totally reflected to the other. It is said that the stereoscopic effect can , be immediately produced when using this prism by merely so arranging the inter- pupilary distance that the outer halves of the beams coming from each ocular are used by the eye ; and, moreover, that by altering such distance in the opposite direction so as to employ the inner portions of each beam, the reverse effect, called " pseudoscopic vision," becomes at once apparent. This, it is said, can equally well be produced by the use of Abbe's diaphragms, of which we have just spoken. Fig. 141. CHAPTER XII MEASURING OBJECTS "WITH THE MICROSCOPE AND THE UNIT OF MEASUREMENT USED BY MICROSCOPISTS It not infrequently happens that it is required for scientific purposes to obtain the exact dimensions of a given object — such as a diatom, for example, or of a minute organism like a bacillus. These objects, being in the microscopist's point of view com- paratively large, do not offer so very much difficulty after a certain amount of practice has been attained ; but when extremely minute details have to be measured, some of which are even commensurate with the wave-lengths of light — as, for example, the dots in Amphipleura pellucida — the operation taxes the powers of the operator to the utmost extent. The method of carrying out these measures is by the use of IfrrillilliMiMUli Fig. 142. Spider-line Micrometer. an instrument called a Spider-line Micrometer (Fig. 142), which is placed in the draw-tube instead of the ordinary ocular. It may be sufficiently described for the present purpose by saying that such is a contrivance by which two wires are viewed 24s 246 MEASURING OBJECTS simultaneously with the object to be measured, through lenses which form part of the arrangement. One of these wires, although capable of a limited amount of adjustment when ■necessary, is fixed when a measure is being taken, being called the " fixed " wire or thread ; whilst the other, working in a separate frame, can be moved by a delicate screw, a hundred threads to the inch, across the field. The screw itself ends outside the eyepiece in a divided head, shown in the figure, called the drum, the circumference of which is engraved with exactly a hundred divisions, for the purpose of showing portions of one entire revolution of the screw. To make the webs appear distinctly sharp, the eyepiece containing the lenses is capable of being pulled out or pushed in, so that, when the observer looks through the apparatus, he sees the wires distinctly in focus ; and, if not so, he proceeds to make them so before putting the arrangement ■on to the microscope. The actual number of complete revolutions of the screw is known by looking into the eyepiece, and counting how many notches in a comb stretching across the field of view (and also in focus with the wires) have been passed over by the movable thread.^ This is the usual form of instrument ; but there are many variations in detail which are not mentioned, to avoid any complication arising in the reader's mind, inasmuch as it is only the principle of the construction that is really neces- sary for him to understand at the moment. A little consideration, and it is readily understood to make a measurement all that is necessary is to arrange the micrometer in such a position that the fixed wire shall lie apparently in contact with one end of the object, whilst the movable one is run across the field so as to enclose the other. A count of the notches of the comb over which this latter thread has travelled in its passage across the field to enclose the object represents the total number of whole revolutions of the screw, whilst the readings on the drum-head furnish the hundredths in excess that have to be subsequently added to complete the measure- ment. The figures thus obtained are necessarily in terms of the revolution of the screw, so that to make them of practical value they must be reduced into those of the inch, millimetre, ' The threads or wires of a micrometer are really constructed of exceed- ingly fine cobwebs. Originally they were made with the finest wires or silk threads procurable ; hence the origin of the term in question. DESCRIPTION AND USE OF MICROMETER 247 or micron, whichever is desired. This conversion implies the ascertaining of the value of a single revolution of the screw, and is called " orienting or evaluating the micrometer." It is one that obviously must be very carefully executed, for otherwise all measurements taken are practically valueless. Before commencing, however, it is absolutely necessary for the observer first of all to make sure his fixed thread is correctly placed with respect to the movable one; for it is evident if this be not so placed, an error in all measurements must take place. To test it, let the drum be set exactly at o, and the observer look through the ocular. Presuming the wires are in focus, the movable web should be seen exactly over the fixed one. If this be not the case, it must be made to take up that position by means of the little adjusting-screw to the fixed thread, provided for the purpose outside the apparatus. Having now set the draw-tube to such a length that the ocular is very approximately the correct distance from the shoulder of the objective for which the latter is corrected, a stage micrometer is placed on the stage and illuminated in the ordinary^ manner. The rulings usually selected, when it is desired to measure the object in English units, are those a ten- thousandth part of an inch apart when employing a twelfth, but of course of greater interval with lower power objectives. The rulings on glass usually have a somewhat granulated appearance under the microscope, and are mostly wider — that is, broader — when a high power is used than either of the fine spider webs ; hence it is necessary to place each web in the centre of the line so as to bisect it its entire length. To do this from the upper to the lower end of the field requires a little patience, turning and twisting the micrometer about the optical axis until it is accomplished. Having by means of the ordinary stage screws apparently placed the fixed wire of the micrometer on the first line of the stage micrometer (which is called o), the movable web is shifted along by means of the micrometer screw until it rests upon the tenth division, care being taken in each case that the wire bisects the line upon which it apparently rests from its upper to its lower end, as explained above. The number of notches in the comb ' The Stage Micrometer is the name given to a cover-glass ruled with lines a certain distance apart, and mounted in balsam on to an ordinary 3 x i in. slip- 248 USING SPIDER-LINE MICROMETER qetween these threads is then counted and noted. Let this, for example's sake, be supposed to be 14. Then we count the hundredths on the drum (if there be any)— which we may by way of illustration say are 41 in number— and add them to the 14, making a total of 14-41. But if the pointer to the drum shows an excess over the 41, and yet not enough to call the reading 42, this quantity must be then estimated by the eye and finally added to the I4'4i- Suppose it is considered as equal to 'S of a division} then "005 is added to the 14-41, making a grand total of I4'4IS- The micrometer should now be moved away at random from the lines on the stage micrometer, and the whole process — beginning with the resetting of the fiducial wire— repeated again at least four times, if possible, over different rulings ^ of the micrometer. Presuming the readings ran thus :— 14-415 14-390 14-550 14-452 14-428 5)7£235 14-447 mean, then I4'447 represents the mean value of -001 in. (10 intervals of TWffw in-), ^"d therefore that i revolution = -00006921, or _^j^^^th of an inch. The above figures show that either the rulings were not exactly equal or the observations were not absolutely accurate ; in reality, however, the errors are not so large as they at first sight appear, for the difference if worked out is exceedingly small.' Without touching the draw-tube the object can now be measured and its dimensions in terms of the inch estimated, several settings and estimations being made and their mean taken. In carrying out this measurement, it will be found exceedingly difficult in ' This of course means -^, or half one of the hundredth divisions. ^ Sometimes the stage micrometer does not furnish more than ten intervals. Injthis xase change the lines from above downwards or vice versd, any method being adopted to secure a " fresh place." ' If it be desired to show with what degree of accuracy the measurements have been made, the absolute values of the deviations from the mean are added together and their mean obtained, which is stated. In the above the " average deviation from the mean" is =!= -043. USING SPIDER-LINE MICROMETER 249 many cases to know which is really the edge of the object, for diffraction phenomena may prevent such being exactly seen ; hence an element of doubt always exists in the measurement taken of extremely minute objects. Then too the shake of the tube when using the micrometer makes the act of setting difficult. Mr. Nelson's suggestion to support the micrometer on a separate stand, so that, although in alignment with the optical axis, the micrometer never touches the draw-tube at all, is a valuable one. We have found it facilitates obtaining accurate measures, and is one to be cordially recommended. As we have said before, it is difficult to be certain of the real edge of the object. The following are Mr. Nelson's suggestions : — (i) Use objectives with as large an aperture as possible with the largest illuminating cone procurable. (2) Measure from the Inner edge of the inner di&xzctlon band to the inner edge of the inner diffraction band on the opposite side. (3) In measuring the diameter of a hole, measure from the outer edge of the outer black diffraction band to the outer edge of the outer diffraction band on the opposite side. (4) The focus of the object to be chosen is what may be termed that of the " black dot " ; in other words, if the object were a slender filanient it would be represented white with black edges. The.se black edges are due to diffraction. If the filament is very slender and the illuminating cone small, there may be seen a white diffraction edge outside the black one, and perhaps another faint black one outside it again. The result, as we have said, is in terms of the inch, but if later on it be desired to convert the same into proportional parts of a millimetre, then the result must be divided by '03937, or multipliedhy 25-4. If desired in microns ^ (/a), further multiply the result by 1000, or divide the original figures in inches by ■00003937, or multiply by 25,400. If it be required in the first instance to obtain the measure in terms of the millimetre, the micrometer should be oriented by means of a stage micrometer divided in millimetres. Figures so obtained can be changed into microns by multiplying hy a 1000. To change millimeter readings into inches multiply by "03937, and to convert microns into inches, by -00003937. ' The Micron, usually written p, is the thousandth part of a millimetre : it will be explained further on. 2SO UNITS OF MEASUREMENT If the object be a large one, and yet requires for certain reasons a high power, it will be found more convenient to set back the fiducial line some given distance — that is to say a certain number of notches in the comb. Mr. Nelson has arranged a micrometer for this special purpose.- Other devices are also made, but it is the principle upon which these instruments are used and evaluated which most concerns us in this work, and which we hope we have intelligibly explained, so no further details will be necessary. Occasions may arise when the microscopist is desirous of obtaining the number of lines to the inch in a given specimen. Having obtained the value of one revolution of the screw, five lines (or more) are taken of the specimen — that is to say one wire is placed on number one line and the second on number six, and the distance carefully measured ; let us say they are contained in '00006 of an inch. Then we say — As '00006 : 5 : : I = -wuhns = 83,300 to the inch. If desired in terms of a millimetre the figures must be divided by 25*4, thus showing that there are, roughly speaking, 3280 to the millimetre, and a little over 3 to the micron (which we have said is the thousandth part of the millimetre). From what has been said it is obvious that the valuation of one turn of the micrometer must always be taken upon every use of the instrument — we mean of course if the microscope in the interval has been employed for other purposes in the ordinary way, and the micrometer eyepiece removed between different measurements being taken. Units of Measurement In the previous section the means of converting measures expressed in inches into terms of the millimetre have been given. The reason for so doing is the fact that a growing feeling is rapidly gaining acceptance for all dimensions in scientific matters to be expressed in the metrical system. Since microscopical objectives have in later years been so much improved, both in defining as well as separating power, the possibility of measuring small objects has become greater and greater. This being so, the inch as a unit of measure has been METRICAL UNITS 251 found to be inconveniently large seeing that some of the small objects, or portions of them to be measured, may be commen- surate even with the wave-length of light. Consequently scientific authorities have sought about for a more suitable standard, one so much smaller than the inch that it would permit an expression of measurement of an object in less figures, and so in a more ■convenient form than hitherto. Selection fell on what is called the Micron — usually expressed by the Greek letter fs. {mu) — which is the thousandth part of a millimetre, or the twenty-five thousand four hundredth part of an inch.^ Seeing that there may be some readers to whom the metrical system may not immediately appeal, we append the following explanation in the hope it may furnish the information desired : A metre was originally intended to be the Txr.TnnjjrTrir P^rt of the distance from the pole of the earth to the equator, measured along a given meridian. Owing however to an error, it is known now to be in reality too short ; hence the metre, strictly speaking, is merely the length of a given definite standard kept in Paris. In Fig. 143 the numeral i — to represent the metre — is seen mm. u. iiji loth metre. I I II I' 000 000 0000 Fig- 143- to be separated by the decimal point from the ten following cyphers. The third cypher indicates the position of the milli- metre (written mm.) because it is the thousandth part of the metre. Hence this quantity is expressed in decimals (in terms of the metre) as o'OOi. If we proceed to the sixth cypher we arrive at the micron (written ya), which is therefore the thousand- thousandth (millionth) part of the metre, whilst being the thousandth part of the millimetre. In decimals then it is ' It should be mentioned here perhaps, although hardly in logical sequence, that even the n or micron is not small enough a unit for the physicist when dealing with the measurements of the wave-lengths of light. In this case the German savants employ what is called the double mu (written fi^i), which is the thousandth part of the micron; but the English scientist adopts a smaller unit still, called the tenth-metre, which is the ten thousandth part of ihe micron, the raison detre of the term being that 10'" (lo at the tenth power) go to a metre. 2S2 METRICAL UNITS expressed as 'oooooi in terms of the metre, but as '001 in those of the millimetre. Continuing to the ninth cypher, we have the position of what is called the double inu — a still smaller unit of measurement — (written yu./i), which in decimal parts of a metre becomes oooooooooi, in that of a millimetre as O'oooooi, and of a micron as O'OOi. The last cypher of all in the figure indicates the position of the smallest unit in existence, being the tenth part of the double inu. It is called the tenth-metre. In decimals, with respect to a metre, this is written O'oooooooooi, in terms of a millimetre as O'ooooooi, of a micron as O'oooi, and of a double mu as O'l. Hence ten of these tenth-metres make one double mu, ten thousand a micron, and ten million a millimetre. As we have said already, the micron is the now almost universally adopted unit of measurement for the microscopist, but is found too large for spectroscopy when dealing with the wave-lengths of differently coloured light. We have mentioned too that in Germany the unit for this branch of science is the double mu, whilst, in England it is the tenth-metre. The position of both these units has been shown with respect to the metre, but we might, to make our meaning quite clear, illustrate for a moment the difference of expression according to the two standards. Take the wave-length of the F line in the spectrum. In this country it would be written approximately as 4862,^ measuring four thousand eight hundred and sixty-two tenth- metres, whilst in Germany it would appear as 486'2 double mu, or four hundred and eighty-six decimal two double mu. This * will be readily understood by the reader remembering the change in the position of the decimal point between the two standards. Although what follows has already been stated elsewhere in this book, still it may be convenient to repeat that at times it is a convenience to be at once able to convert tenth-metres into terms of the inch or vice versd. This can readily be done by dividing 254,000,000 by the expression in tenth-metres. ' Perhaps it ought to be mentioned that in addition, decimal portions of the tenth-metre are frequently added when great exactitude is required j hence the exact wave-length of a Fraunhoffer line in the F region might appear 4862'23, CONVERSION OF MEASURES 253 Thus 4862, the approximate length of the waves of F Hght in tenth-metres, would become — expressed in terms of the inch — as 52,241 waves to the inch — i.e. fifty-two thousand two hundred and forty-one ; vice versa, if it be desired to express in terms of tenth-metres a measurement written in those of the inch, the same nine-figured quantity must be divided by the quantity expressed in terms of the inch, when the quotient furnishes the measurement in tenth-metres. When dealing with expressions written in terms of double mu, one cypher must be taken off the above-mentioned nine-figured quantity, the proceeding for conversion — either way — being carried out in a similar manner. Notwithstanding the explanation given for conversion of the inch and parts into the millimetre or micron or vice versd, it may be sometimes convenient to use the following tables, even if only as a check upon any conversion that might otherwise be made : Table for Conversion of British and Metric Measures f- inch I = •000039 2' = ■000079 3 = ■0001 18 4 = •000157 5 = •000197 6 = •000236 7 = •000276 8 = ■000315 9 = ■000354 10 = •000394 20 = ■000787 30 = ■ooiiSi 40 = ■001575 50 = ■001969 60 = ■002362 80 = ■003150 100 = •003937 1000 ^ iTnm. mm. inch I = ■039370 2 = ■078741 s = ■196852 10 (l cm ■) = •393704 20 = ■787409 50 = 1-968522 100 = I decimetre Example. — What is the equivalent in inches to 21 fi. ? 20 II. = ^00078 7 I (u. = ^000039 ■000826 a tenth-metre = a 250 millionth of an inch nearly. a double mu =a 25 millionth ,, a micron =a 25 thousandth ,, ,, 254 CONVERSION OF MEASURES Inches into Microns and Millimetres inch Ii. Tih^ = '028222 ^-^Ts = roi599l ¥*ir = '031750 ^i-tra = r269989 ^^^ = -050800 ttjW = 1-693318 T*D = "253998' nrW = 2-539977 ^ = 2-539977 Wuir = 2-822197 i = 3-174972 Udw = 5'o79954 i = 5'079954 rsW = 25-399772 f = 9524915 a micron (usually written fi) = t^ millimetre = -00003937 inches a millimetre = ,V centimetre = t-^jsh metre = '03937 „ a centimetre = ^u decimetre = t4tt metre = '39370 „ a decimetre = -^^ metre = 3'93704 „ Inches and Millimetres 5000 lines per inch = 197 lines per mm. loooo „ „ = 394 „ „ 30000 „ „ = 1,181 „ „ 50000 „ „ = 1,968 „ 25399-77 lines in an inch = i line to the fi. 50799 )» „ = 2 IOI599 )» » = 4 152399 )j „ = 6 „ 203198 5) » = 8 253998 » » = 10 Wjnrth of an inch = 5-08 /i". TTttim „ = 2-54 „ T^OTTU „ = I '27 „ 60000 1. = '508 ,, 70000 _ .. 1 ., = '363 „ » = •254,, lUOOOO Square i inch = 10-08045 square millimetres )) TT JJ = 6-45148 „ )» JT tV J> = 4-48021 „ Jl !J tJ-¥ )) = ■06451 „ )> Square /i. = -00155 square tiAft inch. io>. = ■1500 )j 100 IX. = 15-5003 5) Multiples of the above may be found by multiplying the values given by the square of the multiplier. Thus, square j-*jy inch = -j^^ X 4 ; the square of 4 = 4x4= 16, and 645148 x 16 = 103-22368 square millimetres (" Carpenter" abridged). CHAPTER XIII THE MICROSCOPE AND OBJECTIVES SUITABLE FOR DIFFERENT PURPOSES The selection of a suitable stand and objectives depends upon the special purpose for which they are intended to be employed. The different classes of subject will therefore be treated seriatim. Botany, and as an Instrument for the Textile Trade For these purposes the simplest type of stand is all that Himmler's Stand. 2S6 LOW-POWER MICROSCOPES is required. A good coarse adjustment should be provided, preferably of the rack form, but the sliding tube will do very well if the microscopist is " handy with his hands." The fine adjustment is not really needed seeing the objectives are all very Fig. 145. Bausch & Lomb's Stand A. low powers, a 2-in., ij-in. and l-in., but it is not to be despised, especially when only a draw-tube takes the place of a rack form of coarse adjustment as above stated. The mirror should have a concave and flat surface and also be provided with cap of opal glass that can take the place of LOW-POWER MICROSCOPES 257 Fig. 146. R & J Becks No 1124 Stind the silver surface when needed. This is usually employed ^ when the light is found to be too powerful and wants softening ■ Occasionally it is used to obtain polarised light, as explained in the chapter devoted to that class of illumination. 17 258 LOW-POWER MICROSCOPES down ; but some botanists prefer to place a thin piece of ground glass between the illuminant and mirror under these circum- stances instead. The instrument need not have a joint, as an upright position is quite as convenient for botanical and textile Fig. 147. Reichert's Stand. Studies, indeed at times rather more so than an inclined one, for it prevents specimens, temporarily under examination, slipping off the stage. Otto Himmler, Fig. 144, makes a very cheap effective little stand, whilst one of much the same design is pro- vided by Messrs. Bausch & Lomb, shown in Fig. 145, Stand A. LOW-POWER MICROSCOPES 259 Messrs. R. & J. Beck supply a different and more perfect model (Fig. 146), called their No. 11 24 Stand. It is a cheap form of their " London " Microscope, and has a fine adjustment in addition. Reichert (Fig. 147) likewise sells a very firm type (non-inclinable) that has no rackwork to the coarse adjustment, but has a fine one as well as substage arrangements, by which means the microscope can be used for higher powers when required. It is a very excellent little production, and reminds one of the original Oberhauser model. Those who desire a modest form of stand, but one that is easy Pig. 148. Baker's Plantation Microscope. to carry about and suitable for quite low-power work, should see the Plantation Microscope made by C. Baker. It is not provided with a fine adjustment, and it has only a draw-tube for a coarse one. It drops into a case of exceedingly small dimensions (Fig. 148). Most other manufacturers supply cheap stands that are equally efficacious. The objectives required by the student in Botany and for the Textile Trade need not be of the very finest quality, and a 2-in., i|-in., and a i-in. are all that is necessary. Messrs. R. & J. Beck make a series of this description, and so do Messrs. 26o PHARMACY AND DAIRY MICROSCOPES Watson & Sons, and others. If more perfect combinations are desired, most opticians' productions are equally excellent. The wide-angled Holoscopic objective 24 mm. N.A. 0-24 is a favourite lens as it has such a very flat field, about ytj in- diameter, whilst its great aperture f— j makes it exceedingly serviceable for photography if used with a suitably deep green screen.'' The Zeiss 3S-mm. apochromatic that the firm used to make (and we presume would do so still to order) is, we have found, a most valuable and useful little objective, whilst the ij-in. of Beck and the 2-in. of Wray ^ have given us great satisfaction for years. Carl Zeiss also makes a useful combina- tion that by simply turning a ring — rotating it like an objective collar — causes the magnifying power to be increased about double. This objective produces with ocular i a magnifi- cation of 3 to 8, whilst the limit is 33 when used with ocular 5, intermediate magnification being, of course, obtained by the use of the ring in conjunction with oculars of intervening powers. If the work upon which the student is engaged demands the very highest quality of definition, the i-in. apochromat made to order by Carl Zeiss, when employed with a compensating ocular, yields a magnificent image, an example of its performance being given in Fig. 4, Plate VIII. This arrangement forms a valuable one for photographing with, as no screen is required, and such is the excellence of the objective that any compensating ocular can be employed to raise the magnification without producing any deterioration of the definition. For Pharmacy, and as a Dairy Teacher's Microscope For these purposes the student requires a rather more elaborate class of instrument, for he must expect to employ objectives up to a half-inch or even a quarter-inch. An Abbe (chromatic) type of condenser too is also required, but a modified form of non- ' The Fiontispiece was photographed with this objective and two green screens. ^ This combination is corrected for photography, but the under-correction caused thereby for visual purposes is but little noticeable owing to the long focus. It is a convenience to be able to use it for both purposes. Its performance with the camera is shown hi Fig. 5, Plate VIII. PHARMACY AND DAIRY MICROSCOPES 261 centring substage will in most cases fulfil all his requirements. Suitable stands are made by the following firms, although of course the list is not meant to be of an exhaustive nature. A particularly convenient variety is to be found in the model Histological Microscope by Baker, shown in Fig. 149 ; also a Fig. 149. Fig- I5°' Baker's Histological Microscope. superior one still is made by the same firm. They can be supplied with a swinging substage, shown in Fig. i SO. Another stand by Leitz, Stand lU, is of excellent construction and illustrated in Fig. 151. This microscope is really an exceedingly useful piece of apparatus, and quite equal to the preceding. A somewhat more elaborate and very solid stand is " The Fram," sold by Messrs. Watson & Sons, and it can be supplied 262 PHARMACY AND DAIRY MICROSCOPES Fig. 151. Leitz's Stand 113. with substage arrangements of suitable quality when required. The illustration (Fig. 152) shows the excellency of the details and the general firmness of the model. Zeiss's Stand V.A. is an Fig. 152. Watson's "Fram." Fig. 153. Zeiss's Stand V.A. PHARMACY AND DAIRY MICROSCOPES 265 exceedingly useful type (Fig. 153). Constructed upon the latest (1905) lines, it is most easily held in the hand for carrying about. We believe this to be one of the finest models in existence, being well balanced and exceedingly solid, and having a large Stage. The objectives for the study of Pharmaceutical specimens should be really good ones, an inch, |, |, and a 5 being often used ; but for dairy work the last mentioned is rarely required. The inch and the thirds are mostly of good quality with all opticians, but the finest achromatic combination g-in., it has been our lot to examine is that of the Holoscopic series by Watson & Sons. We have treated this lens in an absolutely cruel way in our endeavour to break down the image, but we have failed. Indeed, if employed with an F-line screen, it is hard to dis- tinguish any difference between the irriage it produces and that furnished by the |-in. apochromatic by Zeiss, employed in the same manner, and that is saymg a good deal. A fine quarter is made by Swift, and we have much pleasure in saying that with the same tests applied to it as to the Pfoloscopic we have just mentioned, we failed to break down the image, save perhaps under the most unfair conditions, which out of sheer desperation were tried. Reichert makes an objective (a little over a quarter), called the Ja, usually listed as a seventh, which is an excep- tionally fine lens, especially for colour correction without loss of blackness in black-dot effects, and the extra magnification might at times be serviceable.^ Leitz also makes a first-rate combination of this focus, and all of Zeiss's low-power achro- matics, which to keep pace with rriodern nomenclature should be called " semi-apochromats," are of the very finest excellence, and the images produced by them are absolutely irreproachable in every respect. Their sixth with a collar adjustment is a lens, if the pharmaceutical student desires more amplification than afforded by the quarter, well worth buying, as in our opinion it is the finest in the market, being only equalled by the Reichert 6a and the Watson Holoscopic 4-mm. We have also tried to dis- tinguish the performance of these lenses by every artifice possible, and have failed, and it is a matter for congratulation that com- peting opticians as the outcome of their labours should produce such magnificent results. The Zeiss has a little extra working 1 Those who will turn to the chapter upon the " Testing of Lenses " will better appreciate the meaning of this remark. 266 THE BREWER'S MICROSCOPE distance, which is an advantage sometimes, but the Watson is provided with a collar adjustment that admits of the objective being used as well on the short-tube instrument as on the long, which is a great convenience.^ If the student desires to photograph his specimens, we recommend the half-inch and the quarter-inch apochromats by Zeiss, but it should be recollected both are only made for the long tube, so a lengthening adapter must be employed with the Continental form of instrument; or the transformer recommended by Dr. van Heurck (see Index). If he elect to employ only apochromats for the short tube, the third and sixth are extremely useful. Of these combinations the third by Koristka and Zeiss are most excellent lenses, and with reference to the sixth, those by Reichert, Koristka, and Zeiss perform in a manner indistinguishable (see Plates at the end of the book). The Brewer's Microscope The Brewer needs a stand that will lend itself to the use of a twelfth, as his studies are carried into the subject of bacteria. We do not think, however, he need purchase such a fine instru- ment as that demanded by the bacteriologist (to be dealt with shortly), because the latter uses his instrument so much more than the former. Still, however, the Brewer's Microscope must be a good one ; such, for example, as the very best employed for pharmaceutical purposes. We recommend the following : The small model No. 1129 of R. & J. Beck and Bausch & Lomb's BB stand. Baker's special Brewer's model, arranged^ almost exclusively for the purpose, and those by Leitz, Reichert, Zeiss, and Watson. With respect to objectives, those required by the pharma- ceutical student suit the brewer, but the student will have to add a twelfth. We have already spoken of the first-mentioned ' Whilst going to press Signer Koristka sends us for examination one of his latest productions of similar focus. It ranks as a model combination of the highest order, in fact, we feel we cannot praise it too highly ; like- wise we have carefully tested a semi-apochromat by Himmler of Berlin. This objective furnishes remarkably fine images particularly free from colour, exceptionally so in fact, without any " greyness in the blacks " (see chapter on Testing Objectives). Its performance places this optician in the front rank of manufacturers. THE MEDICAL MICROSCOPE 267 combinations ; but details concerning the semi-apochromatic twelfth will be found in the article devoted to medical purposes (Bacteriological section), and those relating to the apochromatic 2-mm. in that devoted to critical work by the amateur. We might mention that for some reason, not easily discoverable, an eighth or even a ninth seem favourite dry lenses. For Medical Purposes The student in Medicine has to use the instrument for Biology, Histology, Pathology, and Bacteriology. For the first two purposes nothing but a reasonably good stand is required, one indeed not quite so good as that we have recommended for the Pharmaceutical student of advanced type ; but seeing that for Pathology and Bacteriology — especially the latter subject— a really fine, steady and solid instrument is a sine qua non, it is better for the beginner to purchase, once and for all, the best type of instrument at the first, rather than sell his cheap instrument at a loss when he requires a better one later on in his career for the purposes we are now about to consider. The Pathological and Bacteriological stands — for they may be considered' together — should have a very large stage, one in fact far larger than needed by the ordinary user of the microscope. Seeing it has to accommodate what may be called the mostly used size of Petrie dish, its dimensions should never be less than six inches square, and larger would be of greater convenience still. It is a subject of regret that manufacturers do not grasp this necessity, and we very earnestly call their attention to it, for in some of the stands we are recommending now the stages are far too small. We are fully aware arranging for so large a stage to a microscope involves a good deal of trouble, as it demands : a longer arm to hold the tube further from the body ; a consequent alteration in the mechanical details of the fine adjustment ; and a reconstruction of the understage arrangements. When this is grasped it becomes readily under- stood why the addition we speak of has not been hastily under- taken by opticians, for it adds to the cost of the instrument and involves considerable thought and trouble to arrange. We particularly call attention to this matter, because it has come to our knowledge that some students, those who happen not 268 THE BACTERIOLOGICAL MICROSCOPE to be possessed of mechanical knowledge, having asked the manufacturers ^^just to alter their stage to take a Petrie dish," have been somewhat surprised and annoyed at being told that Fig. 154. Baker's "D.P.H." Microscope. such could not possibly be done with their instruments in question. The difficulty is obvious when what we have stated is understood. The stands which we believe are suitable for the purpose of the Bacteriologist are several in number — arranged in alpha- betical order. We commence with that by C. Baker (Fig. 1 54), THE BACTERIOLOGICAL MICROSCOPE 269 called the "D.P.H." Microscope, which is a thoroughly sound and useful model, and one that has given great satisfaction ; whilst Messrs. Bausch & Lomb (English agents : Messrs. A. E. Staley il^ ^'S- 155- Bausch & Lomb's "C.A. " Microscope. & Co., Thavies Inn, E.C.) make" another, called " C.A.," with exceptionally large stage (Fig. 155), which is also well spoken of Messrs. R. & J. Beck also construct a model with a large stage, No. 1 152, called the ''London" Microscope, which has many admirers (Fig. 1 56), and is wonderful value for its cost. Signor Koristka, an Italian maker resident in Milan, not much known in this country, but whose work is of the most excellent type, we believe, supplies a stand especially constructed for numerous bacteriological laboratories abroad, having a 270 THE BACTERIOLOGICAL MICROSCOPE F'g IS6 R &J Becks 'London' Microscope Large Model. yulcaxiite stage of large dimensions (Fig. 157) u ;= called " Stativo modello grande I." ^-^57)- U is called THE BACTERIOLOGICAL MICROSCOPE 271 The well-known firm of Leitz also supply a special model which has a stage of considerable size peculiarly constructed so Fig. 157. ICoristka's " Stativo modello grande I." as to admit of exceedingly large preparations like brain sections. It is called "Dolken's Microscope" (Fig. 158). We believe this Fig. 158. "Dolken's Microscope/ 274 THE BACTERIOLOGICAL MICROSCOPE stand has given very great satisfaction, especially for the par- ticular purposes for which it was designed. Reichert furnishes an instrument called his II B Model, with a vulcanite stage 90 by 9S mm. (Fig. 159). It has a swing-out substage condenser, and is spoken very highly of. Messrs. Swift & Sons construct a special bacteriological stand of very great excellence, which was selected for the laboratory of the ship Discovery, of Antarctic fame, from which it takes its name. It is shown in Fig. 160. The substage arrangement as represented is exceedingly primitive, but there is no doubt it could be added to. Messrs. Watson & Sons' " Edinburgh Students' Model " used to enjoy a great fame, but recently their " Bactil " Microscope seems competing to take its place, and is certainly a most ! excellent design with mechanical stage and a first-rate substage , equipment. The mechanical stage has two inches of movement and its upper part takes away when not required, leaving a large stage available (Fig. 161). Carl Zeiss's " Model III.," although of the old type, is a most excellent one, being a practical and useful stand (Fig. 162). We know of no fault with this arrangement save that it is so unpleasant to take hold of. This is entirely remedied in their new 1905 model, which besides being of an entirely novel ; construction as to form, contains the firm's new fine adjustment, i which is perhaps one of the best in existence (Fig. 163). ' It seems a matter of considerable difference of opinion amongst bacteriologists as to whether a mechanical stage is wanted for every-day work or not. Some think that it is objectionable because, if, when using corrosive chemicals — such as hydrochloric or acetic acids — any of the fluid runs into the slides of the stage, or upon the finely made screws, such are seriously injured unless immediately cleaned, which is a nuisance and a hindrance. Others are of exactly opposite opinion, notwith- standing the objections just mentioned, holding that with reason- able care such accidents should never happen. A third class, however, seem to take an intermediate position, considering that for every-day work nothing mechanical is required, but that facilities should be always at hand to place upon the stage one of the numerous forms of au.xiliary mechanical contrivances already described, so as to obtain the advantages derivable Fig. i6o. Swift & Son'- ' Di-covery " Microscope. Fig. i6i. Watson's "Bactil Fig. 162. Carl Zeiss's "Model III.' Fig. 163. Carl Zeiss's new " 1905 Model." OBJECTIVES FOR MEDICAL WORK 279 therefrom when absolutely necessary ; as, for example, in making a " blood count," or when it is urgently required to hunt seriatim through a specimen. In recommending an auxiliary stage, however, the remarks | made when speaking of the different kinds in a previous part of this work should not be overlooked. We recommend them for the special object just mentioned, their performance for these Occasional purposes leaving little to be desired; but when they are proposed for use regularly in the place of the stage built into the microscope — when they are, in fact, to be daily used, and more especially to register by their verniers, important positions in particular specimens — we abruptly dis- continue our recommendation. After a little use, the continued taking off and putting on to the stage appreciably alters their register with the axis of the tube, and hence positions obtained to-day may very likely be of no use a month hence. Besides, their mechanical construction is not such as to recommend them for hard work, a rapid " loss of way " and an increasing " shake " becoming more and more manifest when they are submitted to the heavy work of a laboratory. (For Zeiss's new Auxiliary Stage see Chapter XVII.) As regards the fine adjustment of the bacteriological micro- scope, we think it is pretty universally acknowledged one of medium speed is the best, unless the instrument is intended for ! photomicrographical use, when the finest is usually desirable. The objectives mostly required by the student are the inch (or two-thirds), a sixth, and a semi-apochromatic twelfth ; a 2-mm. apochromatic being added where expense is no object. , We have no more to say about the inch, two-thirds, and the sixth than mentioned in the preceding sections, with foot- note ; but as respects the one-twelfth semi-apochromat, we have made no remark up to the present. It may be considered as true for \}s\& general ^xs& of- the I laboratory the microsc&pe is mostly employed to distinguish j differences of form rather than refinements of detail, so that really a very highly apertured twelfth is practically not needed, i This is readily understood to be the case from the simple fact that nothing but dry condensers are ever seen in the bacterio- logical laboratory under its normal working conditions. This implies, of course, that no matter what the aperture of the 28o OBJECTIVES FOR MEDICAL WORK objective be that is in use, whether a r25, 1*30, r3S, or r40, it only works with a dry condenser nominally ^X N. A. i*o.^ We fear that this fact may have escaped the attention of some users of the microscope, who, in a passing moment of laxity of thought, have dwelt upon the advisability of having immersion objectives of N.A. i"33 because of their high numerical aperture ! Seeing that combinations working at N.A. i"i are so much cheaper than those ranging from N.A. v^o to V/^o, and that accidents to the former cost so much less to rectify than with the latter, we cannot help thinking this cheaper type of lens, provided the quality is as good, is all that is necessary for the rough hard work of the student in bacteriology. When, however, structural formations are under the consideration of professors, and when the highest resolution and very likely the highest magnification possible are sought after for the elucida- tion of certain details, then, instead of using a r35 or vofi semi-apochromatic, we venture to point out the real utility of the 2-mm. apochromatic with the oiled condenser steps in. We mean that it should be used as a court of appeal. In making these remarks we are fully aware our suggestions may be at variance with the ideas held by those doubtless better able to judge. Some, for example, whilst agreeing with what we have proposed in theory, think in actual practice it is more economical that the 1-35 semi-apochromatic should be purchased, and that it should be of the highest quality obtainable ; and that, although the combination is cut down, it is true, by the dry condenser, to really work usually at about N.A. 10, that it can be used at full aperture when so required by merely oiling the slip to the condenser, provided such illuminator be of the immersion type. To this we feel bound to demur. It may be advisable to buy the high aperture, because perhaps it performs better when cut down than an objective made to work at N.A. ri or N.A i-20 would do, and to this we agree ; but to think for one moment its full working aperture as a court of appeal is equal to the finest apochromatic where all the secondary spectrum is eliminated and the zonal corrections are brought to their highest correction possible, is to our mind an opinion too hastily arrived at. If both objectives are used with green ^ The reader's attention is particularly directed to the chapter on the Use and Abuse of the Substage Diaphragm with respect to this matter. OBJECTIVES FOR MEDICAL WORK 281 screens, such as the Gifford's F-line, or the pot-green glass recommended by us before, then, and only then, we do allow the performance of the two objectives may.be difficult, save to the experienced eye, to disseverate. But can this always be done ? It certainly cannot with many different kinds of staining, for the green screen will not suit every colour. Further, it has been 1 suggested that water immersions, seeing they have a numerical j aperture of i"20, should suffice for ordinary bacteriological work. ^ We must confess to have fallen in with that opinion at first, if only for the fact that tliey need no wiping after use ("as distilled water dries without leaving any stain), or the specimens either, a very considerable inducement lor their adoption. But one fatal objection, however, has become apparent to us in the practical application of the water objective before recommending its adoption, and it is this. Seeing the refractive index of the ordinary cover-glass is approximately rj, and that water is only r33, an alteration has to be effected in the length of the draw- tube (or the collar adjustment must be altered) /or ^f^ry different thickness of cover with which the objective is employed — that is, if the best performance be required. This is at once a nuisance and a hindrance in daily work, and one never required (save under very unusual circumstances) with the homogeneous immersion, simply because the cedar oil and the cover-glass having both approximately the same index of refraction, small differences in thickness of cover cause no appreciable effect in the definition of the object. In selecting a twelfth for bacteriological purposes, a large working distance is a great convenience, for the constant use of the instrument — not, by the way, as a pastime, but as a daily routine — is very apt to breed a certain amount of contempt, if not a certain amount of carelessness, in the use of the delicate combination. Hence we do not unfrequently hear of broken cover-glasses, and what is worse still, of crushed-in "fronts," especially by commencing students, who may have never seen or used a microscope before. Swift makes a special long-distance working bacteriological twelfth which answers the requirements of the bacteriologist very well, and so also do Leitz (a great favourite), Himmler of Berlin, Hartnack, Koristka of Milan, Messrs. Bausch & Lomb, Baker, Ross, Reichert, and several others, all for about the sum 282 OBJECTIVES FOR MEDICAL WORK of £s. Of course if the vefy best type of semi-apochromat be desired, then the still more expensive type must be sought after, such as those made by Zeiss and Reichert, which are most magnificent tools and of the very highest quality attainable, even rivalling in performance, when used with a proper screen to cut off the secondary spectrum, that of tlie finest apochromats. Watson & Sons also sell a very good lens at the more expen- sive rate, and Beck has another which pleases many users. We ought to mention also that the old-established firm of Messrs. Powell & Lealand comparatively recently have introduced a new £i) twelfth, which performs in accordance with other recent lenses made by the same firm. Some bacteriologists complain of feeling considerable fatigue in the eye when they have for long periods to examine specimens, as necessary, for example, when searching for the presence or absence of bacilli tuberculosis in several specimens. The comfort of using a suitable monochromatic screen is not so generally known or fully appreciated as it should be. The best we know is either the Gifford's F-line filter or a piece of the pot-green glass ' of which we have already spoken. Either of these makes a red-stained organism quite black and very easily detected, whilst the field is of a soft monochromatic green. Either of these contrast-screens affords very great relief, and enables the observer to use his eye much longer without fatigue. With bacteria that are not of a red colour, however, these filters are not of quite so much use — for example, with specimens stained with methylene blue. Here a contrast-screen of great con- venience is formed by using a gelatine plate stained with* aurantia. An easy way of preparing such is to place an ordinary lantern slide-plate straight out of its box into an aqueous solution of any strength of hyposulphite of soda (of course in the dark-room) until it completely clears, and after washing well in water, say for half an hour, into a solution (aqueous) of the dye mentioned, film uppermost. Left in this solution all night, it is rinsed \h& next morning in plain water and allowed to dry. Should a single glass not be of sufficiently deep a colour, two may be united by Canada balsam and dried. If the microscopist finds the heat of his lamp is apt to melt this ' This special green glass, to which attention is called by the writer, is sold by Baker or Watson, of Holborn. THE PETROLOGICAL MICROSCOPE 283 screen it should be, after the rinsing, allowed to rest in a solution of formalin (equal parts of formalin and water) for about five minutes and then dried. This may make the colour much fainter. To meet the difficulty it is best to use a solution of the aurantia made with spirits of wine and water, which will stain the gelatine very much more than will the simple aqueous solution, and consequently the screen is of a deeper colour after treating with the formalin. Too powerful a light is really not required by the bacteriologist. It is the fault of the five-shilling Nernst lamp for ordinary work. A substitute, we have elsewhere stated, is to use a 16 or 32 candle- power incandescent lamp of Steam's make (because of his peculiar arrangement of the filaments) with an intervening slip of ground glass. Some laboratories use the ordinary oil-lamp, whilst others prefer an incandescent gas-lamp to all other illuminants ; but their great heat offers a considerable objection, in our opinion, to their use. The remarks to those about to commence with the microscope concerning not only keeping both eyes open, but properly focussing them both also, is well worthy of perusal by the commencing student, and may even be of comfort to some more experienced, saving them possibly some diplopia or double vision, which occasionally makes itself manifest, it is thought by some from this .cause. The Petrological Microscope The particular application of the microscope to the subject of petrology has been growing of late ; but until recent years the special requirements of the petrologist — which are not a few in number — have never been found embodied in one instrument alone. Several manufacturers have now, however, taken up the subject somewhat warmly ; hence several highly complicated and beautifully ingenious stands have recently been put upon the market. We mention a few only of the more modern. In doing this we have thought it desirable to state in several instances more details than we have hitherto mentioned in the previous stands, where the figures mostly explain themselves. The first is by Messrs. Bausch & Lomb, Fig. 164 (agents, 284 THE PETROLOGICAL MICROSCOPE Fig. 164. Pelrolog'cal Microscope by Bauscli & Lomb. Staley, Thavies Inn, Holborn Circus), which we briefly describe as follows : — THE PETROLOGICAL MICROSCOPE 285 Base, horseshoe form. Pillar, finished same as base. Stage, circular, revolving, with vulcanite stage-plate, having scales graduated in millimetres at right angles for the location of the specimen, spring clips, circumference graduated to 360°, with vernier; centring screws. Substage, a modification of the complete substage, with rack and pinion adjustment for vertical movement. Focussing adjustments, coarse adjustment by standard rack and pinion ; fine adjustment by standard micrometer screw movement, having pointer and graduated milled head of extra large size. Adjustment of Bertrand lens by rack and pinion. Main tube with society screw, slots for quartz wedge and Bertrand lens, sliding prism-box, iris diaphragm between prism-box and Bertrand lens, draw-tube nickelled, carrying standard size eyepieces. Nosepiece with centring adjustment. Polarising apparatus. The polariser and analyser are extra large Nicol prisms. The polarising prism is carried in a revolving mounting, with pointer and silver circle graduated to 360°. Directly above the prism is a divisible condenser for convergent light. By an ingenious device the upper lens of the condenser can be instantly thrown to one side without disturbing any of the adjustments. An iris diaphragm is mounted below the polariser to modify the light. The polarising prism is carried in sliding prism-box in the main tube, so arranged that it can be thrown into the optical axis of the instrument when polarised light is desired or thrown to one side when the microscope is used m ordinary work. Herr Leitz is of opinion that the many requirements for a perfect petrological microscope demand an in.strument of larger size than hitherto constructed for the purpose. Hence his latest model — suggested we believe by Dr. Lincio and shown in Fig. 165 — has been specially designed of a much more massive and solid character than any of his previous instruments. The boldly contrived upper portion affords more room for the manipulation of specimens which may be of very considerable size, and moreover the arch itself affords a convenient handle by which the microscope can be carried about without risking any injury to, or straining of, the fine adjustment as hitherto was likely to occur in the former type of stand. No change is made in the arrangements for the coarse move- ment of the tube, but the new type of fine adjustment lately devised by the firm takes the place of the older form more commonly met with. The tube and its draw-tube are very large in diameter. This 286 THE PETROLOGICAL MICROSCOPE is a convenience when using the instrument for the purposes of photography, as it thereby prevents any curtailment of the field of view when low powers are employed. Further it affords — Herr Leitz thinks — more room for a better designed fitting to hold the analyser with its circle divided to 360°, enabling the various measurements carried out by its use to be more easily and efficiently effected. A Bertrand lens slides into the tube, the carrier made to hold the same being capable of removal when the lens, is not required to be in use. The nosepiece, of a very solid character, is provided with centring adjustments and the usual universal thread. The instrum.ent has a large revolving stage, the upper plate being divided by rulings to facilitate the fixing in position of slides on the stage, centring screws being added for bringing into adjustment the whole arrangement so as to obtain perfect alignment with the optical axis. The ordinary rectangular movements arc present, and verniers, divided into millimetres, are attached to different parts of the instrument so as to record the position effected by any cf these three motions mentioned. The substage arrangements are modifications of the usual form, but a fine helical wheel-rim is placed beneath the stage that can be made to engage itself at pleasure with an endless screw, so as to assist the operator in obtaining the exact adjust- ment of an object during any operation involving goniometrical measurements. We have not been able to find that there are adjustments for the substage, condenser, which we hope can be easily added. Swift & Son, too, have paid much attention to their petro- logical stand illustrated in Fig. 166, which has been built after the design of Mr. Allan B. Dick. This instrument differs from most petrological microscopes hitherto con- structed in having a fixed stage, and instead of rotating the object, the two polarising prisms with the eyepiece are made to revolve together. The spider lines in the eyepiece therefore turn on the object which remains stationary, so that the most minute specimen is maintained in position during the entire rotation, and hence the necessity for delicate centring adjustments to ensure accurate concentricity of revolution is altogether obviated. A circle divided to 360° rotates simultaneously with the prisms. A converging lens is fitted over the polariser, and another, mounted in the Fig. 165. Petrological Micio^cDne (new model) by Leitz. Fig. i66. Petrological Microscope by Swift (Mr. Allan Dick's Design), THE PETROLOGICAL MICROSCOPE 289 slide A, can be combined with it when greater convergence is required. G and H are two horizontal slides in the optic tube of the microscope, each of which is furnished with a lens and a clear aperture. The lower one, G, is for showing rings round the optic axis of crystals ; and the upper one, H, is for exhibiting optic images in very minute crystals. Both have adjust- ments in the vertical plane. The stage is divided to millimetres in both directions for recording the position of an object. E is a slot for the insertion of a micrometer, undula- tion plate, or quartz wedge ; the two latter can also be used over the eyepiece. The fine adjustment is a differential screw motion, with milled head divided into 80 parts, each division being equal to o'oi mm., thus enabling it to be used for finding the refractive index of any transparent mineral. The polarising and analysing prisms may be revolved indepen- dently of each other. The polariser is mounted upon an arm which allows of its being turned out of the axis of the microscope. A Klein's quartz plate is made to drop into the open aperture of the slide G, and it can also be used in a holder on the stage. An analysing prism can be mounted below the slide G (which can be readily thrown out). For those who require to photograph slides under observation the analyser fitted as above would be of considerable advantage, the one fitted over the eyepiece not being suitable for the purpose. If the microscope is required for non-petrological studies the analyser is thrown out of position, the polariser removed, and the achromatic condenser A inserted in its place. The condenser is furnished with an iris diaphragm and two stops — one for oblique and the other for dark-ground illumination. Messrs. Watson & Sons have constructed of late years what they call an «^z'«««,^ petrological stand (Fig. 167), which must not be overlooked. In this instrument everything is excellently arranged, and the various contrivances to meet the requirements of the most critical users are carefully looked after. It is shown in Fig. 167. The stage is a circular brass one, finished dead black, having a sliding bar to carry the object. It is divided to millimetres in horizontal and vertical directions. A separate mechanical stage, as figured, with divisions, and giving a long range of motion, is included, and can be attached at once when required. The circumferential edge of the stage is divided to degrees, and a vernier is fitted reading to five minutes. The stage rotates con- centrically completely, and centring screws are provided for adjustment to the axes of different objectives. The substage has screws to centre, rackwork to focus, and can be lifted aside with the apparatus contained in it upon a hinged joint ; when set in position it is securely fixed by means of a clamping lever. The body is provided with one draw-tube actuated by rackwork. At the lower end of this tube the universal thread is fitted to carry a Bertrand's 19 Fig. 167. Watson & Sons' Advanced Petrological Stand. METALLURGICAL MICROSCOPES 291 lens, etc. At the lower end of the body is a Klein's quartz plate, and above it an analyser fitted in boxes, which can be instantly withdrawn when not required. The eyepiece is provided with cross webs, and above it is fitted a rotating circle divided on silver reading against a fixed bevelled circle at the top of the draw-tube, and carrying an accurately adjusted analyser prism and calcspar plate, which may be used either separately or in combination. A polariser having a specially large prism is included, the rotating circle of which is divided on a silvered edge, each quarter-circle being indicated by a spring catch. A removable condensing system of high angle is fitted above the prism for showing brushes in crystals, etc. The Microscope for Metallurgical Use The study of Metallurgy by the aid of the microscope has been increasing very rapidly indeed of late ; so much so that the investigations by Sorbey about 1864, Martens in Germany about 1878, followed by Stead, Roberts, Austen and others, have raised what might have been called in olden days nothing but an interesting study, into an exact and far-reaching science. So much is this the case that within the last ten years consider- able inventive skill has been brought to bear upon the subject of furnishing an instrument which would meet the requirements peculiar to the study in question. Of these there are several. For instance, it is requisite, of course, to use reflected light, because the specimens are necessarily opaque,^ and this can be only perfectly effected by the employment of what is called the vertical illuminator, already described. But this very little piece of apparatus is itself a troublesome arrangement to deal with. Attached to the nosepiece of the microscope at one end, it receives the objective in the other, the light from the illuminant being projected into it through a small hole (guarded by one or more diaphragms) in its side. Arranging an auxiliary bull's-eye condenser to throw the beams of light exactly into this little hole just mentioned (from which it is reflected on to the specimen) is in itself a somewhat troublesome and fidgety affair, hence, when once set in order, the tube of the instru- ment must not be touched. This forbids the use of the coarse adjustment ; hence, as the microscope cannot be lowered to the 1 Occasionally, for exceptional reasons, plates of metal may be ground so extremely thin as to transmit light— anyhow, through certain parts— in whjch case they can be used on an ordinary instrument. 292 METALLURGICAL MICROSCOPES specimen, arrangements have to be made to raise the specimen up to the objective, which means the construction of a special form of stand altogether different in build from any of which we have spoken. Then, to use the vertical illuminator successfully, the objectives have to be specially made in very short mounts, so that the back lens of each shall be quite close to the illuminator. In addition, provision has to be made not only for the examination of slices of metals, but of sensible-sized pieces of material. Other details have also to be considered, so the result is an instrument that is highly complicated. That devised by Martens some ten years ago seems to have satisfied every requirement possible save those of certain faddists, and is used indeed in a very large number of technical colleges. Quite recently, however, Messrs. R. and J. Beck have constructed the " Rosenhain " model, which is said to have improvements of great importance ; but concerning these we have not space to discuss, although we are bound to admit we are not persuaded of the utility of one particularly mentioned, that of the ''per- manently fixed tube," for it is obvious such large pieces of metal cannot be as easily accommodated as they would be in the Zeiss model after Martens, where it can be additionally raised to a considerable extent. Seeing this has a special screw to fix it when everything is set in readiness for use, so it cannot subsequently slip, what is the advantage of depriving the instru- ment of a more liberal adjustment ? We also illustrate a very excellent stand made by Messrs. Watson & Sons, which, judging by the number of institutions they have supplied, seems to be a great favourite. All these three instruments we propose to describe at some length as the subject in recent years is claiming so much attention, especially in the discovery of effects of sudden cooling, slow cooling, and medium cooling of steel, the arrangement of the ferric structure in ferrite, cementite, the properties of cast iron, showing how it differs from malleable cast iron, and the different qualities possessed by the various kinds of metals, such as molybdenum, chrome, tungsten, copper, and aluminium steels, let alone the signs of stress and fatigue in iron girders, and many other interesting subjects connected with metallurgy. It should be mentioned that in the construction of the Zeiss model ("Fig. i68) its adaptability for plwtographing the specimen METALLURGICAL MICROSCOPES 293 as well as regarding it visually is particularly taken into account ; hence many of the extra details relate more to this side of the question than they do with respect to purposes of simple inspection. We feel, however, a full inclusive description is desirable. J.C^'^^^- ,; ui .ic mpnf' ii "Mif'Ti III Fig. 168. Zeiss Metallurgical Microscope after Martens. In external appearance the stand differs greatly from the more usual forms. A square foot, which can be fastened by four screws to the sole-plate of the protection table or on any other suitable base, supports a massive horizontal rail. A carrier, to which the tube is attached in horizontal position, is screwed to one end of this rail. The tube is provided with only a coarse adjustment by rack and pinion T', and is principally intended for work by 294 METALLURGICAL MICROSCOPES transmitted light. A slide, worked by a second rack and pinion movement T'\ is situated at the opposite side of the rail ; a lever H, on the lower side of the rail, gives facilities for securing this slide at any point in the course of its movement. This slide includes the bearing for a second, a smaller slide, which can be moved in the most exact manner by the micrometer screw M. The head of this micrometer screw bears a divided scale, by which movements of the slide by 0005 mm. (5 n) can be immediately read off. The edge of the micrometer screw consists of a crest of oblique teeth into which a pinion Tr engages. This pinion can be set in motion from the position of the focussing screen of the camera by means of Hooke's key, which is joined to a removable wooden rod St. The pinion is con- nected with a revolving arm : when the micrometer screw is to be moved directly by hand, this arm is turned aside after easing the screw S. A special form of stage, suggested by the Royal Institution for Technical Research, Charlottenburg, can also be added to the stage (after removal, if necessary, of the Abbe illuminating apparatus). This appliance is fitted with adjusting-screws, so as to enable the surface of metalliferous prepara- tions, held in position by spring stage clips, to be adjusted vertically to the optical axis. The illuminating accessories for reflected light are attached to the tube, whose rack and pinion action for focussing the preparation is not required for this manner of illumination. With higher magnifications the vertical illuminator is employed. For low magnifications, obtained by means of objectives giving sufiicient object distance, either a plane or a concave mirror is used, or a thin plane-glass, inclined at 45° to the axis, is placed between object and objective so as to partially reflect upon the object the light falling vertically to the axis. The plane and concave mirrors are mounted together in a gimbal in the usual manner, so that they can be conveniently turned in any direction (Fig. Sp). The gimbal is joined to a rod, which is secured by a clamping-screw at the upper end of the small stem SI. This stem is vertically movable in a cylinder— not seen in the illustration — and secured by a second clamping- screw at any desired elevation. The cylinder itself is situated on a slide — screwed on to the lube parallel to the optical axis — which is also movable by hand and is secured by a third clamping-screw. In this manner pro- vision is made for a very extensive movement of the mirror. The plane glasses are attached in exactly the same manner as the mirrors. A large or small plane glass is to be used, according to object distance and extent of the field to be illuminated. The " Rosenhain " Metallurgical Microscope This microscope is built on quite different lines from the preceding. The limb has been designed to constitute a properly proportioned truss. It has a T-girder section throughout, the upper front portion having the body rigidly attached, and the lower front portion having a wide dovetail fitting upon which a solid bracket holding the stage racks up and down. METALLURGICAL MICROSCOPES 295 Fig. 169. R. & J. Beck's "Rosenhain" Model. Besides it is jointed on a centre so arranged that the instrument is almost in balance from the vertical to an angle of about 30°, and at the horizontal 296 METALLURGICAL MICROSCOPES position for photomicrography it rests on a projection of the base, which forms a cradle to support it. Thus, it is claimed, there is no strain on the joint fitting when used for visual purposes and when horizontal for photo- micrography. The limb is provided with a socket and clamp for holding bull's-eyes, etc. The coarse focussing adjustment is by means of a spiral rack and pinion, raising and lowering the stage for a distance of 3-I in. when the instrument is vertical, and a further I in. when the instrument is at a slight angle or horizontal. The fitting is i| in. wide, and fits by means of a broad dovetail. The fine focussing adjustment is by means of a micrometer screw which is situated in the optic axis, immediately under the object, where it is claimed to be of special utility, but for what reason is not immediately apparent. The body consists of a very thick tube, at the lower end of which is a nosepiece for carrying the object glass with centring adjustments, by which different object glasses can be adjusted to the exact axis of the microscope around which the stage rotates. An iris diaphragm actuated by a lever is fixed immediately behind the nosepiece, by means of which the aperture behind the object glass can be constricted for increasing its depth of focus or for cutting off reflections. Three dovetailed fittings are supplied at the lower end of the body, into which all illuminating appliances and their diaphragms are attached to the instrument. These include various thin glass and prism illuminators for throwing light through the object glass. The parabolic speculum, the thin glass illuminator, and the Sorbys' ^-field flat speculum for use between the object glass and the object, also the coloured glass screens for simultaneously illuminating with light of different colours in different directions, an amici prism or bull's-eye for further illumination — all can also be attached by these fittings. A supplementary draw-tube is provided for lengthening the body-tube when required. At the extremity of this tube a ring with the standard object- glass thread is provided, so that extra focussing adjustment can be obtained when using very low power or photographic lenses which might not focus in the ordinary way. The stage has a complete rotation, which may be clamped, for watching the effect of illumination at different angles and for placing the object in any required position. The centre of rotation is in the exact optic axis of the instrument, and any variation of different object glasses can be compen- sated by the centring nosepiece on the body. Mechanical motions in both directions, by spiral racks and pinions of 2-in. travel, are provided in the complete form of the instrument, and they are so arranged that a complete rotation, which is always concentric with the optic axis, can be obtained when the motions are used for i in. of their travel. The adjustments of the stage are so designed that, with the exception of the stage springs, which can be removed, there is no projection to interfere with the illumination or cast shadows when a very oblique pencil of light is employed. A transparent attachment is supplied for use with transparent objects with the same efficiency as that obtained with standard model microscopes. METALLURGICAL MICROSCOPES 297 It fits above the level of the stage, and a supplementary table which bridges it over fixes on to the stage of the microscope and partakes of the mechanical movements and rotation possessed by the stage itself, while the illuminating apparatus remains a fixture, as the latter is fixed not to the stage but to the stage bracket. The whole instrument is well thought out and finished. A parabolic Lieberkuhn, Sorby silver reflector with special objectives are supplied, including a |-in. oil immersion object glass constructed, not for the purpose of giving an increased angular aperture, but to avoid reflections and to give greater depth of focus or penetration than is possible with a similar angle dry glass. This appears to be a very useful addition. Quite a different class of instrument is made by Swift in two forms, the first being designed by Mr. J. E. Stead, F.R.S., etc., for use in workshops, and the other a Compound Metallurgical Microscope designed for the Royal Arsenal, Woolwich. The first (Fig. 170A) is arranged to be employed in engineering works where large forgings, etc., require examination when in the lathe or when laid on the ground. It is specially massive. A solid stage is made to swing round so that the object glass can be brought into focus on the steel or iron forging or casting, upon which the foot or fork rests. To effect this, an inside tube carrying the object glass slides within the outer barrel, and can be lowered to a sufficient distance. By means of a simple wire rope strap the stand is rigidly held in any position required on the massive piece of metal under examination. When in focus the position of the barrel is fixed by a screw at one side of the rack and pinion. When so fixed the conical camera (Fig. 170B) is placed on top of the barrel, and a photograph can then be taken. When not employed in the fitting shop, the microscope can be used in the laboratory or office, and is suitable for all metallographic work. The second variety. Fig. 171, is the New Compound Metal- lurgical Microscope designed specially for the Royal Arsenal, Woolwich. The coarse adjustment is by spiral rack and pinion, and the optical tube 2J in. diameter ; when the draw-tube is removed it allows of photographs being made of large or coarse objects with the smaller type of photographic lenses. The draw-tube takes the ordinary oculars. The slow motion is by the "Ariston" lever fine adjustment, described elsewhere in this book, and the stage is of entirely new and original design which admits of the object, after having been focussed in the horizontal position, being tilted or turned in any direction, so that the light impinging on the object from any source is maintained, thus enabling objects to be thoroughly examined at any point of inchnation without being thrown out of focus, and so entirely doing away with the different types of supplementary levelling stages. This is effected by the base of the stage holding the part of 298 METALLURGICAL MICROSCOPES specimen under examination moving in the segment of a circle or basin, a corresponding segment working in it carrying or holding the specimen, the point at which the object is viewed being the centre of the circle. The stage is fitted with mechanical movements for shifting the object in rectangular Fig. 170A. Swift & Son's Compound Metallurgical 170B. Microscope. directions and the specimen can be entirely revolved round the optic axis of the microscope. It is also provided with a rack and pinion for moving the object up or down from the objective. The ordinary 3 in. x i in. slide is held upon the top of the stage by means of two steel springs which are removable. Pieces of metal, etc., are held in position by four clamping Fis. 171. Swift & Son's New,.Compound Metallurgical Microscope. 300 METALLURGICAL MICROSCOPES dogs sliding in dovetails and are held in position by small clamping-screws. The optical tube is divided to show the position at which any objective will allow of an object being tilted without going out of focus. Metallurgical Microscope By Messrs. Watson & Sons A pattern of instrument differing in appearance from any of the preceding is sold by Messrs. Watson & Sons under the name of the "Works" Microscope. It is shown in Fig. 172. Made originally according to the specification of Mr. H. L. Heathcote, research student to Messrs. Rudge-Whitworth, Ltd., Coventry, it seems to have met with a very pronounced approval both in this country and abroad, for it has been supplied to such firms as Messrs. Armstrong, Whitworth & Co., Messrs. Vickers, Sons & Maxim, not to mention the Mint and several of the Railway Companies in England, whilst the Imperial Japanese Navy are in possession of two for their works. The foot is of the tripod pattern, which affords great stability no matter at what angle the instrument may be inclined. The stage is mounted on a very substantial bracket, which at the back is fitted by dovetailed grooves into a frame, in which, by rack and pinion, it can be raised or lowered to or from the body of the microscope. It is usually supplied with mechanical motion and is provided with verniers. Complete rotation can be made so that specimens may be examined under every aspect of illumination. A sliding bar is fitted to a recess in the stage ; this bar may be instantly removed so that either a levelling stage or metal holder may be substituted. All the necessary auxiliary apparatus are supplied with the instrument and means provided for their separate use ; whilst a substage with rackwork, a mirror, and other details are added so that the microscope can be employed for examining extremely thin sections of metal or for any other purpose where transmitted light is used. There seems no doubt that a considerable time must have been spent in devising and perfecting this arrangement, more especially in rendering it both a practical and portable one, devoid so far as possible of additions that may be regarded by some as superfluous and perhaps troublesome in every-day use. Fig. 172. Watson & Sons' "Works'' Microscope. 302 PORTABLE MICROSCOPES Portable Microscopes Of recent years the want of a microscope tiiat was built especially for the purpose of being easily carried about has been much felt. This has originated, of course, from the fact that the instrument being now so much used in the arts and sciences may often be wanted when the user is away from home, and as respects the medical profession when the prac- titioner is on his rounds. Further still, the researches carried on upon the subject of malaria, and other diseases of a similar character which require investigation in remote parts of the world, demand the use of an instrument that is not a mere toy but one of somewhat superior type. For this reason Fig. 173. Leitz's Hand Microscope. portable microscopes are of two classes, those suitable for low-power work, and those adapted for critical e.xaminations. These in the following iigures can be disseverated by mere inspection. PORTABLE MICROSCOPES 303 One of the most useful for the first purpose is shown in Fi§- ^7^1 by Leitz : we have employed one for years and can find no fault with it of any description. It is called a demonstration microscope. A chromatic Abbe condenser with iris diaphragm is provided, and a substantial handle so that the fine adjustment by means of a ring just above the objective can be easily actuated. Coarse adjustment by a sliding tube. Another entirely different model is the " Diagnostic " by C. Baker, Fig. 174. Dimensions given below show how very lightly and consequently how very portably it is made. Fig. 174. Baker's "Diagnostic" Microscope. The dimensions of this httle instrument rnay be mentioned : width of stage, 2f in. ; depth, 2 in. (from back to front) ; spread of feet, 7 X 7 in. Although exceedingly light this arrangement is far steadier than it looks. It folds into a very small case, 10^ X 4 X 3 in. 304 PORTABLE MICROSCOPES Messrs. Watson & Sons (make another form 'of instrument for the same purpose, but which is of a rather more substantial Fig. 175. Watson & Sons Portable Micioscope. character. It can be used for many purposes, is of a heavier type of construction, and is consequently a little more steady (Fig. 175). PORTABLE MICROSCOPES 30s The coarse and fine adjustments are of standard patterns and the highest powers can be advantageously worked. The fittings are of the " universal " size throughout, so that the full-sized apparatus can be used with it. It can be made to take either the Continental size of eyepiece, large eyepieces, i'27 in. diameter, or any other gauge. For packing, the underfitting and mirror are removed and the tailpiece and tripod legs folded forward under the stage, making an exceedingly compact arrangement. It is usually supplied in a mahogany case, measuring outside about 8^ x 6x3! i"-j but a solid leather case may be had if desired. Fig. 176. Swift's Small Portable Microscope. One of the smallest microscopes ever manufactured is very probably that designed by Swift (Fig. 176). It has a mechanical 20 3o6 PORTABLE MICROSCOPES stage and a centring substage, and altogether is an arrange- ment admirably suited to the medical practitioner, being fit for examination of blood in malaria, anaemia, and inflammatory- conditions. It may fairly be called a pocket instrument, as the case, made to hold both the instrument and bottles of solutions and reagents, blood-counting slide, pipette and other Fig. 176A. details, only measures 8 in. x 4 in. x if in. and weighs under 2 lb. If the microscope be intended for use by the amateur, where the above additions are not requisite, the case only measures 6^ x 3^ x ifV in. and the weight with two objectives is under i^ lb. This is an arrangement we cor- dially recommend to the medical profession for all-round clinical work, where a very expensive instrument may not be PORTABLE MICROSCOPES 307 desired. We have with this arrangement used a twelfth without diiificulty, although we admit a certain amount of extra care has to be employed. Fig. 177 Leitz's Portable Microscope. Of the more severe types of stand, one of the most perfect of the portable variety is that by Leitz (Fig. ] ^^). 3o8 PORTABLE MICROSCOPES This instrument is suited for the most critical work, the case being constructed to hold several accessories. It is somewhat heavy ; but where weight is not of material importance, the advantage of greater steadiness is readily felt. It has a fairly good substage but no mechanical stage, the makers relying upon the addition of the auxiliary form when necessity demands. Fig. 177A. It packs away in a case, shown in Fig. 177A, that measures II X 7f X 3i in. approximately. Messrs. Watson & Sons have recently introduced a model they call their High-power Portable Microscope, which meets the special want of those who require an exceptionally strong instrument and one that can be employed when using high Fig. 178. Watson & Sons' High-power Portable Microscope. 3[o PORTABLE MICROSCOPES powers for really critical work. This is an ideal microscope, the makers say, for those who have to travel abroad, up-country perhaps, where travelling is heavy and the baggage may receive some rough usage, such as would imperil the safety of an instrument unless specially constructed for the purpose. It is shown set up for use in Fig. 178 and closed in 178A, the case Fig. 178A. measuring only nf x 7| x 4| in., and the total weight not exceeding 8 lb. 13 oz. Lightness and rigidity such as to obtain a really useful and efficient instrument seem to have been the aim of the makers. The stage is of ebonite and measures 3J in. square. Substage condenser, with means of adjustment. Several other opticians now sell equally good patterns, notably Messrs. R. & J. Beck and Reichert — limits of space only precluding the possibility of illustrating their excellent productions. MICROSCOPES FOR CRITICAL WORK 311 Microscopes for Critical Work The class of instrument suited to the amateur, apart from the professional or business man, depends almost entirely upon whether his hobby is for low-power work, medium or extreme magnifications. If his amusement and intellectual enjoyment are to be reaped from the vegetable kingdom, such as the study of botanical specimens and such-like, we have already said the objective and the instrument need not be of the very highest class or of the most expensive type ; but if, on the other hand, he elects to study fungi or such-like, he will require a fairly good installation, both as respects the stand as well as the objectives, and some of those we have already recommended will probably suit him. But should his bent be tov/ards the examination of pond life and other small objects in the animal kingdom, he may prefer a stand more of the portable type, or he may perhaps find a somewhat cheaper kind still is all that is necessary, as very high powers are never required for this class of work. As regards the objectives necessary, most authorities rarely employ more than three, a one-and-a-half, two-thirds, and a quarter. Of the first two, no more need be said ; but as regards the quarter, the student will be well satisfied with what he obtains from Watson's Holoscopic series, Sv^ift's best type, and Zeiss's achromatics, as they are all of excellent quality, as well as those by Leitz, Reichert, and Koristka, for they leave nothing to be desired. For the selection, identification, and mounting of diatoms a |-in. and often an objective of still lower power are mostly selected. When we come, however, to the study of minutia; of any kind, whether it be of the animal or vegetable king- doms, but especially with respect to the secondary markings of Diatoms, nothing short of the finest possible .stands and the finest of objectives are demanded. It is critical work of the highest order. It will be necessary, therefore, for us now to consider very carefully these first-class stands, after which we will discuss the finest objectives made, those which are called " the apochromatics." It is but a fair remark to make that the typical English stand (Fig. 35), which we believe has been before the micro- scopist for a very great number of years — viz. that by 312 MICROSCOPES FOR CRITICAL WORK Messrs. Powell & Lealand — although designed so long ago when objectives were not made of such high power as at present are in daily use, still fulfils the requirements demanded by microscopists up to the present moment ! One would be tempted to say the designer lived before his time ! Handsomely made throughout of hand-finished brass, it is necessarily ex- tremely expensive, and consequently out of the reach of many. One of the earliest of the Continental models, so different in aspect from the former, is shown in Fig. 1 79. Though others may equal, none can surpass the make of this firm (Carl Zeiss). We have had two of their earlier models in very constant use for several years, and we have yet to find any fault with their performance. The figure shows the latest improvement, which is especially seen in the handle for lifting, which removes an objection to their previous designs. If the firm would arrange an extra draw-tube to enable the instrument to be used for " long-tube " objectives it would be a great convenience, and we regret the absence of centring adjustments in the sleeve of the substage condenser. Several additional stands, well designed and beautifully finished and generally of the very highest order of merit, are also made by other firms. One by C. Baker is called the " Nelson " model, and claims considerable attention as being designed by one of our greatest living microscopists who as a mechanician is only excelled by his adroitness as an observer. It is essentially a universal form of stand, for it can be used for all low-power work as well as for the most critical ; besides," it is so arranged that both long and short-tube objectives can be used with it as well as very extremely low powers — a com- plete combination not too often met with. There is one notice- able feature in its construction we have never met with elsewhere, and that is the fine adjustment is placed at the lower end of the body instead of in the ordinary position, as is seen by the most casual inspection of Fig. 180. Every movement is present in the mechanical stage with complete rotation, but any screws for centring the rotating stage should it by wear become eccentric do not seem to be present, which seems an oversight.^ The substage is complete with a ' We learn that in recent models these have been added. Fig. 179. Zeiss Stand I. 314 MICROSCOPES FOR CRITICAL WORK Fig. i8o. C. Baker's " Nelson " Model. fine adjustment. A tripod foot is usually supplied, although a horseshoe can be substituted if desired. We know this stand gives the greatest satisfaction. The American firm of Messrs. Bausch & Lomb (Agents, Staley & Co., Thavies Inn, Holborn Circus) sell a most magnifi- MICROSCOPES FOR CRITICAL WORK 315 cent first-class instrument (shown in Fig. 181) called "Stand CD." It has every adjustment we could possibly wish for, including a centring arrangement to the substage, although we regard this as the feeblest part of the instrument. This model has a novelty in the centring screws to the stage, which are pro- vided with micrometers so that the extent of their mov^ent, once ascertained to centre the stage in the optical axis, can be registered for further use ; hence the stage, once carefully set, can in the future be readjusted without any further trouble. This is a most useful addition. If any alteration were con- templated, we should prefer smaller milled heads to the stage screws — especially that for transverse movement, as its large size we look upon as very inconvenient ; but of course this is a most trivial objection. We should like, too, the adjustment for the substage condenser improved. Beck's " London " Micro- scope ("Iris" model. Fig. 182) is a good piece of work. The stage is 4 in. x 4 in. and surfaced with ebonite, four clip-holes being pro- vided. The mechanical stage is removable, which we have said before we object to save for bacteriological purposes. It has a travel of 2 in. horizontally and I in. laterally. An extra iris is contained in the substance of the stage, being placed there to avoid any accidental injury. The body can only be extended to 200 mm. (about 8 in.), so a lengthening tube would have to be added for the instrument to be used with English objectives of the long-tube correction. Fig. 181. Bausch & Lomb's "Stand CD.' Fig. 182. R. &'J. Beck's "London" Microscope ("Iris" Model). Fig. 183. Leitz's " Universal Microscope Stand I." 3i8 MICROSCOPES FOR CRITICAL WORK No centring screws are provided to the substage condenser so far as we are aware. The "Universal Microscope Stand I," by Leitz (Fig. 183), is provided with his new fine adjustment already described, has a standard type of revolving centring stage provided with a removable mechanical one, and is arranged for the short-tube work only, and so would need a lengthening tube when using English long-tube objectives. No centring screws to substage condenser. This stand is a practical one and a favourite with many, but for the highest type of instrument we should like the firm to arrange a model where the stage is built into the frame- work and an arrangement provided for centring the condenser. Reichert's Stand No. I A, Fig. 184, is an entire departure from the usual Continental model, the body taking the form of a handle, which so many opticians are now recognising to be of great service to the practical microscopist. In this instrument, as in the new Zeiss model, the use of the handle in no way threatens the safety of the fine adjustment. A circular centring stage is provided as well as the firm's new fine adjustment, but no centring arrangements for the condenser. It is constructed for the short-tube objective only. We believe this stand affords great satisfaction, especially for work of large, dimensions, such as the study of brain sections ; hence its use for the amateur as well as for bacteriological and pathological purposes, qualifies it to be called a first-class all-round instrument. Swift & Son's Portable Histological Microscope is of great excellence. Although primarily designed for the study of Histology, it is perfect as an all-round instrument. It has the " peculiar feature first of having four legs, and secondly of being collapsible, for it can be packed away in the smallest amount of space imaginable, although a little practice is necessary to do this, as a study of the diagram will lead the reader to understand. It may therefore claim admission into the class of Portable microscopes. Constructed for the short tube, it can be extended for an optical tube-length of 10 in., which makes it just a trifle too short for the convenient and scientific use of long-tube objectives, without an additional draw-tube or the use of Zeiss '' sliders " or a revolving nosepiece, either of which just increases the length sufficiently. It is shown in- Fig. 185, and packed away in Fig. 186. Fig. 184. Reichen's Stand No. Ia. Fig. 185. Swift & Son's Portable Histological Micioicope. MICROSCOPES FOR CRITICAL WORK 321 Messrs. Watson & Sons' " Royal " and " Club " Microscopes are to our mind of a more convenient pattern than their Van Heurck. They are both new models, being much alike. We describe the " Royal," Fig. 187. It is a remarkably well-made instrument, being of very perfect construction, and, as the makers say^and this we can easily believe — " the outcome of numerous experiments." The fine and coarse adjustment are of the usual type supplied to the Van Heurck. The body tube is of large diameter, taking the English form of eyepiece (r27 in.). Two draw-tubes are provided (one having rackwork), so the instrument can be used with both Continental and English form of objective, seeing it Fig. 186. Microscope shown Folded in Cabinet (size, 7| in. x 6} in. x 4 1 in.). closes to 142 mm. and extends to 305 mm. Centring screws to the substage are provided. This we believe to be a practical instrument and to have justly obtained considerable acceptance. With respect to the objectives used for the highest power critical work, there is no doubt the apochrpmat leads the way. We have spoken already of the semi-apochromat, and explained how perfect its performance is when well made and used with a suitable screen to cut off the secondary spectrum, but for the critical work of the advanced student, or for the minute investi- gation of the philosophical enquirer, the more expensive rival must take the precedence. Seeing apochromats were originated by the genius of the late Professor Abbe, and manufactured 21 Fig. 187. Watson & Sons' "Royal" Microscope. APOCHROMATS FOR CRITICAL WORK 323 first by the justly eminent firm of Carl Zeiss, it is only to be expected that the productions of this firm should be, as indeed they truly are, of the highest order of merit. The excellence of definition of these objectives coupled with the absence of practically all colour when dealing with specimens of all sorts, renders these combinations of the very greatest possible value for final examinations and critical work of all sorts, whether it be of objects requiring low-power magnifica- tions or those that demand the greatest resolution and amplifi- cation possible. The 3-mm. and 2-mm. combinations are especially superb in their performance, and were it not for their necessarily high price, would be in more common use. Their outer zones being as near perfection as it seems possible for the mathematician to compute and the optician to construct with our present knowledge, so their performance with oblique light leaves but little, if anything, to be desired, although we trust a time will come when with direct light they can be used with a full cone as well as they can be now with a f one. A reputation of this description, so justly held by this firm for now so many years, has necessarily led others to make very strenuous efforts to compute objectives of the same merit. Indeed Messrs. Powell & Lealand constructed, shortly after the advent of the apochromat, a competing lens — a wonderful one, we have been told, at the time, but which the same firm has long since replaced by others more perfect. One of these latter constructions we used with much profit wherewith to take a very large proportion of the photomicrographs in the Atlas of Bacteriology published by the Scientific Press some years ago, being especially designed to give a large flat field. But Continental manufacturers — of late especially — have been exceedingly hard at work raising the tone and quality of their apochromats until at length they have reached a goal of perfection that defies description. To these we feel bound in common fairness at once to refer. SiGNOR KORISTKA OF MILAN produces apochromats which — aftera very extended and severely conducted series of experiments both with the test-plate and with test-objects — are all oi the very highest possible order of excellence. We have seen, through his courtesy, all his manufactures, and all are equally good. The I'S-mm., a sp^cialit^, v/ith. a very long working distance for so 324 APOCHROMATS FOR CRITICAL WORK high a power, is an exceedingly fine lens and produces an image so absolutely perfect as to render any distinction between it and that displayed by two of the finest apochromatic twelfths — one for the short and one for the long tube — by Zeiss in our possession impossible. Herr Leitz of Wetzlar, too, has given much attention in the same direction, and produced magnificent specimens of work- manship that are beyond praise. His 2-mm. is one of the finest combinations we have met with both when using the test-plate as well as test-objects ; and the rendering of the dots in an excellent specimen of Amphipleura pellucida mounted in realgar by Dr. van Heurck leaves absolutely nothing that can be desired by the most critical observer. Herr Reichert of Vienna has notbeen neglectful in bringing up his apochromats to the level of excellence attained by others of which we have justly and truly spoken so highly. His 2-mm. is one of the most remarkable combinations that have ever passed through our hands. Whilst showing the tertiary spectrum with the plate— an explanation of which is spoken about at some length in the article devoted to the testing of lenses — - its performance as a combination for producing resolution of the finest details of the minutest structure has no superior in the world, the image being so crisp and beautiful. It is a very remarkable lens. His 4-mm. objective is one, too, that effectu- ally competes with those of similar focus and aperture by Zeiss and Koristka. Speaking of the 2-mm. as made by these four manufacturers, Koristka, Leitz, Reichert and Zeiss, the manner in which they show the dots in Amphipleura pellucida even with green light and the extra powerful Nernst lamp, must be seen to be fully appreciated ; the reproduction in Fig. i, plate VI., of a photo- graph taken with the Zeiss 2-mm. apochromatic and blue light furnishing but some idea of the images of which we speak. This photograph was awarded (with some others) a Gold Medal at the St. Louis Exhibition, 1903, and we have often felt that the honour should have been placed in the manufacturer's hands rather than in those of the simple photomicrographer, seeing it is not so difficult to take a photograph — although at this great amplification it is not quite an easy matter — as to compute and construct a lens that will plainly show dots not much more APOCHROMATS FOR CRITICAL WORK 325 than TTTTjWirth of an inch apart in the wonderful manner ex- hibited. We have also taken photographs of the same diatom with 2-mm. objectives by Koristka, Leitz, and Reichert equally perfect, and it is only the limits of space that preclude the possibility of illustrating the excellent work that can be carried out by these wonderfully fine combinations. When the optician's art rises to this pitch of excellence, and a difference is required to be shown between objectives where possibly no distinction exists, and a selection to be made where all appear to be of equal merit, the task of the expert becomes simply an impossible one, and the only thing open to him is to con- gratulate each manufacturer and acknowledge his inability.' For specimens of the photographic performance of these apochromats the reader is referred to the Plates at the end of this book. So many are the varied uses to which the microscope can be employed, that the reader can readily understand the difficulty we should experience if we attempted, alone and unassisted, to state very positively the objectives most suitable for every particular line of investigation. We have felt this so strongly that, fearing we might unintentionally lead the student astray by our attempting to do so, we have written to several micro- scopists whose experience and work upon special subjects justify their speaking with the voice of authority. Doubtless we have not made an exhaustive list of enquiries, hence we should like to add, if we have failed to apply to any specialist upon any given subject, whose aid we ought to have sought, he must regard it not as a sin of commission, but merely as one of (^mission on our part, that has simply arisen from an unfortunate oversight. We met with a hearty response, and the substance of ' Dr. Hartnack, the representative of the old and distinguished firm in Potsdam, near Berlin, whose name is a household word to the older microscopists, has lately forwarded for our inspection, just as we were going to press, one of his recently arranged 2-mm. apochromats. It is a very fine combination, and resolves the tests to which we have applied it in a very creditable manner. Its performance on the test-plate shows certainly more colour than we are accustomed to see, but the dots in amphipieura stand out with an appearance that is very remarkable. His series do not extend to objectives of longer focus, for indeed he only makes one other apochromat, a fifteenth. We prefer the twelfth to this lens, but both must be classified as very good combinations. 326 OBJECTIVES FOR VARIOUS PURPOSES the replies we now append ; taking this opportunity of thanking the writers for allowing us to lay before our readers their individual experiences, which we know will be highly appre- ciated. Mr. F. P. Smith, Hon. Editor to the Quekett Microscopical Club, writes : " I usually use a 2-in., i-in., and frds for ordinary spider work, employing a ;|-in. for detailed examinations. By far the best way to examine a spider is to put it into a pomade-pot lid, cover it with methylated spirit, and treat it as an opaque object, using of course .low powers. If suitable for preservation it can be subsequently mounted and used as a transparency, when I employ the j-in." Mr. Charles D. Soar with the Hydrachnidae uses a i^-in. and ^-in., and sometimes a ^th, employing dark-ground illumination whenever possible. The i|-in. serves to identify species and the ^-in. supplies details especially for " drawing '' purposes. The |th, however, is more or less exclusively employed for the examina- tion of skin texture. Mr. W. WeschiJ has three objectives in constant use for his well-known anatomical researches. An inch he employs upon the Binocular Microscope ; a frds as a finder, and a yth, with as great a working distance as possible, for details of structure. Mr. A. E. Hilton — concerning the study of Mycetozoa — writes: "For sporangia I use a 2-in. and a i-in., and mostly these are sufficient for my purpose, as great magnifications for my class of work in general are not required. When, however, the Capillitia and spores have to be studied, I employ a dry ^th,' although I should recommend in preference an immersion Ath, and I gather Mr. Massee is of the same opinion, for occasionally we require a magnification of I200 diameters." Mr. Richard Lewis, who from his long experience is a distinctive authority, says he has a set of objectives ranging from 3 in. to ^ in., all of which he has found of frequent use in the study of Ixodidse and the sense organs of insects. For the majority of Ticks the 2-in. and i-in. are sufficient if employed on a binocular stand, but when details have to be searched for, a ^-in. is more useful. This may not always be of sufficient power, and if expense is of no object the higher power apo- chromats will be found most serviceable. OBJECTIVES FOR VARIOUS PURPOSES 327 Mr. James Burton for work on Algse and Fungi employs low powers, but occasionally a ^th and a Jth and rarely an ^th. He prefers all objectives with low numerical aperture so that very great depth of focus is obtained. Mr. H. E. Freeman, who is interested in and has studied at some length the Acarina, with the life history in general of microscopic insects, employs a 3-in., i|-in.,and frds with opaque objects in small sunk cells. He objects to the use of very high powers because of the difficulty in following a moving object about the field of view. Mr. T. R. ROSSETER for his well-known researches upon Entozoa, especially, perhaps, the avian Cestoda, employs a 2-in. and i-in. ol second-class type for rough use, and an inch, \-m., \-\n., and |th of high-class make, with a yyth water immersion occa- sionally to study the details when in search of minutiae. Mr. Herbert S. Martin, when working at his favourite study of Petrology, finds an inch and a 2-in. of sufficiently high power for ordinary examinations of rocks, reserving a ^th for "viewing the interference figures formed at the back of the objective when convergent polarised light is used." Mr. Albert Ashe (whose experience is somewhat unique, his studies having been directed more especially to animal, vegetable, and mineral substances for industrial purposes, such as adulterations) rarely employs other objectives besides a second-class frds and a ^th, quite a plain form of stand being sufficient. But for delicate work arising occasionally, he in- variably employs apochromatics, presumably of the same focus with a suitable condenser and critical illumination upon a first- class stand. Mr. E. Leonard, who has given so much attention to the mounting of diatoms and their selection, says his battery con- sists of a i^, I, \, \, and yVh oil immersion. For mounting, the two lowest powers are employed, the i^ for searching over the " drop " on the slide, the | for the actual mounting. Occasion- ally the \-\x\. has to be used for the " drop " searching, and of course, for subsequent work of a more delicate nature, the yVth. For "picking up" the best objective is the i^-in., and for dark- ground illumination the |-in. He adds, "the best bristles for mounting with I obtain from the back of my fox terrier ! " Mr. Frank Earland, Hon. Sec. to the Quekett Club, whose 328 OBJECTIVES FOR VARIOUS PURPOSES extensive work upon Foraminifera and Radiolaria is too well known to need any remark, says he rarely employs any other objective save a i|-in., a frds, and a ;|-in. Mr. C. F. ROUSSELET, one of our greatest living authorities upon Gastrotricha and the Rotifera, mostly uses a J-in., and very frequently only one of 37 mm. focus, both of which are apochromats, but adds that occasionally a higher power apochromatic has to be employed. Mr. G. C. Carop, M.R.C.S., L.S.'A., formerly so many years the valued and highly esteemed Secretary to the Quekett Club, an amateur who has devoted his attention, it may be said, to almost every variety of subject, and whose experience is con- sequently almost unique, writes : " If I were asked the two most useful objectives for an amateur to purchase they would be a frds and a ^th. If I had to select three, I should add a yVth, and if yet one more, it would be a i|-in." Mr. H. MoRLAND, in his work upon the Diatomaceas, more especially relating perhaps to their classification and mounting, rarely finds he requires objectives other than a quarter-inch as a high power, and, say, an inch for other purposes. He does not make so especial a study of the secondary markings, and so has no need for very high-power immersion objectives. Mr. A. Still finds for his work upon Microalgae and Desmids an inch, frds, and a ^th all he requires, the low powers being more especially for searching and the fth for examining details. Mr. G. Massee, past-President of the Quekett Microscopical Club (four years), says : " The objectives I find most useful for work on Fungi and Myxomycetes are : "(i) For a general aspect of the superficial structure a i|-in. "(2) For histological details, measurements of spores, a ^th, as by common consent a magnification of 400 diameters is used. " (3) In the systematic study of the Myxomycetes, and in some special groups of fungi where the so-called species run very close and the finest details are required, I use a ^s^h." Mr. David Bryce finds in his work upon Rotifera he mostly uses two objectives, a i-in. and a :|-in. : the former for searching through specimens and the latter for examining details. He adds : " The student should recollect my subjects are alive, and average about ^Vth of an inch extreme length, so that every movement takes them out of focus," which, he subsequently points out, / / OBJECTIVES FOR VARIOUS PURPOSES 329 prevents the employment of higher power objectives. Occasion- ally, however, he has required a |th. Mr. Robert Paulson, speaking of the Laboratory, London County Council Technical Institute, Lalham Crescent, W., says he has usually found a |-in. and a dry ^th all he requires for his work in biological study, but occasionally, however, he employs a i\th. Mr. Arthur Cottam, F.R.A.S., whose opinion commands immediate respect, says he usually employs a Zeiss A (15-mm.) objective for selecting and mounting his diatoms, as its shape is peculiarly convenient, but with very small specimens he employs all types of the highest powers suitable to the difficulties of the situation. Mr. Holder, who pays so much attention to biology, and is such a successful microtomist, seems to use exclusively an inch and a ^th for all work in general. Mr. SiDWELL, whose work upon the Entomostraca, is so well known to microscopists, writes to the effect that as regards the best objectives for pond life — for the examination of Entomo- straca— he finds an inch N.A. '28 used on the binocular the most useful, but employs a half-inch apochromatic for objects possess- ing smaller details. Occasionally, however, it is necessary to use a higher power still when he resorts to a xV^h immersion. With respect to the study of the Diatomacese, the author of this work is bound to admit the use of all types of objectives ranging from the lowest to the highest powers. A ^th apochromat is a very excellent one to employ upon diatoms for primarily studying their forms, but their secondary markings require the finest apochromatic 2-mm. or i'5-mm. with the aid of green or (better still) blue illumination. The quarter-inch apochromatic by Zeiss on the long tube is a much neglected objective, and is one especially convenient, having a longer working distance (some specimens mounted years ago having rather thick covers) than a ^th. So, too, for the same reason the 3-mm. apochromatic may often be more useful than the 2-mm. The third or half-inch for sorting specimens are both of service ; and the i-in. apochromatic (used with a high-power ocular) shows the colours of diatoms remarkably well. . CHAPTER XIV TESTING OBJECTIVES The testing of objectives has always been an interesting though difficult subject. It used to consist in examining the perform- ance of the lens upon certain specimens called test-objects, but nowadays, besides this method, there is one of a far more searching character originated by the late Professor Abbe, called after him " The Abbe Test-plate," a description of which we at once proceed to furnish. The Abbe Test-plate In the construction of this excellent and useful little piece of apparatus the special aim of its inventor. Professor Abbe, was to artificially produce an object as full of pronounced contrasts as possible. For this purpose advantage was taken of the densely opaque character of a chemically deposited layer of pure silver on a piece of glass, for it is evident if a film of the nature described be ruled in such a manner as to remove the deposit and leave clear glass in certain lines — the film bein^ left untouched between — the result would appear under the microscope as a kind of coarse grating. Now, an object consisting of an alternating series of dark and bright lines fulfils the very ideal required, for it is difficult to imagine one that could be constructed having greater contrasts. The deposit on the Abbe plate is not always absolutely black although exceedingly dense, and may then be described as consisting of a dull grey semi-opaque " filling " transmitting but very little light indeed, in which are closely scattered numerous black irregular-shaped particles of silver deposit. Although these are closely packed together in the filling, still they appear sufficiently discrete to offer every facility for accurate focussing. 33° TESTING OBJECTIVES, ABBE PLATE 331 This is the kind of plate we prefer, but sometimes the so-called black lines are black indeed, in which case the particles are indistinguishable, and only the actual edges of the lines are capable of being focussed. With a superficial examination, the test-plate appears to consist simply of an ordinary 3 x i in. glass slip, having cemented upon its upper surface six small circular silvery-looking cover-glasses (Figs. 4A and 4B, Plate I.) : but on closer inspection each one exhibits, even to the naked eye, a faint indication — plainly seen with a hand magnifier — of the minute rulings above spoken about. All the cover-glas.ses are of specified thicknesses varying from ■09 to "24 mm., the exact measurements of each being etched in white figures beneath it on the slip. Upon looking at any one of these six covers — preferably the one marked "iS — with, say, a iV-i"- semi-apochromatic, it will usually be found to present four batches of lines, each batch consisting of eleven white-space rulings, called technically " the white lines," between twelve black or opaque ones. The white spaces and the black lines are not of quite equal width, the former being the little narrower of the two in most instances that we have met with, although such is not always the case. Further it will be seen whilst using direct light, that when the black lines are out of focus, the white ones immediately appear to have coloured fringes at their upper and lower borders and that the tint of these fringes varies according to whether the objective be pushed within the focus, or pulled without it. If the former, the upper and lower borders in question show purple fringes (appearing as if actually coming from the black lines adjacent) ; whilst if the latter position has been taken for the objective, the purple colour has vanished and apple-green has taken its place. Putting this in short, the colours exhibited are purple within the focus and apple-green outside it. It will also be noticed by the careful observer that whether purple or apple-green be in evidence, both sides of the white lines are similarly coloured. This is technically called " symmetrical colouring of the lines." Should, however, direct light be now changed into oblique light — and here it is necessary for accurate explanation that such shall be produced by placing a card over the lower two-thirds or three-fourths of the condenser between it and the light, so that 332 TESTING OBJECTIVES, ABBE PLATE illumination can only enter through its uppermost third or fourth (appearing as the lowest third or fourth of the back lens of the objective as seen when looking down the tube of the microscope) — the arrangement of the colour effects becomes entirely different.^ First. The colours at the upper and lower borders of the white lines respectively are now no longer symmetrical, for with a visually corrected semi-apochromatic objective of the best quality, apple-green usually appears at the upper border, whilst purple is seen at the lower one of each of the white spaces. Secondly, it will be found that no alteration of the objective, that is to say whether it is placed within or without the focus, causes any change of colour effect as it did when using direct light ; and — Thirdly, that no alteration of colour can be produced by any means whatever excepting by admitting light from the exactly opposite third or fourth of the substage condenser to that employed as we have just stated. It will be of interest before proceeding further, and to make what follows better understood, if the cause or causes of these colour effects be carefully explained. For that purpose, before actually commencing to do so, the reader is referred to Figs. 72-73, 74-75 in the chapter upon the improvements effected in the construction of modern objectives. In this chapter it has been explained achromatism consists in a folding over of the spectrum at the particular colour selected by the optician for the best correction, and that the rays of this " preferred colour " then have the shortest focus, the otherS meeting at intervals along the axis forming the colours of the secondary spectrum? The point then here to bear in mind is that the apple-green has the shortest focus and the purple the ' This can be done with the Abbe illuminating apparatus by simply closing the iris and by turning the milled head which puts the iris out of axial centrality. ' The so-called primary colours are those which come into evidence when a prism or grating breaks a beam of white light into its components- rainbow colours, as they are often called— consisting of red, orange, yellow, green, blue, violet, and uhra-violet ; but the secondary colours .are those formed by unions of these different residuals, such as apple-green being formed by the joining of yellow and green, and purple by the union of red and violet. TESTING OBJECTIVES, ABBE PLATE 333 longest, the intermediate mixture of orange and blue being omitted for clearness of description. Let Fig. 188 be now considered. We have here a point of light P situated upon the axis of a semi-apochromatic combination roughly shown at L. In an exaggerated, manner the yfellow-green rays— because they have the shortest focus in the construction selected — are seen focussing at A, whilst the red and violet forming the purple, having the longest focus, meet at A'. If now a section of the beam of light were possible at A, we should see an apple-green point of light surrounded by a faint haze of purple ; whilst if we examined a section at A' we should see a purple point surrounded by an apple-green halo (the rays forming this halo being shown to have crossed after forming a focus at A). Within the focus at a plane marked A" we should see an apple-green disc of light surrounded by a distinct and well- marked halo of purple, whilst considerably without the focus at A'" a purple disc surrounded by a halo of apple-green. Although in the Abbe test-plate a white line of sensible area between two black ones is the object, instead of a discrete point of light, a little thought will suffice to show that the same reasoning affords an equally correct explanation of the colour phenomena in this instance, as in the previous one. Perhaps the easiest way to understand this is to remember in the first case the image of the point was formed in the yellow-green, hence in the Abbe plate the image of the white line is really in apple-green also. Now when the objective was lowered in the first experiment the image of the point became blurred into an apple-green disc with a halo or fringe of purple around it ; so in the second, the image of the white line following the same course becomes blurred and the purple fringe makes its appearance at the edges of it. Likewise also, when the objective was raised in the first 334 TESTING OBJECTIVES, ABBE PLATE instance outside the focus, tiie purple point became blurred into a disc and had an apple-green halo around it ; so in the second, the image of the white line becomes blurred and the apple-green fringe forms above and below it. When employing oblique light formed in the manner already described, the conditions were materially changed. Fig. 189 is drawn in exaggeration to explain the situation. The rays from the edges of the white line AA are shown as entering and leaving the back lens of an objective at its lower third, as would be seen in fact if the observer were looking down the tube of the microscope, the ocular having been removed. -3ffi — ,^__^ TVii» Ray la oirAwh as it n^peiun -— APPAfKHTLY COMING TMIfOuaM "mt RV Black UNt, THE Red-Violkt BUKGuosT •ntis Ray is drawn as \t Appears APFARCNTLV COWING TPROycn THl Black UNt,THK YcLLOn-GREcrt beiix. lost Fig. 189. The image of the white line AA is shown diagrammatically at A' A". Here at A', the upper edge, the yellow-green colour appears because it is the most refracted of any of the colours of the spectrum, and having the shortest focus, so lies at the very edge A' : whilst at A" we see the purple tint because that colour, being the least refracted (longest focus) consequentlj*. lies at the lowest limit of the image. The red-violet ray is lost in the former case and the apple-green in the latter because of the brilliancy of the white line.' That in this case no change of position of the objective causes any alteration in the colour fringes is accounted for by the fact that no movement of the microscope up or down alters the condition of things in the slightest manner, hence the absence of any change of colour. The exact reversal of colour effect produced by changing the card beneath the condenser, and so allowing the light to enter • With practice, however, these colours can be distinctly though faintly seen, notwithstanding the general brilUancy of the white line. TESTING OBJECTIVES, ABBE PLATE 335 from the opposite side, is readily understood, because tlie position of the least refracted ray becomes that of the most, and vice versa. This concludes an explanation, in general, how the tinted fringes are formed both with direct and oblique light in the Abbe test-plate. The next point which strikes the observer, even if it has not been noticed before in this cursory examination, is that the whole field of view has never been in focus at one and the same time. It is not so even if a lower power ocular than the x 12, which is supposed to have been used throughout these experi- ments, be tried. Indeed it would seem as if nothing more than about the central and intermediate zones of the field can be focussed sharply simultaneously. We believe that, so far as at present is known, no hope can be held out for anything better. It is this inability to produce a flat uniformly defined field at one and the same moment, that has led several microscopists of the old school to say that they consider, in their opinion, the modern objective is retrograde, adding that they do not hold much improvement has been effected by the optician in recent years, seeing that the field of perfect definition is so much smaller than in some of the old objectives with which they are acquainted. To this it must be replied that at all times, whether now or in the past, the equali- sation of the definition in all three zones of the field of view is the effect of a compromise. If the best definition is required in the central and intermediate zones (occupied alone by most objects of microscopical interest), then the outer one must be left to suffer, with the possibility of being immediately brought into focus by a touch of the fine-adjustment screw ; whereas if the whole field be required to be equally well defined, it must and can only be produced by lowering the quality of the definition of the central and intermediate zones. In the present day the former state of things being preferred by most microscopists is the cause for the apparent falling off of the performance exhibited by this outer zone so noticeable in modern lenses. It is needless to remark that the three zones of the field must not be confused with the three zones of the back lens of the objective, for they have no relation one with the other, otherwise cutting off the outer zone of the back lens by the iris would cause a contraction of the field of view, which it does not 336 ABBE PLATE, PRECAUTIONS BEFORE' USING Precautions to be Observed before Commencing to Test the Performance of any Objective with the Abbe Test-plate 1. The draw-tube must be set the exact distance for which the objective is corrected : it is frequently engraved upon the side of the mount.' 2. The back lens of the objective must be filled with light ; hence every objective over N.A. j-q must be used with an immersion condenser oile'd to the slip and of approximately equal N.A., to make the observation of scientific value. The condenser should be carefully centred. ' 3. The cover-glass of the test-plate to be selected should be •18 mm. or thereabouts, because that is the average thickness selected by most manufacturers.' 4. The compensating ocular is to be eniployed for all apochro- matics, no matter what their focus, and with semi-apochromats of over, say, -5 N.A. ; but the ordinary achromat and the low- power semi-apochromats below the N..^. mentioned perform best in most cases, although perhaps not in all instances, with the ordinary Huyghenian ocular. 5. The magnifying power of the ocular is to be such that multiplied by the initial of the objective, the total amplification should numerically equal the N.A. x 1000 ; hence a y^th of, say, r4 N.A. requires a x 12 ocular. 6. The illumination must be critical and very brilliantly white so far as possible. There must be no obliquity in the direction of the light from off the mirror, by which is meant the beams from the illuminant should pass centrally through the condensei". Testing Objectives Examination of Semi-apochromatics : jV-in. or tV-in., N.A. 1-3 TO 1-4 A. With the Abbe Test-plate. B. With Special Test-objects. A. With the Abbe Test-plate.— The list of precautions given in the preceding section having been duly read and observed, the examination of an objective N.A. vt, or i'4, say a jV*^) ' A qualification of this statement is made later. TESTING OBJECTIVES WITH ABBE PLATE 337 iVth, or |-th is carried out in the following manner for two pur- poses : to ascertain the correction — (a) For chromatic aberration (testing for colour). (i) The appearances presented with direct light. (") » „ „ oblique light. (J)) For spherical aberration and definition, (i) With direct light, (ii) With oblique light. {a) (i) When the edges of the black lines are in accurate focus, care being taken that a white space occupies as nearly as possible the true diameter of the field ; no colour phenomena should be visible. If much be present, it may be due to the compensation of the ocular not quite suiting the individual objective under observation. Let the former be removed and replaced by a Holos' compensating eyepiece of similar magnifying power. If the ocular has been at fault, adjustment of the component lenses of this ocular will be found to correct it. If, however, no improvement takes place, this appearance does not betoken a good objective ; but it must be borne in mind the accurate focussing of tfie edges of the black lines bordering the white space must be carefully sought after, for it is only at the very moment of accurate focus with the fine adjustment that a colourless image is seen.^ The instant the objective is lowered beneath the focus or raised above it, colour should appear. What colours are to be expected depends upon the position chosen by the computer of the system for the folding over of the spectrum ; in other words, which colour shall have the shortest focus, and consequently in what colour the image shall ' These are sold by Messrs. Watson & Sons and Messrs. Swift & Son, although under a different name. ' Another word of caution might be mentioned. We have spoken of the necessity of having critical light ; but it is important also to see that the mirror does not reflect the beams of the lamp with any degree of obliquity at all upon the condenser. By this we mean that if, for example, a point of light from the illuminant were in use, the microscopist should see that that point is in the centre of the field of view when the plate is in use with direct light. Should any colour (otherwise than the folding-over one) be seen then upo}t focussing the lines (which we have explained should not be the case), it is possible for it to be caused by the mirror being a little obliquely placed ; hence, before coming to any conclusion on the matter, the simple experiment of shifting the mirror a trifle should always be made, to see if that does not at once remedy the fault in question. 22 338 TESTING OBJECTIVES WITH ABBE PLATE be formed. If he select what is often called the apple-green correction, then such folding over usually takes place about wave-length 5500 in the ordinary spectrum, and the colours exhibited on the borders of the white lines, symmetrically placed, are purple within and apple-green without the focus. This class of correction is a great favourite, but a few makers pitch their folding-over point slightly nearer the green, which produces a redder purple within the focus and a deeper green outside it. This is called a slightly under-corrected combination, a term to be explained a little later on. Sometimes the colour outside the focus is a very light yellow- green indeed, and quite a blue-purple within it. This type is called a slightly over-corrected objective, a term also needing explanation hereafter. Lastly, an objective might present (although they must be very rare and few in number in the case of ^i^th or ^th, for we have never yet met with one) the white lines bordered with blue outside the focus, but a red orange within it. This denotes a correction for photography only, and would be a wretched objective for visual purposes. («) (ii) The objective has now to be tested with oblique light, and it is important that this should be obtained in the following manner:— The condenser must be covered up by a card throughout its lower two-thirds or three-fourths, preferably one with a curved edge — crescent-moon shape — so that when looking at the back lens of the objective down the tube with the ocular removed for the moment, light only appears to enter by a little portion at its lowest limit. On returning the ocular and looking at the lines, care should be exercised that one of the white spaces should occupy as nearly as possible the true diameter of the field ; that is, cen- trally from side to side. Three white lines are usually capable of being seen with the X 12 ocular and the yVth objective; but occasionally the screen- ing diaphragm of the eyepiece may cut off a portion of the white spaces at the upper and lower parts of the field. The fringes on the upper and lower borders of the central white line will now be found to be of different colour, the upper being of apple-green and the lower of purple ; that is, of course, presuming the objective to be the best visual type. There TESTING OBJECTIVES WITH ABBE PLATE 339 should be no fluffiness, and the edges of the lines should be capable of being sharply focussed. It is possible by this time that the student may have noticed the colours in the upper white space may not be quite the same as those in the central, and again those in the central may not be quite the same as those in the lowest. This arises from the eyepiece not being quite in compensation v/ith the objective. Indeed, it may be said to be almost an impossibility to prevent a little difference ; but if it is very pronounced the ocular is probably the cause of trouble and not the objective. This may be proved by altering the adjustment of a Holos eyepiece, when it will be found it can nearly always be greatly modified. It would seem then to be a constant form of fault with the ordinary compensating eyepiece, but the high-power Holos, although it can usually be set to rectify the fault, is not a very suitable ocular to be used for ordinary work on account of its very near eyepoint. To remedy this disturbing effect with the ordinary compensating ocular whilst testing an objective, we have already said, the border of the central white space under observation at the moment should be placed in the exact diameter of the field and then the colour carefully noted, the test-plate being shifted so as to put the other border in the same position before noting its colour. By this means any change of colour due to the eyepiece is eradicated. To test independently the three zones of the objective for colour correction it is almost imperative for the microscope to have an Abbe substage illuminating arrangement, as the iris diaphragm when shut somewhat closely — in fact, down to the size of a large pinhole — has to be shifted from centrality across the field from above downwards to the periphery of the lens, whilst the eye is placed at the ocular, noting any changes of colour during the operation. The precaution above explained, to eliminate any error in the compensation of the ocular by keeping the colour under observation in the exact diameter of the field, should be rigidly carried out. It will be usually found that when the little aperture of the iris is placed in the central zone, the lines are dull and ill-defined. This is caused by the bright reflecting surface of the upper face of the silver. When the lighting is perfectly straight, some of the rays passing through the slits (or white spaces) are reflected from the inner 340 TESTING OBJECTIVES WITH ABBE PLATE surface of the front lens back again upon the cover-glass, the silvered portion of which turns them back again into the objective, and thus fogs the dark lines. As the small illuminated area (caused by the pinhole iris) traverses the intermediate and especially the outer zone of the back lens of the objective, the colours of each border of the white line may slightly alter in some lenses, but in the very finest it remains nearly — if not actually — constant. This means that in many lenses the outer zone is not corrected quite so accurately as the rest: in point of fact it has appeared to the writer this zone is often slightly under-coxx^oXtA} The upper border of the white line with oblique light, we have already stated, shows the point of folding over of the spectrum, and thus indicates whether the ob- jective be over or under corrected ; but when using this exceedingly small point of light, the illumination is always so faint that it becomes very difficult to say whether the upper border is fringed with apple-green, a lighter yellow-green, a deeper green, or very dark green ; hence it will be found practically to be of more utility for a beginner, in this case, to be guided by the colour presented by the lower border of the white line instead — it being placed of course in the true diameter of the field. If this appears of a purple colour throughout the movements of the pinhole iris, the three zones are perfectly corrected ; if the purple becomes redder and redder, perhaps a distinct red, then the objective shows a slight ««flfer-correction ; whereas if it change to violet instead — or blue — then ^z^^r-correction is present. Sometimes the colours are violently different in the central intermediate and outer zones ; this is bad, for in a really fine objective, as before stated, there should be but little if any change — anyhow, not of that violent nature. Seeing the terms " under " and " over corrected " have not as yet been explained, it may be well at once, before proceeding further, to do so. It has been mentioned in the visually constructed objective that the position mostly chosen for the folding over of the spectrum is in the apple-green, say about the wave-length SSOO in the normal spectrum ; but if now the folding over takes place nearer the violet end, it is called under-coxr^c\Aox\, whilst if towards the red end, over-corre.c\!\ox\. To make what follows ' These terms of under and over correction will be explained very shortly. TESTING OBJECTIVES WITH ABBE PLATE 341 more easily understood, it is a convenient method to take a slip of paper some 8 in. in length, and to draw a line along it for 6 in., marking off seven dots at a space of i in. apart, as shown half size in Fig. 190. Commencing at the right-hand end of the line, let the follow- ing letters— R, O, Y, G, B, V, and UV— be affixed to the dots in succession. Midway between Y and G, at right angles to this line, let another be made, marking it with the words I « I 8| I UV V B G Y O R P'ig. 190. " Best Visual." A bending over of the slip of paper at this achromatising line plainly illustrates how Fig. 74 was obtained in theory, for it immediately indicates by mere inspection how the folding together of the different colours has caused the blending about which mention has been made ; in other words, it reveals the formation of the secondary spectrum. Let, now, three additional lines be drawn at right angles to the long horizontal one, the point at G being marked " slight a^i^^r-correction," the second at Y "slight i9f^r-correction," and the third at B, "photo correction." When a folding over of the slip is made at G — as occurs in slight under-coxxe.z\XQn — a union of yellow and blue and of orange and violet will follow, whilst it will be observed red and ultra- violet are left outstanding. The latter colour (UV) is so feebly perceived by the human eye that it may be left out of con- sideration for our present purpose. Hence when the white line in the Abbe plate illuminated by oblique light (in the manner prescribed) is looked at with an under-zoxr&c\.zA objective, its lower border will have a reddi.sh fringe, whilst its upper one w'ill have a pronounced green tint. With an iiz/^^-corrected lens, where the folding over takes 342 TESTING OBJECTIVES WITH ABBE PLATE place in the yellow, the slip of paper will now show, if bent at that position, a union of orange with green, and of red with blue, leaving violet outstanding; hence the lower margin of the white line will now exhibit a colour more nearly violet than purple, and its upper margin a fringe composed of almost a pure yellow. With a photographic correction (rarely to be met with in high powers, or indeed any over, say, a half-inch), where B is the folding-over point, the slip will indicate a union of violet with green, whilst yellow, orange, and red are left outstanding. Hence the upper border of the white line shows blue, and the lower one a mixture of the three colours yellow, orange, and red. Arranged in the form of a table for convenience of reference, these different colour-effects become as follows : Exhibition of Colours at Upper and Lower Borders of the Central White Line with Oblique Light obtained in the Special Manner described. Point of folding over. Upper border shows — Lower border shows- Visual correctioti of what is mostly Apple-green. Apple-green. Purple. called the highest order. Slightly under-zm- rected combination. Green. Green. Reddish purple. Slightly over - cor- rected combination. A purely photographic Yellow or very yellow-green. Blue. Yellow or very yellow-green. Blue. Very blue-purple or violet. Orange-red. , correction. It is evident from this table, and from what has been said, that when using oblique light in the manner described, the tints exhibited respectively by the upper and lower borders of the centrally placed white line afford most valuable information to the examiner of the objective. The colour exhibited by the upper border shows three things at one and the same time : (i) The colour in which the image is formed. (2) The colour having the shortest focus. (3) The point of folding over of the spectrum. TESTING OBJECTIVES WITH ABBE PLATE 343 Moreover, if this colour be yellow, it shows owr-correction. » ,, „ green, it shows «;^(/^r-correction. » J. ,, apple-green, it shows usual visual correction. » >, „ (5/»£, it shows a purely photographic correction. The colour exhibited by the lower border, if it be — Blue-purple or blue shows over-zoxxe.c\!\ox\. Reddish purple to red „ 2i!« x 750. ' Fig. 3.— COSCINODISCUS OPTHALANTHUS. The central portion of the diatom is shown in the centre of the photograph, and the arrangement of the specimen is such that one focus of the object is seen on the right hand and the other on the left. It may be compared with Fig. i, Plate VIII. Photographed with a Reichert 2-mm. apochromat N.A. 1-35 X 750- PLATE IV. Fig. i. Within the Focus. FiS- 3- Kit;. 2 PLATE V. NAVICULA LYRA. This is a favourite specimen to examine the colour-correction of a semi-apochromatic objective. When well made and taken at the moment of focus, but little colour of the secondary spectrum should be visible ; but the diatom appears tinted according to the colour having the shortest focus : apple-green is that mostly chosen. With an apochromat this tinting should be entirely lost, and the valve ought to look the purest white, whilst the dots are colourless also. With those apochro- mats that exhibit the tertiary spectrum (see text, page 365) the dots may show a little colour, but it is open to question whether this type of combina- tion is not more perfect than that in which such exhibition is entirely absent. To test its superiority in definition monochromatic illumination is necessary. No fuzziness whatever should be present, and the dots ought to appear very neatly defined and crisply i-endered. Photographed with a Zeiss 3-mm. apochromat N.A. v\o x 500 and subsequently enlarged x 2. PLATE V. PLATE VI. Fig. I— AMPHIPLEURA PELLUCIDA. In dots of about r^-uhn; of an inch diameter. These are very difficult to see without the use of oblique green light, even when employing the finest objective. A first-class semi-apochromat should then show the dots furnishing an image almost as good as that afforded by the apochromat, although a certain distinction can in most cases be recognised, and the illumination is certainly less than with the higher corrected combination. This photograph was taken (using blue light) with a Zeiss 2-mm. apochromat N.A. 140 x 2800. Fig. 2.— PLEUROSIGMA ANGULATUM ; the white-hexagon focus. In some parts where the upper layer of the diatom is denuded, the " black- dot effect" can be seen. Postage-stamp fracture is visible in the little lozenge and elsewhere at different places. The image with a good objective of either variety ought to be clean, sharp and clear, with but a very moderate closing of the substage iris diaphragm. Photographed with a Leitz 2-mm. apochromat N.A. i'3o x 2000. Fig. 3.— PLEUROSIGMA ANGULATUM showing in the centre of the photograph minute (apparent) apertures surrounded by a limiting boundary which is semi-transparent and not so black as represented in the p>revious ■fncture. It is open to question whether this is not really the correct focus of this difficult diatom. The tube-length may require attention, as the perfectness of rendering and the cleanness of the image (its freedom from fog and greyness) are the real use of this test. Poor combinations will not furnish an image anything approaching the beauty shown in this photograph. Taken with a Reichert's 2-mm. apochromat N.A. i'35 x loop. PLATE VI. Fig. I Fin Fi-. 2. PLATE VII. PLEUROSIGMA ANGULATUM. An enlargement of a photograph ^ made with a 2-mm. apochromatic objective by Leitz of N.A. i'35 to show the (probably) spurious markings which can be seen in the walls forming the hexagons when a certain focus is obtained. This photograph has not been taken with the aid of any specially shaped substage diaphragm or other arrangement, but merely in the ordinary manner at one particular focus. We have usually noticed that to see these peculiar diffraction effects well shown the specimen must be mounted in realgar, and it is also necessary for the objective to be one of the finest computation and workmanship. If the components of the combination be not accurately centred or if the objective be poorly corrected, the image will not bear enlargement anything equal to the photograph as shown in this repro- duction ; about x gooo. PLATE VII. PLATE VIII. Fig. I.— COSCINODISCUS ASTEROMPHALU.S— like the Opthalan- thus — has two distinct planes of focus, both being illustrated in Fig. 3, Plate IV. In this photograph however only one is shown, the situation selected being a point midway between the centre of the valve and its periphery, where specimens of this type are all for the most part flatter than elsewhere. Photographed with a Zeiss 3-mm. apochromat N.A. i"40 x 1000. Fig. 2.— PODURA SCALE. With a well-marked specimen a good apochromatic objective shows a constriction around the neck or upper part of the white interior of the " note," the white portion itself tapering off insensibly to a point at about the lower two-thirds of the note itself If the objective be semi-apochromatic, much the same appearances should be present, especially if used with green light. Badly corrected combina- tions in the preferred colour even then render the white interior very fluffy as a rule, and indefinitely defined. Photographed with a Zeiss 3-mm. apochromat N.A. r4o x 1000. Fig. 3. A portion of Fig. 2 enlarged. Fig. 4.— SURIRELLA GEMMA. " It is somewhat difficult to obtain a really flat specimen mounted in realgar. The dots should appear perfectly sharp and free from fuzziness at their edges. Photographed with a Zeiss 3-mm. apochromat i'40 x 3000. Fig. 5.— FRUSTULE SAXONICA or VAN HEURCKIA CRASSI- NERVIS. The white dots are exceedingly minute. A good apochromat shows them well defined with oblique white light, and a semi-apochromat almost equally well with green illumination. Photographed (green light) with a Zeiss 2-mm. apochromat N.A. 140 X 1200. [Figs. I, 2, 3 and 4 have been kindly lent by the Scientific Press from the author's book Photomicrography. ] PLATE VIII. Fig. 4. l-'ig- 5- PLATE IX. Fig. I.— NITZSCHIA OBTUSA. This diatom is a searching test for a good 2-mm. apochromat or a fine semi-apochromat of the same focus. The strias are fine, about 26 or 27 to the 0003937 of an inch (Van Heurck), and there are about 1 5 dots in each. Ahhough these can be seen with almost any reasonably good objective of the focus mentioned with direct white light, still to show them sufficiently separated and discretely defined •to permit of their being counted with ease requires the use of an objective that is well corrected and free from aberrations. Consequently a running together of the dots betokens a poor specimen of the optician's art. With an apochromat, the dots when focussed for the white effect should appear distinctly white— like pearls — and the background somewhat grey ; but with a semi-apochromat they will be coloured by the secondary spectrum, which spoils their distinctness. With a green screen however they should be shown almost as distinct with either class of objective. The dots in the black-focus effect should look (with a good specimen) as if they had been punched out of black paper and laid upon the surface of the diatom. The apochromat must be expected to show them better than its rival when using white light, but with oblique green illumination the difference should not be anything like so striking. Photographed with a Reichert 2-mm. apo- chromat N.A. r35 X 1240. Fig. 2.— BREBISSONIA BOECKII. This is a remarkably delicate test, the exceedingly small dots constituting the costas being very difficult to resolve distinctly. With an apochromat and suitably adjusted oblique light (white) and a x 12 ocular they should be plainly visible in parts of the diatom, but with* a semi-apochromat, unless it is a specially fine one, definition usually suffers more especially on account of the interfering effects of the secondary spectrum, although not from that cause entirely. With oblique green illumination the image produced by the cheaper type of combination should be vastly improved, but it usually even then is inferior to that furnished by the more highly corrected objective. This diatom offers, it can be understood, a good test to ascertain the fineness of the image in the preferred colour of any semi-apochromat. Photographed with a Leitz 2-mm. apochromat N.A. 1-35 x 1440. Fig. 3.— SYNEDRA CRYSTALLINA. When using white light and X 18 ocular, to break up the transverse strias into dots requires a well- corrected objective, with semi-apochromats especially. The black dots do not ever look so " punched out " as in the case of the Nitzschia obtusa, even with the best apochromats, unless green light be used, and even then they do not possess that marked circumscribed effect so particularly noticeable in that object. A poorly made semi-apochromat will be thrust out of its trials with this test-object, for the dots may appear as if sur- rounded by a thick fog. Photographed with a Koristka N.A. I's-mm. apochromat x 1200. Fig. 4.— CYMBELLA GASTROIDES (small variety). There are not many diatoms that exhibit conical-shaped secondary markings such as can be seen in parts of this object. These, as well as others of differing form— some being more or less rectangular— should appear, when viewed with a first-class objective, as if "lifted out" from the background, which ought not to exhibit a trace of fluffiness or fog. Photographed with a Hartnack 2-mm. apochromat N.A. 1-40 x 1440. PLATE IX. i--ig. I. I'lg- 3- •ig- 4- PLATE X. NAVICULA SMITHII. The double row of circular dots in each costa should be well defined, anyhow in certain portions of the field of view. Van Heurck says : " The exact nature of these markings was not known until the introduction of the homogeneous objective." We have never been able to obtain an objective that will show the dots better than those exhibited in the photograph. A poor semi-apochromat — even with green light — gives an exceedingly foggy image, the dots being perhaps hardly visible. The test, though a severe one, is of a very reliable nature. As the valve is very saucer-shaped, it is impossible to photograph it in its entirety at one plane of focus. Photographed with a Koristka 1'5-mm. apochromat N.A. i'4o x 1200 and subsequently enlarged x 2, PLATE X PLATE XI. Fig. I.— NAVICULA FIRMA. The exceedingly small dots in the floor of this diatom ought to appear discretely separated, free from all fuzziness and crisply defined. As the valve is not flat, both the white and the black dot " effects " are visible at the same focus in different parts of the specimen. Photographed with a Reichert 2-mm. apochromat N.A. i'35 X 960 and subsequently enlarged x 2. Fig. 2.— EPITHEMIA TURGIDA. The double row of irregular-shaped markings in this diatom, when magnified sufficiently, should appear well " lifted out " above the floor ; and there should be no flufifiness of the background. The valve is so bent as to make it almost impossible to photograph satisfactorily, and it is not easy to be certain which is the correct focus, for at one plane the dots appear circular, at another hemi- spherical, whilst irregular-shaped ones also can be seen scattered about. The cleanness and whiteness of the entire object make it a good one to ascertain the type of the colour correction of a semi-apochromat, and the perfection of the correction in an apochromat, Photographed with a, Leitz 3-mm. apochromat N.A. i'35 x 1300, X < PLATE XII. Fig. I.— NAVICULA RHOMBOIDES. This is an old but still very favourite test-object with many opticians to test the type of colour correction of a semi-apochromat, and also the perfection brought about in the computation and workmanship of an apochromat. The black and white dot "effects " are visible with this diatom by focussing the different planes. The dots at the black focus should be intensely black, and the whole diatom should look particularly brisk and bright, with an entire absence of all traces of fluffiness when using a well-made objective of high aperture. So too the white dots ought to appear like pearls laid upon the surface of the valve, no appearance of fog being visible. To objain perfect definition with a semi-apochromat it may be necessary to use green light to remove the secondary spectrum. Photographed with a Zeiss 3-mm. apochromat N.A. I '40 X 1200. Fig. 2.~CYMATOPLEURA SOLEA. A most useful and delicate test- object. If looked at with a three-quarter cone and a x 12 ocular — direct white light — faintly marked transverse striae should just be visible when employing a fine semi-apochromat or an apochromatic objective. Oblique white light reveals these striations — towards the median line particularly — as abruptly interrupted. Each striation should be so distinctly defined that it can be seen to terminate in rather a round-shaped extremity. An inferior combination will most likely fail to show the blunt ends, or perhaps may even fail to show the striations at all, the floor of the valve appearing a foggy desert void of detail. With a three-quarter cone (which is usually necessary) this object is a very searching test, and may enable the microscopist to differentiate between objectives which otherwise appear to perform equally well. Photographed with a Koristka i"5-mm. apochromat N.A. I -40 X 1200. Fig. 3.— EUPLEURIA PULCHELLA (Arnot). This diatom is not frequently mentioned in the literature of the subject. When examined with direct white light (the outer zone being cut off by the iris substage diaphragm) it appears to be divided into about eighteen sections, most of which are quadrilateral, although a few are triangular in shape. Each section, if the upper surface be carefully focussed, presents numerous extremely minute dots crowded together. Even with full aperture the finest of apochromats will give faint though distinct indications of these dots. With oblique white illumination they should appear very distinctly separated with both types of objectives, green light of course rendering their presence far better. Second-rate combinations will show the dots, it is true, but they appear melted together and far from distinctly separated. Third-class objectives may fail to reveal their presence even with oblique green illumination. This diatom is also a very good test for ascertaining the quality of the definition in the outer part of the field of view. If the diatom be placed at the extreme edge of the field, and an objective be used in which the sine law has not been properly fulfilled, no amount of focussing ivill bring the dots to a focus. The quality of the definition affords the microscopist a good means of classifying objectives that otherwise perform very sensibly equal. PLATE XII. Fig. I. Fig. 2. Fig. 3- PLATE XIII. Fig. I.— NITZSCHIA SIGMA is a very small and exceedingly trans- parent diatom with minute dots. These should be completely and very distinctly resolved by a first-class 2-mm. objective with the iris diaphragm partially closed, a test more especially for central and medial zones. Photographed vifith a Powell & Lealand ^Vth apochromat N.A. i'4o X 1440. Fig. 2.— NITZSCHIA SCALARIS. This diatom is an exceedingly good test for a 4-mm. (^th) objective, whether an apochromatic or semi- apochromatic combination. The dots should not only be seen, but they should be distinctly separable, provided the ocular be of sufficient power and the specimen a good one. No oblique light should be necessary, and (for the test to be critical) care must particularly be taken that the light from the mirror does not impinge with any obliquity upon the substage condenser. Photographed with a Zeiss 4-mm. apochromat N.A. o'95 x 8co. Fig. 3.— NITZSCHIA CURVULA. Another test-object for a 4-mm. almost as difficult as the preceding. The dots in this case are usually exceedingly faint, hence if the combination be not well corrected, the resulting fluffiness may quite hide the secondary markings. Photographed with a Leitz 4-mm. apochromat N.A. o'95 x 1000. Fig. 4.— NITZSCHIA MAXIMA. Although the dots in this diatom are resolved fairly easily, a good objective is required to show them without the use of green light, as displayed in the accompanying photomicrograph. There should be an entire absence of all haze, which is readily visible if the correction of the combination be of a feeble character. Photographed with a Reichert 4-mm. apochromat N.A. o'95 x 720. PLATE Xlli. Fig. I. Fig. 2. Fig- 3- Fig. 4- PLATE XIV. Fig. i.-PLEUROSIGMA ANGULATUM : the "black-dot" appear- ance. To show this focus well, with a 4-mm., the correction of the combination must be very good, and the better the objective the less the cutting down by the iris required. This is a point to be recollected. In the accompanying photograph the diaphragm was only closed a very small amount. Photographed with a Koristka 4-mm. apochromat N.A. o'95 X 1000. Fig. 2.— NITZSCHIA OBTUSA. This diatom, before mentioned as a good test for a 2-mm., is also a very valuable one for a ^th. Using oblique light it should be just possible to see the lines distinctly separated, if the combination be a fine one ; but second-rate objectives will almost certainly fail in this respect. It is a most searching test, and will prove the superiority of one combination over another when many other tests fail. Owing however to its great transparency and the theoretical limit of resolving power being somewhat nearly reached, the valve should be a well-marked one. Photographed with a Zeiss 4-mm. apochromat N.A. 0'95 X 360 and subsequently enlarged x 3. PLATE XIV. Fie. I. Fig. PLATE XV. VAN HEURCKIA LOUISIANA. An excellent test-object for a 6-mm. objective, whether apochromatic or semi-apochromatic. Presuming the combination be one of high numerical aperture and used with a x 12 ocular, the faintest signs of secondary markings should be visible even at full aperture anyhow at the edges of the valve. With direct light and a small amount of cutting down with the iris substage diaphragm (not less than about 7), the transverse striae should be visible and well defined when the light is made oblique and green illumination employed (see photomicrograph). When the light is distinctly oblique and turned in the correct azimuth, the lines ought immediately to appear broken up into distinctly defined dots. A considerable difference of rendering will be noticed by different objectives, especially between the semi-apochromatic and the true apochromatic. The apochromatic by Zeiss with which the accompanying photomicrograph was taken (and subsequently enlarged twice) is perhaps the finest quarter it has been our privilege to test, but several semi-apochromats approach it very nearly, notably those by Bausch & Lomb, Swift, and the Holoscopic by Watson. PLATE XV PLATE XVI. Fig. I.— PROBOSCIS OF THE BLOW-FLY. A common test for objectives of low power such as a i or 2 in. The best combination shows the object crisply defined, without a trace of fog, especially if the iris be closed a very small amount. The "blacks" should look exceedingly black, and not as if dusted over with a fine white powder or covered with a fog. No halo about the tracheae should be observable. If the magnification be sufficient, the minutest hairs between the lobes should " rise up " as if growing from parts beneath. When properly illuminated no double tips to the hairs ought to be seen, and the large hairs should not show with an apochromat anything but a trace of colour along their edges. Colour may be seen to a limited amount with the best semi-apochromat. This object is also a very good one for testing the size and flatness of field in a low-power objective, and the Frontispiece (taken with a Holoscopic 24-mm. semi- apochromatic N.A. '24 and two green screens) illustrates the perfection arrived at in a modern combination. Photographed with a Zeiss 24-mm. apochromat N.A. o'3 x 600. Fig. 2.— THE TONGUE OF THE CRICKET. A common test- object for very low powers such as a 2 or 3 in. The remarks given above as to the absence of fog and crispness of image equally apply to this specimen. The curved linear markings should be distinctly and briskly defined. Photographed with a Wray photographic 2-in. objective x 20. [Figs. I and 2 have been kindly lent by the Scientific Press from the author's book PhotOTnicrography. ] PLATE XVI. Fig. I. Fig. 2