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PHOTOGRAPHIC 
 
 OPTICS. 
 
PHOTOGRAPHIC OPTICS; 
 
 INCLUDING THE DESCRIPTION OF 
 
 LENSES AND ENLARGING APPARATUS. 
 
 By D. VAN MONCKHOVEN, 
 
 DOCTOR OF SCIENCE. 
 
 WITH FIVE PLATES AND EIGHTTSEVEN WOODCUTS. 
 
 TRANSLATED FROM THE FRENCH. 
 
 Ons, 
 
 Hh 
 
 5AO ■ 
 lb 
 I6G7 
 
 LONDON: 
 
 ROBERT HARDWICKE, 192, PICCADILLY. 
 
 1867. 
 
PRINTED BT WILLIAM CLOWES AND SONS, STAMFORD STREET, 
 AND CHARING CROSS. 
 
 TOE GETTY CENTER 
 
 LIBRARY 
 
PREFACE. 
 
 To show clearly the principles on which the optical instru- 
 ments used by photographers are constructed is the object of 
 this little volume. Treatises on physics — nay more, treatises 
 exclusively on optics — are silent about these instruments, and 
 about terms — such as chemical focus , depth of focus, distortion , 
 &c. — which are in daily use among photographers. This is 
 because modern optics has been hitherto confined to the 
 study of telescopic and microscopic lenses, which never, 
 like photographic lenses, receive pencils very oblique to 
 their principal axis. The consequence is, that the aberrations 
 which must be destroyed in these objectives, namely, spherical 
 aberration and chromatic aberration , have alone been studied. 
 At most, the other aberrations, — namely, distortion , curvature 
 of the field, and astigmation , — have been made by a few authors, 
 such as Airy and Gauss, who have studied them in connexion 
 with eye-pieces , the subject of some rare memoirs, of which, 
 moreover, no mention is made in any work on physics or 
 optics. 
 
 This volume is divided into two books ; the first (and 
 this is the principal one) the optics of photographic objec- 
 tives, the second that of enlarging apparatus. 
 
 The first book is divided into chapters in which we de- 
 scribe the principles of general optics. We dwell particu- 
 larly on points imperfectly known, or directly related to pho- 
 tography, — such as the chemical action of light ; the images 
 produced by small apertures ; the absorption of light by 
 
VI 
 
 PREFACE. 
 
 transparent media; the reflecting power of mirrors; the 
 position of maximum chemical action in the spectrum on 
 substances sensitive to light ; photographic achromatism ; the 
 manufacture of lenses ; the law of conjugate foci, and the size 
 of images at the foci of lenses ; the determination ofthe abso- 
 lute focus of simple lenses and of optical combinations of 
 several lenses, &c. 
 
 The five aberrations of most interest have been the object 
 of our especial care. 
 
 A radiating point (of homogeneous colour) being placed at 
 infinity, and in the axis of a convergent lens, emits parallel 
 rays, which on emerging from the lens do not meet at one 
 point in the axis ; and therefore the image of the point is 
 surrounded by a circle of diffused light, called the circle of 
 spherical aberration. If the point is placed some degrees out 
 of the axis, the circle of aberration becomes elliptical ; and 
 if the point is very obliquely placed, its image takes the form 
 of a comet. We have carefully examined the conditions 
 necessary to reduce this spherical aberration to the minimum 
 by the employment of the diaphragm, or better by joining 
 to the convergent lens a divergent lens, with appropriate 
 radii of curvature, which makes the combination aplanatic, 
 that is, free from spherical aberration along its axis. 
 
 If the radiating point is not of homogeneous colour — if, for 
 instance, it is white — for one ray incident on the lens there 
 are several refracted rays of different colours which cut the 
 axis at different points, — a phenomenon which has received 
 the name of chromatic aberration , and which is corrected by 
 joining to the convergent lens a divergent lens formed of 
 another kind of glass, and with suitable radii of curvature. 
 But a lens achromatic for incident rays parallel to its axis, 
 cannot be so for rays oblique to this axis ; and the optician 
 has therefore to solve the problem of reducing the chromatic 
 
PREFACE. 
 
 All 
 
 aberration to tlie minimum for the latter while annulling it 
 for the former, a problem which we shall examine in detail. 
 
 If instead of a radiating point placed at infinity, we take, 
 for example, a plane situated at infinity, and if we reduce the 
 lens to its optical centre, we shall find that the image, at 
 the focus of the lens, cannot be received on a plane surface — a 
 curved surface being necessary to receive it : this is the aber- 
 ration of form, or the curvature of the field. Further, the two 
 meridians of the lens have, for pencils oblique to its axis, 
 different focal lengths, and thence two different fields of curva- 
 ture — an aberration which has received the name of astigmation. 
 
 Lastly, another aberration results from the thickness of the 
 lens, and from the position of the diaphragm, the effect of 
 which is to render the straight lines of the object to be 
 reproduced curved in the image, — an aberration which has 
 received the name of distortion. 
 
 All these aberrations are called positive when they are 
 applied to single convergent lenses, and negative to single 
 divergent lenses. All are corrected in an optical combina- 
 tion of divergent and convergent lenses (which in practice is 
 always convergent) ; but the corrections may be excessive 
 or insufficient, and then the aberrations may be, in a con- 
 vergent optical combination, either positive or negative. 
 
 The study of aberrations is followed by that of photo- 
 graphic lenses, which we divide into two classes, — aplanatic 
 objectives, which give sharp images over a small field with 
 their entire aperture ; and non-aplanatic objectives, which give 
 sharp images only on the condition of being limited by a 
 diaphragm to a very small fraction of their aperture, but 
 which generally include a large angle, and consequently give 
 a sharp image over a large field. 
 
 Many new non-aplanatic objectives have been produced 
 in late years, but we positively condemn their introduction 
 
Vlll 
 
 PREFACE. 
 
 among photographers, and regard them, not as a step in 
 advance, but the reverse, and for the following reasons : — 
 
 The practice of photography has established that, when the 
 image at the focus of a lens is wanting in intensity, the pho- 
 tographic reproduction of this image is itself wanting in 
 relief, the foregrounds being too black, the objects situated 
 in the horizon confounded with the sky, and the clouds in 
 the sky replaced by a plain ground of uniform tint : the 
 proof, in a word, is wanting in aerial perspective, and, if it be 
 a portrait, in vigour and relief. For, to give sharp images 
 non-aplanatic objectives require very small diaphragms, and 
 generally of from £ to / being their focal length : hence 
 an insufficient intensity in the image and the defect which 
 we have just pointed out. But, exempt from distortion, and 
 including a considerable angle, they are useful in some special 
 cases, such as the reproduction of cartes , buildings situated a 
 very short distance, or landscapes and buildings strongly 
 illuminated by a powerful sun. 
 
 Aplanatic objectives, under the head of which rank the 
 triplet , include a less angle, but do not require diaphragms 
 exceeding and therefore they give more artistic photo- 
 graphic proofs, in which the foregrounds and the horizons 
 are well brought out, and the skies have clouds. If the light 
 is insufficient, they are employed with a larger diaphragm ; 
 and the sharpness of the image is not destroyed as with non- 
 aplanatic objectives, but only limited to a smaller field. 
 They can be used for portraits in the open air, groups, and 
 animated scenes, with their entire aperture, — an advantage 
 which is invaluable in practice. Lastly, the angle they 
 include, being between 50 and 60 degrees, is more than suffi- 
 cient, because if this angle is more considerable the effect of 
 the perspective is doubtless more astonishing than agree- 
 able. 
 
PEEFACE. 
 
 IX 
 
 In onr opinion, therefore, the nse of non-aplanatic objectives 
 — -such as the single lens , the globe lens , Mr. Ross's doublet , and 
 that of M. de Steinheil — should be abandoned (except in some 
 special cases which we have enumerated above) for that of 
 aplanatic objectives among which the triplet is the best, as 
 being free from distortion. 
 
 For portraits the only possible lens is PetzvaVs doublet , but 
 we are able to state that this form itself will soon be aban- 
 doned for a combination recently invented by M. de Steinheil 
 of Munich, which is free from spherical and chromatic aber- 
 rations both along its axis and obliquely to it, from distortion 
 and from astigmation, and which, further, reduces the curva- 
 ture of the field to a much smaller quantity.* This lens, 
 the fruit of immense and ingenious calculations, will not fail 
 to attract the attention of all photographers, as in every 
 respect it deserves to do. 
 
 It is not enough to be in possession of good objectives, it 
 is necessary to know how to use them, — a thing about which 
 ninety-nine photographers out of a hundred are in ignorance. 
 To use a lens improperly is to produce portraits false in per- 
 spective, buildings and houses falling into the street, &c. 
 We point out, in a special chapter, how an objective should 
 be employed and under what circumstances. 
 
 The second book of this work treats of enlargements. In 
 it we examine the history of enlarging apparatus, the theory 
 of them, their setting-up, their management, and the appli- 
 cation to them of the heliostat and of artificial light. 
 
 We therein clearly establish the principle that the origin 
 of the want of sharpness in the images produced by most 
 enlarging apparatus is due to the circle of aberration of the 
 
 * The author of this work is in possession of one of these new objectives 
 through the courtesy of M. de Steinheil. These objectives are not as yet 
 on sale. 
 
X 
 
 PREFACE. 
 
 condensers which illuminate the negative to be enlarged, the 
 effect of this being to cause diffraction-blurrings or multiple 
 lines in all the sharply defined outlines of the enlarged image. 
 By destroying this circle of aberration, either by the em- 
 ployment of condensers of small diameter, or of aplanatic 
 condensers, the production of these diffraction-blurrings is 
 prevented, and the enlarged images then become admirably 
 sharp. 
 
 Such are the principal contents of this little volume, 
 which is not, indeed, to be considered as more than the 
 summary of a more complete work ; but which, we hope, 
 will be of some use to the amateur, the professional pho- 
 tographer, the physicist, the optician, and all others in- 
 terested in the progress of modern optics. 
 
 D. YAN MONCKHOYEN, 
 
 Doctor of Science. 
 
CONTENTS, 
 
 BOOK I. 
 
 PHOTOGKAPHIC LENSES. 
 
 CHAPTER I. — Preliminary Ideas. 
 
 PAGE 
 
 light— Optics 1 
 
 The Sources of Light — tlieir In- 
 tensity ... 2 
 
 Chemical Action of Light 3 
 
 Movement of Light in Straight 
 
 Lines 4 
 
 Umbra and Penumbra 5 
 
 Images produced by Small Open- 
 ings — Effects of Diffraction ... 5 
 
 PAGE 
 
 Opaque, Translucent, and Trans- 
 parent Bodies 6 
 
 Absorption of Light by Trans- 
 parent Media 7 
 
 Reflection of Light ..= 10 
 
 Mirrors and their Reflecting 
 
 Power 10 
 
 Adjustible Mirrors 12 
 
 Heliostats 16 
 
 CHAPTER II. — Refraction of Light. 
 
 Refraction of Light 16 
 
 Law of Refraction 17 
 
 Index of Refraction 17 
 
 Refraction by Transparent Plates 
 with Parallel Surfaces 18 
 
 Refraction by Prisms 19 
 
 Graphical Construction of a Ray 
 
 refracted by a Prism 20 
 
 Calculation of a Refracted Ray . . 21 
 
 CHAPTER III.— Chromatics. 
 
 The Solar Spectrum 23 
 
 Lines of the Spectrum 27 
 
 Chemical Action of the Spectrum 
 
 — Extra-Prismatic Rays 27 
 
 On the Colour of Bodies 29 
 
 Dispersion 29 
 
 Achromatic Prisms ... ... ... 31 
 
 Photographic Achromatism, or 
 Actinism 34 
 
 CHAPTER IV.— Lenses. 
 
 Section I . — Definitions concerning Lenses. 
 
 Convergent and Divergent I Principal Axis and Optical Centre 
 Lenses 35 J of Lenses 36 
 
12 
 
 CONTENTS. 
 
 Section II. — Manufacture of Lenses. 
 
 PAGE 
 
 Manufacture of Optical Glass ... 37 
 The Grinding Tools fitted for 
 Working the Surfaces of Lenses 40 
 
 PAGE 
 
 Smoothing and Polishing of the 
 
 Surfaces of Lenses 42 
 
 Centering and Mounting of Lenses 44 
 
 Section III. — Law of Conjugate Foci, and the Magnitude of Images at the 
 Focus of Lenses. 
 
 Assimilation of Lenses to Prisms 47 
 Calculation of the Focal Length 
 of Lenses — Principal Focus 
 
 and Conjugate Focus 48 
 
 Formulae determining the Princi- 
 pal Focal Lengths of Lenses 
 for Kays parallel to the Axis... 51 
 Focal Length of Lenses 54 
 
 The Focal Plane 56 
 
 Experimental Determination of 
 the Absolute Focal Length of 
 
 Lenses 56 
 
 Determination of the Conjugate 
 Focus and of the Size of the 
 Image 58 
 
 CHAPTER Y. — Aberrations. 
 
 Definition of Aberrations 
 
 64 
 
 Section I. — Spherical Aberration . 
 
 Spherical Aberration, Lateral and 
 Longitudinal, Positive and Ne- 
 gative ' ... 65 
 
 Spherical Aberration varies with 
 the Aperture and Index of Re- 
 fraction of the Glass of the 
 
 Lens ... 66 
 
 Minimum of Spherical Aberration 67 
 Destruction of Spherical Aberra- 
 tion by the Diaphragm 68 
 
 Destruction of the Spherical 
 Aberration of a Lens by a 
 
 second Lens of contrary cha- 
 racter ... 69 
 
 Spherical Aberration of Pencils 
 Oblique to the Axis — Coma ... 71 
 Destruction of Aberration of Pen- 
 cils Oblique to the Axis 73 
 
 Effect of Spherical Aberration in 
 Photographic Objectives, and 
 
 how it is proved 74 
 
 Spherical Aberration serves to 
 divide Photographic Objectives 
 into two very distinct Classes .. 75 
 
 Section II. — Chromatic Aberration. 
 
 Visual Focus and Chemical Focus 76 
 Destruction of Chromatic Aber- 
 ration 77 
 
 Destruction of Chromatic and 
 Spherical Aberrations in 
 
 Lenses of large aperture ... 80 
 Chromatic Aberration of Pencils 
 
 Oblique to the Axis 81 
 
 Position of the Chemical Focus 
 as regards the Visual Focus ... 83 
 
 Section III. — Aberration of Form of the Image, or Curvature of the Field. 
 
 The Curved Image 84 I The Diaphragm .89 
 
 Depth of Focus 85 Destruction of Aberration of 
 
 Effect of Depth of Focus on the Form 92 
 
 Curvature of the Field 88 
 
CONTENTS. 
 
 13 
 
 Section IV. — Aberration of Thickness of Lenses, or Distortion. 
 
 page | PAGE 
 
 Distortion 96 I Destruction of Aberration of 
 
 1 Thickness 99 
 
 Section V. — Astigmation, or Aberration of Position of Lenses. 
 
 Experimental Procedure to de- 
 monstrate Astigmation ... 102 
 Theoretical Explanation of As- 
 tigmation 103 
 
 Reduction of Astigmation to the 
 
 Minimum ... 104 
 
 Calculation of the Primary Fo- 
 cus and Secondary Focus ... 104 
 
 CHAPTER VI. — Description of Photographic Objectives. 
 
 Division of Objectives into Non-Aplanatic and Aplanatic 112 
 
 Section I. — Non-Aplanatic Objectives. 
 
 Single Combination (for Land- 
 scapes) 113 
 
 Mr. Dallmeyer’s New Single 
 
 Objective 120 
 
 The Globe-Objective or Globe- 
 Lens ... 124 
 
 Mr. Sutton’s Panoramic Lens... 129 
 The Periscope of M. A. de 
 
 Steinheil 130 
 
 The Doublet of Mr. Thomas 
 Ross 133 
 
 Section II. — Aplanatic Objectives. 
 
 The Orthoscopic Lens ... ... 134 I The Triplet 141 
 
 The Double Portrait-Lens . . . 136 { 
 
 CHAPTER VII. — The Employment of Photographic Objectives. 
 
 The Camera ... 145 
 
 The Focussing 146 
 
 Calculation of the Time of Ex- 
 posure 148 
 
 Trial of the Chemical Focus of 
 
 the Objective 149 
 
 The Employment of the Objec- 
 
 tive for Taking Portraits ... 150 
 Reproduction of Landscapes ... 151 
 Architectural Reproductions ... 152 
 Reproduction of Engravings, 
 Drawings, Maps, Pictures, 
 Photographic Proofs, &c. . . . 153 
 
14 
 
 CONTENTS. 
 
 BOOK II. 
 
 APPARATUS FOR ENLARGEMENTS. 
 
 CHAPTER I. — On the Negative intended for Enlargement. 
 
 Section I. — The Optical Apparatus suitable for producing a very small , 
 perfect Negative . 
 
 PAGE 
 
 Influence of the Focal Length 
 
 of the Objective 156 
 
 Influence of the Diameter of the 
 
 Objective 157 
 
 Apparatus suitable for Portrait- 
 
 PAGE 
 
 Negatives 158 
 
 Apparatus suitable for Land- 
 scape-Negatives .158 
 
 Self-acting Camera of M. Bertsch 158 
 
 Section II. — The Photographic Process. 
 
 The Glass 159 | The Process 160 
 
 CHAPTER II.— History and Summary Description of thf 
 Apparatus for Enlargements. 
 
 Section I. — Woodward's Apparatus and its Modifications. 
 
 Modifications introduced into the . I Solar Camera -without a Reflector 166 
 Solar Camera of Woodward... i.65 | Solar Camera of M. Liebert ... 167 
 
 CHAPTER III. — Theory of the Formation of the Enlarged 
 Image in Woodward’s Apparatus. 
 
 Theory of M. Claudet ... ... 170 I M. A. Thouret’s Observations... 174 
 
 Observations of M. Bertsch ... 171 | Theory of M. Foucault 174 
 
 CHAPTER 1Y. — Imperfections of Wood ward’s Apparatus. 
 
 Blurs of Diffraction produced by Imperfections of the Objective. . . 187 
 
 the Circle of Aberration of Suspension of the Negative ... 189 
 
 the Condenser 177 
 
CONTENTS. 
 
 15 
 
 CHAPTER V.— The 
 
 PAGE 
 
 Differences between it and the 
 ordinary Solar Camera ... 190 
 
 CHAPTER YI. — Description and 
 
 RATUS, AND IN GENERAL OF ALL 
 
 The Premises intended for the 
 
 Apparatus 198 
 
 Description of the Adjustible 
 
 Mirror 200 
 
 Setting-up of the Adjustible 
 Mirror 208 
 
 Dyalitic Apparatus. 
 
 PAGE 
 
 Summary Description of the 
 Dyalitic Apparatus 190 
 
 Setting-up of the Dyalitic Appa- 
 Apparatus for Enlargements. 
 
 Description of the Solar Camera 205 
 Setting-up of the Solar Camera . 207 
 
 The Negative-Holder 208 
 
 Description of the Proof Frame 209 
 Setting-up of the Proof Frame . 212 
 
 CHAPTER VII. — The Management of the Enlarging Apparatus. 
 
 Management of the Adjustible 
 
 Mirror 213 
 
 Adjustment of the Negative ... 214 
 
 Adjustment of the Lens and the 
 Frame — Focussing the En- 
 larged Image 215 
 
 CHAPTER VIII. — The Setting-up the Enlarging Apparatus in 
 
 Winter. 
 
 Alterations to be made in the setting-up of the Pieces constituting the 
 Apparatus 217 
 
 CHAPTER IX. — Setting-up of the Moveable Dyalitic • 
 Apparatus. 
 
 Description of the Apparatus ... 218 | Management of the Apparatus . 219 
 
 CHAPTER X. — Application of the Heliostat to Enlarging 
 Apparatus. 
 
 August’s Heliostat 221 
 
 The Heliostat of M. Leon Fou- 
 cault 221 
 
 Fahrenheit’s Heliostat modified 
 
 by M. Van Monckhoven 
 Management of the Heliostat 
 Setting the Heliostat 
 
 225 
 
 230 
 
 230 
 
 CHAPTER XI. — Setting-up of the Heliostat with the 
 Enlarging Apparatus. 
 
 Section I . — Apparatus inclined to the Horizon. 
 
 Description of the Apparatus ... 234 1 Management of the Apparatus .. 238 
 Setting the Apparatus 236 | 
 
16 
 
 CONTENTS. 
 
 Section II. — Apparatus with the Heliostat of Two Mirrors. 
 
 PAGE 
 
 Application of the Heliostat to 
 Apparatus with ordinary Ad- 
 justable Mirror 239 
 
 PAGE 
 
 Operations preliminary to the 
 setting-up the Heliostat ... 240 
 Application of the Heliostat . . . 241 
 
 Section III. — Another Disposition of the Apparatus with the Heliostat of 
 Two Mirrors. 
 
 Description of the Apparatus ... 243 I Management of the Apparatus .. 246 
 Setting the Apparatus 245 ( Site of the Apparatus 246 
 
 CHAPTER XII. — The Parallel Solar-Light Apparatus of 
 M. Bertsch. 
 
 The Parallel Solar-Light Apparatus of M. Bertsch 248 
 
 CHAPTER XIII. — Indirect Enlargement by the Sun or by 
 Diffused Light. 
 
 Inferiority of this Method to the 
 
 direct Method 250 
 
 Conversion of the original Ne- 
 gative into a Positive by 
 Transparency • 251 
 
 Enlargement of the Positive by 
 means of the enlarging Appa- 
 ratus 252 
 
 Enlargement of the Positive by 
 the Camera Obscura 253 
 
 CHAPTER XIV. — Application of Artificial Light to 
 Enlarging Apparatus. 
 
 Necessity of a Light of very 
 great brilliancy within very 
 
 small Surface 254 
 
 Disposition of the Optical Appa- 
 
 ratus 256 
 
 Choice of the Photographic Pro- 
 cess 258 
 
THE 
 
 PRACTICAL OPTICS 
 
 OF 
 
 PHOTOGRAPHY. 
 
 BOOK I. 
 
 PHOTOGRAPHIC OBJECTIVES. 
 
 CHAPTER I. 
 
 PRELIMINARY IDEAS. 
 
 Light.- — Optics. — When we place our hand near a stove, 
 we experience a peculiar sensation which we call heat ; when 
 our ear perceives a sensation, we say it is produced by a sound 
 or noise; so in like manner, if we distinguish the colour 
 and outline of an object, it is because this object sends us 
 lights for in darkness we do not even recognise its presence. 
 By day we easily see all objects which chance or our will 
 throws in our way, because they all reflect light ; but at night 
 we lose sight of them. From this it evidently follows that 
 they do not shine by their own light, but that they borrow 
 their light from a source, which everybody knows is the sun. 
 In fact, some hours before the rising of this body we begin 
 to discern objects indistinctly, and the nearer we approach 
 the hour of its rising the more we distinguish with clearness 
 everything about us ; at length, when his brilliant disc ap- 
 pears above the horizon, light floods with the fullest intensity 
 all parts of the space which surrounds us. It seems, therefore, 
 
 B 
 
2 
 
 PHOTOGRAPHIC OPTICS. 
 
 that there exists, necessarily, between the sun and ourselves 
 some mode of communication of which our eyes are the inter- 
 medium ; it is this mode of communication which constitutes 
 what is called light. 
 
 But, inasmuch as, according to what we have just said, 
 objects at the surface of our globe cease to be visible with the 
 disappearance of the sun below the horizon, light which shows 
 them to us so varied in aspect must, to do so, be also sus- 
 ceptible of various modifications. Now, the sun is white, and 
 yet the trees appear green, the sky blue, and buildings of a 
 hundred other tints. Is it not evident, then, that if the white 
 light of the sun did not contain all these colours we should 
 not perceive them ? The study of all phenomena relating to 
 light is called “ optics' 1 
 
 The Sources of Light; their Intensity.— The sun 
 
 shines with a splendour peculiar to itself ; terrestrial objects 
 with a borrowed brightness. It is not meant by this that there 
 are not on the surface of the earth self-luminous bodies, for that 
 would be very erroneous, as material bodies become luminous 
 when their temperature is sufficiently raised ; thus the jets 
 of gas which at night light the streets of our large towns 
 shine by their own light (for they are visible by day as well 
 as by night), and continue to do so as long as the cause which 
 produces them continues to act. Artificial lights are, besides, 
 capable of producing photographic images as well as the light 
 of the sun, or objects illuminated by it ; but at all times, their 
 intensity being relatively very feeble, their action on sensitive 
 substances is very slow. 
 
 Among the sources of artificial light, of which photographers 
 make use when sunlight or daylight fails them (as for ex- 
 ample when reproducing the interiors of grottoes, the crypts 
 of a church, &c.), we shall mention, in the first place, the flame 
 obtained by the combustion of a wire of magnesium . This 
 flame is of considerable brightness, and, moreover, emits a 
 very large number of chemical rays, of which we shall pre- 
 sently speak. 
 
PRELIMINARY IDEAS. 
 
 A stick of compact magnesia (obtained by the calcination of 
 the nitrate of magnesia) substituted for the stick of chalk in the 
 Drummond light emits a very vivid light also, and one quite 
 comparable to that given out by magnesium in combustion. 
 
 The electric light, though of exceeding brightness, exerts 
 but little action on photographic surfaces. But the light 
 obtained by the mercury-lamp of Way, though not so bright 
 as that obtained between the charcoal points of the ordinary 
 electric lamp, is much more intense in relation to such surfaces. 
 
 Chemical action of Light. — When a very young plant is 
 placed in a cellar, if is observed that as it becomes developed 
 all its shoots are directed not towards the openings by which 
 the air enters, but towards those which admit the light- 
 Moreover, the leaves of the plant in place of being green, like 
 those of our garden -pi ants, are white or slightly yellowish. 
 But if it be exposed to the sun, its leaves at the end of a few 
 hours will have become green under the influence of solar 
 light. 
 
 Chloride of gold dissolved in ether and exposed to the solar 
 rays slowly decomposes and deposits metallic gold. 
 
 White chloride of silver blackens in the light by losing 
 chlorine. 
 
 These, therefore, are examples of the chemical action of 
 light. This action, however, is not due to any elevation 
 of temperature ; for when, for instance, the chloride of silver 
 is placed in a liquid in which a thermometer is plunged, no 
 change of temperature is observed : besides, the chloride 
 remains white when it is heated in darkness. Light, there- 
 fore, induces a true chemical action. The list of substances 
 sensitive to light is extremely long ; and it is even supposed, 
 with some show of truth, that there probably does not exist 
 a single substance in nature which is not affected by light. 
 Although the chemical properties are often changed, the altern- 
 ation is not always apparent. It is thus with mercuric nitrate 
 when submitted to light, which does not visibly appear to 
 change its properties ; but the action of the light is revealed 
 
 B 2 
 
4 
 
 PHOTOGRAPHIC OPTICS. 
 
 by chemical reagents of proto-salts of mercury, which form an 
 image wherever the light has acted. The same thing may 
 be said of the bitumen of Judaea, which is so changed by light 
 as to lose its solubility in its ordinary solvents. 
 
 Among the bodies which are rapidly decomposed when 
 exposed to the solar rays we may mention the salts of gold, 
 silver, mercury, chromium, uranium, and a great number of 
 organic substances. The salts of silver are nearly all decom- 
 posed, more or less rapidly, when exposed to the solar rays. 
 Nearly all these salts are white, but there are also some 
 which are red, yellow, or green ; which exceptional colours, 
 however, do not preserve them from decomposition. 
 
 What is more curious is, that it is not the illuminating part of 
 light which acts chemically in the examples we have just given. 
 For a clear yellow glass, which allows illuminating light to 
 pass very readily, altogether stops chemical light, or that light 
 which decomposes chloride of gold and chloride of silver ; and 
 on the contrary, a very deep violet glass, through which we 
 can see with difficulty, hardly intercepts the chemical rays 
 at all. So that chloride of silver blackens almost as quickly 
 under a violet glass as under a clear one, and not at all 
 behind a yellow glass. 
 
 Movement of Light in straight lines. — Light moves in 
 a straight line ; hence we cease to perceive an object when 
 any obstacle is placed between the object and our eye. 
 
 A luminous point, a (fig. 1), emits luminous rays , ah, ac, ad, 
 l in all directions. A pencil, c a b, 
 is composed of several rays, a h, 
 a c, proceeding from a luminous 
 point a, and forming with each 
 Fig. 1 . other a very small angle, cab. 
 
 A bundle, bad, is composed of several pencils. 
 
 We usually treat of the straight lines ab , ac, which include a 
 pencil , b a c, as if they were parallel. To allow for this supposition, 
 the angle bac ought to be very small : less than half a degree, 
 for instance. 
 
PRELIMINARY IDEAS. 
 
 5 
 
 Every point of an illuminated object sends out rays of 
 light in all directions, for it can be seen by a great number 
 of persons at once. 
 
 Shadow and Penumbra. — An opaque screen placed before 
 a luminous bundle prevents it from passing. From this results 
 a shadow , which fills the whole space which would have been 
 occupied by the intercepted bundle. If, for instance, the 
 hand is held in the rays of the sun at a little distance from a 
 wall, the shadow of the hand is seen on the wall. In pro- 
 portion as the hand is moved away from the wall the outline 
 of the shadow is less clearly defined. This is because the 
 sun is not a luminous 'point , but a disc of sensible diameter, 
 every point of which produces a shadow. The true shadow 
 or umbra of the hand is that part of the shadow from w T hich 
 no portion of the solar disc is visible ; and the penumbra the 
 ill-defined border which surrounds the umbra. 
 
 If a sunbeam be allowed to enter a darkened chamber 
 through a small square hole, or one of any other shape, a 
 screen placed very near the hole receives an image of it 
 on a shadowed ground ; but if the screen be moved back, the 
 image of the hole disappears in the penumbra, and a perfectly 
 round image of the sun takes its place. 
 
 Images produced by small openings. — Effects of 
 Diffraction. — Every luminous ray w T hieh meets an obstacle 
 to its course forms an image there, and illuminates it. It is 
 just the same with any union of rays. A luminous object— a 
 candle-flame, for example — may be considered as made up of 
 an infinity of luminous points, each of which sends a pencil 
 of rays to our eye, so that an image of the flame is formed 
 therein. Similarly, any external object — a church, for example 
 (fig. 2) — may be considered as formed of an infinity of 
 luminous points,, each of which sends rays to all objects sur- 
 rounding it. In fact, if we place ourselves facing the church 
 in a darkened room having a small hole bored in the direc- 
 tion of the building through the window-shutter, we shall 
 see an image of the church formed in an inverted position 
 
6 PHOTOGRAPHIC OPTICS. 
 
 upon a screen opposite tlie hole. For the rays emanating 
 from the top of the steeple pass through the hole and light 
 
 up the screen 
 with their own 
 colour ; those 
 emanating from 
 the wall do the 
 same ; and so 
 on with the rest 
 of the building : 
 thus an in- 
 verted image of 
 the church is formed on the opposite screen. If the hole in the 
 shutter were very large, then each spot in the screen opposite 
 would receive light from a great number of different and 
 distant points of the object outside, all the images thus formed 
 would overlap each other, and the image would be an ill- 
 defined one. The smaller, therefore, the hole is, the sharper 
 but fainter is the image; and conversely, the larger it is, the 
 worse defined but brighter is the image. The size of the image 
 evidently depends upon the distance of the church from the 
 hole, or of the screen which receives the image from the hole. 
 
 When the external object possesses very great luminosity, 
 and when the opening into the dark chamber is very minute, as, 
 for example, when the image of the sun is received into the 
 chamber through a thin sheet of copper pierced with a fine pin- 
 hole, the image is perceived to be not sharply marked out, but sur- 
 rounded by a series of coloured rings which confuse its outline. 
 This phenomenon has received the nameof diffraction of light. 
 
 Opaque, translucent, and transparent bodies. — A body 
 is opaque if it arrests the passage of rays which strike it ; 
 transparent if it allows them to pass freely. There are no 
 bodies either absolutely opaque or absolutely transparent. 
 Opaque bodies when reduced to sufficiently thin laminae 
 always transmit some of the light which strikes them ; and 
 transparent bodies in great thickness arrest part of the light 
 
 Fig. 2. 
 
PRELIMINARY IDEAS. 
 
 7 
 
 which traverses them, this action being what constitutes 
 absorption of light by media said to be transparent. Trans- 
 lucent bodies are those imperfectly transparent. The metals 
 are said to be opaque ; glass, silicates, crystallized bodies, 
 liquids and gases are generally transparent ; organic sub- 
 stances non-crystalline in texture, such as wood in thin layers, 
 horn, gold-beater’s skin, &c., are translucent. 
 
 Absorption of Light by transparent media. — When a 
 pencil of light falls on the surface of a transparent medium, 
 a part of this pencil is reflected, and in quantity so much the 
 greater as the surface of the medium is more oblique to 
 the incident ray ; another part is diffused through the medium ; 
 and, lastly, a third is transmitted. Supposing the incident 
 ray to be perpendicular to the surface of the medium, absorp- 
 tion depends almost entirely on the more or less transparent 
 nature of the medium, on its thickness, and on its tint. 
 With respect to glass, which may be looked upon as sensibly 
 colourless, Bouguer has found, that a thickness of six super- 
 posed sheets, forming a total thickness of only twenty-six 
 millimetres, causes a loss of seven-tenths of the light. Only 
 a third, therefore, of the light is transmitted ; but, in this 
 case, the great loss of light depends principally upon the 
 reflection produced by the twelve surfaces of the medium. 
 
 The air itself arrests a certain part of the light emanating 
 from the sun. Bouguer gives the following table of the 
 intensity of the suns light at different elevations : 10,000 would 
 be the intensity of this light if air were absolutely transparent. 
 
 Sun’s Altitude. 
 
 Intensity. 
 
 Sun’s Altitude. 
 
 Intensity. 
 
 0 ° 
 
 6 
 
 20 ° 
 
 5474 
 
 1 ° 
 
 7 
 
 25 ° 
 
 6136 
 
 2 ° 
 
 192 
 
 30 ° 
 
 6613 
 
 3 ° 
 
 454 
 
 40 ° 
 
 7237 
 
 4 ° 
 
 802 
 
 50 ° 
 
 7624 
 
 5 ° 
 
 1201 
 
 70 ° 
 
 8016 
 
 10 ° 
 
 3149 
 
 90 ° 
 
 8123 
 
 15 ° 
 
 4535 
 
 
 # 
 
8 
 
 PHOTOGRAPHIC OPTICS. 
 
 This table is very instructive, because it serves to show us 
 the immense difference which exists between the intensity of 
 the sun’s light in summer and in winter. Thus, at Paris, on 
 June 21st, the elevation of the sun at noon is about 64° 17', 
 and the intensity of his light is then, in round numbers, 
 7800. In winter, on the 21st of December, the sun’s elevation 
 is 17° 43', and the intensity of his light is then no more than 
 5000, being but f of what it is in summer. In this com- 
 parison the atmosphere is supposed to be very clear; but if 
 we reflect that very often in winter, in our climates, the 
 atmosphere is misty, we can easily understand the great 
 difference in the intensity of the light radiated by this body 
 in winter and in summer. 
 
 We have seen that the chemical rays of light, that is to say, 
 that part of light (the blue and violet) which acts on photo- 
 graphic surfaces, differs from the illuminating (red and 
 yellow) part of light. We have a very striking example 
 of this in investigating the absorption of chemical rays by 
 media, such as glass, very transparent to luminous rays. 
 The more or less perfect 'polish of the surface is found, parti- 
 cularly, to greatly influence absorption. The more perfect the 
 polish, the less considerable is the absorption, all things 
 else being equal. This is explained by the well-known fact, 
 that ground glass arrests a great part of the chemical rays 
 of light ; for a surface imperfectly polished is a surface slightly 
 ground. 
 
 Secondly, absorption depends a great deal upon the 
 colour of the medium. For this reason, glass completely 
 colourless, like the light kind of flint-glass, allows two 
 or three times as much chemical light to pass through as 
 the very heavy kind, which is yellowish, and one and a 
 quarter times as much as crown-glass, which is of a greenish 
 tint. 
 
 When transparent plates are colourless they all transmit 
 chemical light to almost the same extent. Tn consequence of 
 .this, lenses of the same shape in quartz, rock-salt, flint-glass. 
 
PRELIMIN' ARY IDEAS. 
 
 9 
 
 and crown-glass show no difference in their power of trans- 
 mitting chemical light.* 
 
 The thickness of the medium exercises a great influence on 
 the absorption of the chemical rays (or such rays as act on pho- 
 tographic surfaces). The law discovered by Bouguer applies 
 here as well as in the case of the absorption of radiant heat, 
 namely, that the intensities of the transmitted rays form a 
 decreasing geometrical progression when the thicknesses form 
 an increasing arithmetical progression. 
 
 If the absorption were simply proportional to the thickness 
 of the medium, a very thick layer of the medium would be 
 opaque. Thus let us take, for example, sea-water. If a 
 metre of this absorbs one-twentieth of the incident light, 
 twenty metres will, on the above supposition, absorb twenty- 
 twentieths, or the whole of the light, and at this depth there 
 will be total darkness ; but such is not the case. If the first 
 metre of water absorb one part out of 20 of incident light, 
 there will be 19 which have traversed this medium ; the 
 second metre will absorb only one-twentieth of these 19 parts, 
 leaving therefore 18*05 ; the third metre will absorb only 
 one-twentieth of the 18*05 parts of light transmitted by the 
 second, and so on ; so that, even if a hundred, a thousand, oi 
 even a million metres of water were traversed, there would 
 still be a certain quantity of light transmitted, as in fact we 
 find by experience. It follows from this, that, in a very 
 thick transparent plate, the first layers, when traversed by 
 
 * The author has had constructed by M. Secretan lenses, with a diameter 
 of 1 inch and a focal length of 6 inches, in flint, white crown-glass, 
 colourless quartz, and colourless rock-salt, and has compared them together 
 by mounting them all in a camera and receiving the image of external 
 objects on the same photographic surface. The four photographic images 
 were of apparently equal intensity. Although these media, as Dr. Allen 
 Miller has shown, exert a different absorbent power on certain rays of very 
 high refrangibility (and situated entirely beyond the violet end of the 
 spectrum), it does not therefore follow that they also absorb differently less 
 refrangible rays, such as the blue, violet, and indigo, and thus Dr. Miller’s 
 experience in no way invalidates the results obtained by the author. 
 
10 
 
 PHOTOGRAPHIC OPTICS. 
 
 the incident light, absorb the greatest part of it, the others 
 absorbing much less. 
 
 From this it also follows, that of two transparent plates, one 
 of which is twice as thick as the other, the first will not 
 absorb twice as much of the incident light as the second. 
 On the contrary, the absorption will be nearly equal if the 
 thickness of the plates do not exceed a few centimetres, and 
 if they are without colour. 
 
 Reflection of Light. — A surface reflects when it sends 
 back- some of the light impinging upon it. All bodies reflect 
 light more or less. However, by the name of reflecting 
 surfaces are usually meant polished surfaces. But, even when 
 a ray of light meets a perfectly polished surface, only some 
 of it is reflected ; for a part is absorbed by the medium which 
 forms the substance of the polished surface, another is diffused, 
 and another is transmitted if the medium be transparent. 
 
 The study of the reflection of light from the surface of 
 polished plates bears the name of “ catoptrics .” Let A B (fig. 3) 
 
 be a plane reflecting surface, and 
 EOa ray of light, incident upon 
 it ; that ray will be reflected in 
 the direction O R' in the same 
 plane as the incident ray — the 
 plane being perpendicular to 
 the reflecting surface, and making 
 with that surface an angle E'OA 
 equal to the angle ROB. The 
 normal N O is the straight line 
 perpendicular to the surface A B, 
 which makes with the incident ray R 0 and the reflected ray 
 R' 0 equal angles. 
 
 In this way we can determine the path of light reflected 
 from any geometrical surfaces whatever; but this study is 
 quite foreign to the optics of photographic instruments. 
 
 Mirrors and their reflecting power. — A polished me- 
 tallic surface is called a mirror. The quantity of light 
 
 Fig. 3. 
 
PRELIMINARY IDEAS. 
 
 11 
 
 reflected from the surface of a mirror depends on three 
 elements : the degree of perfection of its polish, the colour of 
 the surface, and the incidence of the luminous rays which 
 strike it. 
 
 The more perfect the polish, the less is the loss of light in 
 the act of reflection. Metallic surfaces being polished with 
 great difficulty, and, besides, soon becoming tarnished in the 
 air, we usually substitute for them plates of polished glass, 
 backed up with mercury, or, still better, with silver. In this 
 case the metal partakes of the admirable polish so easily given 
 to glass. 
 
 On the colour of the metal depends, in great part, the colour 
 and the intensity of the reflected ray. Thus copper, which 
 is polished with difficulty, and the colour of which is red, 
 reflects rays of light imperfectly, and gives to them its red 
 tint. In the same way gold gives the reflected light a yellow 
 colour. Of all metals silver is the whitest; this is why 
 silvered glasses make the best mirrors. They reflect, according 
 to M. de Steinheil, ninety per cent, of the incident rays ; 
 while glasses backed with mercury reflect only sixty-five per 
 cent. And, as the sole employment of mirrors in photo- 
 graphy is to send the solar rays into the apparatus for 
 enlarging, and as the sun very soon destroys glasses backed 
 with mercury, causing the mercury to run into globules, 
 all the advantage is in favour of silvered glasses. 
 
 Lastly, the more obliquely the light falls on a reflecting 
 surface, the less it diminishes in intensity by reflection. 
 Further, if it falls so as to make a very acute angle with the 
 reflecting surface it is entirely reflected. We have a very 
 evident proof of this, in looking at a white object reflected by 
 a polished plate of copper or of gold, which then appears 
 red or yellow ; but when we incline the plate in such a way 
 as that the reflecting plane is directed towards the object, so 
 that the rays emanating from it just graze the plate, the 
 object will no longer appear coloured, but white. Now, this 
 is because, in such a case, the whole of the light coming 
 
12 
 
 PHOTOGRAPHIC OPTICS. 
 
 from the object is reflected, no matter what may be the colour 
 of the plate ; in other words, the light suffers total reflection. 
 
 It is generally imagined that the more nearly the rays of 
 light fall perpendicularly on a reflecting surface the greater 
 is the portion of light reflected; but the contrary is the 
 case. In fact, representing by 100 the intensity of the solar 
 rays falling at an angle of from 60° to 90° (that is, nearly 
 perpendicularly) on a quicksilvered mirror, the intensity of 
 the solar rays reflected is 60 ; so that 40 per cent, is lost 
 in the act of reflection. If, on the other hand, the solar rays 
 make with the mirror only an angle of 5°, the intensity of 
 the reflected rays is 70; so that there is only 30 per cent, 
 of loss. With silvered mirrors, as we have seen above, the 
 loss is much less. 
 
 Adjustible Mirrors. — The instruments which serve to 
 
 reflect solar light 
 in optical appara- 
 tus are called 
 adjustible mirrors. 
 We give here the 
 description of two 
 of the forms most 
 frequently used. 
 BODE (fig. 4) 
 ff is a square plate 
 of bronze or iron, 
 which is fixed by 
 the screws J I to 
 the shutter of a 
 darkened room. 
 This plate is 
 pierced by a round 
 opening, which re- 
 ceives a disc of 
 Fig. 4 . the same shape, 
 
 toothed at its periphery, and pierced at the centre by a 
 
PRELIMINARY IDEAS. 
 
 13 
 
 circular opening. Lastly* to maintain this disc in position, 
 and to keep it from falling out, it is covered by another, 
 attached to the square plate. A pinion, with milled head, 
 F, works in' the teeth of the circular disc, and enables us 
 to turn it round. 
 
 To the revolving disc is attached a small arm, which is seen 
 under the letter a. The mirror A is fixed into a small toothed 
 wheel, the axis of which is held by the arm. A pinion, of 
 which the milled head is seen at G, works in the small toothed 
 wheel a, so that all imaginable inclinations to the plane 
 BODE can be given to the mirror ; and as, on the other 
 hand, the milled head F allows the disc to which the mirror is 
 attached to be turned round, it follows that the mirror can 
 receive all required positions. 
 
 This instrument, as we have said, is fixed to the shutter 
 
 > 
 
 of the dark chamber. By turning simultaneously the milled 
 heads F and G, the solar rays can be thrown through the 
 opening in the centre into the dark chamber, and the desired 
 direction, which is usually a horizontal one, be given to the 
 reflected rays. 
 
 The circular opening which gives passage to the reflected 
 rays ought to have a diameter equal to the breadth of the 
 glass ; but as to the length which the glass ought to have in 
 order to reflect a cylinder of solar rays equal in diameter 
 to the opening, this depends on the aspect of the shutter 
 and the height of the sun above the horizon. The most 
 convenient aspect is a southern one (a northern one in 
 places situated in the southern hemisphere, as in the East 
 Indies, Cape of Good Hope, &c.) The height of the sun 
 depending on the latitude of a place, the higher the latitude 
 the longer the mirror must be. In our climates (between 40° 
 and 60° of latitude) it is sufficient if the length is three times 
 the diameter of the aperture for the rays reflected by the mirror 
 to cover the aperture in spring and summer (from March 1st 
 to September 30th) ; but in winter, particularly in from 50° to 
 .60° of latitude, this length is quite insufficient, and even a 
 
14 
 
 PHOTOGRAPHIC OPTICS. 
 
 mirror ten times longer than the dimensions indicated above 
 would still be too short. 
 
 The adjustible mirror represented in fig. 5 is more convenient 
 for winter, but it requires a special arrangement and a dark 
 chamber, built expressly for it in a garden or on a terrace. 
 
 This chamber should be very low, in order that the solar rays 
 
 may pass, even in 
 — [ winter, above the 
 roof which covers it, 
 
 y 
 
 the summit of which 
 roof is directed to- 
 wards the south, 
 
 
 while the lowest 
 
 
 part, raised at the 
 
 
 most six feet from 
 
 
 the ground, looks 
 
 j J 
 
 towards the north. 
 The optical appa- 
 ratus is no longer 
 directed towards the 
 
 
 south, but towards 
 the north ; and it is 
 
 . 1 | II 
 
 at two or three me- 
 
 j i ii 
 
 tres to the north of 
 
 
 the building that 
 
 U ||r 
 
 the adjustible mir- 
 
 
 ror is placed, of 
 
 
 which the follow- 
 
 
 ing is the descrip- 
 tion : 
 
 Fig. 5. 
 
 The mirror L is 
 
 either square, or, still better, circular. 
 
 Its diameter ought 
 
 to be double that of the lens on which the solar ra}^s 
 will be reflected. This mirror, mounted in wood, is attached 
 by means of four screws to the ends of the toothed semicircle 
 K, the (horizontal) axis of which turns in two uprights of 
 
PRELIMINARY IDEAS. 
 
 15 
 
 iron. A small toothed wheel, I, is in gear with the semicircle, 
 and is placed a little on one side, for the rod a must occupy 
 the vertical axis of the foot of the mirror, and it is from 
 an endless screw which terminates this rod a that the small 
 wheel I, and from it the semicircle K, receives its movement. 
 
 The fixed pedestal of the instrument is formed by the iron 
 plate c c turned upon both its upper and lower faces, by the 
 plate of cast iron H, and by the three feet D, of iron or wood, 
 which join the two plates. 
 
 The rod a is terminated below by a small conical toothed 
 wheel, the lower part of which turns in a small bearing fixed 
 to the plate IT. One extremity of the horizontal rod G- passes 
 into the dark chamber, where it terminates in a key-piece, 
 which is moved by the hand ; the other (seen in the figure 
 above the letter H) ends in a conical toothed wheel working in 
 that of the rod a. By turning, therefore, the rod Gr, movement 
 is communicated to the rod a, and consequently to the wheels 
 I and K, in such a way that the mirror receives a motion in a 
 vertical plane. 
 
 The two uprights, E E, which sustain the mirror, are fixed 
 on a plate of turned iron, of which the margin rests on the 
 upper part of the plate c c, which presents a central circular 
 opening equal to half its total diameter. The plate which 
 carries the uprights, E E, can therefore turn freely on the plate c ; 
 but, to communicate movement to it from the dark chamber, 
 another plate, B, is placed on its lower part, of which the 
 toothed circumference works in the endless screw terminating 
 the rod A which passes into the dark chamber. The plate c is 
 therefore held, with gentle friction, between the margin of the 
 upper plate and the plane of the toothed wheel B, so that 
 the system of uprights E E is solid ; the plates also give free pas- 
 sage to the rod a. The mirror, in addition to the movement in 
 the vertical plane, has therefore a movement in the horizontal 
 plane also ; so that, in relation to a given point, it can take all 
 positions imaginable. 
 
 The reflecting part of the mirror being turned towards the 
 
16 
 
 PHOTOGRAPHIC OPTICS. 
 
 sun, it suffices to communicate from the dark chamber a con- 
 venient movement to the rods A and G, in order that the solar 
 rays may be reflected horizontally into the optical apparatus. 
 
 Heliostats. — Heliostats are adjustible mirrors which receive 
 their movement from clock-work in such a manner that the 
 solar rays reflected remain motionless in a given direction. 
 
 As the minute description of those instruments, the use of 
 which in photography is important, occupies a very consider- 
 able space in this work, a special chapter has been devoted to 
 it, which will be found in the book treating of enlarge- 
 ments. — (See the Table of Contents.) . 
 
 CHAPTER II. 
 
 REFRACTION OF LIGHT. 
 
 The study of the path of light through transparent media bears 
 the name of “ dioptrics .” This study, which is very complicated, 
 extends to all imaginable media, crystallized or amorphous, 
 transparent or opaque, liquid, solid, or gaseous. We have, 
 however, but to consider, and shall only in this work treat of, 
 one class of transparent media, namely, the non-crystalline, 
 and more especially glass. 
 
 Refraction of Light. — Light, in consequence of passing 
 from one medium into another, is refracted — it changes its 
 velocity. If it fall normally (that is to say, perpendicularly) 
 on the surface of a medium, it continues through this medium 
 its course in a straight line, although refracted. But if it fall 
 obliquely, its direction is changed, and it deviates from its 
 rectilinear path. As an example, we may cite the case of a 
 stick which, when plunged half-way into water (fig. 6), appears 
 broken at its point of contact with the water. 
 
REFRACTION OF LIGHT. 
 
 17 
 
 The point where the incident ray cuts the surface of the 
 refracting medium is called the point of 
 incidence or point of immersion. The name 
 of point of emersion or emergence is given to 
 it when the ray is leaving the refracting 
 medium. The angle which the refracted 
 ray makes with the normal (or perpendicu- 
 lar) to the surface of the refracting 
 medium has received the name of angle of 
 refraction. 
 
 Law of Refraction. — 1st. The incident 
 
 ray , the refracted, ray, and the normal , are all 
 in the same plane. 2nd. For the same two media , the ratio of the 
 sine of the angle of incidence to the sine of the angle of refraction is 
 constant, whatever may he the angle of incidence. This law has 
 received the name of the Law of Descartes.” Let us give an 
 example of it : — 
 
 A ray of light, R 0 (fig. 7), passing from air into water, 
 is refracted along 0 R', in the same plane 
 as the incident ray. If, at the point of 
 immersion 0, where the incident ray 
 R O touches the water, we raise a per- 
 pendicular, or normal, A B, to the line 
 n m, which represents the surface of the 
 water, we shall find that the refracted 
 ray is bent towards it. Conversely, a 
 ray, R' 0, passing from water into air is 
 refracted in a direction, 0 R, which bends 
 away from the normal. For air and water, the ratio of the 
 sines of the angles R 0 A and R' 0 B is constant, whatever 
 may be the incidence of the ray R 0. 
 
 Index of Refraction. — If, in place of water, we use essence 
 of turpentine, ether, or other liquids, we shall always find for 
 the same liquid a constant ratio between the sine of the angle 
 of incidence and the sine of the angle of refraction ; but this 
 ratio differs with the nature of the liquid, being, for example, 
 
 c 
 
 Fisr. 7 
 
18 
 
 PHOTOGRAPHIC OPTICS. 
 
 much greater for ether than for water, and therefore ether is 
 said to he more refractive than water. This ratio has received 
 the name of index of refraction. The higher therefore the 
 index of refraction possessed by a medium — in other words, 
 the more refractive it is — the more it deviates the incident luminous 
 ray from its primitive direction . 
 
 Works on physics,* particularly works on optics, contain 
 different methods by the aid of which the index of refraction 
 of transparent substances can be measured ; it is therefore not 
 necessary to describe these methods here. We shall only 
 remark, that (as we shall afterwards see) the refraction of 
 white light is always accompanied by dispersion , that is, by 
 decomposition ; and that, ordinarily, the ray which corresponds 
 to the yellow is taken for the refracted ray. We shall, how- 
 ever, return to this subject. 
 
 The following is a table of the index of refraction of a few 
 substances : — 
 
 Vacuum .. 0*000 
 
 Diamond 2*47 to 275 
 
 Flint-glassf 1*57 to T60 
 
 Rock-crystal 1*547 
 
 St. Gobain glass (crown) J .. .. 1*5 
 
 Congealed water (ice) T31 
 
 Liquid water (at 0° C.) 1*333 
 
 Liquid water (a^20° C.) .. .. 1*332 
 
 Refraction by transparent plates with parallel sur- 
 faces. — Let fig. 8 be a transparent plate with parallel faces 
 — a sheet of glass, for example, — and R a ray of light incident 
 upon it. The ray, which would pursue its course in a right 
 line if the glass were not in the way, suffers deviation 
 towards the normal, N, on entering the plate, and away from 
 
 * See Daguin, Traits de Physique, tome iv. p. 155 (2nd edition). 
 
 + There are varieties of flint-glass, containing lead, of which the index 
 of refraction is even higher than 1*6. 
 
 X The index of refraction of crown-glass varies also with the composition 
 of the glass : it is most often higher than 1*5. 
 
REFRACTION OF LIGHT. 
 
 19 
 
 it again on leaving it. Now, since the sheet of glass, taken as 
 an example, has its faces parallel, it 
 follows that the normals N and N' 
 are also parallel. As it is easy to 
 conceive, the deviation on leaving 
 the glass is precisely equal to the 
 deviation on entering it, and the 
 ray R is parallel to R' ; therefore, 
 when a refracting plate with parallel 
 faces is placed in the path of a lumi- 
 nous ray , the ray preserves its di- 
 rection , although its first position is 
 changed. It is evident that if the ray fall perpendicularly on 
 the glass plate, along N for example, it would leave it without 
 deviation, because it is coincident with the normal. 
 
 In place of a plate of glass, one of rock-crystal, rock-salt, or 
 any other transparent material, may be taken for illustration. 
 In using these materials, for the same thickness and inclination 
 of the plate to the incident ray, the displacement will be variable 
 in extent, because their refractive power is different. 
 
 Refraction by Prisms. — Let us now consider the case of 
 refracting media, with plane faces inclined to each other, such 
 media having received the name of prisms. 
 
 Let CAB (fig. 9) be a prism, and Roa ray of incident light. 
 On entering the prism, 
 this ray is deviated 
 along o o' (unless it 
 fall perpendicularly 
 on the face A C), and 
 on leaving the prism 
 it is again deviated 
 along o' R'. The two 
 deviations on en- 
 trance and exit are identical as regards the normals N o, NV, 
 as in the example of the plate with parallel faces ; but as the 
 faces A C, A B here make an angle with each other, the two 
 
 Fig. 9. 
 
20 
 
 PHOTOGRAPHIC OPTICS. 
 
 rays, Ro and o’ R' will also make an angle with each other. 
 Bnt this angle will not ho the same as that (CAB) of the 
 prism, for it depends on tho refractive power of the material 
 which forms the prism, and on the size of the angle (CAB) 
 of the prism* Prisms, then, deviate towards their base rays 
 incident npon one of their faces. 
 
 Graphical construction of a ray refracted by a Prism. 
 — This is very easy when the index of refraction of the mate- 
 rial of the prism is known. Let it, for example, he supposed 
 to he glass with an index of 1*5. This index is absolute, that 
 is, expressed in relation to a vacuum, hut, as in most cases, 
 the luminous ray has passed through the air, it would he 
 necessary t6 take into account the index of refraction of this 
 medium, were it not that it is so small that it may nearly 
 always he neglected. 
 
 Draw on a sheet of very smooth Bristol-board the angle A 
 (fig. 10), which forms the edge of the prism. At the point 
 
 of immersion o, draw 
 the normal N o perpen- 
 dicular to the l ight line 
 A C, which represents 
 one of the faces of the 
 prism. Let R o he the in- 
 cident ray, making with 
 the normal N a given 
 angle. From any point 
 R on the incident ray, let fall cn the normal the perpen- 
 dicular NR, which is the sine of the angle of incidence 
 N a R. Make N a in the ratio of unity to the index of 
 refraction, which in the present example is the ratio of 1 
 to I'd or of 2 to 3. Therefore, make N a equal in length to 
 two-thirds of N R. Draw the right line a o, which represents 
 the refracted ray. 
 
 In o , the point of intersection of ao prolonged, with AB 
 (the other face of the prism), raise the normal NV perpen- 
 dicular to A B. From any point a, on the refracted ray a o', 
 
 Fig. 10. 
 
INFRACTION OF LIGHT. 
 
 21 
 
 let fall on the second normal N'o' the perpendicular a N' ; 
 this is the sine of the angle of incidence. Prolong the 
 sine to b', so that «N' = 2 and N' b' = 3, and draw the right 
 liue b' o', which, when prolonged, will give o' R', This is the 
 emergent ray. 
 
 The explanation of this diagram is simple. It is necessary 
 to effect for the face A B the converse of what is done for the 
 face AC. Now, RN is the sine of the angle of incidence, and 
 N a the sine of the angle of refraction. The ratio of these is 
 known, for it is the index of refraction. If, then, the lengths of 
 N a and N R are made corresponding to this ratio, the refracted 
 ray a o' is evidently obtained. By proceeding similarly, but 
 in the inverse way, to get the emergent ray, O' R' is obtained. 
 
 Calculation of the refracted Ray,— Let MN (fig. 11) 
 
 Hg. 11. 
 
 be the incident ray, making the angle of incidence i with 
 the normal BND; NP the refracted ray, making the angle 
 P N C = r with the same normal ; P Q the emergent ray, 
 making the angle EPQ = r' with the normal P E to the 
 second face ; NPC = f the angle of incidence of N P with this 
 normal, a the angle of the prism, and n the index of re- 
 fraction : * the incident ray M N prolonged will meet the 
 
 * In England the index of refraction is generally symbolically repre- 
 sented by the Greek letter \x ; on the Continent it is invariably, as in this 
 treatise, represented by the letter n. 
 
22 
 
 PHOTOGRAPHIC OPTICS. 
 
 emergent ray P Q in F, and the angle G- F Q of these two rays 
 will he the angle of deviation d, which has to he calculated. 
 
 Now, in the triangle PFN, the sum of FNP-f-FPN is equal 
 to the exterior angle d , therefore d = FNP + FPN = (i-r) + 
 (r'— ■»') = — (r+i') ; hut the angle DCP of the two 
 
 normals is equal to the angle a of the prism ; further, in 
 the triangle NPC, the sum of r-\-i is equal to the exterior 
 angle a ; we have, therefore, 
 
 d = i -f- r' — a (1). 
 
 By another calculation, the laws of refraction give the 
 formulas — 
 
 Sin r - n sin (a — r) ...... (2). 
 
 Sin r=!“i (3). 
 
 n 
 
 The formulas (1), (2), and (3), are general, and enable us 
 to calculate the deviation of any incident ray, situated in a 
 plane perpendicular to the edge of the prism : for, the angle 
 of incidence i and the index of refraction n being known, 
 the angle r can he found by formula (3) ; knowing this, 
 and the angle a of the prism, we can calculate r by the 
 aid of formula (2), and after that we may eliminate d by 
 formula (1). 
 
 If the angle a be very small, and the incident ray be 
 nearly perpendicular to the bisector of this angle, then i is 
 also a very small angle. In formula (3) the ratio of 
 the sines may be replaced by that of the arcs, so that 
 
 we have r = - ; for the same reason, formula (2) gives 
 n 
 
 r =n ( a — r ) = n (a — l -)=na — i-, and, in consequence, formula 
 \ w 
 
 (1) becomes 
 
 d = i + r' —a — i -f- (na—i)—a = (n — 1) a . 
 
 If, a being very small, the incident ray be not nearly per- 
 pendicular, but oblique, to its bisector, then the angle i ceases 
 to be very small, and the simplest means of calculating d is 
 to make use of formulae (1), (2), and (3). 
 
CHROMATICS. 
 
 23 
 
 CHAPTER III. 
 
 CHROMATICS. 
 
 Hitherto we have considered the passage of light through 
 transparent media, from a geometrical point of view only, as if 
 a ray of incident light gave rise to but a single refracted ray. 
 This is true, were the simple ray homogeneous, that is, of a simple 
 colour , (we shall see presently what this term means) ; but if 
 the incident ray be composed of white light instead of a single 
 refracted ray, then, after refraction an infinity of refracted 
 rays is obtained — a phenomenon which has received the 
 name of dispersion. 
 
 The Solar Spectrum. — Into a dark chamber, suitably 
 arranged, let a bundle of horizontal solar rays a (fig. 13), be 
 
 Fig. 12. Fig. 13. 
 
 allowed to enter through a circular hole one centimetre in dia- 
 meter, by means of an adjustable mirror. A round image of the 
 sun a ' (a" in fig. 12) will thus be formed on the wall opposite 
 
24 
 
 PHOTOGRAPHIC OPTICS. 
 
 the shutter. If, in the path of the rays a a', a glass prism be 
 placed in the position shown in the figure, instead of getting, 
 after refraction of the rays, a circular white image as before, we 
 obtain at c' d' ( cd in fig. 12) an elongated and coloured image 
 called the Solar Spectrum. This spectrum is composed of the 
 following colours, beginning from above — red, orange, yellow', 
 green, blue, indigo, violet. The red, being less deflected than 
 the violet, is said to be less refrangible. Each of these colours 
 is called “ simple,” because if a bundle of rays of one of them 
 be isolated, by passing it through a hole in the centre of a 
 disc of blackened copper, and received on a second prism, it is 
 of the same colour after this second refraction. 
 
 The coloured rays which emerge from the prism are un- 
 equally refrangible — that is to say, if they fall at the same 
 angle of incidence on the surface of a refracting medium they 
 will each pursue, in this medium, a different path. Thus, in the 
 example of the refraction of an incident ray by a transparent 
 medium quoted at page 17, if R Obe a red ray of which 0 R' is 
 the refracted ray, 0 R' would approach nearer to the normal 
 0 B if R 0 were violet, because the violet is more refrangible 
 than the red. 
 
 When it is wished to study with care the physical constitu- 
 tion of the solar spectrum, or the action of the spectrum on 
 substances sensitive to light, it is necessary, in order to produce 
 a suitable spectrum, to make the following arrangements. 
 
 In the shutter of a room completely darkened (fig. 14) a 
 plate of brass is placed vertically, having a rectilinear aper- 
 ture, very narrow, (not less, however, than one millimetre), 
 and two or three centimetres high. Two thin plates of copper 
 which form the opening are also made moveable and capable 
 of being separated or approximated, according as the spectrum 
 is to be more or less intense. 
 
 The solar rays are reflected horizontally through this 
 rectilinear opening by a plane mirror of silvered glass, 
 polished on its upper surface. If wished, an ordinary mirror 
 may be employed ; but in this case a part of the chemical rays 
 
CHROMATICS. 
 
 25 
 
 of light is absorbed by its passage through the glass of the 
 mirror. 
 
 The prism (of 
 which the sec- 
 tion is an equi- 
 lateral triangle) 
 of flint-glass, 
 quartz, or any 
 other transpa- 
 rent material, 
 and mounted on 
 a foot resting 
 on three screws, 
 is placed ver- 
 tically in the 
 path of the lu- 
 minous ray. 
 
 The luminous 
 band must fall 
 on only one of 
 the faces of the Fig. 14 . 
 
 prism, and near 
 
 its edge. The vertical position of the prism is tested by 
 comparing the height of the spectrum with that of the slit 
 above the floor ; the two heights ought to be equal. 
 
 On turning the prism upon its axis (and its mounting is dis- 
 posed so as to easily permit such a movement), the spectrum 
 is seen to approach the luminous ray a a (fig. 13), but a point 
 is soon reached when it begins to move away again from it, 
 even on turning the prism in the reverse direction. There is, 
 therefore, a position of the prism, called the position of mini- 
 mum of deviation ,* which it is essential to fully realise, else 
 
 * In this case, the angle of dispersion is the smallest possible, and the 
 spectrum the shortest possible. To realize this position of the prism, 
 the incident ray R o (fig. 9) and the emergent ray 0 ' R' must make equal 
 angles with the bisector of the angle A of the prism. 
 
26 
 
 PHOTOGRAPHIC OPTICS. 
 
 the colours of the spectrum will he mixed with white 
 light. 
 
 The spectrum thus obtained has not a sharply defined out- 
 line, hut on receiving it into a photographic apparatus,* 
 through a double objective, as shown in fig. 14, the slit can be 
 brought to a focus through the prism, and when this is done it 
 takes a rectangular form. By moving the rack-work of the 
 objective, the different colours may be successively brought to 
 a focus, for the focus of each is different. 
 
 The camera which serves to receive the spectrum must 
 be capable of being shortened and elongated to a sufficient 
 extent, and must be supported by a stand susceptible of the 
 movements necessary to place it horizontally. The ground- 
 glass screen should be about ten centimetres high by fifty 
 broad. 
 
 The prism must always be placed as near as possible to the 
 objective. 
 
 The nearer the objective and the prism are approximated to 
 the slit, the broader and longer is the spectrum ; and the fur- 
 ther they are moved from it, the smaller and brighter is the 
 spectrum. It follows from this, that when experiments are 
 to be made on the chemical action of the spectrum with 
 substances very sensitive to light, the first arrangement is to 
 be employed ; and with those, on the contrary, little sensitive, 
 the second. In the first case, this spectrum should be three or 
 four decimetres long ; in the second, one decimetre, and in 
 this case the slit in the shutter may even be a little enlarged. 
 
 The various colours of the solar spectrum are more or less 
 elongated, according to the dispersive power of the prism 
 employed. We have already named the principal colours of 
 which it is formed; we may now mention that Sir John 
 Uei'schel has added to these two others, very difficult to 
 observe well, but which, however, are to be seen if the 
 
 * The reader is here supposed to be familiar with the practical 
 proceedings of photography. 
 
CHROMATICS. 
 
 27 
 
 chamber is well darkened : they are, the one crimson, beyond 
 the red ; the other grey (crimson and lavender) beyond the 
 violet. 
 
 Lines of the Spectrum. — When the solar spectrum, pro- 
 duced in the way we have just described, is examined with 
 attention, an infinite number of dark lines in the direction of 
 its breadth are to be observed, which were discovered by 
 Wollaston and Frauenhofer . These lines, for solar light, and 
 the same refracting substance, always have the same relative 
 order — a fact of the utmost value, because these lines serve to 
 specify exactly the parts of the spectrum in which they occur. 
 
 In fact, the passage from one colour into another being 
 insensible, the designation, yellow, red, &c., is vague. Pre- 
 cision is obtained by stating the line or group of lines which 
 exactly characterise the place of that part of the spectrum 
 which it is wished to indicate. 
 
 At M. Secretan’s, optician, Pont Neuf, a Paris, a coloured 
 lithograph of the spectrum may be obtained, which contains 
 all the principal lines of the spectrum with their designations. 
 This plate, which is more than a metre in length, and of 
 which the price is only six francs, is indispensable to every 
 one studying optics. 
 
 Chemical action of the Spectrum.— Extra-prismatic 
 Rays. — We have already spoken of the chemical action of 
 light at p. 3. 
 
 If chloride-of-silver paper be exposed for some minutes to 
 the action of the solar spectrum, kept motionless, and if, from 
 time to time a ground-glass be interposed between the spectrum 
 and the prism (which permits the successive action of the 
 light, otherwise invisible, to be seen), it will be found that 
 the action begins in the indigo and violet, and then passes on 
 into the blue, and far beyond the violet, where, nevertheless, 
 no light can be distinguished by the eye. In the red, orange, 
 yellow, and green there is no action at all, so that the paper 
 at that part remains white. 
 
 On substituting for the silver-chlorised paper, a paper of 
 
28 
 
 PHOTOGRAPHIC OPTICS. 
 
 the bromide of the same metal, the action extends a little way 
 into the green. 
 
 Figure 15 represents this experiment. The rectangle on 
 
 the right of the figure 
 represents the seven 
 colours of the spectrum, 
 of which the names are 
 printed on the left. The 
 dark rectangle on the left 
 represents a strip of 
 silver - bromised paper, 
 and the next rectangle 
 a paper of the chloride 
 of the same metal, after 
 having been both sub- 
 mitted for a long time to 
 the action of the spec- 
 trum. 
 
 Most substances sensi- 
 tive to light behave in 
 the same manner. The 
 experiment is of the 
 highest importance in 
 photographic optics. It 
 demonstrates at once, that 
 the most brilliant colours 
 of the spectrum, that is, 
 those which are most 
 diffused throughout na- 
 ture — namely, the red, 
 orange, yellow, and green 
 — have no action on sub- 
 Flg * 15 ‘ stances sensitive to light ; 
 
 and that, on the contrary, the colours the least brilliant — blue, 
 indigo, and violet — have on these substances a very intense 
 action (the maximum being in the indigo) ; and, lastly, that 
 
CHROMATICS. 
 
 29 
 
 there exist in solar light, rays invisible to the eye, which 
 have on these substances a very intense action also. These 
 invisible rays have received the name of extra-prismatic 
 rays. 
 
 On the colour of Bodies. — Bodies in nature, illuminated 
 by solar light, present all colours imaginable. This is because 
 the light of the sun, or that of the clouds, which strikes them 
 is decomposed at their surface ; they absorb all the simple 
 lays of which white light is formed, except those they reflect. 
 •"W hite bodies reflect all rays which strike them ; black bodies 
 absorb all. 
 
 Coloured bodies, however, absorb only a part of the coloured 
 rays which strike them, a great part of the white light which 
 illuminates them being reflected in a diffused state, and 
 without being decomposed. It is more especially red, yellow, 
 and green bodies which act in this way, and it is owing to 
 this property that they are reproduced on photographic 
 surfaces * Blue and violet bodies, which, on the contrary, 
 scarcely reflect any white light, are, on the other hand, very 
 photogenic or actinic .f 
 
 Blue and violet are even so photogenic that they are 
 reproduced on photographic surfaces as if they were white. 
 Bed and yellow are so little so that they are reproduced as 
 if they were black. There are, however, ways of modifying 
 these phenomena so as to make the reproduction of colours 
 more conformable to truth. (See Traite general de Photographies 
 5th edition, p. 28). 
 
 Dispersion. — We have already defined the term dispersion , 
 p. 18. The dispersion of refracting media is measured by the 
 length of the spectrum which is furnished by them. Thus 
 flint-glass is said to be more dispersive than crown-glass, 
 
 * We employ this term to indicate the surfaces of iodide, bromide, 
 chloride of silver, &c„ of which photographers make use, and which, as is 
 well known, are very sensitive to light (which blackens them). 
 
 f Terms used by photographers to indicate rays of fight having a 
 powerful action on photographic surfaces. 
 
30 
 
 PHOTOGRAPHIC OPTICS. 
 
 because the spectrum which it furnishes is longer than that of 
 crown-glass. 
 
 Yellow, being the most brilliant colour of the spectrum, is 
 that which approaches nearest in intensity to white. It is 
 also the ray of this colour which has been selected as the 
 refracted ray in measuring the refractive power (index of 
 refraction) of transparent media, the incident ray being white. 
 All indices of refraction given in tables are therefore too high 
 if the refracted ray under consideration is red, and all are 
 too low if the ray under consideration is violet ; seeing that, 
 out of the infinite number of refracted rays to which a white 
 ray gives rise, the red is that which is the least refracted, and 
 the violet the most. 
 
 But the numerical value, to express which all these indices 
 are too high for red and too low for violet, varies with the 
 nature of the medium to which the index refers, according as 
 the different media elongate more or less the colours of the 
 spectrum. 
 
 The co-efficient of dispersion (or simply the dispersion) of a 
 medium is indicated by the difference between the index of 
 refraction of the red (or of the yellow in photographic optics), 
 and the index of the violet, (of the indigo in photographic 
 optics). 
 
 No. 
 
 Names of Substances. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 9 
 
 10 
 
 Heavy boraeic acid flint-glass (Guinand) 
 
 Flint-glass (Frauenhofer) 
 
 Flint-glass (Bontemps) 
 
 Ordinary flint-glass (Guinand) 
 
 Boracic acid flint-glass (Guinand) 
 
 Venetian glass 
 
 Boracic acid crown-glass (Guinand) 
 
 Crown-glass (Dollond) 
 
 Boracic acid glass with, a base of zinc (Maes) 
 Crown-glass (Bontemps) 
 
 Density. 
 
 Index 
 
 of 
 
 Refraction. 
 
 3417 
 
 1*72339 
 
 2*135 
 
 1-63913 
 
 2-011 
 
 1*62847 
 
 3*610 
 
 1*62730 
 
 4-322 
 
 1*62696 
 
 2-713 
 
 1-53445 
 
 2*362 
 
 1*53455 
 
 2-484 
 
 1*53113 
 
 2*835 
 
 1*52401 
 
 2-447 
 
 1-51921 
 
CHROMATICS. 
 
 31 
 
 No. 
 
 rin 
 
 n 0 
 
 
 n e 
 
 n d 
 
 n c 
 
 n b 
 
 1 
 
 1*7637 
 
 1-7486 
 
 1-7320 
 
 1-7234 
 
 1-7144 
 
 1-7070 
 
 1-7049 
 
 2 
 
 1-6679 
 
 1-6573 
 
 1-6454 
 
 1-6392 
 
 1*6324 
 
 1-6272 
 
 1-6256 
 
 8 
 
 1-6558 
 
 1-6457 
 
 1-6346 
 
 1-6285 
 
 1-6222 
 
 1-6172 
 
 1-6154 
 
 4 
 
 1-6542 
 
 1*6443 
 
 1-6331 
 
 1*6273 
 
 1*6209 
 
 1-6160 
 
 1*6144 
 
 6 
 
 1-6539 
 
 1-6439 
 
 1-6328 
 
 1*6270 
 
 1*6205 
 
 1-6158 
 
 1-6140 
 
 6 
 
 1-5480 
 
 1-5433 
 
 1-5375 
 
 1-5344 
 
 1-5309 
 
 1*5284 
 
 1-5273 
 
 7 
 
 1*5478 
 
 1-5430 
 
 1-5374 
 
 1-5345 
 
 1-5311 
 
 1-5285 
 
 1-5275 
 
 8 
 
 1-5444 
 
 1-5393 
 
 1-5341 
 
 1-5311 
 
 1-5277 
 
 1-5247 
 
 1-5240 
 
 9 
 
 1-5466 
 
 1-5325 
 
 1-5271 
 
 1-5240 
 
 1-5207 
 
 
 
 10 
 
 1-5322 
 
 1-5275 
 
 1-5222 
 
 1-5192 
 
 1-5160 
 
 1-5134 
 
 1-5124 
 
 This table gives for the above ten kinds of glass the indices of reiraction of the seven 
 lines of the spectrum of IVauenhofer. 
 
 In treatises on physics, the index of refraction is designated 
 by the letter n. And when regard is to be had to dispersion, 
 the colour of the refracted ray selected for the index of refrac- 
 tion is indicated by a small letter at the side. Thus n r , 
 express the index of the red, the blue, the violet ; or, if 
 greater exactitude be desired, at the side of the n is placed the 
 letter indicating the line in the spectrum whence the refracted 
 ray has been taken. 
 
 We shall see, further on, for what end this is necessary. 
 
 The two preceding tables give — the first, the indices of 
 refraction of ten kinds of glass ; and the second, the variable 
 index for each kind in reference to the line of the spectrum 
 indicated at the side of n. 
 
 The angle of dispersion is the angle under which the different 
 rays are elongated. The dispersive power is the ratio of the 
 dispersion to the index of refraction shortly so called, minus 1. 
 
 4 .x. r n„ — n r 
 
 It is written, therefore : — • 
 
 n y — 1 
 
 Achromatic Prisms. — A system of prisms is achromatic 
 when it deflects rays of white light without colouring 
 them. 
 
 An achromatic prism (fig. 16) is obtained by associating 
 with a prism of crown-glass, A B C D, a prism of flint-glass, 
 C D F E, the angle of which and the material are suitably 
 
32 
 
 PHOTOGRAPHIC OPTICS. 
 
 chosen. If in such a system an incident white ray, R o, falls 
 on the face, A B, of the prism of crown-glass, the refracted 
 
 the red the direction ro'; so that the emergent ray, o' R', 
 will he colourless. 
 
 It is to be observed that the compound prism, which 
 is achromatic, for the ray R o, or for rays of the same 
 incidence, would not be achromatic for rays of another 
 incidence. 
 
 We propose now to find the angles which the two prisms 
 ought to have, in order that their union may constitute an 
 achromatic prism. Because this investigation is only the intro- 
 duction to that of achromatic lenses, we shall suppose the 
 angle a of these prisms so small, that the deviation, D, which 
 they produce on incident rays is equal to (n — - 1 ) a ; n being 
 the index of refraction of the material of which they are made. 
 Further, we shall suppose the rays which traverse them to 
 be very nearly perpendicular to the plane bisector of their 
 angle a. 
 
 We have for the deviation D of the red by the two united 
 prisms, — 
 
 n r being the index of refraction of the red for the first prism, 
 of which the angle is a; n r that of the second, of which the 
 angle is a'. 
 
 For the deviation D' of the violet we have — 
 
 D' = (n 0 — 1) a + (n' v — 1) a. 
 
 Fig. 16. 
 
 ray will be decom- 
 posed, and or will 
 be the red refracted 
 ray, and ov the vio- 
 let refracted ray. On 
 entering the flint- 
 glass prism the vio- 
 let ray will take the 
 direction v o', and 
 
 D = ( n r — 1) a + ( n r — 1) 
 
CHROMATICS. 
 
 33 
 
 Since these deviations ffiust he equal, we have — 
 
 (n r — 1) a + (n' r — 1) a' = ( n v — 1) a -f (n v — 1) a\ 
 
 whence we get — 
 
 (i). 
 
 Cl 71/y “ Wy 
 
 (X Ifl v — W f 
 
 The angle a is known, seeing that it is chosen arbitrarily ; 
 d ' will therefore be negative (that is to say, the second prism 
 must be reversed in* relation to the second), for n r — n v is 
 negative, whilst n v — n' r is positive. 
 
 But if the dispersive power of these two prisms be but slightly 
 different, their union will form a plate with faces sensibly 
 parallel, which will scarcely deflect rays of light, a result 
 which it is necessary to avoid. 
 
 Let us write, therefore, 
 
 D _ n' r — 1 a’ 
 
 (n r — l)a~ n r — 1 ' a 
 
 For, when we consider that experience proves that the yellow 
 is always very close to the red in the solar spectrum, and that 
 consequently n r is sensibly equal to n y , we can write : 
 
 D 
 
 (n r — 1) a 
 
 = 1 + 
 
 n y ~~ 1 
 % “ 1 
 
 Replacing - by its value above given, and indicating, by 
 p and p r , the dispersive powers, — — and ^ of the 
 
 two prisms, this becomes — 
 
 n'y- 1 
 
 [ <*> •>-*<— »(>-!■)• 
 
 This value, D, would still be nothing, if the dispersive- 
 powers p and p' were equal, or slightly different ; but in 
 practice the kinds of glass selected are such as experience 
 shows to be suitable for this object, namely, a colourless crown- 
 glass, very slightly dispersive but strongly refractive, and a 
 
 D 
 
34 
 
 PHOTOGRAPHIC OPTICS. 
 
 light* flint-glass, nearly colourless, and rather highly dis- 
 persive. 
 
 The preceding formulas give, therefore, — the first (1), the 
 relative angle of the two prisms ; the second, the deviation that 
 their combination will produce in incident rays. A white ray 
 will emerge sensibly white from such a compound prism, 
 which will therefore be achromatic. 
 
 Photographic achromatism or actinism. — But, for 
 photography, the preceding formulae must undergo a slight 
 modification ; for the two kinds of rays that must be brought 
 to coincide are not the red and the violet, but the yellow, the 
 dominant colour of the spectrum, and the indigo, where the 
 maximum chemical action of the spectrum is found. The dis- 
 persive powers must therefore be written— 
 
 and 
 
 And the first formula (1) becomes 
 a ' rii — n y 
 a n'i — n'y ’ 
 
 This obliges opticians to select for photographic instru- 
 ments special kinds of crown and flint glass, different from 
 those required for astronomical objectives. 
 
 In all cases, the achromatism determined by calculation is 
 never exact ; because for this it would be necessary to have 
 an accurate knowledge of the indices of refraction, and the 
 dispersive powers, which the methods employed for this pur- 
 pose do not give. Further, the angle of the prism should be 
 infinitely small, (and it has always an angle relatively large) ; 
 and, lastly, the incident rays have not, as they should have, 
 a constant direction perpendicular to the plane bisector of the 
 angle of the prisms. But the optician modifies by practical 
 experience the results furnished by calculation. With two 
 prisms, only two colours can be achromatised, or at most three, 
 
 * The heavy kinds of flint-glass would suit better, but they are generally 
 yellow-coloured, which is above all to be avoided in photographic objectives. 
 
LENSES. 
 
 35 
 
 by a good selection of the flint and crown glass ; for, to obtain 
 complete achromatism it would be necessary that the ratios 
 of dispersion of the substances which form the prisms should 
 be equal in all parts of the spectrum ; and, hitherto, no such 
 substances have been discovered. But two prisms, suitably 
 chosen as to angle and material, are sufficient for practical 
 purposes. 
 
 CHAPTER IY. 
 
 LENSES. 
 
 Section I . — Definitions relating 5 to Lenses. 
 
 Convergent and divergent Lenses. — Lenses are trans- 
 parent media, bounded by spherical surfaces, of which the 
 intersection is a line without sensible thickness. The latter 
 condition is important, as otherwise we should have a prism 
 with spherical surfaces, and not a lens. 
 
 Lenses are divided into two very distinct classes : the first 
 contains convergent lenses , thicker 
 at their central part than at their 
 margins ; the second, divergent 
 lenses , thinner, on the contrary, at 
 their central part than at their 
 margins. 
 
 Figure 17 represents in section 
 the different kinds of lenses ; the 
 three upper being divergent, and 
 the three lower convergent. The 
 first (that on the left) is bi-concave ; 
 the second, plano-concave ; and the 
 third has received the name of a divergent meniscus ; the 
 
 D 2 
 
 Fig. 17. 
 
36 
 
 PHOTOGRAPHIC OPTICS. 
 
 fourth, is bi-convex ; the fifth, plano-convex ; and the sixth is a 
 convergent meniscus . 
 
 Principal axis and optical centre of Lenses. — The 
 
 right line a a’ (fig. 18 ), which joins the centres of curvature a 
 
 and a of the spherical surfaces 
 of a lens, is the principal axis of 
 the lens. If one of the faces 
 of the lens he plane, the prin- 
 cipal axis passes through the 
 centre of curvature of the spheri- 
 cal face, and is perpendicular to 
 the plane face. 
 
 For every lens there exists a point, situated in its principal 
 axis, so that every incident ray which passes through it 
 does not undergo deviation. This point is called the optical 
 centre of the lens. 
 
 To find the optical centre of a lens (fig. 18 ), through the 
 centres of curvature a and a' of its surfaces draw two radii a V 
 and a b parallel to each other but oblique to the axis a a , then 
 join their extremities b b'; this line will cut the principal axis 
 at c, which is the optical centre. 
 
 If the lens be a meniscus, prolong the straight line b b 1 to 
 the point where it meets the principal axis, which will be the 
 optical centre. 
 
 The same construction gives the optical centre of bi-concave 
 and divergent meniscus lenses. As to plano-convex and 
 plano-concave lenses, the optical centre is determined by 
 the intersection of the spherical surface with the principal 
 axis. 
 
 A straight line passing through the optical centre of a lens, 
 and making with the principal axis an angle more or less 
 large, is called the “ secondary axis.” 
 
 Fig. 18. 
 
LENSES. 
 
 37 
 
 Section II . — Manufacture of Lenses * 
 
 Manufacture of Optical Glass.— It is a preliminary 
 necessity for the manufacture of lenses, to have a good 
 homogeneous glass, free from striae, perfectly colourless, and 
 transparent. Bubbles, lines, and even the presence of opaque 
 particles in glass, merely intercept a portion of the light 
 proportional to their size, whilst striae are a certain indication 
 of an imperfect mixture of the substances composing the 
 glass, and are productive of unequal refractions. These 
 striae may be compared to tho^e produced by the mixture of 
 two solutions of unequal density, such as gum-water and 
 pure water, alcohol and water, &c. The best way to see 
 if a glass lens is free from striae is to mount it in a 
 wooden frame, which is fixed to the shutter of the dark 
 room in such a way that it may receive the daylight. The 
 eye being placed at the focus of the lens, the smallest striae 
 are easily perceived. Veins in glass may also be discovered 
 by looking at it very obliquely opposite a feeble light in a 
 well-darkened room. 
 
 Transparency of the glass is a condition essential for 
 a lens ; if within it there exists^ a cloudiness, it will be 
 useless. It should also be colourless. Certain kinds of 
 glass are yellowish (particularly flint-glass), reddish or 
 greenish (crown-glass), and thus arrest — especially the 
 yellowish and reddish kinds — a considerable part of the che- 
 mical rays of light. 
 
 There are great difficulties in obtaining discs of glass of 
 large dimension quite free from striae. At present, however, 
 a great part of these difficulties has been overcome, and there 
 
 * Pretchl, Prdktische Dioptrih. Vienna, 1828. 
 
 Smith, Treatise on Optics, 1767. 
 
 Laboulaye, Dictionnaire des Arts et Manufactures, tome ii., art. Verre. 
 
 Hekschel, Treatise on Optics. 
 
 Hekschel, The Telescope ( Encyclopedia Brit.), 1861. 
 
 H. Papin, La Lunette d’approche. Lausanne, 1861. 
 
38 
 
 PHOTOGRAPHIC OPTICS. 
 
 are to be bad, for photographic purposes, discs of crown-glass at 
 from five to six francs per kilogramme, and discs of flint-glass 
 at fourteen francs per kilogramme,* for sizes of from one to six 
 inches in diameter. Crown-glass more commonly costs from 
 three to six francs per kilogramme ; but then it is greenish, 
 and always contains some striae, particularly when the discs 
 are of large dimensions. 
 
 Bontemjps and Guinand are the two makers of optical glass 
 who have done the most to advance this branch of industry. 
 
 The crucibles employed for the fusion of optical glass are 
 of sorted fire-clay, capable of receiving a charge of about 250 
 kil., with covers to keep out the smoke, and having somewhat 
 the form of very short-necked retorts. 
 
 The furnace is vaulted, and capable of being raised to a 
 very high temperature. The crucible, well covered, is first 
 heated to whiteness in the furnace ; then, when the fuel ceases 
 to give off smoke, it is charged successively with 10, 20, or 
 40 kil. of material, and after each charge the crucible is 
 covered again, to avoid the smoke (putting the charge into it 
 only when the fuel does not emit smoke). At the end of from 
 eight to ten hours the furnacing is finished. The crucible 
 being now raised to a white heat for four hours, the material is 
 stirred for some minutes with a rod of pottery-clay attached 
 at its upper extremity to a bar of iron. Six times, from 
 hour to hour, the stirring is repeated, smoke always being 
 avoided. Then the heat is reduced, in order that the bubbles 
 of the melted mass may rise to the surface. At the end of 
 two hours, the furnace is again raised to full activity for five 
 hours, so that the glass regains its fluidity. It is again 
 stirred for two hours, the stirring-rod is removed from the 
 crucible, which is then closed up, as also the various openings 
 
 * At M. Sautter’s, manufacturer of glasses for light-houses, Avenue 
 Montaigne a Paris ; also at Chance and Co.’s of Birmingham. French makers 
 generally use glass of the former kind ; English makers that of the latter 
 kind. But many foreign opticians already ask for glass of French manu- 
 facture, the prices of which are lower, while the material is very perfect. 
 
LENSES. 
 
 39 
 
 of the furnace, and, lastly, all is left to cool for eight days. 
 The crucible is taken out and broken, and the mass of glass 
 divided into pieces. The operation is the same for flint-glass 
 as for crown-glass. 
 
 The divided pieces of the mass of glass are examined and 
 sorted. The purest are used for astronomical objectives, 
 the next quality for photographic objectives, and a third for 
 ordinary lenses ; the rest being waste, which is added to the 
 next meltings. 
 
 The pieces are then softened in a kind of muffle, and made 
 into square plates of a variable thickness (commonly of from 
 half an inch to two inches). 
 
 The plates destined for astronomical objectives are ground 
 with wet sand in cast-iron grinding tools, to give them pretty 
 nearly the shape indicated by theory. As regards the other 
 plates, they are softened by heat, and cast in moulds of clay 
 or of iron, coated with sand, so as to give them very nearty 
 the form which they must have. There may be formed in 
 this operation streaks and striae in the glass, and therefore 
 opticians prefer grinding to moulding. For the large lenses 
 employed as condensers in apparatus for enlargements, mould- 
 ing is had recourse to, striae in these lenses not having very 
 troublesome consequences. 
 
 The following is the composition of the glasses of Guinand 
 and Bontemps. 
 
 FLINT-GLASS. 
 
 
 Bontemps. 
 
 Guinand. 
 
 White silicious sand 
 
 261 
 
 225 
 
 Eed oxide of lead 
 
 261 
 
 225 
 
 Potash (1st quality) 
 
 60 
 
 52 
 
 Borax 
 
 18 
 
 4 
 
 Nitre 
 
 
 3 
 
 Manganese 
 
 
 1 
 
 Arsenious acid 
 
 « m 
 
 1 
 
 Waste pieces resulting from previous meltings . . 
 
 
 89 
 
40 
 
 PHOTOGRAPHIC OPTICS. 
 
 CROWN-GLASS. 
 
 White silicious sand . . 
 Carbonate of potash . . 
 Carbonate of soda . . 
 Carbonate of lime . . 
 
 Borax 
 
 Red oxide of lead . . 
 Peroxide of manganese 
 Arsenic 
 
 Bontemps 
 
 ( 1846 ). 
 
 360 
 
 150 
 
 84 
 
 6 
 
 Guinand 
 
 ( 1840 ). 
 
 400 
 
 160 
 
 20 
 
 20 
 
 1 
 
 Bontemps has observed that crown-glass is less liable to 
 exfoliate under the influence of damp, by introducing into its 
 composition borax with carbonate of soda, not in excess, 
 however, or else the same inconvenience is produced. 
 
 Lastly, Faraday, Dutirou, and several other savans and 
 practical men, have made many researches on very heavy 
 kinds of flint and very refractive kinds of crown-glass, with a 
 view of making the relations between the various colours 
 of their respective spectra the same ; but these researches, 
 although very interesting in the optics of astronomical tele- 
 scopes, are of little use to photographic opticians, in whose 
 hands ordinary crown-glass, united with light flint, produces 
 excellent results. Recourse is rarely had to the heavy kinds 
 of flint, which generally present a yellowish colouration — a 
 colour which, above all, is objectionable for photographic use. 
 
 The grinding Tools fitted for working the surfaces of 
 Lenses. — The lenses being brought to a shape approximate 
 to that which they are to have, either by casting, or by grind- 
 ing with wet sand in convex or concave tools of cast-iron, are 
 now to be brought to the form calculated by theory or indi- 
 cated by practice. For this purpose they are ground with fine 
 emery, in spherical tools of brass or iron, with given radii 
 of curvature, a little larger than the lens to be ground, other- 
 wise the surface of the outer part of the lens would not be 
 spherical. 
 
LENSES. 
 
 41 
 
 A sufficient thickness is given to these tools to enable them 
 to resist flexion. When small, they are cast in a single 
 piece of a sufficient thickness ; but when they are large — 
 over six or eight inches in diameter, for example — they are 
 made only half an inch thick, and cemented solidly to a thick 
 stone, or to a second tool of cast iron, or some such thing.* 
 
 To make the tool, the iron is first cast in a mould made from 
 a model in wood and is then finished in a lathe. 
 
 It is necessary to give to the tools the radii of curvature 
 which the surfaces of the lens must have. For this purpose, 
 by means of a beam-compass, an arc of a circle, double the dia- 
 meter of the tool, is drawn on a plate of copper, made very 
 flat by hammering, and followed up carefully with a file, so as 
 to have an exact shape. Two of them are made, the one con- 
 cave, the other convex ; then, after having fixed one on the 
 table, the other is rubbed against it with emery. The two 
 gauges are thus rubbed one upon the other, so as to give 
 them accurately the curvature which they must have. 
 
 These gauges are applied against the tools (the one convex, 
 the other concave) whilst they are being worked in the lathe ; 
 an operation which gives them, approximately, the radius of 
 curvature which they ought to have. The tools, thus finished, 
 are rubbed the one in the other with emery, until they touch 
 each other at all parts, by which means they are made spheri- 
 cal. It is necessary to have two tools, — the one convex, the 
 other concave,— because during the process of grinding the lens, 
 the tool with which this is done loses its shape, and then 
 requires to be rubbed with the other in order to restore to it 
 its primitive curvature. 
 
 The roughly fashioned lens is fixed by means of soft pitch, 
 spread out in separate drops on one of its surfaces, to a plate of 
 brass, rounded and worked in the lathe in such a way as that 
 the glass adapts itself to it as closely as possible. For this end 
 
 * The method adopted by Mr. Ross is not to cement them down on a 
 thick stone, but to support the entire tool by means of iron ribs cast to it. 
 
42 
 
 PHOTOGRAPHIC OPTICS. 
 
 the glass and the plate should be previously warmed. The 
 plate holds the glass, and prevents its yielding under the pres- 
 sure of the hand. Before pursuing these operations, the edge 
 of the glass is ground down so as to make it quite circular, 
 which is done by fixing it in the lathe and turning it true 
 with the point of a diamond or other hard stone. 
 
 It is from this moment that the most delicate operations in 
 the manufacture of the lens begin. 
 
 Smoothing and polishing of the surface of 
 Lenses. — The tool, either concave or convex (according as 
 the face of the lens is to be convex or concave), being fixed 
 in a very solid block, receives a little moistened fine emery. 
 The lens, fixed on its plate, is taken in the right hand (there 
 is often attached to the plate a handle to render its manage- 
 ment more easy), and moved about in the tool with more 
 or less pressure. The glass is moved about in the tool five or 
 six times in a circle, and two or three times in different direc- 
 tions. Great care must be taken, never to go beyond the edge 
 of the tool (which, for this object, should be a little larger than 
 the glass) and, to keep the emery always damp. At the 
 end of a period varying with the extent of the surface to be 
 worked, and when the glass touches closely at all points 
 of the surface of the tool, the emery is changed for finer and 
 finer kinds, and the smoothing is continued until all the 
 lines and marks have quite disappeared from the surface of 
 the glass. It is necessary, from time to time, to retouch the 
 tool (supposing it to be concave) with the convex tool, so as 
 to preserve its curvature. It is especially when the work 
 is advanced that this retouching becomes often necessary. 
 Lastly, after the emery, very fine pumice-stone is used, 
 which renders the grain still finer, and begins the polishing. 
 At this stage the lens is detached from its plate with the* 
 point of a knife, and the other surface is worked in the same 
 manner. Before commencing, it is necessary to examine, by 
 means of the lathe, if the lens be well centred on its plate, or 
 at least approximately so. This is done by looking at the 
 
LENSES. 
 
 43 
 
 margin of the lens, which should then have throughout the 
 same thickness. 
 
 The lens, after the grinding, has curvatures really spheri- 
 cal ; and now commences the difficult operation of polishing, 
 for which extremely skilful workmen are necessary, the polish- 
 ing very often altering the spherical surfaces of the lens. 
 
 There are several methods of polishing, a succinct idea of 
 which is here given. A melted mixture of equal parts of pitch 
 and resin is passed through a piece of linen. The tool is 
 gently heated, and the preceding mixture (somewhat cooled 
 so that it may have lost its previous fluidity) is spread over 
 it in sufficient quantity to cover it to a thickness of three or 
 four millimetres. The resinous mixture is spread in a 
 uniform layer by means of the other tool, which for this pur- 
 pose ought to be very cold and thoroughly clean. The first 
 tool is then plunged into cold water to harden the resinous 
 mixture, a little very fine rouge, is spread over its surface, and 
 the lens carefully polished by proceeding in the same way as 
 for the smoothing previously described, until the operation 
 is completed. It is necessary to take care that the glass do 
 not get hot, and to exert a uniform pressure with the hand 
 over all the surface of the lens, otherwise certain parts of the 
 surface will be polished before the others, and the surface thus 
 lose its sphericity. To avoid this defect, some opticians add 
 round the lens, which they fix in the resinous mixture on the 
 block, segments of the same radius of curvature, so that the 
 lens occupies the centre, and the intervals between the seg- 
 ments absorb the excess of the rouge. In this way a surface 
 very nearly spherical is obtained, but the operation is a more 
 tedious one.* 
 
 In following the preceding method (without additional 
 segments), it is necessary to trace in the cement some furrows 
 at a distance from each other of half an inch, about a line 
 broad, and crossing each other perpendicularly. All the 
 
 * The author has seen this method practised at Mr. Boss’s establishment 
 in London. 
 
44 
 
 PHOTOGRAPHIC OPTICS. 
 
 superfluous parts of the rouge collect in these, as well as 
 the fragments of cement which become accidentally detached. 
 
 It is also necessary, as in the smoothing, to preserve the 
 curvature of the tool by applying from time to time the other 
 tool to it, and rubbing them together with a little fine rouge, 
 which is then removed with water. 
 
 Another method of polishing consists in spreading on the 
 tool a sheet of damp paper, which is made to adhere by 
 applying the other tool to it, and which is lightly rubbed 
 with moist rouge. The lens is then polished in this paper 
 tool. It is stated that German opticians employ, instead of 
 paper, fine cloth, and that they thus obtain a very fine 
 polish. 
 
 Whatever method of polishing be employed, the lens still 
 has not an absolutely spherical surface, unless a series of 
 precautions be taken, which renders the lens of a very high 
 price, and which is only adopted by opticians of the highest 
 rank, for the polishing of astronomical objectives. 
 
 The spherical curvature of the lens, polished as has been 
 just described, is, however, sufficiently correct for the pur- 
 poses of photography, where images have not to be magnified 
 by powerful eye-pieces, like those formed in the focus of 
 telescopes. 
 
 Lastly, to avoid the flexion of the glass during the smoothing 
 and polishing, the margin of the lens is always left of a certain 
 thickness. 
 
 Lenses with convex surfaces are the easiest to work ; 
 convergent and divergent meniscus lenses are much more 
 difficult to manipulate. Such lenses are even difficult to 
 obtain of correct surfaces; for example, the three lenses 
 constituting the wide-angled lens of Dallmeyer , those consti- 
 tuting the globe-lens of Harrison , and the doublet of Boss , 
 objectives of which we shall shortly speak. 
 
 Centering and mounting of Lenses. — When the centres 
 of the two surfaces of the lens are in the same right line, 
 perpendicular to the plane of the circumference of the lens, 
 
LENSES. 
 
 45 
 
 the lens is centered, and has the same thickness at all parts 
 of its margin. When less than two inches in diameter, the 
 lens is put in the lathe and fixed in it with mastic as 
 solidly and as centrally as possible. On making it revolve, 
 and observing in its two faces the reflected image of a 
 distant candle-flame, the two images produced by the surfaces 
 should not be displaced from each other. If the centering 
 is imperfect, one or both of the images describes a circle. 
 It then becomes necessary to move the lens until the 
 centering is perfect, that is, until the images remain motion- 
 less, and then to grind with copper and emery the margin of 
 the lens. 
 
 If the lens be more than two inches in diameter, it is again 
 placed in the lathe on a chuck capable of universal adjustment. 
 A peculiar construction of callipers, the legs of which are of 
 unequal length, is then fixed to the bench of the lathe, in such 
 a way that the lens near its margin may run between the 
 two shortest legs, the two others being provided with a spring, 
 which tends to separate them from each other. If now the 
 lens be revolved, the extremities of the callipers separate or 
 approach, if the lens is not centered. The chuck is then re- 
 adjusted until the callipers record the uniform thickness of the 
 lens at its outer parts. In this position the lens is made cir- 
 cular, by giving it a rapid rotary movement, and by rubbing 
 it gently at the margin, without shocks or jolts, which would 
 displace it. By such means the lens is centered. 
 
 We operate in the same manner for convergent and diver- 
 gent lenses, and as most usually a convergent lens is combined 
 with a divergent lens in the same ring (called a cell), we 
 give them the same diameter, taking care that the edges 
 are at right angles to the plane of the circumference, that is, 
 parallel to the axis of the lenses. 
 
 The two lenses are often cemented together, and must then 
 present a common surface. To effect this, they are warmed, a 
 little Canada balsam is poured into the concave surface, and 
 then, after applying to this the convex surface, the two lenses 
 
46 
 
 PHOTOGRAPHIC OPTICS. 
 
 are pressed together, so as to force out the excess of the 
 liquid. When cooled, the lenses hold firmly together (for they 
 cannot he separated without heat), and form but a single 
 one. 
 
 Frequently also, when the two lenses have not a common 
 surface, three small pieces of tin-foil are introduced at equal 
 distances asunder, between their margins, so as to separate 
 them ; or a brass ring is employed for this purpose. The 
 objective which photographers call the “ the double combination ” 
 offers an example of these two ways of mounting lenses ; those 
 in front, which look towards the object to be reproduced, are 
 cemented together, while the two behind are separated in 
 their common mounting by a ring. 
 
 When the lens is fixed in its brass ring, so that it can- 
 not be taken out without raising the bent edge of the brass 
 with a knife, it is said to be set. Most usually, it is kept in 
 place by a second ring, which can easily be unscrewed. 
 
 Section III.— -Law of conjugate Foci, and the magnitude of Images 
 at the focus of Lenses. 
 
 In this chapter we treat of the course of luminous rays 
 through lenses. But, in order not to uselessly complicate this 
 study, we suppose two conditions, from which we shall free 
 ourselves presently, but of which the reader ought not to lose 
 sight. The first is, that incident rays are composed of simple 
 light (for, as we have already seen, the refraction of a ray of 
 white light is always accompanied by its decomposition). 
 The second is, that lenses have, at their central part, an 
 extremely slight thickness, or even none at all * ; or, in other 
 
 * That, at least, is the condition commonly set forth in treatises on 
 physics. But it is a very erroneous one when applied to meniscus lenses, of 
 which the radii of curvature are very short and the diameter is considerable, 
 although the thickness of such lenses is slight. To illustrate this, fig. 19 
 represents a convergent meniscus, of which C R and C' R' are the radii of 
 
LENSES. 
 
 47 
 
 words, that the radii of curvature of the faces are very great 
 relatively to their diameter. 
 
 Assimilation of Lenses to Prisms. — In studying the 
 course of luminous rays through lenses, it is always supposed, 
 which is, moreover, true, that the infinitely small portion 
 of the lens struck by the ray may be replaced by a tangent 
 plane. 
 
 A convergent lens may thus be considered as formed of 
 prisms united at the base, and a divergent lens of prisms 
 united at the summit. Thus, a bi-convex lens, A (fig. 20), 
 may be assimilated 
 to two prisms (B) 
 joined at the base; 
 and a divergent lens 
 
 (C) , to two prisms 
 
 (D) united at the 
 summit. This ex- 
 plains how it is that the former (and all convergent lenses, 
 in general) causes rays, rr, incident upon it, to meet in /, 
 and that the latter causes them to separate along r'; since 
 we know that prisms deviate towards their base rays which 
 traverse them. 
 
 To find geometrically the course of a luminous ray, ED, 
 (fig. 21), falling parallel to the axis C C, on a lens L M, 
 (bi-convex for example, but the thickness of which we shall 
 neglect), take the radius of curvature, I) C', of the face M, and 
 
 curvature. Now, if C C' is small the thickness will be small, and could 
 be regarded as nothing if the lens were 
 bi-convex. However, on applying to this 
 lens the ordinary formulae which determine 
 the focal distance, the expression of its aber- 
 ration, &c., a relatively considerable error 
 comes out. This is why the definition, “ no 
 thickness,” is erroneous. It is necessary that 
 the versed sine a 6 of the radius of curva- 
 ture may be treated as nothing in relation 
 to this radius, particularly in calculations relating to aberrations. 
 
 Fig. 20. 
 
48 
 
 PHOTOGRAPHIC OPTICS. 
 
 the radius of curvature, C E, of the face N, the two making 
 with the axis C C' equal angles. To these radii of curvature 
 
 Fig. 21. 
 
 draw the tangents DA and E A. We have, then, no longer 
 to consider the lens, hut the prism A. Now, the angle 
 A being infinitely small (since we regard the lens as very 
 thin), the deviation which it produces on the ray which falls 
 normally to its bisector AB, is equal to (n — T) A. The 
 emergent ray E B ' will then cut the axis in a point f. 
 
 If in place of the incident ray B D any other is taken (but 
 always parallel to the axis) more or less removed from the 
 centre of the lens, it is found, on converting the angle A into 
 figures, that all the emergent rays cut the axis of the lens 
 at the same point, /, which constitutes its principal focus. 
 
 Calculation of the focal length of Lenses; Princi- 
 pal Focus and conjugate Focus. — Let AB be the spherical 
 
 Fig. 22. 
 
 surface, infinitely small, of a medium more refractive on the 
 right of A B than on the left ; let D be a radiating point, 
 emitting an incident ray, DA. Join the centre of curvature, 
 
LENSES. 
 
 49 
 
 C, of the surface A B to the points A and D ; the axis will be 
 D C, and A C the normal, to which the refracted ray will 
 approach, cutting the axis in /'. Let us determine the relation 
 of B D to B /'. 
 
 From the point C let fall on the incident ray and on the 
 refracted ray the perpendiculars C H, C I, and consider A B 
 as a straight line ; which may be done, it having been consi- 
 dered as an arc infinitely small. The right-angled triangles 
 D A B, D H C, are similar, the angle at D being common, and 
 give the proportion DC:DA::CH:AB, and by suppos- 
 ing (the angle f being very small) I) A = D B=p (the distance 
 of the radiating point from the spherical surface ), and BC being 
 equal to R ( the radius of curvature of the spherical surface ) 
 DC=p-fR, and this proportion may be written p+R :p : : 
 C H : A B. 
 
 The similar triangles f I C, /' A B (being rectangular, and/' 
 common), give, f'C :/'B :: IC : A B. Now, /'A =/' B 
 (/' being, like D, very small), f~B=p' {focal distance of AB), 
 therefore p' — R : p : : I C : A B. 
 
 Dividing the two proportions, term by term, we get 
 p + R p C H 
 
 ! " 1 ‘ CT 
 
 : 1. C H and C I are the sines of the angle 
 
 p' - R p 1 
 
 of incidence and the angle of refraction ; their ratio is there 
 
 fore the index of refraction n, therefore 
 which we get 
 
 P + R 
 p '- R 
 
 £5; from 
 
 V 
 
 1 n 
 
 1 7 
 
 p p 
 
 n — 1 
 
 . . (i). 
 
 Now, in a similar way it may be shown that if the ray 
 is refracted behind the incident ray, the formula becomes 
 
 1 n n — 1 
 
 p p R 
 
 We see, therefore, that whatever may be the incidence of 
 the ray D A, for we have chosen it arbitrarily, /' B or p 
 
50 
 
 PHOTOGRAPHIC OPTICS. 
 
 remains constant, since the preceding equation does not 
 mention the incidence ; therefore all rays emitted from a radiat- 
 ing point to the infinitely small spherical surface of a medium are 
 refracted to a common point , called the focus. 
 
 We have supposed the incident ray D A oblique to the axis 
 D 0, but if we had supposed it parallel to the axis, as D' A, we 
 should get for the refracted ray A P instead of A F, and the 
 point P determines the principal focus of the medium. 
 
 n P, 
 
 In this case, (BP) = — .... (2). 
 
 n — 1 w 
 
 Let us take, now, the case of a lens (fig. 23), which we shall 
 
 Fig. 23. 
 
 suppose bi-convex, with equal curvatures, sufficiently thin for 
 its thickness to be neglected, and with very small aperture, 
 precisely as we made it for the preceding case. The letters 
 from fig. 22 indicate the same things. Let A B, A' B' be the 
 two surfaces of the lens ; C, C' the centres of curvature ; C A, 
 O' A' the radii of curvature R, R' ; Df the axis ; D A an inci- 
 dent ray coming from a point, X), situated on the axis : the 
 refracted ray will be, as in the preceding case, A /, and we 
 shall have, supposing the medium to the right of A B to be of 
 indefinite extent, 
 
 CO • • • -\ + l’ 
 
 n — 1 
 
 "IT' 
 
 But the refracted ray meets the face A'B' in A! and cuts 
 the axis in /'. Let us now suppose the medium to be of in- 
 
LENSES. 
 
 51 
 
 definite extent to tlie left of A' B' ; /' as the radiating point ; f A! 
 an incident raj ; A' A the refracted raj : its prolongation will 
 
 • 1 Tb 71 "J_ 
 
 cut the axis in /. We should thus have -~ r — — 
 
 Let /' B' = p, and B '/ = p ; and this proportion becomes 
 
 ( 2) . . . . I _ “ = . 
 
 p p R' 
 
 Neglecting B B', which we regard bj hjpothesis as in- 
 finitelj small, and adding the two equations together we get 
 
 1,1 __n- 1 ( n- 1 (n— 1) (R + R') 
 
 ^ ; * * * * p p' R + R' RR' 
 
 It is plain that p and p f — that is to saj, the distance of the 
 radiating point from the lens , and the focal distance of it — do not 
 depend at all on the incidence of the raj D A, but onlj on the 
 radii of curvature R and R' of the lens, and the index of 
 refraction of which it is formed. Which was to be demon- 
 strated. 
 
 If the incident raj D A is parallel to the axis, p is infinite, 
 and p' represents the principal focal distance of the lens, in this 
 case p' or / becomes 
 
 RR' 
 
 ; (ti-i) (R + R') ’ 
 
 Formulse determining the principal focal lengths 
 of Lenses for Rays parallel to the Axis. — Knowing the 
 index of refraction n of the material of which the lens is 
 formed, and its radii of curvature R and R r , its principal focal 
 distance / is given for the different kinds of lenses b j the fol- 
 lowing formulae. We have to remark, however, that the value 
 of/ is onlj approximate, because we take no account in them 
 of the thickness of the lens. For a closer approximation, see 
 the Treatise on the ^Reflection and Refraction of Light , bj Henrj 
 Coddington, Cambridge, 1829, pages 94 et seq. 
 
 N'B. — The focal length / is reckoned from the optical 
 centre of the lens. — {See p. 36.) 
 
 e 2 
 
52 
 
 PHOTOGRAPHIC OPTICS. 
 
 00 
 
 ( 2 ) 
 
 ( 3 ) 
 
 (O 
 
 ( 5 ) 
 
 ( 6 ) 
 (0 
 ( 8 ) 
 
 Bi-convex lens (R > R' or R' > R). 
 
 RR ; 
 
 n — 1) (R -j- R') 
 Equi-convex lens (R = R'). 
 
 J 2 (n - 1) 
 Plano-convex lens. 
 
 / = 
 
 E 
 
 0 - 0 
 Convergent meniscus (R' > R). 
 
 -RR' 
 
 1 (n — 1) (R — R'* 
 Bi-concave lens (R > R') or R' > R). 
 
 -RR' 
 
 J (n-i) (R + R'’ 
 Equi-concave lens (R = R'). 
 
 J 2 (n - 1 ) 
 
 Plano-concave lens. 
 
 -R 
 
 / 
 
 o-o 
 
 Divergent meniscus (R > R'). 
 
 -RR' 
 
 1 (»- 1) (R-R')' 
 
 Examples of these calculations. — 1. "What is the focal length 
 of a bi-convex lens, of which the radii of curvature are respec- 
 tively 6 metres and 1 metre, and the index of refraction 
 1 - 5 ? 
 
 6X1 6 
 
 Formula (l) gives/ = 
 
 metres. 
 
 ( 1-5 - 1 ) (6 + 1 ) 3*5 
 
 = 1*714 
 
 2. What would be the focal length of a convergent menis- 
 
LENSES. 
 
 53 
 
 cus, having the same radii of curvature and index of refraction 
 as in the preceding example ? 
 
 It is necessary to take [formula 4] R'> R; therefore R' = 6, 
 and R = 1. If not, instead of a convergent meniscus, we 
 should have a divergent one. — (See the next example.) 
 -1X6 -6 
 
 /= 7 
 
 2 * 4 metres. 
 
 (1*5- 1) (1 - 6) -2*5 
 
 3. What would be the focal length of a divergent meniscus 
 with the same radii of curvature and the same index of refrac- 
 tion as before ? 
 
 It is necessary to take (formula 8) R>R ; therefore R- 6, 
 and R = 1 ; and we have — 
 
 -6x1 —6 
 
 / = 
 
 = — 2 • 4 metres. 
 
 (1-5 - 1) (6 - 1) 2-5 
 
 4. I wish to have made by an optician a bi -convex lens of 
 1*714 metres focal distance, the two radii of curvature being 
 to each other as 1 to 6. What will be the lengths of the radii 
 of curvature, the index of refraction being 1*5? 
 
 Since one of the radii of curvature is 6 times as long as the 
 other, R' = 6 R. 
 
 In formula (1) we replace / by its given value (1*714 
 metres), and R' by its value 6 R, and we shall get 
 
 W14 metres = 
 
 0*o x 7R 3*5 
 
 whence 6 R or R' = 1*714 metres x 3*5 = 6 metres, 
 
 and R = 1 metre. 
 
 5. I possess a bi-convex lens, and I wish to know the 
 index of refraction of the material of which it is formed. I 
 have measured its focal length, which is 1*714 metres, and 
 its two radii of curvature, which are respectively 1 metre and 
 6 metres. What is this index? (formula 1), 
 
 6x1 6 
 
 ’14 
 
 (n — 1) (1 + 6) 7n-7 
 
 whence (7 n 
 
 7) 1 * 714 = 6 ; whence n = — or 1 * 5. 
 
 £ 
 
54 
 
 PHOTOGRAPHIC OPTICS. 
 
 Fig. 24. 
 
 It is seen, therefore, that these formulas always enable n, 
 E and B', or/ to be found, two of the three elements being 
 known. These formulas are therefore in frequent use. 
 
 Focal length of Lenses.* — Let us suppose, first, the 
 most simple case, namely, that of luminous rays r (fig. 24) 
 
 emanating from a point infinitely 
 distant— of a star, for example- — 
 and falling parallel to the axis of 
 a convergent lens A. In this case 
 the emergent rays all converge to- 
 wards a single point, / in the axis, 
 which has been named the principal 
 focus of the lens, and at which an image of the point is 
 formed, 
 
 Conversely, a luminous point /(fig. 25)— a candle, for ex- 
 ample — placed in the principal focus 
 of a convergent lens A, emits diver- 
 gent rays which, after having tra- 
 versed the lens, all emerge from it 
 along r, parallel to each other and 
 to the axis. 
 
 The principal focus of a convergent 
 lens is therefore always very easy to determine approximately 
 by experiment. It is sufficient for this to present the lens to 
 the solar rays in such a manner that these fall perpendicu- 
 larly upon it, and to measure the distance which separates 
 the centre of the lens from the sharpest image of the sun 
 which is formed at its focus. — (See p. 65). There is, however, 
 a slight error which results from the thickness of the lens, 
 particularly if it is a convergent meniscus. 
 
 Instead of a radiating point situated at infinity, let us take 
 a point nearer to the lens, but situated in its axis. In this 
 case, the rays emitted by the luminous point are no longer 
 
 Fig. 25. 
 
 * This paragraph is only an elementary enunciation of that which has 
 been demonstrated geometrically in the preceding paragraphs. 
 
LENSES. 
 
 55 
 
 parallel ; they diverge, and fall divergently on the lens, and 
 their focus is formed so much the farther beyond the lens the 
 more the point approaches it. If the radiating point is at a 
 distance from the lens equal to double its principal focal 
 length, then its image is formed at a distance precisely 
 equal behind the lens. The more it approaches, the farther 
 off its image is formed ; and there comes at last a moment 
 — that at which the radiating point is at a distance from 
 the lens equal to its principal focal length — when the rays 
 emerge parallel to each other, and no longer form any image 
 at all. 
 
 Divergent lenses form no images at all, whatever the dis- 
 tance of the radiating point. Hence it is (fig. 26) that the 
 rays r r, parallel to the axis, A /, 
 of a lens A, emerge along r diver- 
 gent. There is therefore formed 
 no real image behind the lens. 
 
 If we prolong the rays r' until 
 they meet the axis, as shown in 
 the figure, A / will be the prin- 
 cipal focal length of the lens A. 
 
 The same relation which exists between the variable focal 
 length of convergent lenses, and the distance of the radiating 
 point, exists for divergent lenses ; only that, instead of a focus 
 forming behind the lens, none at all is really formed, but one 
 is said to be formed virtually . 
 
 Just as the deviation of a luminous ray produced by a prism 
 depends on the angle of the prism, and the index of the 
 material of which it is made, so the principal focal distance 
 of a lens depends on the radii of curvature of the spherical 
 surfaces which form it and on its index of refraction. It is 
 dear, in fact, that the shorter the radii of curvature are the 
 shorter will be the focal length. Also, of two lenses with 
 equal curvatures, that which is formed of the most highH 
 refractive material will have the shortest focal length. — 
 (See p. 67.) 
 
 Fig. 26. 
 
56 
 
 PHOTOGRAPHIC OPTICS. 
 
 The focal Plane. — If, instead of a single luminous point 
 situated in the axis of the lens, we consider an object, C D 
 (fig. 27), of a certain size, we find sensibly the same results if 
 
 the extent of the ob- 
 ject is not very great. 
 For let us consider 
 a point D in this ob- 
 ject (which we shall 
 suppose situated at 
 infinity) sending to 
 the convergent lens 
 A B a pencil of rays 
 oblique to the axis a C ; its image will be formed at p', 
 sensibly in the same plane (perpendicular to the axis a 0) as 
 the focus p of the rays parallel to the axis of the lens and 
 coming from the point C. The plane p p' is called the focal 
 plane. 
 
 It is seen, therefore, that the image p p' is formed inverted 
 behind the lens, and that its size evidently depends upon the 
 size of C D, and also upon the distance, a C, of the object from 
 the lens, and on the focal length of the latter ; since in the 
 two similar triangles p p' a and C D a there is the propor- 
 tion — 
 
 C D : pp’ :: C a : ap. 
 
 The shorter, therefore, the focal length of a convergent lens 
 (the object C D remaining at a constant distance), the smaller 
 will be the image of the object. The farther the object is 
 removed from the lens A B (its focal length being given), the 
 smaller, again, will be the image of the object. 
 
 Between the focal length of a lens, the distance of the object 
 from the lens, and the size of the image, there are, therefore, 
 geometrical ratios, which we must further study. The law 
 which connects these distances is called the law of conjugate 
 foci. 
 
 Experimental determination of the absolute focal 
 
 Fig. 27. 
 
LENSES. 
 
 57 
 
 length of Lenses. — We have given at page 51 formulae by 
 the aid of which the principal focal length of a lens was 
 easily determined, and at page 52 an experimental process for 
 the same purpose ; but neither the one nor the other of 
 these methods is sufficiently exact if it be applied to a 
 system of lenses having a common axis — for example, to 
 photographic objectives. In this case the following method 
 is applied : — 
 
 Let A, B (fig. 28) be objects widely separated, situated in the 
 horizon, 0 the objective screwed A D 
 on to a camera placed on a well- 
 levelled table. On bringing them 
 to a focus on the ground-glass, 
 we find that the objects D and E 
 form the limit of the image on the 
 ground-glass. D C E is the angle 
 included by the lens. Draw on 
 the middle of the ground- glass a 
 vertical right line, and turn the 
 camera until the point E falls on 
 this line. With a pencil pressed 
 against the side of the camera draw 
 the right line c e. Turn the camera towards the point D until 
 this point falls on the line traced on the ground-glass. Draw 
 the right line c d in the same way as c e was done. If this line 
 does not cut e e, prolong it until it does. It is clear that the 
 angle ecd is equal to D C E. Therefore, by placing the centre 
 of a protractor at c, the number of degrees, e d , is read off, 
 that is, the angle included by the lens. 
 
 Its absolute focal length is thus obtained : — Measure on the 
 ground-glass the distance of the points D E with a compass, 
 and take the half of them. Bisect the angle e c d by a straight 
 line c /, against which place a square rule. Carry the half- 
 distance D E (measured on the ground-glass) on the square 
 rule, and make / g equal to this half-distance and perpendi- 
 cular to cf. Then fc will be the true focal length of the 
 
 B 
 
 Fig. 28. 
 
58 
 
 PHOTOGRAPHIC OPTICS. 
 
 objective, which, once known, permits the size of images to 
 be calculated. — (Grubb, British Journal of Photography.) 
 
 Determination of the conjugate Focus and of the 
 size of the Image. — First, let us recall this fact : that if 
 in a well-darkened chamber (fig. 2, page 6) we make a small 
 aperture, external objects will be represented on a white 
 screen placed behind this aperture. The greater the distance of 
 these objects , the smaller their image is; but this image can be 
 enlarged or diminished by withdrawing or advancing the screen 
 which receives it. If, at the aperture, we place a convergent 
 lens, we shall observe that there is a place behind the lens 
 where the image is the best defined : on advancing or with- 
 drawing the screen, the image will lose its primitive sharp- 
 ness. 
 
 If the fixed object, which, in our figure (2, page 6) is re- 
 presented by a church, is replaced by a moving figure — by 
 a man who is walking, for example — we can prove that, 
 if the man moves away, the image on the screen, to be the 
 sharpest possible, approaches the lens, and diminishes in 
 size ; and that, conversely, if the man approaches, the focus 
 moves off from the lens, and the image increases in size. 
 
 Now, there are, between the focal length of the lens, the 
 size of the image, and the distance of the object from the lens, 
 very simple ratios, by the aid of which, knowing two of the 
 ratios, the third can always be found. Let / be the principal 
 focal length of the lens (or system of combined lenses), p the 
 distance of the object from the lens, p' the focal length of 
 the lens at which the image is sharply defined. We have the 
 ratio : — 
 
 11 1 
 
 7~ p + p r 
 
 If the objective has a focal length of 24 centimetres, the 
 distance of the object from the lens being 400 centimetres, 
 we shall have for the distance p at which the image is 
 represented with clearness on the ground-glass : 
 
LENSES. 
 
 59 
 
 1 
 
 24 
 
 i + ?’ or40 ° 
 
 24 = 
 
 24 x 400 
 
 whence p' = 25*5 centimetres. The focal distance will there- 
 fore, in this case, he elongated 1-5 centimetres beyond the 
 principal focus. 
 
 The ratio of the size of the image to that of the object will 
 be as p ' : p , or as 25*5 to 400 ; that is, the image will be 
 aj)proximately X V of the size of the object. 
 
 It is therefore always easy, knowing the focal length of the 
 lens we make use of, the dimension of the object and its dis- 
 tance from the lens, to calculate exactly the dimension of the 
 image. Or, changing the problem, and wishing with a given 
 objective to obtain an image of definite size, to find out at 
 what distance it will be necessary for the object to be placed. 
 But, to save our readers this labour, we extract from the ex- 
 cellent pamphlet of M. Secretary entitled, “ Be la distance focale 
 des systemes optiques convergents ” the following tables (pp. 
 60, 61, 62), with the explanation of the mode of using them/" 
 
 The first vertical column contains the focal lengths of the 
 lenses, increasing by 5 centimetres, from 10 to 100 centimetres; 
 for intermediate focal lengths, the results can be interpolated 
 or rather calculated by the rules already given (see page 58). 
 The second vertical column, which has at the top the fractional 
 number p, gives for a full-sized image, and for the focal length 
 of each lens opposite to it in the first, column, two numbers : 
 the first is the distance of the object from the lens ; the second 
 that of the ground-glass from the lens. The third vertical 
 column gives the same distances, but for a half-sized image ; 
 the fourth column gives them for the ratio •*-, and so on. 
 
 * Opticians, in their catalogues, generally give, in place of the true focal 
 length of their objectives, that measured from the face of the lens which 
 is directed towards the ground-glass. There is thence no very sensible 
 error for the simple landscape objectives ; but for all others it is necessary, 
 either to measure the focal length in the way we have indicated above, 
 or else to add to the figures given by opticians half the length of the tube 
 in which the objectives are mounted. 
 
60 
 
 PHOTOGRAPHIC OPTICS. 
 
 
 1/1 
 
 1/2 
 
 1/3 
 
 1/4 
 
 1/5 
 
 1/6 
 
 1/7 
 
 1/8 
 
 1/9 
 
 o-io | 
 
 O ' 20 
 0*20 
 
 0-30 
 
 0*15 
 
 0-40 
 
 0-13 
 
 0-50 
 
 0*13 
 
 0*60 
 
 0*12 
 
 0-70 
 
 0*12 
 
 0-80 
 O ' 11 
 
 0'90 
 
 0*11 
 
 1*00 
 
 0-11 
 
 0*15 | 
 
 0-30 
 
 0-30 
 
 0*45 
 
 0-23 
 
 0-60 
 
 0-20 
 
 0-75 
 
 0-19 
 
 0-90 
 
 0*18 
 
 1-05 
 
 0*18 
 
 1-20 
 
 0*17 
 
 1*35 
 
 0*17 
 
 1-50 
 
 0-17 
 
 0-20 < 
 
 0-40 
 
 0-40 
 
 0*60 
 
 0-30 
 
 0-80 
 
 0-27 
 
 1-00 
 
 0-25 
 
 1*20 
 
 0*24 
 
 1*40 
 
 0-23 
 
 1 '60 
 0'23 
 
 1-80 
 
 0-23 
 
 2*00 
 
 0*22 
 
 0-25 . 
 
 0*50 
 
 0-50 
 
 0-75 
 
 0-38 
 
 1-00 
 
 0*33 
 
 1-25 
 
 0-31 
 
 1*50 
 
 0-30 
 
 1-75 
 
 0*29 
 
 2 '00 
 2-29 
 
 2-25 
 
 0-28 
 
 3*50 
 
 0-28 
 
 0-30 - 
 
 0-60 
 
 0-60 
 
 0-90 
 
 0*45 
 
 1-20 
 
 0-40 
 
 1-50 
 
 0*38 
 
 1-80 
 
 0*36 
 
 2-10 
 
 0-35 
 
 2 '40 
 0'34 
 
 2-70 
 
 0*34 
 
 2-00 
 
 0-33 
 
 0-35 < 
 
 0-70 
 
 0-70 
 
 1*05 
 
 0*53 
 
 1-40 
 
 0-47 
 
 1*75 
 
 0*44 
 
 2-10 
 
 0*42 
 
 2*45 
 
 0-41 
 
 2-80 
 
 0'40 
 
 3-15 
 
 0*39 
 
 3*50 
 
 0-39 
 
 0*40 - 
 
 0-80 
 
 0-80 
 
 1*20 
 
 0-60 
 
 1*60 
 
 0-53 
 
 2-00 
 
 0*50 
 
 2-40 
 
 0-48 
 
 2-80 
 
 0*47 
 
 3*20 
 
 6-40 
 
 3'60 
 
 0'45 
 
 4*00 
 
 0*44 
 
 0*45 ■ 
 
 0*90 
 
 0-90 
 
 1-35 
 
 0-68 
 
 1*80 
 
 0*60 
 
 2*25 
 
 0*56 
 
 2-70 
 
 0-54 
 
 3*15 
 
 0*53 
 
 3'60 
 
 0*51 
 
 4*05 
 
 0*51 
 
 4-50 
 
 0'50 
 
 0-50 | 
 
 f 1*00 
 { 1-00 
 
 1-50 
 
 0*75 
 
 2*00 
 
 0-67 
 
 2*50 
 
 0-63 
 
 Voo" 
 
 0*60 
 
 3-50 
 
 0-58 
 
 4-00 
 
 0*57 
 
 4*50 
 
 0-56 
 
 5*00 
 
 0'55 
 
 0-55 \ 
 
 f 1-10 
 [ 1*10 
 
 1*65 
 
 0-83 
 
 2*20 
 
 0-73 
 
 2*75 
 
 0*69 
 
 3-30 
 
 0-66 
 
 3-85 
 
 0*44 
 
 4-40 
 
 0*63 
 
 4*95 
 
 0-62 
 
 5-50 
 
 0'61 
 
 0-60 j 
 
 f 1*20 
 [ 1*20 
 
 1*80 
 
 0-90 
 
 2*40 
 
 0-80 
 
 3-00 
 
 0-75 
 
 3*60 
 
 0*72 
 
 4-20 
 
 0-70 
 
 4-80 
 
 0'69 
 
 5*40 
 
 0'68 
 
 6-00 
 
 0-66 
 
 0*65 < 
 
 f 1-30 
 ( 1-30 
 
 1*95 
 
 0-98 
 
 2*60 
 
 0*87 
 
 3-25 
 
 0 - 8 ] 
 
 3-90 
 
 0-78 
 
 4*55 
 
 0-76 
 
 ~ 5 : 2 (T 
 
 0-74 
 
 5'85 
 
 0*73 
 
 6'50 
 
 0-72 
 
 0-70 - 
 
 f 1-40 
 ( 1-40 
 
 2-10 
 
 1*05 
 
 2-80 
 
 0*93 
 
 3*50 
 
 0*87 
 
 4*20 
 
 0-84 
 
 4*90 
 
 0-82 
 
 5'60 
 
 0-80 
 
 6 t 30 ” 
 
 0-79 
 
 7'00 
 
 0'77 
 
 0*75 • 
 
 ( 1-50 
 ( 1-50 
 
 2*25 
 
 1*13 
 
 3*00 
 
 1-00 
 
 3-75 
 
 0*94 
 
 4-50 
 
 0-90 
 
 5-25 
 
 0*88 
 
 6*00 
 
 0'86 
 
 6*75 
 
 0'84 
 
 7*50 
 
 0*83 
 
 0-80 • 
 
 / 1*60 
 \ 1*60 
 
 2-40 
 
 1-20 
 
 3-20 
 
 1-07 
 
 4*00 
 
 1*00 
 
 4-80 
 
 0*96 
 
 5-60 
 O ' 93 
 
 6'40 
 
 0'91 
 
 7*20 
 
 0'90 
 
 8*00 
 
 0*88 
 
 0-85 
 
 / 1*70 
 \ 1-70 
 
 2-55 
 
 1*28 
 
 3*40 
 
 1-13 
 
 4-25 
 
 1*06 
 
 5*10 
 
 1-02 
 
 5*95 
 
 0-99 
 
 6 80 
 0-97 
 
 7 65 
 0*96 
 
 8-50 
 
 0-94 
 
 0*90 
 
 / 1-80 
 \ 1-80 
 
 2-70 
 
 1-35 
 
 3-60 
 
 1-20 
 
 4-50 
 
 1-12 
 
 5-40 
 
 1-08 
 
 6-30 
 
 1-05 
 
 7*20 
 
 103 
 
 8-10 
 
 l'Ol 
 
 9-00 
 
 0-99 
 
 0-95 
 
 / 1-90 
 \ 1-90 
 
 2*85 
 
 1*43 
 
 3-80 
 1 - 27 
 
 4-75 
 
 1*19 
 
 5-70 
 
 1-14 
 
 6*65 
 
 1-11 
 
 7'60 
 
 1-09 
 
 8*55 
 
 1*07 
 
 9-50 
 
 1'05 
 
 1-00 
 
 / ~ 2 t 00 ~ 
 \ 2*00 
 
 3-00 
 
 1*50 
 
 4-00 
 
 1-33 
 
 5*00 
 
 1-25 
 
 6-00 
 
 1*20 
 
 7 '00 
 117 
 
 8'00 
 
 1*14 
 
 9-00 
 
 1*15 
 
 10*00 
 
 1*10 
 
 • 
 
LENSES, 
 
 61 
 
 
 1/10 
 
 1/15 
 
 1/20 
 
 1/25 
 
 1/30 
 
 1/40 
 
 1/50 
 
 1/60 
 
 1/70 
 
 o-io , 
 
 l'lO 
 
 0-11 
 
 1-60 
 
 0-11 
 
 2-10 
 
 0-11 
 
 2-60 
 
 0-10 
 
 3-10 
 
 o-io 
 
 4-10 
 
 o-io 
 
 5-10 
 
 o-io 
 
 6-10 
 
 0-10 
 
 7-10 
 
 0-10 
 
 0*15 < 
 
 1-65 
 
 017 
 
 2-40 
 
 0-16 
 
 3-15 
 
 0-16 
 
 3-90 
 
 0-16 
 
 4-65 
 
 0-16 
 
 6-15 
 
 0-15 
 
 7-65 
 
 0-15 
 
 9-15 
 
 0-15 
 
 10-65 
 
 0-15 
 
 0*20 . 
 
 2*20 
 
 0-22 
 
 3-20 
 
 0-21 
 
 4-20 
 
 0-21 
 
 5-20 
 
 0-21 
 
 6-20 
 
 0-21 
 
 8-20 
 
 0-21 
 
 10-20 
 
 0-20 
 
 12-20 
 
 0-20 
 
 14-20 
 
 0-20 
 
 0*25 • 
 
 2-75 
 
 0*28 
 
 4-00 
 
 0-27 
 
 5-25 
 
 0-26 
 
 6-50 
 
 0-26 
 
 7-75 
 
 0-26 
 
 10-25 
 
 0-26 
 
 12-75 
 
 0-26 
 
 15-25 
 
 0-25 
 
 17-75 
 
 0‘25 
 
 0-30 ■ 
 
 3-30 
 
 0-33 
 
 4-80 
 
 0-32 
 
 6-30 
 
 0-32 
 
 7-80 
 
 0-31 
 
 9-30 
 
 0-31 
 
 12-30 
 
 0-31 
 
 15-30 
 
 0-31 
 
 18 t 30 
 
 0-31 
 
 21-30 
 
 0-30 
 
 0-35 . 
 
 f 3-85 
 0-39 
 
 5-60 
 
 0-37 
 
 7-35 
 
 0-37 
 
 9-10 
 
 0-36 
 
 10-85 
 
 0-36 
 
 14 : 3’5 
 
 0-36 
 
 17-85 
 
 0-36 
 
 21-35 
 
 0-36 
 
 24-85 
 
 0-36 
 
 0-40 
 
 4-40 
 
 0*44 
 
 6*40 
 
 0-43 
 
 8-40 
 
 0-42 
 
 10-40 
 
 0-42 
 
 12-40 
 
 0-41 
 
 16-40 
 
 0-41 
 
 20-40 
 
 0-41 
 
 24-40 
 
 0-41 
 
 28-40 
 
 0-41 
 
 0-45 
 
 f 4-95 
 ( 0-50 
 
 7-20 
 
 0-48 
 
 9-45 
 
 0-47 
 
 14-70 
 
 0-47 
 
 13-95 
 
 0-47 
 
 18-45 
 
 0-46 
 
 22-95 
 
 0-46 
 
 27-45 
 
 0-46 
 
 31-95 
 
 0-46 
 
 0-50 < 
 
 f 5*50 
 ( 0-55 
 
 8-00 
 
 0-53 
 
 10-50 
 
 0-53 
 
 13-00 
 
 0-52 
 
 15-50 
 
 0-52 
 
 20-50 
 
 0-51 
 
 25-50 
 
 0-51 
 
 30-50 
 
 0-51 
 
 35-50 
 
 0-51 
 
 0.55 < 
 
 ( 6-05 
 ( 0-61 
 
 8-80 
 
 0-59 
 
 TT 7 55 ' 
 
 0-58 
 
 14-30 
 
 0-57 
 
 17-05 
 
 0-57 
 
 22-55 
 
 0-56 
 
 28-05 
 
 0-56 
 
 33-55 
 
 0-56 
 
 ~39 7 05 
 
 0-56 
 
 0*60 • 
 
 f 6-60 
 
 i 0*66 
 
 9-60 
 
 0-64 
 
 12-60 
 
 0-63 
 
 15-60 
 
 0-62 
 
 18-60 
 
 0-62 
 
 24 t 60 
 
 0-62 
 
 30-60 
 
 0-61 
 
 36-60 
 
 0-61 
 
 42-60 
 
 0-61 
 
 0-65 • 
 
 f 715 
 \ 0-72 
 
 10-40 
 
 0-69 
 
 13-65 
 
 0-68 
 
 16-90 
 
 0-68 
 
 20-15 
 
 0-67 
 
 26-65 
 
 0-67 
 
 33-15 
 
 0-66 
 
 39-65 
 
 0-66 
 
 46-15 
 
 0-66 
 
 0-70 • 
 
 ( 7-70 
 { 0-77 
 
 11-20 
 
 0-75 
 
 14-70 
 
 0-74 
 
 18-20 
 
 0-73 
 
 21-70 
 
 0*72 
 
 28-70 
 
 0-72 
 
 35-70 
 
 0-71 
 
 42-70 
 
 0-71 
 
 49-70 
 
 0-71 
 
 0*75 
 
 / 8*25 
 \ 0-83 
 
 12-00 
 
 0-80 
 
 15-75 
 
 0-79 
 
 19-50 
 
 0-78 
 
 23-25 
 
 0*77 
 
 30-75 
 
 0-77 
 
 38-25 
 
 0-77 
 
 45-75 
 
 0-76 
 
 53-25 
 
 0-76 
 
 0-80 
 
 / 8-80 
 \ 0-88 
 
 12-80 
 
 0-85 
 
 16-80 
 
 0-84 
 
 20-80 
 
 0-83 
 
 24-80 
 
 0-83 
 
 32-80 
 
 0-82 
 
 40-80 
 
 0-82 
 
 48-80 
 
 0-81 
 
 56-80 
 
 0-81 
 
 0*85 
 
 / 9-35 
 \ 0-94 
 
 13-60 
 
 0-91 
 
 17-85 
 
 0-89 
 
 22-10 
 
 0-88 
 
 26-35 
 
 0-88 
 
 34-85 
 
 0-87 
 
 43-35 
 0 87 
 
 51-85 
 
 0-86 
 
 60-35 
 
 0-86 
 
 0*90 
 
 / IkhT 
 
 \ 0-99 
 
 14-40 
 
 0-96 
 
 18-90 
 
 0‘95 
 
 23-40 
 
 0-94 
 
 27-90 
 
 0-93 
 
 36-90 
 
 0-92 
 
 45 90 
 0-92 
 
 54-90 
 
 0-92 
 
 63-90 
 
 0-91 
 
 0-95 
 
 / 10-45 
 \ 1-05 
 
 15-20 
 
 1-01 
 
 19-95 
 
 1-00 
 
 24-70 
 
 0-99 
 
 29-45 
 
 0-98 
 
 38-95 
 
 0-97 
 
 48-45 
 
 0-97 
 
 57-95 
 
 0-97 
 
 67-45 
 
 0-97 
 
 1-00 
 
 / 11-00 
 \ 1*10 
 
 16-00 
 
 1-07 
 
 21-00 
 
 1-05 
 
 26-00 
 
 1-04 
 
 31-00 
 
 1-03 
 
 41-00 
 
 1-03 
 
 51-00 
 
 1-02 
 
 61-00 
 
 1-02 
 
 71-00 
 
 101 
 
62 
 
 PHOTOGRAPHIC OPTICS. 
 
 
 1/80 
 
 1/90 
 
 1/100 
 
 1/120 
 
 1/140 
 
 1/160 
 
 1/180 
 
 1/200 
 
 0-10 
 
 / 8-10 
 \ 0-10 
 
 9-10 
 
 0-10 
 
 10-10 
 
 0-10 
 
 12-10 
 
 0-10 
 
 14-10 
 
 0-10 
 
 16-10 
 
 o-io 
 
 18-10 
 
 0-10 
 
 20-10 
 
 o-io 
 
 015 
 
 / 12-15 
 \ 0-15 
 
 13-65 
 
 0-15 
 
 15-15 
 
 0-15 
 
 18-15 
 
 0-15 
 
 21-15 
 
 0-15 
 
 24-15 
 
 0-15 
 
 27*15 
 
 0-15 
 
 ' Iwas ’ 
 
 0-15 
 
 0-20 
 
 ( 16-20 
 \ 0-20 
 
 18-20 
 
 0-20 
 
 20-20 
 
 0-20 
 
 24-20 
 
 0-20 
 
 28*20 
 
 0-20 
 
 32-20 
 
 0-20 
 
 36-20 
 
 0-20 
 
 40-20 
 
 0*20 
 
 0-25 
 
 / 20-25 
 \ 0-25 
 
 22-75 
 
 0-25 
 
 25-25 
 
 0-25 
 
 30-25 
 
 0-25 
 
 35-25 
 
 0-25 
 
 40-25 
 
 0-25 
 
 45-25 
 
 0-25 
 
 50-25 
 
 0-25 
 
 0-30 
 
 / 24-30 
 \ 0-30 
 
 27-30 
 
 0-30 
 
 30-30 
 
 0-30 
 
 36-30 
 
 0-30 
 
 42-30 
 
 0-30 
 
 48-30 
 
 0-30 
 
 54-30 
 
 0-30 
 
 60-30 
 
 0-30 
 
 0-35 
 
 / 28-35 
 \ 0-35 
 
 31-85 
 
 0-35 
 
 35-35 
 
 0-35 
 
 42-35 
 
 0-35 
 
 49-35 
 
 0-35 
 
 56-35 
 
 0-35 
 
 63-35 
 
 0-35 
 
 ' 70-35 
 0-35 
 
 0-40 
 
 / 32-40 
 \ 0-41 
 
 36-40 
 
 0-40 
 
 40-40 
 
 0-40 
 
 48-40 
 
 0-40 
 
 56-40 
 
 0-40 
 
 64-40 
 
 0-40 
 
 72-40 
 
 0-40 
 
 "Iw-Io 7 
 
 0-40 
 
 0-45 
 
 / 36-45 
 \ 0-46 
 
 40-95 
 
 0-46 
 
 45-45 
 
 0-45 
 
 54-45 
 
 0-45 
 
 63-45 
 
 0-45 
 
 72-45 
 
 0-45 
 
 81-45 
 
 0-45 
 
 90-45 
 
 0-45 
 
 0-50 
 
 / 40-50 
 \ 0-51 
 
 45-50 
 
 0-51 
 
 50-50 
 
 0-51 
 
 60-50 
 
 0-50 
 
 70-50 
 
 0-50 
 
 80-50 
 
 0-50 
 
 90-50 
 
 0-50 
 
 100-50 
 
 0-50 
 
 . 0-55 
 
 / 44-56 
 1 0-56 
 
 50-05 
 
 0-56 
 
 55-55 
 
 0-56 
 
 66-55 
 
 0-55 
 
 77-55 
 
 0-55 
 
 88-55 
 
 0-55 
 
 99-55 
 
 0-55 
 
 110-55 
 
 0-55 
 
 0*60 
 
 \ 0-61 
 
 54-60 
 
 0-61 
 
 60-60 
 
 0-61 
 
 72-60 
 
 0-61 
 
 84-60 
 
 0-60 
 
 96-60 
 
 0‘60 
 
 108-60 
 
 0-60 
 
 120-60 
 
 0-60 
 
 0-65 
 
 / 52-65 
 \ 0-66 
 
 59-15 
 
 0-66 
 
 65-65 
 
 0-66 
 
 78-65 
 
 0-66 
 
 91-65 
 
 0-65 
 
 104-65 
 
 0-65 
 
 117-65 
 
 0-65 
 
 130-65 
 
 0-65 
 
 0*70 
 
 /~ 56 - 70 ~ 
 \ 0-71 
 
 63-70 
 
 0-71 
 
 ~~ 70*-70 
 
 0-71 
 
 84-70 
 
 0-71 
 
 98-70 
 
 0-71 
 
 112-70 
 
 0-70 
 
 126-70 
 
 0-70 
 
 140-70 
 
 0-70 
 
 0-75 
 
 / 60-75 
 \ 0-76 
 
 68-25 
 
 0-76 
 
 75-75 
 
 0-76 
 
 90-75 
 
 0-76 
 
 105-75 
 
 0-76 
 
 I 20 - 75 - 
 
 0-75 
 
 135-75 
 
 0-75 
 
 150-75 
 
 0-75 
 
 0-80 
 
 / 64-80 
 \ 0-81 
 
 72-80 
 
 0-81 
 
 80-80 
 
 0-81 
 
 96-80 
 
 0-81 
 
 112-80 
 
 0-81 
 
 128-80 
 
 0-81 
 
 144-80 
 
 0-80 
 
 160-80 
 
 0-80 
 
 0-85 
 
 / 68-85 
 1 0-86 
 
 77-35 
 
 0-86 
 
 85-85 
 
 0-86 
 
 102-85 
 
 0-86 
 
 119-85 
 
 0-86 
 
 136-85 
 
 0-86 
 
 153-85 
 
 0-85 
 
 170-85 
 
 0-85 
 
 0-90 
 
 / 72-90 
 \ 0-91 
 
 81-90 
 
 0-91 
 
 90-90 
 
 0-91 
 
 108-90 
 
 0-91 
 
 126-90 
 
 0-91 
 
 144-90 
 
 0-91 
 
 162-90 
 
 0-91 
 
 180-90 
 
 0-90 
 
 0-95 
 
 / ~ 76 : 95 ~ 
 \ 0-97 
 
 "86 ^ 
 0-96 
 
 95-95 
 
 0-96 
 
 114-95 
 
 0-96 
 
 133-95 
 
 0-96 
 
 152-95 
 
 0-96 
 
 171-95 
 
 0-95 
 
 190-95 
 
 1-95 
 
 1-00 
 
 / 81-00 
 \ 1-01 
 
 91-00 
 
 1-01 
 
 101-00 
 
 1-01 
 
 121-00 
 
 1-01 
 
 141-00 
 
 1-01 
 
 161-00 
 
 1-01 
 
 181-00 
 
 1-01 
 
 201-00 
 
 1-01 
 
LENSES. 
 
 63 
 
 Suppose that with an objective of 30 centimetres focus it is 
 wished to make a portrait one-sixth the size. 
 
 From the number 30 in the first vertical column, the 
 horizontal line is followed until the vertical line is reached 
 at the top of which there is i ; the square will be thus come to 
 where are the two numbers 2*10 and 0-35 ; the first indicates 
 that the person will have to be 2 metres 10 centimetres from 
 the lens, and the second shows that the ground-glass, when 
 brought to a focus, will be about 35 centimetres from the 
 lens. The results of the table are exact to within less than 
 a centimetre ; greater exactitude would have been useless, 
 particularly for the number which determines the distance of 
 the ground-glass, seeing that this is always regulated by the 
 effective focussing. The latter quantity it is always well to 
 know beforehand, if only to know whether the locality 
 where we are working is large enough to effect a certain 
 reduction of the image with an objective of a known focal 
 length. 
 
 Thus, it is desired to know what is the smallest reduction 
 that can be made with a focus of 40 centimetres, in a room 
 of which the greatest length is 4 metres. We first deduct 
 one metre for space for the object to be represented, and for 
 the operator to focus on the ground-glass, and thus reduce 
 our 4 metres to 3. 
 
 In the horizontal line, which corresponds to the focus of 
 40, make up the sum of the two numbers in each square 
 until the result is obtained which approaches nearest to, but 
 less than, 3 metres. We shall thus arrive at the number 
 2*88, furnished by the vertical column at the head of which 
 is 4. 
 
 Such will be the smallest sized image that could be obtained 
 in this place with this It ns. 
 
64 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTER Y. 
 
 ABERRATIONS. 
 
 Definition of Aberrations. — We have thus far supposed 
 the aperture of lenses to he very small relatively to their 
 focal length, and consequently the meeting at the same point 
 of all the rays refracted by them. But in practice lenses are 
 most often used which have a considerable aperture, and then 
 this result is not obtained, the rays refracted by the margin of 
 the lens meeting at a different point in the axis from those 
 refracted by the centre. This constitutes an aberration , which 
 has been named spherical because it proceeds from the sphe- 
 ricity of the surfaces of the lens. 
 
 We have also supposed that refraction by lenses was not 
 accompanied by dispersion; hut this is not so, since for an 
 incident white ray there are several rays refracted, and these 
 cut the axis in different points. This is what is called 
 chromatic aberration. 
 
 Again, we have admitted that the image of external objects 
 is formed at the focus of a lens on a plane perpendicular to 
 its axis, whereas in reality it is formed on a curved surface. 
 This aberration is that of the curvature of the field. 
 
 We have supposed lenses as infinitely thin, and therefore 
 giving images in conformity with the lines of the object. 
 But lenses have a sensible thickness, which alters the exact 
 form of the image at the edges. This aberration has received 
 the name of aberration of thickness, or more commonly that of 
 distortion. 
 
 One other aberration results from the position of the lens 
 in relation to points situated obliquely to its axis ; the two 
 meridians of the lens having a different focal length. This 
 aberration has received the name of astigmation. 
 
ABERRATIONS. 
 
 65 
 
 Section I . — Spherical Aberration. 
 
 Spherical Aberration, lateral and longitudinal, posi- 
 tive and negative. — The parallel rays of light r r (fig. 
 29), passing through the margins of a convex lens L L', cross 
 each other at /', nearer to 
 the lens than the rays r' r\ 
 which, passing through the 
 centre, cross each other at /. 
 
 This proceeds from the cur- 
 vatures of the lens being 
 spherical surfaces ; hence the 
 name spherical aberration. 
 
 Spherical aberration in a 
 simple convergent lens can 
 easily be observed by receiv- 
 ing the image of the sun at its focus. For this purpose the 
 lens is presented to the solar rays in such a way that they 
 fall perpendicularly to its circumference, and the place where 
 the image is formed with sharpness is sought for by with- 
 drawing or advancing a white paper behind the lens. (To 
 attain this end more easily, reduce the lens to its central part 
 by covering it with a card having a round hole cut in it ; 
 then remove the card.) If the lens has a very short focus, — 
 if, for instance, it is one of those lenses which are used as 
 magnifying-glasses, — we observe that around the best-defined 
 image of the sun there is an aureola, a b (Fig. 29), of 
 white light which constitutes lateral spherical aberration. In, 
 fact, it is at /, the focus of the rays incident on the centre 
 of the lens, that the best-defined image is formed of objects 
 situated at infinity (and the sun is in this condition); whilst 
 the rays r r falling on the margins of the lens L, and having 
 their focus/' nearer, continue their way and form a round 
 aureola, ab, about the point /. The diameter a b of this circle 
 constitutes the measure, or, as it is also called, the expression 
 of the lateral spherical aberration (or diameter of the circle 
 
 F 
 
 Fig. 29. 
 
66 
 
 PHOTOGRAPHIC OPTICS. 
 
 of aberration). The distance,//', (measured along the axis 
 of the lens) which separates the focus / of the central rays 
 from the focus /' of the extreme rays is called the longitudinal 
 aberration . 
 
 The circle of least aberration is between/' and/. It is the 
 smallest section it is possible to make in the cone of rays 
 emergent from the lens. 
 
 In negative lenses the ray /, parallel to the axis c' c of a 
 divergent lens L N, and falling on the central part, emerges 
 
 in the direction o m, which, pro- 
 duced, cuts the axis in /'/', which 
 is therefore the principal focus of 
 this lens. A ray r , parallel to the 
 first, falling on the margin of the 
 lens L, emerges in the direction 
 n q , which, produced, cuts the axis 
 in/. Therefore the focus of the extreme rays is longer than 
 the focus of the central rays. In this case the aberration is 
 said to be negative. 
 
 Spherical Aberration varies with the aperture and 
 index of refraction of the glass of the lens. — Since 
 spherical aberration depends on the sphericity of the faces 
 forming the lens, it is perfectly clear that the more convex 
 these faces are — that is to say, the shorter the radii of cur- 
 vature are relatively to the diameter of the lens — the more 
 considerable are the aberrations of sphericity. 
 
 Lenses which have a short focus relatively to their diameter 
 are in this condition. On the contrary, the spherical aberra- 
 tion is sensibly nothing when the diameter of the lens is not 
 greater than the fifteenth of its focal length. 
 
 Longitudinal aberration increases or diminishes as the 
 square of the diameter of the aperture, and inversely as its 
 focal length. Lateral aberration is proportional to the cube 
 of the aperture, and inversely proportional to the square of 
 the focal length. 
 
 Thus, let us compare two lenses of the same material and of 
 
 Fig. 30. 
 
ABERRATIONS. 
 
 67 
 
 the same radii of curvature, but one of which has double the 
 diameter of the other. The former has a longitudinal aberra- 
 tion four times as great as the latter, and a circle of aberra- 
 tion eight times as great. 
 
 Of two lenses with the same aperture, of which the focal 
 lengths are to each other as 1 to 2, that which has 2 as its 
 focal length has half the longitudinal aberration of the other, 
 and only a quarter of the lateral aberration. 
 
 The greater the index of refraction of the material of which 
 the lens is formed, the smaller will be, for the same given c 
 focal length, its radii of curvature, and consequently its 
 spherical aberration. It follows from this that in objectives 
 which have a given aberration, this could be diminished by 
 employing very refractive transparent bodies. 
 
 Figure 31 strikingly exhibits this fact. A and B are two 
 lenses having exactly the same focal length, 
 but formed of different refractive sub- 
 stances. The first is of glass, of which the 
 index is 1*5 ; the second of diamond, of 
 which the index is 2*5. The radius of cur- 
 vature of the first is three times as short 
 as that of the second, and therefore it pos- 
 sesses an aberration much more consider- 
 able. 
 
 Minimum of Spherical Aberration. 
 -—For a fixed distance of the radiating point 
 situated in the axis of a lens, calculation, agreeing with 
 practice, assigns to it radii of curvature and a position where 
 aberration is the least possible. For this it is necessary to 
 know the index of refraction of the material of which the lens 
 is formed. 
 
 Thus with ordinary crown-glass, of which the index of 
 refraction is 1*5, the two radii of curvature ought to be 
 to each other as 1 to 6, the most convex face (of which the 
 radius of curvature is 1) being turned towards the radiating 
 point which w$ suppose placed at infinity. If the index 
 
 Fig. 31. 
 
68 
 
 PHOTOGRAPHIC OPTICS. 
 
 increases, the ratio of the two radii of curvature increases 
 also. Thus for the heavy kind of flint (1*6), the plano-convex 
 form is the most advantageous. 
 
 For diamond, of which the index of refraction is 2*5, a 
 meniscus would he necessary, of which the convex face should 
 have 2 and the concave face 5 as radii of curvature. 
 
 If the radiating point, in place of being situated at infinity, 
 and consequently emitting rays parallel as regards the lens, 
 is near to the latter, it must be treated as emitting divergent 
 rays, and in order that the lens shall present the minimum of 
 aberration its curvatures must be changed. In proportion as 
 the radiating point approaches the lens, the face which is 
 towards it, and which had in the case cited above 1 for its 
 radius of curvature (the other having 6), becomes less convex 
 in relation to the other ; for example, 2 to 5, 3 to 4, 4 to 3, 
 5 to 2 successively, and lastly, if the radiating point reaches 
 the principal focus of the lens, G to 1. It is seen, therefore, 
 that the lens is now reversed. 
 
 Destruction of Spherical Aberration by the Dia- 
 * phragm. — Any lens, convergent or divergent, of which the 
 radii of curvature are long or short, and of which consequently 
 the aberration is slight or considerable, is reduced by a 
 small diaphragm placed in its axis, to a plate ab d c (fig. 46) 
 which has nearly parallel faces, and thus it is henceforth 
 exempt from spherical aberration. This lens, M, in fact, such 
 as it is represented in our figure, would be reduced to one- 
 sixth of t its diameter, while its focal length remains the 
 same ; therefore, according to what we have just seen, its 
 lateral aberration would be reduced to a thirty-sixth, that 
 is, would be annulled or nearly annulled. We can convince 
 ourselves of this by presenting the lens to the solar rays 
 falling normally (to the plane of its circumference). With 
 the whole of its aperture the image of the sun is fringed with 
 the lateral aureola due to the aberration of sphericity. The 
 diaphragm being then interposed this aureola disappears, and 
 the image thus becomes incomparably sharper because the 
 
ABERRATIONS. 
 
 69 
 
 rays refracted by the margin of the lens, which rendered the 
 image indistinct, are cut off by the stop. 
 
 Nevertheless the diaphragm never destroys completely the 
 spherical aberration of lenses ; it only serves to reduce it to 
 a very small quantity. It is, however, completely destroyed 
 in the following way. 
 
 Destruction of the Spherical Aberration of a Lens 
 by a second Lens of contrary character, — Let us sup- 
 pose a lens, L, (a convergent one, for example,) the aberra- 
 
 Fig. 32. 
 
 tion of which it is wished to destroy completely along its axis. 
 The expression//' of the aberration is furnished to us by the 
 points where a ray infinitely close to the axis and an extreme 
 ray (both parallel to the axis) cut the axis after emerging 
 from the lens. Now let us associate with the convergent 
 lens L a divergent lens M. 
 
 It is easy to conceive that this divergent lens, if its radii 
 of curvature are suitable , will scarcely at all change the 
 direction of the ray b /', which will only be deviated to 
 F, /' F being a very small quantity, whilst it will greatly 
 change the direction of the ray a f (since its prismatic form 
 is greater at the margin than at the centre) so as to direct it 
 also to the point F. 
 
 Such an association of lenses forms, as a whole, a single lens, 
 convergent, but free from spherical aberration. Such lenses 
 are called aplanatic , and calculation indicates with absolute 
 exactitude their numerical data. 
 
70 
 
 PHOTOGRAPHIC OPTICS. 
 
 The divergent lens M may have a common face with the 
 lens L, and the two lenses he then cemented together. The 
 two lenses may also he separated by a larger or smaller 
 interval, and consequently have a different diameter. 
 
 An example of such an aplanatic combination will be found, 
 in the chapter on enlargements, in the dyalitic apparatus. The 
 convergent lens in this system has a diameter of nineteen 
 inches, and a focal length of thirty-eight, and its spherical 
 aberration is corrected by a lens of nine and a half inches, 
 which is hardly one centimetre thick at the margin, and 
 which scarcely lengthens the focal distance of the other. 
 
 The nature of the glass may be the same for the two lenses, 
 or, as is most generally the case, it may be different ; because, 
 as we shall soon see, the negative lens most frequently not 
 only corrects the spherical aberration, but also the chromatic 
 aberration . 
 
 As chromatic aberration always surpasses in importance 
 spherical aberration, and, consequently, as it is desirable above 
 all to correct the former, it frequently happens that the nega- 
 tive lens corrects too much or too little the spherical aberration 
 of the convergent lens with which it is associated. If it cor- 
 rects aberration too much, the system is said to possess spherical 
 aberration of a negative character, because then the rays emerg- 
 ing from the margin cut the axis farther away than those from 
 the centre. If it correct too little, the aberration is positive. 
 
 It is impossible to construct a convergent lens, or to associate 
 two or more of them on a common axis, in such a way as to 
 destroy their spherical aberration. Many treatises on physics 
 contain the contrary assertion,* but this is an evident error. 
 
 It is needless to add, in finishing this paragraph, that it is 
 necessary for correcting the aberration of convergent lenses to 
 
 * M. Daguin and many other authors of works on physics repeat this 
 error, which originated in a memoir of Sir John Herschel, in which the 
 illustrious astronomer, having fallen into an error in interpreting the 
 figures of his analytical formulae, gave combinations of convergent lenses 
 which ought to have been aplanatic, and which are not so. Sir John Her- 
 schel, however, rectified this error in his memoir several years afterwards. 
 
ABERRATIONS. 
 
 71 
 
 associate with them divergent lenses, and conversely for cor- 
 recting the aberration of the latter to associate with them the 
 former. 
 
 Spherical Aberration of Pencils oblique to the axis ; 
 Coma. — We have hitherto only considered the aberration of 
 pencils parallel to the axis of lenses, but in photographic 
 objectives which include a very considerable angle (from 30° 
 to 90°), what we have said is only applicable to a small portion 
 of the objective, namely its central part. We have therefore 
 also to examine the aberration of pencils very oblique to the 
 principal axis of a lens, both by a single lens and by an 
 aplanatic system of lenses. 
 
 When parallel rays of light strike a lens obliquely, the 
 longitudinal aberration alters for two diameters of the lens 
 (perpendicular to each other), and is the greatest in the plane 
 passing through the axis of the lens and the radiating point. It 
 follows from this that the aureola A (fig. 33) — circle of aber- 
 ration — which surrounds the image 
 of a luminous point at the focus of a 
 simple lens, circular if this point is 
 situated in the axis, lengthens ac- 
 cording as the point departs from 
 the axis and takes the forms B, C, D, 
 which lengthen more and more until 
 terminating in a point at their upper part, which has given 
 them the name of Coma. 
 
 An aplanatic system — that is, one perfectly free from 
 spherical aberration along its axis — is no longer free from this 
 aberration if the pencils fall obliquely to its axis. 
 
 Let A B (fig. 34) be a simple plano-convex lens, H F an 
 axis passing through its optical centre, and making with its 
 principal axis D E a considerable angle (15° to 30°, for 
 example), and R I, R I * two parallel rays, striking the lens 
 
 * In figs. 34 and 35, R I indicate the incident rays, R R the refracted 
 rays, M the normals to the convex face, M' the normals to the plane face 
 AC, C B, the tangent planes at the points of incidence or emergence. 
 
 Fig. 33. 
 
72 ' 
 
 PHOTOGRAPHIC OPTICS. 
 
 above and below H F. The upper ray will cut the axis at 
 
 FY and the 
 other farther 
 off at F. The 
 image of the 
 luminous point 
 will no longer 
 be a single 
 point, but will 
 appear to be 
 furnished with 
 a tail or coma* 
 which is di- 
 rected down- 
 wards. In con- 
 sequence, rays 
 coming from 
 the lower part 
 
 of the lens are more condensed in a point F than those coming 
 from its upper part, which are dispersed beneath this point 
 
 after having cut the axis in F\ 
 
 If the lens be turned the other 
 way (fig. 35), so that incident 
 rays fall on its convex face, the 
 coma, in place of being directed 
 inwards, is directed outwards. 
 
 If, instead of considering only 
 two incident rays, we take an 
 infinite number of rays, R 1 , R 2 , 
 R 3 , &c. (fig. 36), striking ob- 
 liquely the plane surface of a 
 plano-convex lens A B, there 
 Fig. 36. will be, for every two rays im- 
 
 mediately adjacent taken in the plane passing through the prin- 
 
 * J. Lister. On some Properties of Achromatic Object-glasses. — Phil. 
 Transactions (1830.) 
 
ABERRATIONS. 
 
 73 
 
 oipal axis, a different focal distance. The construction of the 
 figure shows that R 1 , R 2 , &c., being parallel after refraction at 
 the plane surface of the lens along the dotted lines r, will all 
 emerge along RE 1 , RE 2 , &c., making different angles with 
 the normals n 
 to the curved 
 surface at the 
 points of emer- 
 gence, and with 
 the oblique axis 
 R 1 RE 1 which 
 we have (arbi- 
 trarily) chosen. 
 
 So the incident 
 pencils, R 1 and 
 R 2 , R 2 and R 3 , 
 
 &c., will have for focal distances (fig. 37) the points / 2 , 
 / 3 , &c. 
 
 Destruction of Aberration of Pencils oblique to the 
 axis. — By properly selecting the radii of curvature of the 
 two lenses which form the single combination employed in pho- 
 tography (corrected for chromatic aberration along its principal 
 axis), and by placing in front of it a diaphragm, of which the 
 aperture does not exceed 1-3 Oth of its focal length, its spherical 
 aberration is reduced to a very small amount, both for pencils 
 parallel to the axis and for pencils very oblique. 
 
 The diaphragm must be placed at a suitable distance from 
 the lens. This makes of it, therefore, an assemblage of lenses, 
 each of which has sensibly the diameter of the aperture of the 
 diaphragm, and each of which acts specially on pencils more 
 or less oblique, the centre of the lens receiving rays only from 
 points of the object situated along the axis, while all others are 
 shut off, and the margin receiving them only from points of 
 the object situated very obliquely. 
 
 We shall, however, explain these things more fully when 
 treating of the diaphragm (see p. 89). 
 
 Fig. 37. 
 
74 
 
 PHOTOGRAPHIC OPTICS. 
 
 Effect of Spherical Aberration in Photographic Ob- 
 jectives, and how it is proved. — The effect of spherical 
 aberration in the systems of objectives employed in photo- 
 graphy, is to destroy the sharpness of the image both at its 
 centre and at its margins. We can experimentally prove this 
 by removing the diaphragms of the objective, known among 
 photographers under the name of single landscape lens , and 
 by examining the image the objective gives. It is utterly 
 wanting in sharpness. 
 
 In other objectives in which spherical aberration is cor- 
 rected by the arrangement of the lenses which form them, — 
 for example, in the objective known under the name of the 
 “j portrait combination ” — to discover if this aberration is alto- 
 gether destroyed, examine the image of two small circles of 
 tinfoil* fastened to a window exposed to direct day-light, 
 so as just to touch each other. Whilst the image is being ex- 
 amined with a magnifier, put a diaphragm on the objective so 
 as to reduce its aperture to a half. If, in this case, the image 
 of the circles of tinfoil gain in sharpness, which will be best 
 observed at their point of contact, the aberration is not com- 
 pletely corrected. 
 
 This trial must be made along the axis of the objective, be- 
 cause it is only along the axis that spherical aberration can be 
 completely corrected. 
 
 If, after having put on the diaphragm, it becomes necessary 
 to draw back the focal plane (the ground-glass of the camera), 
 to preserve the primitive sharpness of the image, the objective 
 possesses positive aberration ; if it is necessary to advance it, 
 negative aberration. 
 
 The examination, however, may be made still better by 
 reproducing the wafers by photography, first with the whole 
 aperture of the objective, then with a small diaphragm on 
 the objective, and without changing the focus. The two 
 images should be equally sharp. 
 
 * Two wafers answer equally well. 
 
ABERRATIONS. 
 
 75 
 
 Spherical Aberration serves to divide Photographic 
 Objectives into two very distinct classes. — There are dif- 
 erent forms of photographic objectives. Some can be employed 
 with their entire aperture, and then give a sharp image, but of 
 little extent ; the others (employed with their whole aperture) 
 give only confused images. This is because the former are 
 aplanatic — that is, because their aberration is corrected by the 
 arrangement of the lenses which form them, and the second are 
 not so. The aplanatic photographic objectives comprehend — 
 
 1st. The double lens of M. Petzval. 
 
 2nd. The orlhoscopic of M. Petzval. 
 
 3rd. The triplet of M. J. H. Dallmeyer. 
 
 The non-aplanatic objectives comprehend — - 
 
 1st. The ordinary single lens. 
 
 2nd. The single objective (of three lenses) of M. Dallmeyer. 
 
 3rd. The doublet of Mr. Thomas Eoss. 
 
 4th. The globe-lens of Harrison and Schnitzer. 
 
 5th. The panoramic lens of Mr. Sutton. 
 
 6th. The doublet of M. Steinheil. 
 
 An attentive examination of the latter class of objectives 
 demonstrates that the sharpness of the images which they fur- 
 nish (even when they are employed with very small dia- 
 phragms) is not so perfect as that of the images produced by 
 aplanatic objectives; especially if we compare, in the first 
 series, the orthoscopic and the triplet (which are the most apla- 
 natic), with the globe-lens, which possesses a very con- 
 siderable spherical aberration. We may satisfy ourselves on 
 this point by examining the image of very fine black letters 
 pressed on a very smooth white ground — engraved visiting- 
 cards, for instance. Aplanatic objectives cause no loss of the 
 finest details, whilst the others cause them to disappear. It 
 is particularly at the centre of the image (which corresponds 
 to the axis of the objective) that it is necessary to make this 
 comparison. It is necessary besides, in this trial, to furnish 
 the objectives with diaphragms of which the aperture is pro- 
 portional to their respective focal length (l-30th). 
 
76 
 
 PHOTOGRAPHIC OPTICS. 
 
 Section II . — Chromatic Aberration. 
 
 Visual and Chemical Focus.— The image of a white 
 point, A (fig. 38), situated at a distance from a lens, L, 
 
 which is formed at its prin- 
 cipal focus, E, is deficient in 
 sharpness, because it is there 
 surrounded by a violet au- 
 reola. At V, nearer the lens, 
 the image of the point is 
 surrounded by a red aureola. 
 This results from the fact that the white point, A, emits rays 
 of different refrangibility. After refraction these rays are 
 separated, and the violet, being more refrangible than the red, 
 have their focus at V, while the red have theirs at E. 
 
 If we wish to obtain from the point A a photographic image 
 by using a simple lens, L, we shall find that by placing the 
 photographic surface at E, where the image of the point 
 appears the clearest to us, we shall obtain but a confused 
 image of it, and that, by successively advancing the photo- 
 graphic surface towards the lens, the image obtained will be 
 more and more sharp up to V, where it will be perfectly distinct. 
 
 This is because those rays which have the greatest bright- 
 ness to the eye, and which are found to have their focus pre- 
 cisely at E, where, consequently, the image appears the clearest 
 to us, have scarcely any influence on photographic surfaces ; 
 whilst those the most obscure (blue, indigo, violet), which 
 almost escape our eye, are precisely the most active in regard 
 to the photographic surface. 
 
 If therefore we used as a photographic objective a simple lens, 
 even though this should be limited (as is shown in figure 38) to 
 a very small aperture, so as to reduce the spherical aberration 
 to a small quantity, the exact focussing of the image on the 
 ground-glass, for the eye, would not be so for photographic sur- 
 faces, which give in place of a sharp image a confused one. 
 

 ABERRATIONS- 
 
 77 
 
 Hence the names of visual focus , to indicate the focus of a lens 
 as judged of by the eye, and of chemical focus , to indicate its 
 focus as determined by photographic surfaces. These two foci 
 in a photographic objective ought to coincide, else the objec- 
 tive is said to have a chemical focus. 
 
 If the reader recall to mind what we have said at page 29 
 about dispersion by prisms, and at page 51 about the focal 
 length of lenses, he will very easily determine for himself the 
 value of the difference between the visual and chemical foci, 
 when the focal length of the lens and its index of refraction, 
 or, what comes to the same thing, its radii of curvature, are 
 known. Thus, suppose it is wished to know what will be the 
 chemical focus of a plano-convex lens of which the radius of 
 curvature is 1 metre, the index of refraction of the yellow 
 being 1*5, and that of the violet 1*52. The formula 
 R 
 
 / = gives us for the focus of the yellow 666 milli- 
 
 metres, and for the violet 658 millimetres. The chemical 
 focus thus differs from the visual by 8 millimetres. 
 
 In reality this focus would be much more considerable, 
 because, instead of considering only the central part of the 
 lens, which is free from spherical aberration, account must be 
 taken of the error arising from the margin of the lens, the 
 spherical aberration of which is considerable. The chemical 
 focus would therefore be reckoned from the absolute focus 
 (that of the yellow rays emerging from the central part of the 
 lens), to the focus of the blue rays emerging from the peri- 
 pherical part of the lens — blue rays which cut the axis so 
 much the nearer the lens as its aperture is larger, a fact 
 arising from spherical aberration. Hence the necessity, in 
 achromatising a lens, of first destroying its spherical aberration. 
 
 Destruction of Chromatic Aberration. — The most 
 simple way to achromatise a lens (or a system of lenses) consists 
 in placing in front of it a vessel with parallel glass sides, con- 
 taining a solution of chloride of copper in ammonia. This 
 liquid is of a deep blue. It is, however, diluted with water 
 
78 PHOTOGRAPHIC OPTICS. 
 
 so long as the solution, though being less deeply tinted, 
 allows only blue colour to pass through. This is easily 
 ascertained, by looking through a prism at a strip of white 
 paper placed in front of the vessel. Seen directly, the strip 
 is fringed with red and yellow at one side, and blue and 
 violet at the other. Seen through the blue solution, the red 
 and the yellow disappear completely if the solution be of the 
 proper tint. 
 
 The ammoniacal chloride of copper, therefore, by allowing 
 only the blue to pass through, achromatises simple lenses, and 
 also allows the passage of the chemical rays ; still it absorbs 
 a great part of these, and its use would, besides, be very 
 inconvenient. 
 
 Since the diaphragm applied in front of a lens does not 
 correct chromatic as well as spherical aberration, it is, there- 
 fore, absolutely necessary to proceed with lenses, as with 
 prisms, by associating with them a second lens of different 
 dispersive power. After what we have seen at p. 31 et seq ., 
 the explanation of the achromatising of lenses will present 
 no more difficulty. 
 
 Fig. 39 shows how these lenses are combined. The first, 
 
 of the upper row is a divergent 
 meniscus ; the second, a plano-con- 
 cave lens ; the third, a bi-concave 
 lens with faces equally concave. 
 The lenses beneath are similar, 
 but convergent. Ordinarily, in 
 an achromatic combination, the 
 convergent lens is of crown-glass , 
 the divergent of flint-glass , and 
 the two have one face common, 
 at which they are cemented to- 
 gether. 
 
 Suppose the case of the achro- 
 matism of a bi-convex lens of crown-glass, of which R and R' 
 are the radii of curvature, and n v and n r the indices of refrac- 
 
 Fig. 39. 
 
ABERRATIONS. 
 
 79 
 
 tion for the red and the violet. The focal lengths, / and f l9 
 of this lens will be— 
 
 RR' 
 
 J (n r — 1) (R -j- R') 
 
 /i- 
 
 RR' 
 
 (n v — 1) (R R )» 
 
 Associate with this convergent lens a divergent one, having 
 one face common with it, R', and the other unknown, R". But 
 R' will necessarily be negative, since it belongs to the diver- 
 gent lens. Let n' r and n v be the indices of refraction, and we 
 shall have for their focal lengths — 
 
 % B'R" 
 
 J (n'r - 1) (R' - R") 
 
 // = 
 
 R' R" 
 
 (n' v - 1) (R' — R"). 
 
 Now, let the reader recall to mind the formula which con- 
 nects the distance, p, of the radiating point, and that, p\ of the 
 conjugate focus, with that of the principal focus 
 
 £ + ?“7’ 
 
 and let him take into account that the negative lens lengthens 
 the focal distance p', which becomes p ", by giving a new 
 principal focal length /' for the combination. From this 
 we have — 
 
 w p" y /' 
 
 These two equations added together give — ■ 
 
 1 , 1 1,1 ,11 11 
 
 + p" ~ f + f an p'\~ f’\ 
 
 Vi'i /n /i\ referring to the violet, and p", f and /' to the red. 
 
80 
 
 PHOTOGRAPHIC OPTICS. 
 
 Now, in order that achromatism may result from the asso- 
 ciation of the two lenses, p" and p" must be equal — that is, 
 the focus of the red and that of the violet must form at the 
 same point. These values will be equal if the resulting sys- 
 tem allows us to write — 
 
 i+JUl+1. 
 
 r r /i /', 
 
 In these equations, let us substitute the values of /, /', /-,, 
 //, obtained above as functions of R, R', R", and n , w', and 
 we shall derive from them — 
 
 _ RR ^ r ) 
 
 R ^ ft v — t ) = (R R ^ (pv — % ^ 
 
 R ( n' v - . n' r ) 
 
 (^Ifl ■ u — Mr) — 2 — Tip ) 
 
 Now, R and R' are known, being the radii of curvature of 
 the convergent lens ; the indices of refraction of crown and 
 flint-glass are also known ; and therefore the divergent lens 
 of flint-glass will have for its radii of curvature R' and R". 
 
 We here suppose the aperture of the lens to be very small, 
 for we do not take into consideration the thickness of the lens. 
 
 Moreover, we have not here considered the spherical aber- 
 ration either of the first or second lens, and this ought to 
 have been done. 
 
 Destruction of Chromatic and Spherical Aberrations 
 in Lenses of large aperture. — It is easy to connect together 
 the equations which enable us to construct aplanatic lenses, 
 and those which enable us to achromatise them ; but these 
 equations, otherwise very simple, only apply to the case where 
 the lens has a very small aperture, that is, where its thick- 
 ness can be regarded as nothing.* 
 
 * Equations can be laid down in which a second approximation takes 
 thickness into account. By employing them, the calculation is much 
 abridged. — (See Coddington : Treatise on Optics .) 
 
ABERRATIONS. 
 
 81 
 
 Now, if the lens possesses a considerable diameter rela- 
 tively to its focal length, these formulae, at the most, can 
 only apply to the central part of the aplanatic and achromatic 
 system ; and they therefore serve only to give the numerical 
 elements of this part. But it is essentially necessary that 
 the rest of the surface of the lens should present the proper- 
 ties of its central part ; and it is the accomplishment of this 
 which constitutes the real difficulty for the optician. 
 
 In fact, in an achromatised aplanatic lens, it is not only 
 necessary that the rays falling on its margin and on its centre 
 (parallel to its axis), should emerge from the lens so as to 
 cut the axis at the same point, hut it is also necessary that the 
 rays falling on the intermediate parts of the lens should pre- 
 sent the same property. The negative lens of an achromatic 
 system ought therefore, in the first place, to correct the 
 spherical aberration of the positive lens with which it is 
 associated (without this, perfect achromatism is impossible), 
 and, next, to correct the aberration of refrangibility. It may 
 fulfil the first condition without fulfilling the second; but it 
 cannot fulfil the second without also satisfying the first, at 
 least from a theoretical point of view. 
 
 The formulae which are applicable to an achromatised apla- 
 natic lens of large aperture cannot be converted into nume- 
 rical data, on account of the much greater number of 
 unknown quantities which they contain when a greater 
 approximation is sought. It is necessary, therefore, to have 
 recourse to experiment by re-working the surfaces several 
 times, and this operation is sometimes very long and laborious. 
 
 Chromatic aberration of pencils oblique to the axis. 
 — Since it is impossible to construct a lens free from spheri- 
 cal aberration both along its axis and oblique to it, so 
 lenses cannot be constructed free from chromatic aberration 
 under these same circumstances. For a combination of lenses 
 may be assimilated to a combination of prisms, and we have 
 seen that achromatism of a prism is only possible in rela- 
 tion to rays of a fixed incidence (page 32, line 16). 
 
82 
 
 PHOTOGRAPHIC OPTICS. 
 
 Ficr. 40. 
 
 Let M (fig. 40) be a bi-convex lens of crown-glass, achro- 
 niatised for incident rays parallel to its axis, CC', by the 
 
 piano - concave 
 lens of flint- 
 glass, N, and let 
 EO be an in- 
 cident ray ob- 
 lique to the 
 axis. This ray, 
 on emergence, 
 will be decom- 
 posed in the 
 direction r o' v, 
 which forms 
 
 the angle of dispersion. The part of the lens traversed by 
 the ray may be represented by the prism (of dotted lines 
 in the figure) oao' ; ao, ao\ being the normals drawn to the 
 points of immersion and emersion. Now, the angle, i, which 
 the incident ray, EO, makes with the parallel, oa , to the 
 bisector, a m, of the prism, a , is much greater than the angle, 
 i\ made by the emergent rays with the parallel, o' a', to the 
 same bisector, m a. Now, that the angle of dispersion, r o' v, 
 may be as small as possible, these angles, i and i', should be 
 equal, which would assign the position xy to the bisector, a m. 
 Therefore the lens reversed would fulfil this condition better, 
 and it is in fact in this way that it is employed in the single 
 objective ; but, to fulfil it completely, a meniscus, of which 
 the concave surface facing the radiating point has a short 
 radius of curvature, is more favourable. M. Dallmeyer is the 
 first optician who has constructed the single combination in 
 accordance with this theory. 
 
 The objective which we represent in fig. 41 under the form 
 of a simple lens, although in reality there should be three of 
 them cemented together, is a convergent meniscus, M, of which 
 the face P turned towards the objects for reproduction is 
 concave, and of a radius of curvature relatively very short. 
 
ABERRATIONS. 
 
 83 
 
 Along its principal axis, C C, this objective is quite free from 
 chromatic aberration ; 
 hut for very oblique 
 pencils, such as E 0, 
 achromatism no longer 
 exists. In front of the 
 objective is a dia- 
 phragm, D, which limits 
 the extent of the inci- 
 dent pencils. Let E 0 
 be an incident rav very 
 oblique to the axis, N 0 the bisector of the prism represented 
 by the two faces tangent at the points of immersion and emer- 
 sion of the lens traversed by this ray ; and we shall find that 
 the refracted rays E 0 and E Y form with this bisector, the 
 angles NOE, NO V', sensibly equal to each other and to the 
 angle N OE'.. The angle of dispersion, E'O V', which is the 
 direct measure of the chromatic aberration, is therefore very 
 small, whereas it is very considerable in ordinary single ob- 
 jectives. 
 
 The impossibility which exists of correcting at once, in the 
 same lens, chromatic aberration both along the axis and ob- 
 liquely to it, has a very troublesome consequence. This is 
 why (using the language of photographers) if a sharp image 
 on the ground-glass is likewise so on the photographic sur- 
 face, thus proving that the objective is without chemical 
 focus, such is only the case at the centre of the ground-glass. 
 If this experiment be made at the edges of the ground-glass, 
 an image, perfectly sharp to the eye, is not so for the photo- 
 graphic surface ; because there exists, for pencils oblique to 
 the axis, a chemical focus, often considerable, which it is very 
 important to reduce to the minimum. 
 
 Position of the Chemical Focus as regards the 
 Visual Focus. — It may happen that, the dispersive powers 
 of the materials forming the objective not having been 
 exactly measured, the chromatic aberration may be under or 
 
84 
 
 PHOTOGRAPHIC OPTICS. 
 
 over corrected. In the former case, the violet having its focus 
 nearer the lens than the red, the chemical focus will he situ- 
 ated nearer the lens than the visual focus. If, on the contrary, 
 the chromatic aberration is over-corrected, the red will then 
 have its focus nearer the lens than the violet, and the chemical 
 focus will be situated further away from the lens than the 
 visual focus. From this it will be seen, therefore, that it is 
 exactly the same with chromatic aberration as it is with sphe- 
 rical aberration ; a convergent combination of two lenses, the 
 one convergent, the other divergent (the combination being 
 convergent), may offer the characters of negative aberration 
 proper to negative simple lenses. — (See p. 69). 
 
 Section III . — Aberration of form of the image , or curvature of 
 
 the field. 
 
 The curved Image. — The image of external objects 
 formed at the focus of a lens cannot be received on a plane 
 screen, as we have hitherto supposed it to be (see p. 56) : 
 the screen ought to have a concave form, which constitutes 
 the curvature of the field of the image. Thus, let us select in a 
 plane very distant, three points, ABC (fig. 42), very nearly 
 
 A 
 
 equally distant from the convergent lens, D, one of the 
 points, B, being in the axis of this lens, and the two others 
 without it ; and let us examine the form of the image behind 
 this lens. It is evident that the image of the three points will 
 be formed at distances from the optical centre of the lens, D, 
 
ABERRATIONS. 
 
 85 
 
 nearly equal to its principal focal length. The field, FEG, 
 will therefore he curved, and the image cannot be received 
 on a plane, H I, without sacrificing the sharpness of the image 
 of the points A and C. 
 
 This aberration of lenses is generally attributed by 
 photographers to spherical aberration. They imagine, on 
 seeing the image sharp at the centre of the ground- glass of 
 the camera and confused at its edges, that this effect is due 
 to the sphericity of the faces of lenses. But this has nothing 
 to do with it, for a lens with parabolic curvatures would give 
 the same result. 
 
 Before explaining how the aberration of form is corrected, 
 we must see what is meant by the depth of focus of a lens, and 
 by the diaphragm. 
 
 Depth, of Focus.- — Depth of focus is the property of lenses 
 of giving a clear image in planes of which the distance is 
 unequal. It follows from this that the ground-glass placed 
 at the focus of a lens may be moved to a very slight extent 
 without the image sensibly losing its sharpness. 
 
 To prove this experimentally, bring a camera furnished with 
 a single combination to bear on a landscape. Bring to a focus 
 the objects farthest off. We shall soon remark two things : the 
 first is that the ground-glass can be advanced or withdrawn 
 to a small extent without the sharpness of the image of a 
 fixed plane of the landscape sensibly changing ; the second is, 
 that if we bring to a focus the most distant plane, many other 
 nearer planes will still be in focus. 
 
 The same experiment can be made with an opera-glass, 
 which may be regulated for distant objects so as that they may 
 be seen very distinctly. If you now direct the glass to nearer 
 objects you will also see them with perfect clearness. Simi- 
 larly, by holding the opera-glass directed on a distant object, 
 
 ' you will see that you can move the eye-piece a short distance 
 without lessening sensibly the sharpness of the image by 
 doing so. 
 
 It is to be observed that the depth of the focus varies with 
 
86 
 
 PHOTOGRAPHIC OPTICS. 
 
 the aperture of the lens. Figures 44 and 45 make this very 
 
 plain. In figure 44 we make 
 use of a lens with its entire aper- 
 ture. The rays, rr, emanating 
 £ from a distant point, form, after 
 having traversed the lens D, the 
 
 r 
 
 image of the point at a on a 
 screen or ground-glass A. But 
 »- if the ground-glass be either 
 drawn back or advanced, to C or 
 to B for example, the image of 
 the point immediately spreads 
 out in a circle, because angle a is very large. When the 
 same lens D (fig. 45), is reduced to its central part by a 
 stop, the image of the point is still formed at a, but the 
 ground-glass can be placed at C or at B, without the image of 
 the point becoming now appreciably altered. This is because 
 in fig. 44 the rays, r r , emerging from the lens, are much more 
 convergent than in fig. 45. 
 
 It results, therefore, from the preceding, that a convergent 
 lens is capable of giving a sharp image of planes distant from 
 each other, contrary, apparently, to the law of conjugate foci. 
 But experiment shows that it is only on the condition that 
 these planes are sufficiently distant from the lens that their 
 image may be formed near the principal focus. Thus, the 
 nearer objects approach the lens, the less becomes this depth 
 of focus, as is shown by the following short table, which 
 gives the focal lengths of a lens of 10 cent, focus, for objects 
 of which the distance is constantly diminishing. 
 
 Distance of object. 
 
 Elongation of focal length of the lens. 
 
 10,000 metres. 
 
 0*001 millimetres. 
 
 1,000 
 
 tt 
 
 0*01 
 
 91 
 
 100 
 
 tt 
 
 0*1 
 
 19 
 
 50 
 
 tt 
 
 0*2 
 
 91 
 
 10 
 
 tt 
 
 1*01 
 
 99 
 
 5 
 
 tt 
 
 2*04 
 
 99 
 
ABERRATIONS. 
 
 87 
 
 Distance of object. Elongation of focal length of the lens. 
 
 4 metres. 
 
 2-6 
 
 millimetres. 
 
 3 „ 
 
 3-5 
 
 ?» 
 
 2 „ 
 
 5-3 
 
 .? i 
 
 1 
 
 11*1 
 
 
 50 centimetres. 
 
 25 
 
 •>-> 
 
 40 „ 
 
 33-3 
 
 5 5 
 
 30 „ 
 
 50 
 
 55 
 
 20 „ 
 
 100 
 
 55 
 
 This table is very instructive. It enables us to see clearly 
 that for objects 50 metres distant, for example, the focal 
 length of the lens is increased only two-tenths of a millimetre, 
 a length quite inappreciable ; for 10,000 metres it is increased 
 still Jess, only a thousandth of a millimetre. Therefore, all 
 objects situated more than 50 metres from the lens will be 
 in focus on the ground-glass, however great may be their 
 distance. 
 
 When, on the contrary, the object is situated very near the 
 lens — for example, 30 centimetres from it — the ground-glass 
 has to be drawn out 5 centimetres ; when at 50 centimetres, 
 the glass has to be drawn out 2h centimetres ; when the object 
 is distant one metre, the glass has to be drawn out 11 milli- 
 metres, — quantities relatively great. For this reason, objects 
 situated at a short distance from the lens give sharp images 
 only on the condition that they are very near each other; 
 hence the difficulty of obtaining the image equally sharp 
 if this condition is not fulfilled. 
 
 Thus, then, the depth of focus of the lens varies with its 
 aperture, and the distance of the objects which form the 
 image at its focus. It varies also according to the form of 
 the lens or the optical combination of lenses composing an 
 objective. Convergent meniscus lenses have the greatest 
 depth of focus when their concave face is towards the 
 objects. Among objectives composed of several lenses, the 
 orthoscopic has the greatest depth of focus, and the ordinary 
 double combination the least. This is because the former has 
 generally a small aperture in relation to its focal length, 
 
88 
 
 PHOTOGRAPHIC OPTICS. 
 
 and because, moreover, the divergent lens placed along with 
 the anterior convergent lens renders the emergent pencils less 
 convergent. The second, on the contrary, has generally a 
 very large aperture, and besides, the rays emergent from the 
 first lens (the one which is towards the object) are rendered 
 still more convergent by the second lens. 
 
 Effect of depth of Focus on the curvature of the 
 field. — Figure 42 shows that if a ground-glass, H I, is placed 
 at the principal focus of the lens, D, there is but one point 
 sharply defined in the image of the points A, B, C, which is E ; 
 if the ground-glass is brought nearer to the lens, the point E 
 will then become indistinct, and the points F and G will 
 gain in sharpness, but it will be impossible, with the entire 
 aperture of the lens, to render the image of the three points 
 equally sharp at the same time. But let us see the effect of 
 a stop, D D, placed close in front of the lens (fig. 43), and let us 
 compare the two figui es 42 and 43 with the figures 44 and 
 45, it will be seen at a glance that the ground-glass, II I 
 (fig. 43), on which the point E was alone in focus in the 
 jmeceding example, can be brought a little nearer to the lens 
 without the image sensibly diminishing in sharpness in con- 
 sequence. Similarly, another ground-glass which would pass 
 through the points F and G could be brought a little farther 
 to the lens without the points F and G losing their sharpness 
 on this account. There is, therefore, between F G and H I 
 such a position for the ground-glass that the three points, 
 F, E and G, will all three be approximately sharp. 
 
 The office of the stop which reduces the aperture of 
 a lens to its central part is of great importance. In reality 
 it serves only to increase the depth of focus of the lens, and 
 it is owing to this property that a lens can give a sharp 
 image on a plane surface. The experiment is easily verified 
 by directing on any plane whatever — a geographical map for 
 example — a camera furnished with a reversed single com- 
 bination, all the diaphragms of which have been taken away. 
 We can only succeed in rendering the centre of the image 
 
ABERRATIONS. 
 
 89 
 
 sharp, or a small square situated symmetrically around the 
 centre. Now put on a very small diaphragm, and 
 you will observe that sharpness will be distributed 
 over a surface of the ground-glass much more ex- 
 tended. 
 
 The Diaphragm.* — If the stop, A, be placed as 
 we have shown in fig. 43, that is, close to the lens, 
 
 M, it is the same as if the lens were very small 
 relatively to its focal length. In this case observe 
 that, if it be very small, the lens may be considered 
 as a plate with parallel faces ab, c d (fig. 46), that 
 is, therefore, nearly as if there were no lens there. Flg * 46 ‘ 
 The field of the lens will certainly not be so curved as if the 
 lens were employed with its entire aperture, but it will still 
 be much so, because of the depth of focus ; that is, the extent 
 to which the ground-glass can be safely moved without 
 putting the image out of focus is as a whole very slight, and 
 because the curvature of the field is very great. Let us 
 see what takes place when the stop is removed from the 
 lens to a proper distance. In this case the stop becomes 
 a diaphragm. 
 
 Let A, B, C be three very distant radiating points (fig. 
 47), L L a convergent lens. Let us trace, behind the lens, 
 the course of the rays emitted from the three points, A, B 
 and C. The rays coming from the point B (which we 
 suppose to be situated at infinity and on the axis) reach the 
 lens parallel to each other and perpendicular to its surface, 
 from which they will proceed to form the image of the point 
 B at F, the principal focus of the lens, L L. But it is not 
 
 * In optics, stop and diaphragm are synonyms. But in photographic 
 optics they are only so by an unfortunate confusion of language. The 
 stop reduces the lens to its central aperture; the diaphragm, on the 
 contrary, allows all the segments of the lens to act, hut only on the dif- 
 ferent radiating points placed symmetrically and concentrically in relation 
 to the axis of the lens, or of the system of lenses (of which the axis is, 
 besides, in every case common). 
 
90 
 
 PHOTOGRAPHIC OPTICS. 
 
 thus with the rays which emanate from the points A and C 
 situated without the axis of the lens. The ray A’ will he 
 
 refracted to a; A 2 to b; A 3 to c; A 4 to d; A 5 to N. It is 
 the same with the rays 1, 2, 3, 4, and 5 emitted by the point 
 
ABERRATIONS. 
 
 91 
 
 C. (This effect is due to spherical aberration, of which 
 we have spoken, p. 72.) For this reason, the ground-glass 
 placed at the principal focus, F, will not receive a sharp image, 
 but an indistinct one. The experiment can easily be made 
 by examining the image of a landscape at the focus of a photo- 
 graphic single objective. Even should the ground-glass 
 have the form of a spherical cup, the image would still be 
 indistinct, because all the rays emanating from points out of 
 the axis of the lens arrive at different points behind the lens. 
 To have a sharp image, a diaphragm must therefore be placed 
 in front of the lens ; but where it must be placed and what 
 its aperture is to be, is the question. 
 
 Observe in the figure that the only pencils coming from the 
 points A and C, which arrive and form their focus very near 
 to the focal plane M N, are the pencils A 4 and A 5 , and C 4 and 
 C\ Let us place the diaphragm at 0 P, so as to allow only 
 these pencils to pass, then our figure becomes exactly the 
 other (fig. 46) ; but w r e already know that lenses with a 
 diaphragm have a certain depth of focus, and that conse- 
 quently the ground-glass can be slightly moved without 
 the sharpness of the image sensibly changing. Now, if the 
 distance M d 1 or N d is not greater than the depth of focus, then 
 the dimension and position of the diaphragm will be deter- 
 mined. It is easy to see, that the smaller the diaphragm, the 
 more must the image gain in sharpness ; since the rays which 
 confuse the outlines of the image are arrested by the diaphragm. 
 
 The diameter of the diaphragm necessarily depends on the 
 expression of the spherical aberration for rays oblique to 
 the axis of the lens L L. The smaller the aberration, the 
 greater may be the diaphragm; the greater the aberration, 
 the smaller must be the diaphragm. There is, however, a 
 limit to the smallness of the diaphragm, because of diffraction 
 (see p. 5), which would have the effect of causing in the 
 image a confused outline of very bright objects. The image of 
 a star, instead of being a single point, would be a point sur- 
 rounded by concentric rings. If the diaphragm which is 
 
92 
 
 PHOTOGRAPHIC OPTICS. 
 
 placed in front of lenses be smaller than l-60th of their focal 
 length, the image tends to become less sharp in consequence 
 of diffraction. 
 
 Let us add that, photographically speaking, diaphragms, 
 too small, give flat images, without either relief or effect. It 
 should never be necessary to employ diaphragms of which 
 the aperture was less than one-thirtieth of their focal length ; 
 and it is chiefly for this standard that we prefer the use of 
 aplanatic objectives (see p. 75). 
 
 Destruction of Aberration of Form. — Now that we 
 understand the use of the diaphragm, which divides the lens 
 into as many parts as there are incident pencils more or less 
 oblique, we can examine more precisely the cause of curvature 
 of the field, and how this field may be rendered flat. 
 
 In the first place, experiment has shown that, among 
 simple convergent 1 lenses, convergent meniscuses furnished 
 with a diaphragm properly placed are those of which the 
 field is the least curved, on the condition, however, that 
 their concave face is presented towards the object to be 
 reproduced. The field is even completely flat if the lens 
 does not include a considerable angle (10° or 15°, for ex- 
 ample). But, for the purposes of photography, this lens 
 should include an angle at least double of this. Now, in this 
 case the field becomes much curved, and the image com- 
 pletely loses its sharpness towards its edges. 
 
 Thus, let M L be a convergent meniscus furnished with a 
 
 diaphragm N 0, 
 R a luminous 
 pencil emanat- 
 ing from a point 
 situated at infi- 
 nity in the axis 
 of the lens, and 
 R' an oblique 
 pencil falling on 
 the margin of the lens. The focal plane P F will be deter- 
 
ABERRATIONS. 
 
 93 
 
 mined by tlie focal length of the lens (where the rays R have 
 their focus). The focal length of the obliqne pencil R' 
 will not be equal to the other, but much shorter , M F' ; so 
 that the focal plane F P will be curved, F F x P' F' being 
 the measure of the curvature of the field. Suppose we use 
 a negative lens instead of a positive one, and exactly under 
 the same conditions. It is understood that we should not 
 have a real image, but only a virtual one. In this case the 
 curvature of the field would be reversed, since the margins of 
 the lens have a greater focal length than the centre, a result pre- 
 cisely the converse of that obtained with the convergent lens. 
 
 But simple or uncorrected lenses cannot be employed in 
 photography, because of the chromatic aberration, the result 
 of which would be a considerable distance between the visual 
 and chemical foci. Hence the necessity of employing achro- 
 matic lenses which, as is known, are composed of a positive 
 lens associated with a negative lens. How, by properly com- 
 bining these two lenses, the aberration of form in which is 
 opposed, as we have just seen, we succeed in rendering the 
 field completely flat, that is to say, in rendering their focal 
 length for pencils oblique to the axis equal to that for pencils 
 parallel to this axis. 
 
 There exists, therefore, between the position of the dia- 
 phragm and the negative and positive radii of curvature of 
 the lenses which form an objective, a relation such that the 
 field can be rendered flat at the same time that achromatism 
 is obtained. If the relation between the radii of curvature of 
 the three surfaces forming an achromatic lens be not exact, the 
 field may be curved either like that of a simple convergent 
 lens, or like that of a simple divergent lens. Thus the achro- 
 matic plano-convex lens L M (fig. 50), formed of a plano- 
 concave of flint-glass, and a bi-convex of crown-glass, has for 
 oblique incident pencils, R', a focus, F', nearer the lens than 
 for central pencils, R, of which the focus, F, is farther off. 
 Therefore this lens, although achromatic, possesses the curved 
 field analogous to that of simple convergent lenses. 
 
94 
 
 PHOTOGRAPHIC OPTICS. 
 
 An achromatic convergent lens, L M (fig. 51), of which the 
 
 flint-glass is bi- 
 concave and the 
 ^ crown-glass bicon- 
 vex, may have pro - 
 •° perties the con- 
 verse of those in 
 the preceding case, 
 and have a curved 
 cn field analogous to 
 that of simple 
 divergent lenses, 
 although conver- 
 gent. It is therefore necessary, in the destruction of the aber- 
 ration of form, to avoid going beyond a certain focal length 
 for oblique pencils, or else we fall into the same aberration 
 (of contrary sign). 
 
 It is therefore with this aberration as with spherical and 
 chromatic aberrations, in which we can go beyond the correc- 
 tions, and render the aberrations negative in convergent 
 combinations and positive in divergent combinations. 
 
 The single combination employed in photography, as we 
 shall see in the following chapter, possesses a field tolerably 
 flat, whilst including a certain angle. This objective is 
 necessarily achromatic, like all the objectives employed in 
 photography. It is a convergent meniscus, of which the 
 concave face is turned toward the object to be reproduced, 
 and the convex face toward the ground-glass of the camera 
 in which it is mounted. If this lens were employed in the 
 position in which it offers the least spherical aberration — that 
 is to say, the convex face turned towards the object to be 
 reproduced, like the object-glasses of telescopes — then the 
 field of the image would be very curved. Nevertheless, the 
 part of the field bordering on the axis would have a perfect 
 shatpness, even with the entire aperture of the lens; this 
 is conceivable, seeing that for incident rays parallel to its 
 
ABERRATIONS. 
 
 95 
 
 principal axis, the lens is nearly free from spherical and 
 chromatic aberrations. By associating with snch a lens a 
 negative achromatised lens with appropriate radii of cur- 
 vature, and situated at a certain distance from the first, 
 M. Petzval has succeeded in rendering the field of the entire 
 system very flat. His objective bears the name of the ortho scojoic 
 lens. Fig. 52 explains the principle on which its construc- 
 
 Eig. 5k.. 
 
 tion is based. A is the aplanatic and achromatic convergent 
 lens, the convex face of which is turned towards the object 
 to be reproduced ; B is the equally aplanatic and achromatic 
 negative lens. The lens A, employed alone, would give a 
 very curved image on the ground-glass, since the focal distance 
 A /' of the oblique pencils. R', would be much shorter than that, 
 /, of the axial pencils, R. The negative lens, B, lengthens 
 greatly (from f to F') the focal distance of the former, since 
 it acts on these pencils by its margins, which are strongly 
 prismatic, while it hardly lengthens the focal distance (from 
 / to F) of the latter. The primitive field, / /', is therefore 
 made flat along F F\ 
 
 The triplet of M. Dallmeyer is composed of two achromatic 
 convergent lenses situated at the end of a tube. Such a sys- 
 tem would have a field extremely curved, but a negative lens 
 placed between the two serves to render the field very nearly 
 .flat, as in the case of the orthoscopic lens. 
 
96 
 
 PHOTOGRAPHIC OPTICS. 
 
 Section IY . — Aberration of thickness of lenses , or distortion. 
 
 Distortion. — Stretch horizontally and vertically some 
 threads across a frame, and examine them, through a large and 
 strong magnifying glass, B, mounted in a frame with a handle, 
 A (fig. 53). You will observe, on placing the eye at a distance 
 
 of two or three feet from it, and 
 on a level with the centre of the 
 glass, that the threads which cross 
 in the line of the two perpen- 
 dicular diameters of the glass 
 are the only ones which remain 
 straight, the others appearing 
 curved. Observe in the figure that 
 the upper threads are bent in the 
 reverse direction to that of the lower 
 threads. This is because the 
 upper part of the lens is a prism 
 with curved faces, of which the 
 edge is precisely in the reverse position to that of the prism 
 with curved faces which forms the lower part. Accordingly, 
 on elevating the lens (whilst the eye is kept in the same 
 position), so that the upper thread may be seen through the 
 lower part of the lens, the thread is immediately curved in 
 the opposite direction. This is what constitutes distortion. 
 
 If the two threads in the middle remain straight, it is 
 because the eye is placed just at the level of the centre, and 
 if the eye be displaced these same threads immediately become 
 curved. 
 
 Distortion by divergent lenses is just the reverse of that by 
 convergent lenses. Thus the threads in fig. 53, instead of 
 being bent with their convexity towards the interior, are bent 
 with their convexity to the exterior, like the curved side 
 of a barrel. 
 
 The shorter the focus which the lenses employed in this 
 
ABERRATIONS. 
 
 97 
 
 experiment have, their diameter remaining the same, the 
 greater is the aberration of thickness : this explains itself. 
 
 .big. 04. 
 
 Figure 54 makes the effect of aberration of thickness, or 
 distortion, perfectly intelligible. Let L be a convergent lens, 
 in front of which is placed a diaphragm D,- pierced at its 
 centre by an opening 0" infinitely small." Let A B be the 
 principal axis of the lens L, K M a plane (situated at infinity) 
 perpendicular to this axis, and K' M' the focal plane. 
 
 I say that every straight line, C E, passing through the 
 extremity A of the axis B A contained in the plane K M, will 
 be reproduced as a straight line, n O'. In fact, let us recall to 
 mind that the centres of curvature of the faces of the lens are 
 necessarily in its principal axis; and further, that every 
 refracted ray is always in the plane of the incident ray. Now, 
 the plane of the incident rays C o, E n, which divides the lens 
 into two equal parts, and which is perpendicular to the plane of 
 its circumference , is also the plane of the refracted rays n n 
 and o O', the intersection of which with the focal plane K' M' is 
 the right line n O'. It would be thus, also, with every other 
 straight line — I A, for example — taken in the plane K M, pro- 
 vided that it passes through the extremity A of the axis. 
 
 But it is no longer the same for a straight line, 0 H, taken 
 in the plane K M, which does not pass through the extremity 
 A of the axis of the lens. In fact, a plane drawn through 
 
 H 
 
98 
 
 PHOTOGRAPHIC OPTICS. 
 
 this line and the aperture of the diaphragm will he oblique 
 to the axis, A B, and will cut the lens, at x Z, no longer into 
 two equal, but into two unequal parts. 
 
 Observe that the rays x H and Z 0 coming from the 
 extremities of the line 0 H pass through the lens close to its 
 margins, x and Z, whilst the rays drawn from the aperture 
 of the diaphragm to all the points intermediate between 0 
 and H — I », for example — taken at the middle, pass through 
 farther away from the margin, and where the lens is thicker. 
 The refracted rays, also, which in the preceding case emerge 
 from the lens in a plane perpendicular to that of its circum- 
 ference, now emerge in a plane oblique to this and along a 
 curved surface which cuts the focal plane in x ' i* Z', having 
 its concavity turned towards the principal axis of the lens. 
 If this lens, L, were formed of an infinity of concentric rings 
 having sensibly the same thickness, the refraction through 
 any point in the surface would be, for a like incidence, equal 
 to that produced by a lens infinitely thin. But formed as it 
 is at present of parts of unequal thickness, the refraction for 
 the same incidence is unequal, according as the ray is incident 
 farther or nearer from the margin ; hence the distortion . 
 
 It is very evident that the distance of the diaphragm from 
 the lens causes the distortion to vary, since the nearer this 
 diaphragm is brought to the lens the closer to the centre of 
 the lens do incident rays of a given obliquity to the axis 
 pass. If the diaphragm be in contact with the lens, the latter, 
 reduced to its optical centre, is evidently free from distortion. 
 
 The single objective employed in photography does not 
 
 give images free 
 from distortion ; 
 thus a drawing 
 like that repre- 
 sented in fig. 55 
 is reproduced as 
 in fig. 56. In 
 fact (fig. 58), in the single objective employed in photography, 
 
ABERRATIONS. 
 
 99 
 
 the diaphragm when placed at A in front of the lens B 
 has the effect of causing each segment of the lens to act on 
 a different part of the object to be reproduced, C D. Hence 
 distortion in the direction indicated by fig. 54. By placing 
 the diaphragm behind, that is, between the lens and the 
 ground-glass (fig. 59), the distortion would be of the opposite 
 
 kind (fig. 57), since in the former case the ray coming 
 from D traverses the upper part of the lens, and in the latter 
 case the lower part. 
 
 Destruction of aberration of thickness.— By uniting 
 two single objectives equal to each other, L L' (fig. 60), 
 
 and by placing the diaphragm D in the middle, it is easy to 
 see that the rays coming from the point A of ah external 
 
100 
 
 PHOTOGRAPHIC OPTICS. 
 
 object pass through the two opposite parts of the lenses. 
 The first lens gives barrel-shaped distortion (fig. 56), and the 
 second pincushion distortion (fig. 57), but they neutralize 
 each other by being combined. 
 
 Messrs.. Harrison and Schnitzer of New York (in 1862), 
 and M. Steinheil of Munich (in 1865), adopted this optical 
 system in the “ globe-lens” and the “ jperiscojpic lens .” The two 
 lenses (fig. 60) (identical with each other) have the form of 
 meniscuses with their concavities towards each other. The 
 diaphragm is very small, in order to correct the spherical 
 aberration of the combination, which is considerable. 
 
 The field is flat, owing to the very peculiar form of the 
 lenses, and principally to the very small diaphragms with 
 which these objectives are supplied. 
 
 An English savant , Mr. Sutton, in 1858, recommended 
 placing between the two lenses (identical with each other), 
 and at an equal distance from each of them, a concave lens. 
 In fact, by joining two ordinary lenses, A and B (fig. 61) 
 
 (such as the single objectives employed in photography) 
 the field /' a' is very curved. But by placing between 
 the two a negative lens C, the rays coming from a point a 
 without the axis, in place of having their focus at the point a\ 
 have it at the point b through the etfect of the negative lens. 
 This negative lens increases, therefore, the focal length of 
 the oblique rays. In this case the field is flat, and there is no 
 longer any distortion if the negative lens is bi- concave with 
 
ABERRATIONS. 
 
 101 
 
 faces identical to each other. This objective has received the 
 name of symmetrical triplet. Such, however, is not the 
 triplet of M. Dallmeyer, who was the first who produced this 
 optical system; Mr. Sutton having only indicated the possi- 
 bility of thus correcting the distortion.* 
 
 M. Dallmeyer gives to the two convergent lenses different 
 focal lengths, and places the negative lens between them, the 
 diaphragm being in such a position that the distortion is 
 destroyed, or very nearly so. His system has over that of 
 Harrison and Schnitzer the advantage of a complete absence 
 of spherical aberration ; but the negative lens by its thickness 
 still gives a slight distortion, because it is extremely difficult 
 to give it the exact position assigned by calculation, and which 
 varies with the nature of the glass employed. This distortion, 
 however, is only appreciable where the objective is used for 
 a dimension of picture greater than that for which it has been 
 constructed. 
 
 * The author’s history of the triplet is scarcely so correct as English 
 readers would desire. The following extract, from the seventh edition of 
 Hardwick's Photographic Chemistry , supplies the omission : — 
 
 “ The exact origin of the triplet lens for photographic work is not easy 
 to define, since there are conflicting claims for the honour of first having 
 introduced it. It would appear that, so early as the year 1853, the late 
 Mr. F. Scott Archer was in the habit of using a double combination portrait 
 lens for taking landscapes and interiors, and when thus applied, a stop with 
 a small aperture was placed between the components of the combination, 
 not in the convenient manner subsequently introduced by Mr. Waterhouse, 
 but similarly situated. Mr. Archer, finding that for interiors his lens was 
 sometimes of inconveniently long focus, introduced a slightly convex lens 
 of small diameter instead of the diaphragm, thus shortening the focus and 
 enabling him to include more of the subject on the same-sized plate. 
 Finding this arrangement work satisfactorily, he then substituted, for 
 ordinary landscape purposes, a concave lens of similar dimensions, in the 
 place of the convex, thereby lengthening the combined focus, so as to 
 enable him to use larger plates with the same lens. From evidence still 
 existing, these additions were not empirical, but made with the definite 
 objects in view. The small convex and concave lenses were not at first 
 actinic, from inotives of economy — the requisite slight corrections for 
 variation of chemical focus being made after focussing. Shortly after Mr. 
 
102 
 
 PHOTOGRAPHIC OPTICS. 
 
 The double objective of Petzval, when the diaphragms 
 are suitably placed between the two lenses, is very nearly 
 free from distortion. But if the diaphragms are placed in 
 front of the objective, then the distortion is considerably 
 greater than in the single objective. 
 
 Section Y. — Astigmation , or aberration of position of lenses. 
 
 Experimental process to demonstrate Astigmation. 
 
 — Astigmation is observed with a small portrait combination 
 placed on a large camera, the ground-glass of which is two or 
 three times as great as the surface which this lens ordinarily 
 covers ; thus, for example, a quarter-plate lens on a whole- 
 plate camera. Attach to a white wall a black wafer (or one 
 of any other colour), and examine its image at the centre of 
 your ground-glass, the axis of the apparatus being level with 
 
 Archer introduced the third lens, M. Chevalier constructed something of 
 the same kind for the late Mr. P. W. Fry, and subsequently M. Derogy 
 adopted the same device for obtaining a sort of multum in parvo lens. 
 
 “About four or five years ago, Mr. Thomas Sutton, of Jersey, devised a 
 form of lens which he called the ‘ symmetrical triplet/ which, as its name 
 implies, consisted of one concave and two compound-convex combinations ; 
 the latter being exactly alike, and placed one at each end of the tube- 
 mounting. The object aimed at was to correct the deviation of the pencils 
 of rays, so that they should be incident and emerge in directions parallel 
 to one another. Mr. Goddard, of Isleworth, then constructed some triple 
 combinations, not adhering, however, to the symmetrical form, and subse- 
 quently M. Dallmeyer adopted the same principle of employing for land- 
 scape lenses three actinic combinations ; these, however, were not mere 
 copies of any of the preceding, but the formulae for their construction were 
 worked out quite independently by M. Dallmeyer, so that they only re- 
 sembled the others in consisting of three parts, the central one being a 
 concave lens. 
 
 “ Somewhat later, Mr. Ross adopted a form of lens consisting of three 
 parts, arranged as were the others; but here again the formulae were 
 calculated anew by Mr. Ross, and any person who will take the trouble 
 of examining them will perceive at once that they differ in construction 
 as much from those of M. Dallmeyer as the last-named optician’s did from 
 those of his predecessors.” — Trans . 
 
ABERRATIONS. 
 
 103 
 
 the wafer. You will remark that its image is round, even 
 if you should move your ground-glass behind or in front of 
 the focus, in which case the image only loses its sharpness. 
 But turn the apparatus on its stand so that the image of the 
 wafer comes as nearly as possible on the edge of the ground- 
 glass. You will observe that it is now impossible to get a 
 sharp image of it, and that, by moving your ground-glass in 
 advance of or behind the focus, the image is lengthened in a 
 vertical or horizontal direction. 
 
 Theoretical explanation of Astigmation.— -Fig. 62 
 enables us to explain this result and to analyse its conse- 
 
 Fig. 62. 
 
 quences. Let LOMN be a convergent lens of which the 
 principal axis is A B. Obliquely to this axis, let us take a 
 radiating point R situated at infinity, and sending, conse- 
 quently, parallel rays to the lens. Let us make a plane pass 
 through the axis A B and the point R, which will cut the 
 lens along its diameter L M ; and let us suppose a second 
 plane to pass through the point R perpendicular to the 
 former one, the line of which on the lens will be the diameter 
 NO; let us see the course of the rays emitted by the point R 
 along these two planes, beginning with the first. 
 
 Let us draw, firstly, the ray R C passing through the optical 
 
PHOTOGRAPHIC OPTICS. 
 
 104 
 
 centre of the lens, which undergoes no deviation by refraction 
 at the curved surfaces of the lens, and which prolonged, 
 therefore, will constitute a secondary axis, E P. Let us 
 draw to the two extremities of the diameter L M of the lens 
 the incident rays E L and E M, which after refraction will 
 cut the axis at Q and at P, just as we have seen in the 
 chapter on spherical aberration. But, if the lens has a 
 small aperture, the point of meeting will be sensibly the 
 point Q. 
 
 In , the plane E 1ST 0, which contains also the secondary 
 axis EP, the incident rays EN and EO are symmetrical 
 in relation to the secondary axis, as after refraction they cut 
 the axis at the same point, S. 
 
 Jt is seen, therefore, that there are two focal lengths of the 
 same lens for rays oblique to the axis, falling parallel to each 
 other on the surface of a lens ; the one in the plane passing 
 through the principal axis of the lens and the radiating point ; 
 the other in the plane passing through the radiating point 
 and the optical centre, and perpendicular to the first. This 
 is what constitutes astigmation. 
 
 Reduction of Astigmation to the minimum. — Astigma- 
 tion (that is, the difference between the primary focus and the 
 secondary one) is reduced to the minimum ; firstly, by means 
 of the diaphragm, which divides the surface of the objective 
 into many separate surfaces, each of which acts on radiating 
 points of a different incidence ; secondly, by making the 
 spherical surfaces such that the immergent and emergent 
 rays may make a very small angle with the normals to the 
 spherical surfaces of the lenses. 
 
 Calculation of the Primary Focus and Secondary 
 Focus. — We shall consider the most simple case, that of a 
 simple lens, plano-convex, and furnished with a diaphragm 
 with very narrow aperture, placed at the optical centre of the 
 lens. We suppose the radiating point situated at infinity, 
 and the bundle of parallel rays to be falling on the plane face 
 of the lens. 
 
ABERRATIONS. 
 
 105 
 
 Let C F (fig. 1 , plate I.) be the axis of the lens, A a the 
 axis of the luminous beam after refraction at the plane surface 
 of the lens. Let us make a plane pass through these axes, 
 and let a b be an arc of a circle having its centre at C, 
 representing the section of the convex surface of the lens by 
 this plane. Let us consider in this a second ray, B6, of 
 the beam: the two rays A a, B b, will emerge along a Y and 
 b V, and their point of intersection, Y, will be approximately, 
 and when the two rays are infinitely close will be exactly, 
 the primary focus. 
 
 Let us calculate the distance a Y as a function of the 
 radius, C a = r, of the lens, and make the angles 
 
 Y aF = 0 
 A'aF = r] 
 bCa = (j> 
 b Y a = i (/. 
 
 The triangle Y a b gives 
 
 Y a :ba :: sin Y ba : sin if/ 
 
 Y a = ba 
 
 sin Y ba 
 sin if/ 
 
 Let us calculate each of the factors which enter into this 
 expression. On letting C p fall perpendicularly on the chord 
 ab , the triangle Gpb gives 
 
 ba = 2pb = 2Gb sin 
 
 </> 
 
 2 
 
 2 r sin 
 
 $ 
 
 2 * 
 
 Let us call K the point of intersection of the ray Y b$ 
 prolonged, with the axis aC. The angle Y ba considered as 
 exterior to the triangle K ba is equal to the sum of the 
 opposite interior angles, 
 
 Y ba = YKa + baC. 
 
 But the triangle YKa gives similarly 
 
 YKa = YaF - KYa = 0-if/, 
 
106 
 
 PHOTOGRAPHIC OPTICS, 
 
 and the right-angled triangle C pa gives — 
 
 baC = 90°-|. 
 
 Z 
 
 By addition we find 
 
 4 > 
 
 Y ba = 6 — if/ “J- 90° — — , 
 Z 
 
 whence 
 sin Y ba 
 
 = sin 1 90° — 
 
 t+t- 0 ) = c 4 +, H 
 
 By substituting this in the value of Y a, the latter becomes 
 sin | cos (j, + | - Oj 
 
 Va = 2r 
 
 sin i {/ 
 
 Let us observe now, that the angles if/ and <f> are infinitely 
 small, since the rays A a and B b are infinitely close. We 
 have, thererefore, 
 
 sm 
 
 sin if/ 
 
 2 <£_ 
 
 if/ ~ 2if/ 
 
 Again, by developing the case of the difference of the arcs 
 if/ ~ and 0, by means of the general formula, 
 
 z 
 
 cos (a — b) = cos a sin b + sin a sin b , 
 
 we get 
 
 cos 
 
 (if/ -f y — = cos 6 cos + i/^ + sin 0 sin + if^j f 
 
 whence, by observing that the arc + if/ being infinitely small, 
 
 z 
 
 we can substitute it for its sine, and make its cosine equal 
 to 1 : 
 
 cos 
 
 (if/ + ^ - Oj = cos 0 + if)j sin 6. 
 
 We get, therefore, 
 
 cb i 
 
 Y a = r — cos 0 -f ( ~ 
 
 
 
 sin 6 
 
ABERRATIONS. 
 
 107 
 
 Because of the smallness of the angles 0 and 0, the second 
 term within the bracket may be neglected against cos 0 , and 
 there remains simply 
 
 cos 0 
 
 Y a — r 
 
 * 
 
 0 
 
 There remains only therefore for calculation the ratio — - 
 
 Prolong B b and A a respectively to b B ? and a A'. If we 
 observe that at the point b the luminous ray passes from one 
 medium into another less dense, and that the angle of inci- 
 dence is C b B = E b B', and the angle of refraction Y b E, we 
 shall have, supposing n to be the angle of refraction — 
 
 But 
 
 sin Y b E = n sin E b B'. 
 
 Y 5 E = C&K = YKa — 0 = 0-0- 
 
 and 
 
 E6B' = C&L = B'LF - 0 = A'aF - 0 = v - 0 , 
 Therefore 
 
 sin [0 — (0 4“ i f/j] = n sin ( tj — 0), 
 
 but, because of the general formula 
 
 sin (a — b) = sin a cos b — sin b cos a , 
 
 we have 
 
 sin [0 — (0 + </0] = s i n 0 cos ($ 4- 0) — cos 6 sin (0 + 0) 
 
 sin (rj — 0) = sin rj cos 0 — sin 0 cos rj. 
 
 The angles 0 and 0 being infinitely small, these formulae 
 are reduced to 
 
 sin [0 — (0 — 0)] = sin 6 — (0 + 0) cos 0 
 sin (r) — 0) = sin y — 0 cos >7, 
 and by substitution of the latter values we get 
 
 sin 0 — (0 + 0) cos 0 = n (sin rj — 0 cos >/). 
 
108 
 
 PHOTOGRAPHIC OPTICS. 
 
 Again, the refraction at a gives similarly 
 
 sin 0 = n sin y ; (1), 
 
 which reduces the preceding relation to 
 
 (0 -J- \jf) cos 0 = n cos rj. 
 "Whence we derive 
 
 4> cos 6 
 
 ij/ n cos r] — cos 6 9 
 
 which, by substituting it in the value for Y a , gives 
 
 Ya = 
 
 cos 2 0 
 
 n cos 7] — cos 6 
 
 ( 2 ). 
 
 This value can be also put in another form by replacing n 
 
 by S j n -- ; it then becomes 
 ‘ sin 7] 
 
 Y a = r 
 
 cos 2 6 sin 7] 
 
 sin 0 cos 7] — sin 7) cos 0 
 
 or 
 
 Y a = r 
 
 cos 2 6 sin 7] 
 sin ( 0 — 7j) 
 
 (3). 
 
 If the direction of the axis of the incident pencil A a — that 
 is, if the angle tj — is made to vary, formula (1) will give the 
 angle 0 which fixes the direction of the emergent beam a Y : 
 the position of the primary focus Y will then be known by for- 
 mula (2). If we make rj = o , the luminous beam becomes 
 parallel to the axis of the lens, and the primary focus co- 
 incides with the principal focus F. Formula (2) then gives 
 (by observing that 7] = 0 = o, whence cos tj = cos 0=1), 
 
 Hence the relation 
 
 Y a _ cos 2 0 (n — 1) 
 
 F n cos 7] — cos 0 ' 
 
ABERRATIONS. 
 
 109 
 
 This relation between Y a and 6 is the polar equation of 
 the curve Y F formed of all the primary foci, and makes the 
 curvature of the field of the lens known in so far as these foci 
 only are considered. 
 
 But this curve differs from that of the secondary foci, H F, 
 which we have still to determine. 
 
 Let us consider, at a, a section passing through the axis of 
 the lens and perpendicular to a b , and let us suppose that this 
 section is the arc of the circle a m. If a luminous ray M m 
 be infinitely close to the axis A a of the beam, it will 
 cut the refracted ray in a Y at a point H different from V, 
 and it is this point H which we have called the secondary 
 focus. 
 
 Take M' m' and M m equidistant from A a ; the refrac ted 
 rays are m' H, m H. The plane MiH contains the radius of 
 curvature C m, normal to the point m , and the plane M' m' H 
 contains also the radius C m'. Since these two planes pass 
 through C, their intersection passes, therefore, through the 
 same point, and is no other than the right line C H. But as 
 each of these planes contains a parallel to the incident rays, 
 their intersection C H is likewise a parallel to these rays. 
 Therefore C H is parallel to A a, and the angle H C a = ri 
 (fig. 2, PL I.) 
 
 The triangle H a C gives 
 
 a H sin HC a sin rj 1 
 
 C H d sin CflH ~ sin 0 ~~ n' 
 
 The curve H F of the secondary foci is therefore such that 
 the ratio of the distances Ha, H C, from any one of its points 
 
 to two fixed points a and C, is a constant — , and it is easy to 
 
 demonstrate that such a curve is a circle. 
 
 Let C and a be the two fixed points, and H any point what- 
 ever on the curve. Take the points B and D such that we 
 have — 
 
 a B 1 a D 1 
 
110 
 
 PHOTOGRAPHIC OPTICS. 
 
 From the definition of the curve, this will pass through the 
 two points B and D. 
 
 Let us join B H and D H. The proportions are 
 
 flH _ «B a H _ a D 
 CH"CB and C'H'CD‘ 
 
 The first shows us that B H is the bisector of the angle 
 C H < 2 , and the second that H D is the bisector of the supple- 
 mentary angle a H K. These two right lines H B and H D are 
 therefore perpendicular to each other, and the curve possesses 
 the property, that all inscribed angles, such as BHD, are right 
 angles. It is therefore the circumference of a circle. 
 
 Let us observe now that from the proportion 
 
 CB:Ba:;n:l 
 
 we derive 
 
 CB + Ba:Ba::n-j-l:l, or B a = 
 
 Similarly, the proportion 
 
 C D : aD : : n : 1 
 
 Ga 
 
 n + 1 n + 1 
 
 gives 
 
 CD-aD:aD::n-l : 1, or a D = 
 
 CD— aD r 
 
 n — 1 n — 1 
 
 by adding these equations together we get 
 
 r r 2rn 
 
 Ba + aB = BD = + 
 
 » + 1 w — 1 ?r — 1 
 
 Now, BD is the diameter of the circle BHD; therefore, 
 indicating the radius of the circle by B, we have 
 
 B = 
 
 nr 
 
 w 3 — 1 
 
 When the ray a H falls on the axis a D, the secondary 
 
ABERRATION'S. 
 
 Ill 
 
 focus H forms at D, which is consequently no other than the 
 principal focus, F ; and, in fact, we have found above : 
 
 r 
 
 aT> = — — = F. 
 n — 1 
 
 To find now the value of a H, let us observe that the 
 triangle CHa gives 
 
 a H : C a : : sin rj : sin (Q - 77 ), 
 
 whence 
 
 r sin t? 
 sin ( 0 — rj) 
 
 By comparing this with formula (3) we shall have finally 
 for the ratios of the primary and secondary focal lengths 
 which correspond to a given angle 6 
 
 Ya 
 
 —== = cos 2 6. 
 a H 
 
 To obtain the distance of these foci we deduce from the 
 above proportion 
 
 a H — a Y 1 — cos 2 6 . 0 „ 
 
 aH 
 
 1 
 
 = sm" 
 
 Y H = sin 2 0 x a H = 
 
 r sin rj sin 2 0 
 sin {0 — 7]) 
 
 This formula shows that astigmation is as much more con- 
 siderable as the beam of incident rays is more inclined to 
 the axis. 
 
112 
 
 PHOTOGRAPHIC OPTICS. ? 
 
 CHAPTEE VI. 
 
 DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES.* 
 
 Division of Objectives into non-aplanatic and apla- 
 natic. — We have seen (p. 75 ) that spherical aberration might 
 serve to divide photographic objectives into two great -classes 
 — the one consisting of non-aplanatic objectives, which only 
 give sharp images on the condition of being furnished with a 
 very small diaphragm ; the other of aplanatic objectives, which 
 give with their entire aperture sharp images, but on a focal 
 plane of less extent than those given by objectives of the first 
 class. We shall adopt, then, this division in the present 
 chapter. 
 
 The differences which characterise these two kinds of objec- 
 tives are as follow : — 
 
 Aplanatic objectives are particularly suitable for the repro- 
 duction of animated scenes, because, as they are capable of 
 being used with their entire aperture, they allow of the 
 exposure to light being but short. They only cover sharply 
 a focal plane of which the greatest side is, at the most, half 
 their focal length ; but if furnished with a diaphragm, the 
 extent of sharpness of image is increased. 
 
 With a diaphragm extremely small 
 
 they cover a 
 
 surface almost as great as non-aplanatic objectives, and then 
 
 * Notice. — To avoid repetitions, we shall always indicate the focal 
 length of the objective by /, and the aperture of the diaphragm by the 
 f f f 
 
 fractions &c., which express apertures of the thirtieth, fortieth, 
 
 sixtieth, &c., of the focal length. 
 
 Numerical data will always be expressed as a function of the focal 
 length of the objective employed, which is the only way of comparing 
 different objectives together. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 113 
 
 they are suited for the reproduction of buildings, landscapes, 
 &c. 
 
 Non-aplanatic objectives employed with all their aperture 
 give confused images over the whole extent of the focal 
 
 f 
 
 plane. With a diaphragm equal to-j-^-,the image begins to 
 assume sharpness, but still not of a very marked character. It 
 
 • • • f f f 
 
 is only when the diaphragm is but -j-, and even that 
 
 the image acquires perfect definition. These objectives are 
 therefore very slow in impressing photographic surfaces; but 
 their focal plane is much greater than that of non-aplanatic ob- 
 jectives. They are for the most part (the single combination 
 excepted) free from distortion arid astigmation, whilst among 
 aplanatic objectives the triplet alone is free from distortion. 
 
 As, on the whole, the only advantage of non-aplanatic objec- 
 tives consists in the large angle which they embrace ; as the 
 triplet , without including so great an angle, yet includes one 
 sufficient in practice; and as, moreover, it can give sharp 
 images wfith much larger diaphragms — and even with its full 
 aperture, when the non-aplanatic objective no longer gives 
 images at all— the advantage rests with the triplet, which, in 
 the actual state of optical science, is the best objective there 
 is. But in the preface to this volume the reader will find 
 our opinion more fully justified in this respect. 
 
 Section I. — Non-aplanatic objectives. 
 
 Single (Landscape) Objective. — Jean Baptiste Porta, 
 the inventor of the camera obscura, employed, as objective, a 
 plano-convex lens of erown-glass, of which the convex face 
 was towards the ground- glass, and which was reduced to its 
 central part by a diaphragm in contact with it, of which 
 
 f f 
 
 the diameter was from — to Under these conditions, the 
 
 2i\J dO 
 
 field of the image was very curved, as we have explained, 
 
 i 
 
114 
 
 PHOTOGRAPHIC OPTICS. 
 
 page 84. It resulted from this, that to obtain a focal plane 
 quite defined in all its parts, the greater side of the image 
 / 
 
 could not be more than Nevertheless such an arrangement 
 o 
 
 was almost free from distortion. 
 
 If the diaphragm be moved away from the lens, the field 
 becomes flatter, but the distortion increases, since the lens 
 is now under the conditions represented in fig. 54, and 
 explained at page 97. 
 
 Opticians soon found out that a concavo-convex meniscus, 
 substituted for the plano-convex objective of Porta, gave, with 
 equal focal length, a well-defined image of much greater 
 extent. The concave surface was towards the object to be 
 reproduced, and the convex surface towards the ground-glass. 
 The focal plane was covered with sharpness over a square 
 
 f 
 
 surface, the diagonal of which was equal to The aperture 
 
 f f 
 
 of the diaphragm was and its distance from the lens ~. 
 
 ou o 
 
 Such then was the simple objective at the time of the 
 discovery of the daguerreotype in 1839, and it served to 
 produce the first proofs by this process. But it was soon found 
 out that the image, when sharp on the ground-glass, was not 
 so on the photographic surface; that, in a word, the lens 
 possessed a chemical focus depending on the angle of dis- 
 persion of the glass of which it was made. For the visual 
 focus, corresponding to the yellow rays, differed considerably 
 from that of the blue and violet rays, which was nearer, 
 and which constituted the chemical focus. It became neces- 
 sary, therefore, to graduate the base of the camera, according 
 to the conjugate focus of the lens, and this was a long 
 and difficult operation, so that opticians were appealed to on 
 all sides to obtain objectives free from this chemical focus. 
 
 The first objectives of this nature appear to have been con- 
 structed by the late Charles Chevalier. This optician made use 
 of the achromatised objective of an opera-glass — an objective 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 
 
 115 
 
 formed of a bi-convex lens of crown-glass cemented to a plano- 
 concave lens of flint-glass. Employed with its convex face 
 turned towards the object to be reproduced, the image had a 
 remarkable sharpness and brilliance, since in this position the 
 lens could be employed with all its aperture, spherical and 
 chromatic aberration being corrected in it along its axis. But 
 the extent of the focal plane was very trifling, and at the most 
 / 
 
 its greater side was but 
 
 8 
 
 Charles Chevalier did as opticians 
 
 before him ; he turned the lens, so that its convex face was 
 now towards the ground-glass. In this position the image 
 was much less sharp than in the preceding case, but he 
 furnished it with a diaphragm placed in front of the objective, 
 so that the definition was thus considerably augmented, at 
 the same time that the field of the image was much flattened, 
 to such an extent that the greater side of the focal plane, 
 
 f 
 
 sharply covered, now became 
 
 Fig. 3, plate I., represents the primitive single objective. 
 The achromatic plano-convex lens, A, was placed in a conical 
 mounting of brass, C, furnished with a diaphragm, B, beyond 
 which a circular plate slided, which served as a shutter. 
 
 f 
 
 The aperture of the smallest diaphragm was generally — . 
 
 oO 
 
 There were, besides, several others — of which the greatest had 
 
 f 
 
 an aperture four times as great as that of the first, — , which 
 
 1 5 
 
 could be substituted for this, according to the intensity the 
 image was desired to have. 
 
 The objective was mounted on a camera, F N 0 E', of which 
 the ground-glass, E F', was much smaller than the field, G G' 
 — an inevitable consequence of the too short distance between 
 the lens, A, and the diaphragm, B. The objective only acted, 
 therefore, at its central part, and there was thus lost the half 
 of its diameter, as is well shown in the figure. The spherical 
 aberration for rays oblique to the axis and the distortion 
 were thus reduced to a less amount than if the diaphragm 
 
 i 2 
 
116 
 
 PHOTOGRAPHIC OPTICS. 
 
 had been situated farther in front, and the field was also 
 nearly flat, because the plano-convex form was not the best 
 that could have been chosen ; but at this period opticians were 
 not so skilful as they are at present. 
 
 The plano-convex form is therefore the first which was 
 given to the single objective. Some opticians afterwards 
 discovered that the meniscus form was preferable to the 
 plano-convex. The radius of curvature of the concave face, 
 which looked towards the object to be reproduced, was gene- 
 
 f f 
 
 rally, and is still, from - to the diameter of the objective 
 
 -c o 2 
 
 being -■.* 
 
 * When the face of the lens is thus chosen, the radius of curvature ol 
 the two surfaces in contact is determined by calculation, and then that 
 of the face which is towards the ground-glass. 
 
 Let F be the focal length of the two lenses cemented together ; % the 
 index of refraction of the crown-glass (bi-convex) ; n' y the index of refrac- 
 tion of the flint-glass (bi-concave) ; A the ratio of the dispersive powers ; 
 and R the radius of curvature, arbitrarily chosen, of the concave face of the 
 flint-glass, which looks towards the object to be reproduced. We shall 
 find the other data of the system — namely, R' the radius of curvature of the 
 two surfaces in contact of the crown and flint glass ; R" the radius of cur- 
 vature of the face of the crown-glass which is towards the ground-glass ; 
 / the focal length (negative) of the flint-glass lens; and /' the focal 
 length (positive) of the crown-glass lens, by the following equations : — 
 
 Wrt- •'# 
 
 f = ^ (it ~~ R 7 ) ’ ' ' ' 
 
 J = (n'y - 1 ) (jg - .... ( 4 ). 
 
 If, by the photographic test, this lens is found to possess a chemical focus, 
 it is because A has not been accurately calculated. Then, if this focus 
 falls in advance of the visual focus, substitute for the face of the flint-glass, 
 of which R is the radius of curvature, another face of which the radius of 
 curvature is shorter ; and the contrary if the chemical focus fall behind the 
 visual focus. We shall see, in the following chapter, how the chemical 
 focus is found to fall in front of or behind the visual focus. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 117 
 
 The form of the single objective which is therefore gene- 
 rally adopted is represented by fig. 4, pi. I., the concave face of 
 flint-glass being towards the object to be reproduced, the con- 
 vex face of crown-glass towards the ground-glass. As to its 
 diameter and the position of the diaphragm, these elements 
 depend entirely on the greater or less concavity of the flint- 
 glass face. If a large diameter relatively to its focal length, 
 ab , is given to the lens A, (fig. 5, pi. I.), the diaphragm, D, must 
 be placed at a greater distance from the lens, and such that the 
 circle, MNO, which bounds the focal plane nearly circum- 
 scribes the rectangle, cdef which represents the size of the 
 image for which the objective is constructed. In this case, if 
 the radii of curvature of the objective are suitably chosen, the 
 field is as flat as it can be, but the distortion is considerable. 
 
 If the diaphragm is moved back to the lens — which, for the 
 same size, cdef of image, is thereby reduced to a central 
 part of its primitive surface (as is shown in fig. 5, pi. I.) — 
 the field becomes less flat, but the distortion diminishes. In 
 this case, in order that it may be found in the best possible 
 conditions for sharpness, a more concave face must be substi- 
 tuted for the existing face of flint-glass (the one towards 
 the object to be reproduced). The greater, therefore, the 
 diameter of the single objective, the focal length remaining 
 the same, the more ought the flint surface facing the object 
 to approach to a plane, and then the more considerable 
 becomes the distortion, but the flatter the field; the less the 
 diameter, the more concave this face becomes, and the smaller 
 is the distortion — within, of course, the limits which have 
 been determined by practice with an approximation sufficient 
 for the guidance of the optician. 
 
 In every case the spherical aberration is corrected by the 
 
 f 
 
 employment of a very small diaphragm, and the chromatic 
 
 o(J 
 
 completely so by a proper choice of the flint and crown 
 glasses ; but it is of great importance to render the spherical- 
 aberration as slight as possible, for the following reason. 
 
118 
 
 PHOTOGRAPHIC OPTICS. 
 
 There is required in a photographic proof a very great per- 
 fection in the details, which constitutes its sharpness. Now, 
 we have seen, in the chapter on spherical aberration, that its 
 effect was to destroy this definition over the whole extent of 
 the image ; and that, to avoid this defect, it was necessary to cor- 
 rect the aberration as much as possible, which was done in the 
 single objective by means of the diaphragm. But the more 
 considerable this aberration is, the smaller must the diaphragm 
 be to give the image that definition which is required of it, and 
 the longer therefore must be the exposure to light, since the 
 intensity of the image necessarily depends on the aperture of 
 the diaphragm. It is therefore of very great importance that 
 the spherical aberration should be reduced in the single objec- 
 tive to the lowest possible degree, because it will then be pos- 
 sible to make use of a larger diaphragm. 
 
 As to the spherical aberration, if the optician correct it 
 for pencils parallel to the axis of the objective, he cannot cor- 
 rect it for pencils oblique to it ; and we have seen that, to 
 reduce this aberration to the minimum, the angles of immer- 
 gence and emergence of the pencils ought to form equal angles 
 with the section of the lens traversed by these pencils, 
 which could only be effected with meniscuses, the concave 
 face of which was of a relatively short radius of curvature. 
 
 To attain this end, some opticians of great merit have 
 adopted a new form of single objective (fig. 4 bis, pi. I.), in 
 which the crown-glass lens, B, of meniscus form, has its concave 
 face towards the object to be reproduced.* The divergent flint- 
 glass lens, A, is cemented to the crown-glass lens, and has the 
 same diameter. Its form is also a meniscus. The arrangement 
 is therefore the reverse of that of the old objective, represented 
 in fig. 4, pi. I., in which the flint-glass, B, is turned towards 
 
 * Mr. Grubb, of Dublin, several years ago patented this form of single 
 combination for photographic work, and we believe it is now used by other 
 opticians. A modification of the same system forms one of the components 
 of Mr. Ross’s doublet, and was used in double combinations, and also as a 
 single objective, by the late Mr. Ross, nearly twenty-five years ago. — Trans. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 119 
 
 the object to be reproduced, whilst in this it is the crown-glass. 
 The first end now served by the flint-glass lens is to achro- 
 rnatise the combination for pencils parallel to the axis, and the 
 second to increase the focal length of the combination for inci- 
 dent pencils oblique to the axis and emergent from the crown- 
 glass lens, so as to give a focal plane very flat, and of much 
 greater extent than that obtained with the old objective. The 
 flint-glass lens, if the concave face of the crown-glass lens be well 
 chosen, also renders the value of the spherical aberration much 
 less than it is with the old single objective, which permits the 
 use of larger diaphragms. The objective is thus more rapid 
 (photographically speaking) ; and, further, the image is more 
 brilliant, and possesses more relief, as we have stated at 
 page 92. 
 
 Lastly, this objective having for the same extent of image a 
 focal length shorter than that of the old objective, possesses 
 therefore over the latter all advantages possible. 
 
 There are therefore two kinds of single objectives— the first, 
 that iu which the flint-glass faces the object to be repro- 
 duced ; the second, that in which the crown-glass is turned 
 towards this object. Both have the meniscus form, and in both 
 the concave face is towards the object to be reproduced, and 
 the convex one towards the ground-glass ; but the latter has 
 over the former the advantages of less distortion, a shorter 
 focal length, a greater rapidity, and a smaller bulk. 
 
 The old form — the one not so good — is still generally 
 adopted by French and German opticians, several of whom, 
 however, begin to adopt the 
 other. The new form is adopted 
 by English and American op- 
 ticians. 
 
 Fig. 63 represents the mount- 
 ing of the single objective adopted 
 in France. The flange A is fixed 
 on the camera by means of screws. 
 
 The tube B contains, in the plane of the flange A, the objective. 
 
 Fig. 63. 
 
120 
 
 PHOTOGRAPHIC OPTICS. 
 
 At C this tube is terminated by a circular disc, perforated 
 at its central part ; to which is adapted the small tube E, 
 which contains the brass diaphragms, which a cylinder, E, 
 of blackened brass keeps in place. D is the cap. 
 
 To change the aperture of the diaphragm, the ring F must 
 be removed, but this is inconvenient. 
 
 The English and Americans have adopted as a mounting 
 the form sketched in fig. 64. A A' is the flange which is fixed 
 on the camera, and B C, D E, the cylindrical tube in which 
 the objective, L M, is mounted. F G is a disc of brass pierced 
 with circular apertures, the centres of which are at equal dis- 
 tances from its centre of rotation. It is sufficient therefore, 
 in order to substitute one diaphragm for another, to rotate 
 the disc by sliding the finger on its exterior part F. We shall 
 describe, however, this method more at length at page 125. 
 
 The following are the dimensions of the single objectives 
 adopted by French and English opticians : — 
 
 The diameter of the English objective* is generally the fifth 
 of its focal length, and the greater side of the image is equal 
 to two-thirds of this focal length. 
 
 The diameter of the French objective is generally the seventh 
 of its focal length, and the longer side of the image sharply 
 covered is half this focal length. 
 
 The French objective has less distortion than the English 
 objective, taking as the term of comparison the size of the 
 image ; but it has more, if we take for the term of comparison 
 the focal length of the objective. 
 
 M. Dallmeyer’s new single Objective. —With the 
 object of reducing the distortion to as slight an amount as 
 possible, and of making the objective include a maximum of 
 angle, M. Dallmeyer has sought to give to the single 
 objective a meniscus form more pronounced, and has brought 
 the diaphragm considerably nearer to the lens. If he had 
 
 * It is to be understood that we speak here of the objectives coming 
 from workshops of the first order, such as those of Messrs. Eoss and 
 Dallmeyer. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 121 
 
 adopted the form of objective already existing, he would have 
 been able to attain his end by sacrificing sharpness at the 
 
 margins of the image ; 
 but taking as an es- 
 sential condition the 
 maintaining the image 
 as sharp at the mar- 
 gins as at the centre, 
 he has had to adopt 
 another optical com- 
 bination, which is re- 
 presented by fig. 64. 
 
 Instead of two lenses* 
 the first of crown-glass, 
 the second of flint, 
 M. Dallmeyer employs 
 an additional one of 
 crown-glass, the index 
 of refraction of which 
 is slightly different 
 from that of the crown- 
 glass of the first one. 
 
 This figure represents with very great exactitude the objective arid its mounting of the 
 actual size, the focal length of the objective being 6 '95 inches, and its diameter 1*6. These 
 are the other data of the system, expressed in terms of the focal length : 
 
 Diameter of the lenses 
 
 First lens c — r 1 
 
 (crown -glass!) ( - r r 2 
 
 Second lens c — r 3 
 
 (flint-glass) t r 4 
 
 Third lens c — r 5 
 
 (crown-glass 2 ) \ -+- r 6 
 
 Focal length of the combination 
 
 Index of refraction (yellow) of the flint-glass . 
 
 „ „ crown -glass! . 
 
 ,, „ crown-glass 2 . 
 
 Ratio of the focal lengths to produce achromatism : 
 
 f 
 
 Crownj and flint-glass ~ = 0*706 
 Crown 2 and flint-glass = 0*645 
 
 2302 
 
 6043 
 
 1727 
 
 1*727 
 
 4813 
 
 4813 
 
 2561 
 
 10,000 
 
 1581 
 
 1521 
 
 1514 
 
 We here seize the opportunity of publicly thanking M. Dallmeyer for having given us the drawing and 
 numerical data relating to his single objective, Petzvai’s objective, and his own triplet, by which we have been 
 saved the long and difficult work ol determining them experimentally. 
 
122 
 
 PHOTOGRAPHIC OPTICS. 
 
 The three lenses are therefore meniscnses joined together, 
 and form a single combination, the concavity of which is 
 turned towards the object to he reproduced, precisely as in 
 the ordinary single objective. 
 
 The diaphragm is placed in front of the lens, at a distance 
 equal to the diameter of the lens, to which, therefore, it is 
 much nearer than usual. The aperture of the smallest 
 
 diaphragm is 
 
 OU 
 
 The following are the principal advantages of M. Dall- 
 meyer’s single objective. ^ 
 
 With a diaphragm of it covers with perfect sharpness 
 a circular focal plane 72° in extent ; with a diaphragm of a 
 
 Ob/ 
 
 circle of from 85° to 90°. The field of the objective is there- 
 fore enormous, since the longer side of the image (which, as 
 we know, is always rectangular), is greater than the focal 
 length of the objective, while, in the best single combinations 
 previously constructed, this side was at the most but two- 
 thirds of the focal length. 
 
 This has, in the reproduction of landscapes, a considerable 
 advantage in an artistic point of view, which is, that the fore- 
 grounds are represented in the image, and thus give to the 
 more distant planes an astonishing effect of perspective. It 
 was not thus with the old objectives, the field of which w~as 
 of much less extent. 
 
 The distortion is, for an image of which the greater side is 
 equal to the focal length of the objective, reduced to a small 
 quantity, the diameter of the objective being relatively less 
 than that of the old objective. Besides, the single objective 
 being destined solely for landscapes, the distortion causes no 
 visible defect in the image. 
 
 The chemical focus for pencils oblique to the axis is reduced 
 to a less quantity (see page 82) ; the field is flatter than that of 
 the old single objective ; and, lastly, the image is brighter.* 
 
 * We have seen that a refracting plate reflects a part of the light incident 
 upon it. Now, it frequently happens in optical arrangements that the sur- 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 123 
 
 The new single objective of M. Dallmeyer has, finally, as 
 a last advantage, that of being less in respect of weight and 
 bulk, and of requiring, on account of its shoft focal length, 
 a much shorter camera, which is, in practice, a very great 
 one. 
 
 To terminate this article, we have to examine in what 
 circumstances the single objective is to be prefered to the 
 other systems. 
 
 Like all the non-aplanatic objectives, the single lens 
 having to be furnished with a very small diaphragm (one- 
 thirtieth of the focal length), in order to give sharp images, 
 cannot serve for the reproduction of groups, animated land- 
 scapes, and portraits, except by having at command a bright 
 light like that of the sun, which generally produces effects 
 but little artistic. The triplet is in this case infinitely pre- 
 ferable to it, since, with a diaphragm of double the diameter 
 of the other (one, consequently, four times more rapid), it 
 
 gives images perfectly sharp, the greater side of which is 
 
 / 
 
 2 * 
 
 The single lens not being free from distortion, seeing that 
 it distorts images in the way shown in fig. 56, page 98, cannot 
 be employed for the reproduction of buildings, maps, and 
 in general all objects in which straight lines occur. In this 
 case, again, the triplet is preferable to it. 
 
 On the other hand, the single lens is superior to the 
 triplet for the reproduction of landscapes, because, with equal 
 diaphragm, it is rather more rapid ; firstly, because it offers 
 fewer optical surfaces ; secondly, because the incident and 
 refracted pencils are almost normals to the refracting 
 
 faces of the lenses which form them, acting as reflectors, throw over the 
 image furnished by transmission a diffused light, which tends to fog the 
 image, and which often betrays itself by a very luminous spot at the centre 
 of the ground-glass, particularly if the sky of the landscape occupies a 
 great extent of the image. In M. Dallmeyer’s objective the transmitted 
 and reflected rays are nearly normals to the surfaces, so that the image 
 is free from this fogginess, and consequently is more brilliant. 
 
124 
 
 PHOTOGRAPHIC OPTICS. 
 
 surfaces (on account of its meniscus form). But in this 
 respect it is inferior to the globe-lens. 
 
 The single lens possesses greater depth of focus (see page 
 85), than the triplet, and, generally, than all known objectives 
 except the orthoscopic. 
 
 On the other hand, it covers a smaller angle than the 
 globe , the periscopic , and the orthoscopic objectives. 
 
 It is seen, therefore, that the single objective presents, when 
 compared with other objectives, more disadvantages than ad- 
 vantages. Thus the triplet is preferable to it as regards the 
 absence of distortion, and the power of reproducing animated 
 landscapes ; and the globe , the periscopic , and the orthoscopic ob- 
 jectives are preferable to it as regards the extent of the field. 
 But as, in general, landscapes require a very long exposure 
 to light, and as the extent of the field need not be great for 
 this kind of photography, the triplet, on the whole, is for 
 the reproduction of landscapes, especially animated ones, 
 practically (if not scientifically) preferable to the single ob- 
 jective, even to the new one of M. Dallmeyer, of which we 
 shall speak presently, which has over the triplet but one 
 advantage, that of including a larger angle. 
 
 The Globe-objective or Globe-lens. — This objective, 
 invented by Messrs. Harrison and Schnitzer of New York, 
 and represented by fig. 65, is formed of two achromatic and 
 identical convergent meniscus lenses, the distance between 
 which is such that the external surface of the meniscus lenses 
 prolonged forms one and the same sphere, hence the name of 
 globe-lens or globe-objective. 
 
 The figure shows how the globe-lens is mounted. The two 
 meniscus lenses, each enclosed in a ring, are fixed to the 
 extremities of a brass tube, terminated on the side towards 
 the object to be reproduced by an expanded cone of 
 blackened brass, on which is fitted the cap of pasteboard 
 which serves to close it. 
 
 At the middle of the mounting of the objective is the 
 diaphragm, which is represented separately, at the side of 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES, 
 
 125 
 
 the figure. It consists of a circular plate of brass, which 
 passes out beyond the mounting, and which is perforated by 
 
 Fig. 65. 
 
 Radius of curvature of the 1st surface of crown-glass . . . . 1412 
 
 „ 2nd „ „ .... 2403 
 
 „ 3rd „ flint-glass .... 2403 
 
 4th „ „ .... 1620 
 
 Diameter of the lenses '. 1875 
 
 Thickness of the meniscus (at its central part) 231-5 
 
 Distance, measured along the axis, between the external surfaces 2824 
 
 Absolute focal length 10,000 
 
 / 
 
 Aperture of the largest diaphragm — = 277-7 
 
 smallest 
 
 Density of the crown-glass 2-543 («'h = 1-53) 
 „ flint-glass 3-202 (w' H = 1-60) 
 
 = 138-8 
 
 The two flint and crown glass lenses are cemented together. The two achromatic 
 meniscuses are equal to each other. The diaphragms are situated at equal distances 
 from the two meniscuses. 
 
 These data have been communicated to us by Messrs. Gasc and Charconnet, of Paris, the opticians who 
 introduced the globe-objective into France under the name of lentifcrme de Vceil ; and who construct it with 
 great perfection, and at a price much lower than the original American objectives. 
 
 holes which constitute the diaphragms properly so called. 
 This disc revolves about a centre placed above the axis of 
 the objective, and the holes which constitute the diaphragms 
 are all at equal distance from this centre. The disc turns, 
 
126 
 
 PHOTOGRAPHIC OPTICS. 
 
 with gentle friction, between two circular plates perforated 
 at their central part. A spring acts on the disc, and catches 
 by its extremity in shallow notches, so that when we turn 
 the disc from the outside of the objective, a shock is felt each 
 time that the aperture of the diaphragm corresponds with the 
 axis of the objective. 
 
 In the objective that we have before us, the apertures of 
 the diaphragms are such that the times of exposure are 
 respectively from the greater to the less, 1, 2, 3, 4, 5, that is, 
 that the smallest diaphragm (No. 5) requires five times 
 as much exposure as the largest, of which the aperture 
 is 1 ; the next (No. 2), twice as long ; No. 3, three times, and 
 so on. The objective is screwed to a flange fixed on the front 
 of the camera, a construction identical with those of other 
 systems. 
 
 The mounting of the objective unscrews into three parts, 
 as may be seen in the figure, which allows of the part 
 which carries the diaphragm to be separated from those which 
 carry the lenses. This is indispensable, for the purpose of 
 cleaning the inner surface of the lenses. 
 
 Persons familiar with photographic optics will compre- 
 hend, on glancing at the numerical data enunciated above, 
 the great originality of the globe-lens. The luminous pencils 
 emitted by external objects, situated within or without the 
 axis of the objective, strike normally the external sur- 
 face of the meniscus which is towards them, emerge from 
 the first meniscus, strike almost at the normal incidence 
 the concave face of the second meniscus, and emerge from 
 the entire system, forming with the axis an angle the 
 same as that of their immergence. Hence a complete de- 
 struction of distortion, and an almost complete destruction 
 of astigmation. 
 
 The flint-glass lenses only serve here for achromatism, but 
 the choice of the outer surface of crown-glass is such, 
 that these flint-glass lenses render the field flatter than if, 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 127 
 
 foregoing the destruction of the chemical focus, the objective 
 were reduced to two simple convergent lenses having 1412 
 and 1 620 as radii of curvature. The angle included by the 
 objective is very considerable, and exceeds 75°, so that 
 the length of the greater side of the focal plane sharply 
 covered is greater than the foc^l length of the objective, 
 which has for its measure the distance of the principal focal 
 plane from the diaphragm. The examination of some globe- 
 lenses has proved to us, that an objective of 10 centimetres 
 focal length covers sharply a focal plane of 14 by 12 centi- 
 metres. In this respect, however, the globe-lens is inferior 
 to Mr. Ross’s doublet and M. Steinheil’s periscope; but it 
 possesses over the former the advantage of being perfectly 
 free from distortion, and of being more rapid with equality of 
 diaphragm, and over the latter that of having its chemical 
 and visual foci coincident. 
 
 In all these respects, therefore, the globe-lens would be a 
 precious objective for photographers, did it not possess an 
 exceedingly great spherical aberration. Accordingly, the dia- 
 phragms fitted to the objective must be extremely small (not 
 
 f 
 
 less, however, than — , otherwise the phenomena of diffraction 
 
 72 f 
 
 would be produced in the image), never greater than else 
 
 oo 
 
 the image would be wanting in sharpness over the whole 
 extent of the focal plane. 
 
 This necessity of using very small diaphragms has not 
 only the effect of rendering the objective very slow ; this 
 would be only a defect quite remediable by increasing the 
 time of exposure ; but it has a more troublesome result, that 
 of giving images in which the foregrounds are but slightly 
 developed (are too black), and in which the horizons are 
 solarised , that is, have lost details, in consequence of too long 
 an exposure. In a word, the image is wanting in brilliancy 
 and relief, and possesses these qualities only in the case where 
 the subject to be reproduced offers a very large surface with- 
 
128 
 
 PHOTOGRAPHIC OPTICS. 
 
 out foreground, such as a panorama, a map, or an engraving. 
 This defect is, besides, common to all the non-aplanatic 
 objectives, and the only one which may form an exception is, 
 perhaps, the single objective, and particularly that of M. Dall- 
 meyer, the spherical aberration of both being much less than 
 that of the globe-lens. 
 
 f 
 
 If the smallest diaphragm be employed, that of the 
 
 image has very great sharpness, equal to that of aplanatic 
 objectives. Further, in this case the depth of focus of the 
 globe-lens is so considerable, that all objects situated at more 
 than 70 times the focal length of the objective appear on 
 the ground-glass of the camera perfectly defined. Moreover, 
 the extent of the field is then very considerable, but, at the 
 same time, the image is particularly deficient in that bril- 
 liancy wdiich gives it its artistic value. 
 
 The employment of this objective is limited to the repro- 
 duction of buildings, landscapes, and especially maps and 
 engravings. As it only gives fine proofs on the condition of 
 being furnished with very small diaphragms, it cannot serve 
 to reproduce animated landscapes. It is, therefore, limited 
 to the reproduction of still nature ; which may, without in- 
 convenience, require a long exposure. It is always necessary 
 to employ it with the smallest of the diaphragms it admits, in 
 order to obtain a great sharpness of image over a considerable 
 field. In reproducing a landscape or a building, very near 
 foregrounds, which would come out too black, must be 
 avoided, as well as very distant backgrounds, which would 
 be confounded with the sky, and be wanting in details, for 
 the reason we have stated above. The globe-lens (and the 
 non-aplanatic objectives, the description of which follows) 
 can never reproduce any landscape or view along with clouds. 
 The power of doing this is confined to the objectives of 
 
 f f 
 
 which the diaphragm is at the most from ■— to such as 
 
 A\) oO 
 
 the triplet, the orthoscopic and the single objective. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 129 
 
 Mr. Sutton’s Panoramic Lens. — The necessity that 
 exists of using curved glasses with this objective will always 
 render its employment very limited, consequently we shall 
 not devote much time to its 
 description. 
 
 Fig. 66 represents a section 
 of the lens. Two lenses of 
 glass, A and B, with spherical 
 curvatures, concavo-convex, 
 are fixed in a metallic ring, 
 
 E, which screws on a second 
 flat flange, F, fixed on the 
 camera. The hollow part, C, 
 is filled with water. The 
 surfaces of the glass lenses 
 are concentric, the optical 
 centre of the combination 
 coinciding, therefore, with 
 the centre of the figure. 
 
 Achromatism is obtained by 
 giving to the surfaces of the 
 glass lenses the radii of cur- 
 vature determined by calcu- 
 lation, which, for pure water and for glass having an index of 
 refraction equal to 1*57, is as 1 to 2. 
 
 Such an objective possesses a considerable spherical aber- 
 ration, and a very curved field. Let us see how Mr. Sutton 
 removes these two imperfections. By introducing a dia- 
 
 phragm, of small aperture (— - to ^-) between the two glass 
 
 lenses equally distant from each of them, the spherical 
 aberration is completely destroyed, and the images possess 
 great sharpness. But it is easy to conceive that the ground- 
 glass would be unequally illuminated, inasmuch as, for rays 
 parallel to the axis, the circular diaphragm would present an 
 aperture greater than that for oblique rays, particularly such 
 
 Fig. 66. 
 
130 
 
 PHOTOGRAPHIC OPTICS. 
 
 very oblique ones as those which the lens is intended to 
 include. Now, in place of a single diaphragm, Mr. Sutton 
 takes two, which he places equally distant from the centre of 
 the sphere which constitutes the objective and from the con- 
 cave surfaces of the glass lenses ; and he makes their aperture 
 elliptical, the long axis of the aperture being in the horizontal 
 direction, for he intends his lens to include horizontally a large 
 angle, in other words, to take in panoramic views. There 
 remains now the second difficulty, the curvature of the 
 field. To correct this, Mr. Sutton diminishes in the vertical 
 direction the dimension of his glass, and curves it in the 
 horizontal direction. Hence it follows that the ground-glass, 
 instead of being flat, is a portion of a cylinder. With these 
 conditions the image obtained is, to the image that would be 
 produced on a flat glass (or by a single objective of the same 
 focal length), as 1 to 3. The horizontal angle included by 
 the lens is 100°, and the vertical 30°. 
 
 Mr. Sutton’s objective, like the globe-lens, is free from dis- 
 tortion. But this quality is of little importance, inasmuch as 
 the objective is only intended for panoramic views, in which 
 the effects of distortion are scarcely perceptible. On the other 
 hand, it possesses, viewed in connection with the smallness 
 of its diaphragm, the defects pertaining to the globe-lens; 
 but these defects are here less evident, because panoramas do 
 not generally present foregrounds, and because in all cases, if 
 they did present such, the objective would not reproduce 
 them, since the large angle which it includes is horizontal 
 and not vertical. Further, since panoramas possess a con- 
 siderable luminous power, the image possesses a greater 
 brilliancy than the smallness of the diaphragm would lead us 
 to expect. 
 
 The Periscope of M. A. cLe Steinheil. — This objective 
 (fig. 67), which has only come to our knowledge while this 
 work was in the press, through private letters from the in- 
 ventor, is formed of two meniscus lenses of crown-glass, 
 C E, D F, the concavities of which are identical and facing 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 
 
 131 
 
 each other. Half-way between the lenses are the dia- 
 
 phragms LL'. 
 
 Diameter of the lenses ] 256 
 
 Radius of curvature of the surfaces A and A' H- 1753 
 B and B' — 2076 
 
 A or distance between the two lenses .... 
 Thickness of the lenses measured along the axis 
 Index of refraction : n 0 =■ 1*5233 
 „ nv = 1*5360 
 
 Focal length of the system (visual focus) f 0 
 ,, „ (chemical focus) f v 
 
 f , 
 
 Aperture of the diaphragm 
 
 1256-35 or 829 
 125-6 
 
 10-000 
 
 9-754 
 
 40 
 
 Fig. 67. 
 
 This objective is the best which could be produced by 
 means of two simple non-achromatised lenses. It possesses, 
 indeed, a chemical focus which necessitates a rectification 
 
 after each focussing ; but this rectification is simple and easy, 
 since the distance which it is necessary to advance the focal 
 plane towards the lens is always the same fraction of the focal 
 39 
 
 length, namely, — or 975-thousandths of this length. Besides, 
 
 the depth of focus of this objective is sc considerable, that a 
 slight error in this rectification would scarcely diminish the 
 sharpness of the image. 
 
 The incident pencils, oblique or parallel to the axis, form 
 with it the same angle on leaving the objective as on enter- 
 ing it. The optical centre of the compound system coincides 
 therefore with the point in the figure situated on the axis half- 
 way between the two lenses, where also is the diaphragm. It 
 is thus in all the symmetrical doublets — for example, in the 
 globe-lens — and therefore the periscope is, like the globe, 
 entirely free from distortion . 
 
 The field of the periscope is very flat (in other words, 
 the image is rigorously sharp all over the surface of the 
 ground-glass). Of all known objectives, it is the one of 
 which the focal length is the shortest for the same extent of 
 image sharply covered, since, with a diaphragm of an aperture 
 f f 
 
 of from to it covers an angle of 100°. 
 
132 
 
 PHOTOGRAPHIC OPTICS. 
 
 It is also the one of which the diameter is the least, as may 
 be seen from the following table, which has been communi- 
 cated to ns by M. de Steinheil : — 
 
 j Nos. 
 
 | 
 
 Diameter of 
 the Lens 
 in Millimetres. 
 
 Focal length of 
 the Lens 
 in Centimetres. 
 
 Size of the 
 Image 
 
 in Centimetres. 
 
 1 
 
 8*9 
 
 7*4 
 
 12-2 
 
 2 
 
 11-2 
 
 8*9 
 
 17-6 
 
 3 
 
 18-0 
 
 14*4 
 
 27*0 
 
 4 
 
 22-5 
 
 17-6 
 
 35-2 
 
 5 
 
 33*8 
 
 35-2 
 
 56-8 
 
 6 
 
 56-4 
 
 58-7 
 
 81*2 
 
 7 
 
 i 
 
 47-4 
 
 40-6 
 
 81-2 
 
 It will be seen, therefore, that this objective presents con- 
 siderable advantages. Let ns see its disadvantages, which are 
 common (and will, except the first, be always so) to all non- 
 aplanatic objectives. 
 
 First,' the necessity of correcting the focussing every time, 
 seeing that the objective has a chemical focus. 
 
 Secondly, the forced employment of exceedingly small dia- 
 
 / f 
 
 phragms, the aperture of which will be between and ~ . 
 ■f 
 
 With the largest. the field is much less flat, and the image 
 
 40 
 
 much less sharp, than with the smallest, 
 
 / 
 
 72 
 
 Nevertheless, 
 
 in this respect the periscope is superior to the globe-lens, its 
 spherical aberration being much less considerable. 
 
 But the forced employment of such small diaphragms gives 
 rise to photographic images which are flat, and without that 
 vigour which only the employment of large diaphragms can 
 secure. But, on this question, the reader can refer to what 
 we have said at p. 92, bearing on the same subject. 
 
 The periscope is not so free from astigmation as the globe- 
 lens, particularly if the most oblique pencils are taken into 
 consideration. Still, however, this aberration is scarcely 
 perceptible. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 
 
 133 
 
 This objective possesses, therefore, much the same qualities 
 as the globe-lens. But it will never come into general use, 
 because it requires diaphragms too small. With respect to 
 other qualities of these lenses, we refer to the Preface to this 
 book, in which we give our reasons against the employment 
 of non-aplanatic objectives. 
 
 The Doublet of Mr. Thomas Ross. —This objective, of 
 which the subjoined figure* is a 
 section (representing exactly, 
 and of the actual size, the 
 one of 110 millimetres focal 
 length), is composed of two 
 achromatised meniscuses, N M 
 and H G, (the surface G facing 
 the object to be reproduced). 
 
 Each of these meniscuses 
 can be emplo} 7 ed separate^ 
 as a single objective. The 
 two lenses are fixed in rings 
 which screw into a tube, B B', 
 
 E E', terminated towards the 
 object to be reproduced by a 
 larger tube, E F, on which 
 the shutter fits. The tube 
 screws on the flange A A' Fig. 68. 
 
 fixed to the camera. The diaphragms, of which the maximum 
 
 f 
 
 aperture is and the minimum one 
 
 15 
 
 45 
 
 , are graduated and 
 
 constructed like those of the globe-lens. Further, a sliding- 
 plate, Z, allows of the lens being opened or closed inde- 
 pendently of the shutter. 
 
 This objective is superior to the globe-lens, in that it pos- 
 sesses less spherical aberration, thus allowing of the employ- 
 
 * By a mistake of tlie draughtsman, the position of the two lenses in the 
 woodcut is reversed. Let the subsequent description be read with this 
 correction in view. — Trans. 
 
m 
 
 PHOTOGRAPHIC OPTICS. 
 
 ment of larger diaphragms. It includes an angle of 80°, and 
 is nearly free from distortion. But it possesses the disadvan- 
 tages common to the globe-lens and to the periscope, namely, the 
 forced employment of too small diaphragms — disadvantages 
 which we have dwelt upon in the Preface to this work, and 
 also at p. 91. 
 
 Its use, like that of the globe-lens and of the periscope, is 
 very valuable for the reproduction of inanimate nature, and 
 particularly of buildings, at a very short distance. It gives 
 images of a remarkable sharpness, and possesses a very great 
 depth of focus, qualities which make it rank with the best 
 non-aplanatic objectives.* 
 
 ^Section II . — Aplanatic Objectives. 
 
 The Orthoscopic Lens. — This objective has been in- 
 vented by M. 
 Petzval, of Vi- 
 enna, and it is 
 based on extreme- 
 ly ingenious cal- 
 culations. The 
 subjoined figure 
 shows it as now 
 constructed by 
 Messrs. Harrison 
 and Schnitzer of 
 New York. 
 
 It is formed 
 of an achromatic 
 Fig. 69. meniscus lens, of 
 
 which the convex surface is towards the object to be repro- 
 
 * Several years ago, the late Mr. Goddard, of Isleworth, introduced to 
 the notice of the public a doublet lens for architectural and copying pur- 
 poses ; it differed, however, in form from Mr. Ross’s, and did not embrace 
 so large an angle of view. — Trans. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 135 
 
 duced. This meniscus is not entirely free from spherical, 
 but is completely so from chromatic, aberration. Employed 
 alone, in the position represented by the figure, it would give 
 an image not very sharp at the centre of the focal plane, and 
 in every case very deficient in definition at the margins. 
 But behind this lens, and at a certain distance, is a second 
 but divergent meniscus ; the purpose of which is, firstly, to 
 correct the spherical aberration of the entire system; and, 
 secondly, to extend the focal length of pencils oblique to the 
 axis, in order that the field may be rendered flat, as has been 
 explained at p. 95. 
 
 The second meniscus is formed of two simple lenses, the 
 combination of which is achromatic. The one lens, that 
 towards the anterior meniscus, is bi-concave and of flint-glass ; 
 the other is a convergent meniscus of crown-glass. The two 
 lenses cannot, therefore, be cemented together, like those which 
 form the anterior meniscus. 
 
 f 
 
 The aperture of the orthoscopic lens is about It can be 
 
 o 
 
 employed with its entire aperture, and acts then with very 
 great rapidity, but the extent of sharp image is in this 
 case not more than half its focal length. Between the two 
 lenses is a diaphragm formed of imbricated plates of brass 
 
 f 
 
 which permit of its aperture being diminished to — . With 
 
 this aperture the sharp image becomes of a much greater ex- 
 tent, and equal to the focal length of the objective employed. 
 
 / 
 
 With this aperture of diaphragm (— ), the depth of focus of 
 
 oO 
 
 the objective is very considerable indeed, and the image is 
 also very brilliant, since this diaphragm is, relatively to those 
 employed with the globe-lens and the other non-aplanatic 
 objectives, also very large. 
 
 In a word, the orthoscopic lenif possesses all the advantages 
 of the triplet, of which we shall speak presently, except that 
 of absence of distortion. In fact, the orthoscopic lens repro- 
 duces fig. 55 as fig. 57. It is not, therefore, adapted for the 
 
136 
 
 PHOTOGRAPHIC OPTICS. 
 
 reproduction of buildings, engravings, &c. This is to be 
 regretted, for it possesses some essentially good qualities. 
 
 The double Portrait-Lens. — This objective has been in- 
 vented by Herr Petzval of Vienna, and described by this 
 illustrious savant in a memoir presented to the Academy of 
 Sciences of Vienna — a memoir which is a masterpiece in a 
 mathematical point of view, but of which unfortunately we 
 are unable to give the analysis here, because of the limited 
 space at our disposal, and particularly because of the class of 
 readers to whom this work is addressed. 
 
 Many opticians have claimed priority -of invention of the 
 double objective, on the grounds that they had constructed 
 them with two lenses long before the publication of Herr 
 Petzval’s memoir. But these objectives were not at all in 
 conformity with the compound lens universally adopted at 
 present, were far inferior to it, and admitted of only an 
 
 f 
 
 aperture of jL. They were much like fig. 46, but the menis- 
 cus in front was smaller. These claims have no scientific 
 value, and have besides, on this account, fallen at the present 
 day into oblivion. 
 
 Fig. 70 represents, of the actual size, the double objective of 
 Petzval constructed by M. Hallmeyer, bearing the name of the 
 rapid lens for stereoscopic proofs, and having a focal length of 
 
 4.62 inches. This form unites the greatest perfection with 
 
 f 
 
 the largest possible aperture ( = ^ ). The following are its 
 
 numerical data, the nature of the glass being the same as that 
 of the single objective described at p. 121.*' 
 
 * The following are the indices of refraction of the hinds of optical glass, 
 made by Chance, of Birmingham, which English opticians employ : — 
 
 
 Density. 
 
 index of 
 refraction. 
 
 Dispersive 
 
 power. 
 
 — 
 
 Crown-glass, No. 1 
 
 2*48 
 
 1-50 
 
 0*039 
 
 Crown-glass, No. 2 
 
 2*51 
 
 1-52 
 
 0-04 
 
 Light flint-glass, No. 1 . . 
 
 3-2 
 
 1-57 
 
 0 0473 
 
 Heavy flint-glass, No. 2 
 
 3-64 
 
 .1-64 
 
 0-055 
 
 Very heavy flint-glass, No. 3 
 
 384 
 
 1-64 
 
 0-059 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 137 
 
 This objective is composed, therefore — 
 
 1st. Of an achromatised meniscus, H G (nearly piano- 
 
 Fig. 70. 
 
 Diameter of the anterior combination 
 
 T> 
 
 Bi-convex crown-glass lens j r ' 
 (— R ,r 
 
 Bi-concave flint-glass lens | 
 
 Diameter of the posterior combination 
 
 r , T> 
 
 Divergent flint-glass meniscus j _ 
 
 Bi-concave crown-glass lens -? ((( * ’ ' 
 
 Distance between the two combinations 
 Absolute focal length 
 
 Total aperture of the lens . . . . . 
 -Aperture of the smallest diaphragm . . 
 
 . . 2977 
 
 . . 5585 
 
 . . 3701 
 
 . . 3701 
 
 . . 102662 
 . . 3517 
 
 . . 13030 
 . . 5844 
 
 . . 10195 
 . . 10195 
 
 . . 2424 
 
 . . 10000 
 
 f 
 
 - - 2500 
 
 4 
 
 — = 400 
 
 25 
 
 convex), the convex surface of which is towards the object to 
 be reproduced ; this meniscus, set in a ring, I T, screws on a 
 
138 
 
 PHOTOGRAPHIC OPTICS. 
 
 tube, DEE' D', which receives the larger tube, F F', which is 
 closed by means of a brass or pasteboard cap. 
 
 2ndly. Of a bi-convex combination, NM, formed of a 
 divergent meniscus, M, of flint-glass, placed at a certain dis- 
 tance from a bi-convex lens, N, of crown-glass. The flint- 
 glass, set in a ring, O O', screws into the ring P P', which re- 
 ceives the crown-glass. A ring separates the two lenses to 
 the distance assigned by calculation. This lens is fixed to the 
 other extremity of the tube, DEE' D'. For other parts, the 
 figure, drawn with great exactitude, makes the details of the 
 construction quite clear. 
 
 L L', K K', are two discs between which the diaphragms 
 pass. The aperture of the latter is so graduated, that, 
 knowing the time of exposure required by one of them, that 
 required by another is found by a simple multiplication. 
 
 Let us try to give an idea of the theory of Petzval’s lens. 
 For this purpose, let us remove from the lens the posterior 
 combination (that which is towards the ground glass). The 
 combination in front, the form of which is slightly plano- 
 convex, is very nearly free from spherical and chromatic 
 aberrations. The image that this lens will give of objects 
 situated in its axis , or very slightly oblique to it , will therefore be 
 very sharp, but of very small extent in relation to the focal 
 length. On the other hand, it will be very brilliant. But for 
 objects situated out of the principal axis, the image will be 
 very confused, the field being much curved.* 
 
 * Turned the other way, and furnished with a diaphragm, the lens gives 
 an image less brilliant, but sharp, over a greater extent of the ground- 
 glass. In fact, we have then the single, primitive objective, described at page 
 115. It is for this reason that many opticians recommend their objectives 
 as serving for both portraits and views, by replacing the lens N M (fig. 70) 
 by the lens H G. This can be done by unscrewing the ring PP', and 
 replacing it by the ring E E' : the lens H G then presents its plane or 
 concave face to the object to be reproduced. 
 
 But, as we have seen in the article on the single objective, this system 
 can never be good, inasmuch as the front lens of the compound objective 
 of Petzval has not the form which a good single objective ought to have. 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 139 
 
 The posterior combination (N M, fig. 70) ought therefore 
 to unite the following conditions : — 
 
 1st. That of correcting the spherical aberration (positive or 
 negative) which the anterior combination may possess, and 
 of being itself free from this as well as from chromatic 
 aberration. 
 
 2ndly. That of extending the focal length of bundles oblique 
 to the axis, emergent from the front lens, while reducing 
 astigmation to the least possible degree. 
 
 The front lens, H G, being selected arbitrarily, but as com- 
 pletely free from spherical and chromatic aberration as possible, 
 the posterior combination, NM, is constructed from the formulae 
 of Professor Petzval. If the compound system be not free 
 from chemical focus, another face is substituted for the plane 
 face of the front combination, as we have explained, when de- 
 scribing the single objective, in the noteat page 116, and the two 
 lenses, N and M, are removed from or approached to each other 
 in such a way as to correct the spherical aberration resulting 
 from the preceding operation (that of correcting the chemical 
 focus). If this be not done, the entire system may possess 
 spherical aberration ; and in this case it does not give images 
 of that decided sharpness which a good objective ought to 
 give. 
 
 In all cases, the data relative to the lens must be first 
 very closely obtained by calculation, since the preceding 
 corrections are not practicable beyond narrow limits. 
 
 The second condition is infinitely more difficult to realise. 
 It is the negative lens of the posterior combination which, by 
 its meniscus form, the convexity of which is directed towards 
 the anterior combination, renders the field of the combination 
 entirely flat. But to demonstrate this would need several 
 pages of calculations, which, moreover, are to be found in 
 Petzval’s memoir. 
 
 Generally the anterior lens (that which is towards the 
 object to be reproduced) is a little smaller than the posterior 
 lens, or, if made equal to it, is reduced to a portion of its sur- 
 
140 
 
 PHOTOGRAPHIC OPTICS. 
 
 face by an opaque ring. The consequence of this is an 
 equality of the luminous intensity of the image on a focal 
 plane of a certain extent. For, let A and B (fig. 6 , pi. I.) be 
 the lenses of the double objective, the principal axis of which, 
 H Gr, makes, with the oblique axis, I J, of a bundle, R R', of 
 incident rays, a small angle, GrBI = «, such that the refracted 
 ray, be, meets the upper part, e, of the lens A. It is clear 
 that, if the angle a increases, the image, the luminous inten- 
 sity of which was equal over the focal plane, I J, will be so 
 no longer, since the ray b e , emerging from the front lens B, 
 will no longer traverse the second lens, A, and will strike the 
 mounting, C D. To obtain a great equality of light over a 
 focal plane of 30° in extent (the angle a being consequently 
 15°), it would be necessary either to increase the diameter of 
 the lens A, or to interpose at M M f a diaphragm w T hich limits 
 the extent of the bundle of oblique incident rays. 
 
 The latter method is preferable to the former, because there 
 is great inconvenience in increasing the diameter of the lens 
 A, an inconvenience which consists principally in the great 
 value then assumed by the spherical aberration for rays 
 oblique to the axis and by the astigmation, rendered evident 
 in the image by the thickening of the lines (whether hori- 
 zontal or vertical, according to the position of the ground-glass) 
 of the object to be reproduced. 
 
 The field of the double objective is, with its entire aperture, 
 generally much curved. It could easily be made flat by in- 
 creasing the diameter of the posterior lens A, but for the 
 inconvenience which we have just noticed. It is better to 
 make the field flat (that is, render the image sharp at its mar- 
 gins at the same time that it is so at the centre) by employing 
 a diaphragm, and seeking rapidity in the chemical processes 
 on the photographic surfaces. 
 
 The double objective is intended for portraits, because it is 
 the most rapid of all the optical combinations hitherto invented. 
 
 / / 
 
 Furnished with a very large diaphragm (. 7 : or—), it only 
 
 t) o 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 141 
 
 f 
 
 covers sharply a small part of the focal plane (‘- ), but with a 
 
 / 3 
 
 smaller diaphragm, for instance, the extent of sharp image is 
 
 10 / 2f 
 
 greatly enlarged, and becomes from ^ to — - . Lastly, with a 
 
 2 6 
 
 diaphragm of the extent of the image becomes equal to /. 
 
 The depth of focus of the compound objective is very slight, 
 
 particularly when used* with all its aperture, so that this 
 
 quality is only obtained on the condition of using objectives 
 
 of very short focus, furnished with small diaphragms, which 
 
 f f . f f 
 
 limit the aperture to from ^ to for portraits, from — to 
 
 O j 1/ jLU Zv 
 
 f f 
 
 for groups, and from ^ to ~ for landscapes and buildings. 
 
 The double objective is very nearly free from distortion, on 
 the condition that the diaphragm which it carries is placed 
 between the two lenses, as we have represented at fig. 70 ; but 
 at one time the diaphragm used to be placed (and is still by 
 some opticians behind the time) at the front of the objective. 
 Then distortion of the image occurs as with the single lens. 
 
 The Triplet. — We have already spoken several times of 
 this remarkable objective, and, among others, at pp. 95, 
 101, &c. 
 
 The triplet which we shall here describe is constructed by 
 M. Dallmeyer, who must be regarded as the inventor of this 
 objective.* Fig. 71 represents very exactly the size, having 7 
 inches focal length. The following are the numerical data of the 
 system, the glass employed being that of Chance, of Birming- 
 ham, identical as to index of refraction and dispersive power 
 with that of the single objective described at p, 120. (See 
 also the note at p. 137). 
 
 On inspecting the figure, the construction of the triplet 
 will be at once comprehended, of which, however, the 
 following is the description : — 
 
 * See foot-note, p. 101. 
 
142 
 
 PHOTOGRAPHIC OPTICS. 
 
 G H, IQ, J K, are meniscuses, achromat.ised, and forming 
 single lenses, though each is composed of two cemented toge- 
 
 Fig. 71. 
 
 Diameter of the front lens J K 1714 
 
 / I t 3128 
 
 Bi-convex crown-glass lens | ^ 23g6 
 
 s g t 2386 
 
 Bi-concave flint-glass lens •< ^ 20228 
 
 Diameter of the negative combination I Q 1071 
 
 f-l- R 14200 
 
 Bi-con vex flint-glass lens j ^ ^ 452g 
 
 „ , (_R 4528 
 
 Bi-concave crown-glass lens | ^ 32Q0 
 
 Diameter of the combination H G 2286 
 
 ( — R 30300 
 
 Bi-concave flint-glass lens •<_ . 3557 
 
 s 1 -p # 3557 
 
 Bi-concave crown-glass lens K * 472g 
 
 Distance between the lenses HG, JH 1257 
 
 Focal length of the system 10000 
 
 / _ 
 
 Aperture of the largest diaphragm j - — 1000 
 
 /J 
 
 ” 30 
 
 smallest 
 
 333 
 
DESCRIPTION OF PHOTOGRAPHIC OBJECTIVES. 143 
 
 ther at their common surface. The first and last are conver- 
 gent, and the middle one is divergent. The three are mounted 
 in a tube, C F E D, D E being capable of being covered with 
 a pasteboard cap. This tube screws on a flange, A A', which 
 is fixed to the camera. 
 
 The diaphragms L are graduated, and introduced between 
 two discs, mm', nn. 
 
 When it is desired to make use of this instrument for land- 
 scapes or for reproductions of a natural size, the combination 
 J K (the smallest) ought always to be turned towards the 
 object to be reproduced, and the combination G H (the largest) 
 towards the ground-glass of the camera ; but when it is 
 wished to use it for enlarging, the combination ought to be 
 reversed and turned the other way, G H being towards the 
 object to be reproduced, and J K towards the screen or the 
 sensitive surface placed in the camera. 
 
 For groups and for instantaneous effects, the objective 
 ought to be employed -with the largest possible aperture, 
 so as to obtain the maximum of rapidity. But for land- 
 scapes and for reproductions, when the time of exposure is of 
 less importance, smaller diaphragms may be employed (this 
 is one of the reasons why the triplet will be generally pre- 
 ferred to the globe-lens), by recollecting always that what is 
 called depth of focus can never be obtained legitimately except 
 by using small diaphragms. 
 
 If it is desired, the combination I Q can be removed by 
 first screwing off the combination G H. When the combina- 
 tions G H and I K are alone employed, the focus is found to 
 be reduced to a half, and the rapidity of photogenic action is 
 found to be consequently increased to the same extent ; but 
 though in this case The system may be achromatic, the field 
 produced is much too curved, and the apparatus cannot serve 
 as an instrument for portraits, unless in some special cases. 
 Particularly when it is required for portraits taken out of 
 doors, for groups or reproductions, the three combinations 
 must be employed, arranged as indicated in the figure. 
 
144 
 
 PHOTOGRAPHIC OPTICS. 
 
 < - •• 1 
 
 The advantages and disadvantages of M. Dallmeyer’s 
 triplet are as follow : — 
 
 ls£. With equality of focal length, it covers sharply a focal 
 plane much larger than does the ordinary single objective, but 
 not so large as the new single objective of the same optician, 
 and particularly Mr. Ross’s doublet and M. Steinheil’s peri- 
 scope. 
 
 2 ndly. It is, within practical limits, free from distortion, 
 but not from astigmation, like the globe-lens. 
 
 3 rdly. But it is free, along its axis, from spherical aberra- 
 tion, which is very valuable in the production of animated 
 scenes, portraits, and groups in the open air, &c. In this re- 
 spect it is superior to the orthoscopic lens, and especially to 
 the ordinary double objective, the depth of focus of which 
 with the same aperture is much less than that of the triplet. 
 
 4 thly. With a diaphragm the thirtieth of the focal length, 
 it covers sharply an extent of focal plane of which the greater 
 side equals its focal length, and this aperture of the diaphragm 
 is sufficient for giving brilliant images. If from insufficiency 
 of light, or from any other cause, the diameter of the dia- 
 phragm has to be increased, the sharpness of the image does 
 not diminish (the extent of surface sharply covered on! y 
 diminishes). This advantage is in practice so considerable, 
 that it makes the triplet the most indispensable of all known 
 objectives. The use of the triplet is therefore nearly uni- 
 versal. 
 
THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 145 
 
 CHAPTER VII. 
 
 THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 
 
 In this chapter we purpose to describe the mode of using 
 objectives in the different branches of photography — namely, 
 for portraiture, reproducing landscapes , buildings , maps , pictures , 
 photographs , &c. — and the precepts common to all these 
 processes — namely, the focussing , the time of exposure , varying 
 with the aperture of the diaphragm, the previous trial of 
 the position of the ground-glass of the camera, and the testing 
 of the objective as regards the chemical focus which it may 
 possess. We shall in this description follow the natural order 
 of the operations. 
 
 The Camera. — The camera employed by photographers is 
 so well known that any description of it is needless. The 
 following are the principal points to which we call the atten- 
 tion of the reader :■ — 
 
 ls£. A glass finely ground, which may even be rubbed with 
 a little oil so as to render the grain finer, is necessary for 
 exact focussing. 
 
 2 ndly. It is necessary, before using a camera, to verify if 
 the ground-glass and the glass-plate in the slide occupy ex- 
 actly the same place, and, in order to do this, to measure with 
 a rule their distance from the brass ring of the objective fixed 
 on the front of the camera. 
 
 3 rdly. The objective ought to be fixed to a small board, 
 sliding in two vertical grooves on the front of the camera. 
 This is indispensable for the reproduction of views and 
 buildings. 
 
 4 thly. — In no case ought the plane of the ground-glass to be 
 
 L 
 
146 
 
 PHOTOGRAPHIC OPTICS. 
 
 capable of being inclined to the axis of the lens, as it is 
 made to be in some portrait-cameras.* 
 
 The Focussing. — To focus is to render the image on the 
 ground-glass as sharp as possible. When the objective has a 
 small aperture and a very great focal length this is very easy ; 
 but when the objective has a short focal length and a large 
 aperture, it is infinitely more difficult, because then the least 
 derangement of the ground-glass changes the sharpness of the 
 image, for the reason we have explained at p. 85. 
 
 For rigorous focussing it is well to make use of the magni- 
 fier, represented by fig. 72, It is formed of two plano-convex 
 
 lenses, a and 5, the convexities 
 of which are towards each other, 
 fixed at the extremities of the 
 tube C, sliding with gentle 
 friction in the tube B, screwing 
 into a larger tube A, which is 
 applied, during the focussing, 
 at the part where it may be 
 deemed to be necessary. We first adapt the magnifier to 
 our sight by sliding the tube C in the tube A, taking care 
 that no one disarranges the magnifier afterwards ; for every one 
 must regulate it to his own vision, else a very great error 
 might be caused in the focussing, particularly if the ground- 
 glass is fine and oiled. 
 
 When the camera is directed with its objective towards the 
 object to be reproduced, select in the latter a sharply defined 
 point placed at the centre of the ground-glass, and another 
 placed at its edge, both as nearly as possible in the mean plane, 
 that is to say, chosen between the fore and back-grounds. (In 
 examining the ground-glass, the head is covered by a black 
 cloth, which envelopes the upper part of the body, and also 
 the camera, except its objective). 
 
 * In our Traite General de Photographie we have stated the contrary, 
 but a more attentive examination of this question has proved to us our 
 error. 
 
 Fig. 72. 
 
THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 147 
 
 On advancing or withdrawing the ground-glass and ex- 
 amining with the magnifier the image of the point at the 
 centre, we easily succeed in giving it all the sharpness pos- 
 sible. Passing, then, to the point at the edge of the ground- 
 glass, we see whether the image is sharply defined. Ordi- 
 narily it is not so, but the intermediate points become more 
 defined the nearer they are to the centre. The ground-glass 
 is always, after the focussing, fixed by a pressure-scre'w. 
 
 When the objective is aplanatic (see p. 75), the image 
 can be focussed with a large diaphragm. The image is 
 then better observed, but we must, in this case, choose for 
 focussing a well-defined object somewhere between the fore 
 and back grounds and situated at the centre of the ground- 
 glass. For the large diaphragm there is then substituted 
 a smaller one, which extends the sharpness to a surface 
 of the ground-glass so much the greater as the diaphragm 
 is smaller. But with non-ajolanatic objectives it is neces- 
 sary for exact focussing to make use of one of the smallest 
 diaphragms. 
 
 This is easily conceived, if it be recollected that any point 
 chosen in the object to be reproduced forms the summit of 
 the luminous bundle of which the lens is the base, and the 
 focal plane the point where the rays meet. The diameter 
 of the aperture of the objective has no influence on this 
 point if the objective is aplanatic, so that, with or without 
 diaphragms, the objective must reproduce the object with 
 the same degree of 'sharpness. The employment of the 
 diaphragm only causes the sharpness of the image to be 
 distributed over a greater surface by increasing the depth 
 of focus. 
 
 Properly speaking, when the objective is furnished with a 
 very small diaphragm, the position of the ground-glass for 
 the sharpest possible image is not fixed (see p. So) ; hence the 
 difficulty of focussing with this kind of objectives,, a difficulty 
 which is not experienced with an aplanatic lens previously 
 furnished with a large diaphragm, which gives at once more 
 
 l 2 
 
148 
 
 PHOTOGRAPHIC OPTICS. 
 
 clearness to the image, and limits the sharpness to determined 
 points. This sharpness is extended on the substitution of a 
 small diaphragm for the large one. 
 
 Calculation of the time of exposure. — The time of 
 exposure has the greatest influence on the artistic value of a 
 photographic proof. Too much exposure gives dull proofs, 
 too little exposure harsh proofs, and a proper exposure 
 brilliant images with shaded skies, deep shadows, etc. 
 
 According to M. Leon Yidal, of Marseilles, — who has pub- 
 lished a small work on this subject, entitled Calcul des 
 temps de pose , which is remarkable for precision, and from 
 which this account is only an extract, — the following causes 
 make the time of exposure vary : — 
 
 1st, the intensity of light at the moment of the operation ; 
 2nd, the sensibility of the surface submitted to the impression ; 
 3rd, the greater or less reflecting power of the object to be 
 reproduced ; 4th, the ratio of the diameter of the diaphragm 
 to the focal length of the objective employed. 
 
 M. Yidal measures the intensity of the light by exposing 
 for one minute a piece of ordinary albumenized paper to day- 
 light (in the shade), and afterwards compares it with a series 
 of ten printed shades, selecting that one the coloration of 
 which approaches the nearest to the tone of the paper, the 
 number of which furnishes one of the elements of the calcula- 
 tion of the time of exposure. 
 
 The sensibility of the surfaces submitted to the impression 
 is, as thus determined, in the following ratio \ dry collodion with 
 tannin , 3 ; moist collodion , 24 ; albumen , 1 ; whence it follows 
 that wet collodion is eight times as rapid as dry collodion 
 with tannin. 
 
 The reflecting power of bodies becomes' appreciated by 
 habit ; but attention need only be paid to it in exceptional 
 cases, such as the reproduction of landscapes, where green 
 would be' predominant, that of pictures, where red, yellow, 
 and green would prevail, etc. 
 
 Lastly, the fourth datum is the most important. M. Yidal 
 
THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 149 
 
 at once admits that within a small fraction nearly all objectives 
 are equally rapid if the ratio between the aperture of the 
 diaphragm and the focal length be the same. All objectives, 
 
 f 
 
 therefore, of which the diaphragm is —■ give the same intensity 
 
 oO 
 
 of image, whatever / (the focal length) may be, which is in 
 fact the case. 
 
 But M. Yidal expresses the / in a series of figures which 
 he takes from 10 to 90 centimetres, along with diaphragms of 
 variable apertures; so that, in this way, his tables attain a 
 length which they would not have reached by taking the 
 ratio between the aperture of the diaphragm and /. But on 
 this account his tables are more practical ; for, in our system 
 (and this is an improvement which every optician should 
 carry out) the constructor of the objective ought to adopt, as 
 indeed he does, focal lengths determined by the dimension of 
 the focal plane, and then apertures of the diaphragms which 
 are exact fractional numbers of this distance, such as 
 
 f f f f f 
 
 — , — , tJ-, — , In this way, all imaginable obiectives could 
 40 30 20 10 8 
 
 be compared together just as the variable diaphragms of the 
 same objective. 
 
 However this may be, M. Yidal introduces in his tables the 
 preceding elements, which, in the main, are, for the operator, 
 confined to the measurement of the intensity of the light, 
 a knowledge of his lens, and the consultation of the tables ; 
 and he thus obtains exactly the time of exposure. 
 
 Let us add, further, that if there are some slight causes 
 of error in the calculation of the time of exposure, this 
 may vary within certain limits without very sensibly 
 changing the results. But many who practise photography 
 have only a vague appreciation of such matters ; and, there- 
 fore, real thanks are due to M. Yidal for his remarkable and 
 useful work. 
 
 Trial of the chemical focus of the Objective. — It is of 
 
 the highest importance, before adopting an objective, to try if 
 
150 
 
 PHOTOGRAPHIC OPTICS. 
 
 it has not some chemical focus, and this is how we proceed 
 to test it : — • 
 
 Place at some metres from the objective to be tested the 
 focimeter, the image of which must 
 be formed at the centre of the 
 ground-glass. This focimeter is 
 formed (fig. 73) of eight segments 
 of pasteboard, numbered and placed 
 at equal distances from each other 
 along a cylinder of wood in such a 
 way that their assemblage seen 
 from their face forms a circle. 
 Bring rigorously to a focus the 
 card No. 5, and, in order to avoid 
 all error, use a ground-glass placed 
 in the dark frame which will afterwards receive the sensitised 
 plate. 
 
 This being done, substitute the sensitised plate for the 
 ground-glass, take a proof, and see if the card No. 5 be 
 rigorously sharp. If not, your objective possesses a chemical 
 focus. If the card No. 6, 7, or 8 be the sharpest (instead of 
 No. 5 focussed by the eye), the chemical focus is longer than 
 the visual focus, and after every focussing it would be neces- 
 sary to draw out your camera to an extent variable with the 
 distance of the object to be reproduced. If it be the card 
 No. 1, 2, 3, or 4, the reverse must be done. 
 
 The employment of the Objective for taking por- 
 traits. — The only objectives which should be employed for 
 portraits are : the double lens in the studio ; the triplet and the 
 orihoscopic in the open air. What follows relative to their 
 employment applies to all three, but more particularly to the 
 first, the use of which is the most general. 
 
 Firstly, there must be procured a wooden stand, very 
 massive , in order to avoid vibrations (iron stands are in general 
 to be rejected for this purpose), and which can be lowered or 
 raised so as to bring the lens to the height of the loins of 
 
THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 151 
 
 a person sitting, and to that of the chest of a person standing 
 up. The axis of the objective ought to be capable of inclining 
 downwards to a small extent, but to abuse this allowance is to 
 run the risk of obtaining deformed proofs, for theoretically 
 the axis of the objective ought always to be maintained rigo- 
 rously horizontal. 
 
 To prove this let B C D E (fig. 7, pi. I.) be a person seated, 
 and A the objective placed too high, and consequently re- 
 quiring to be inclined at a downward angle. It is clear that 
 the angle a subtended by the horizontal part, C D, of the legs 
 will be much greater than if the objective were placed at A', 
 at the level of the loins, in which case the angle a is much 
 smaller, and in accordance with truth ; for in the photographic 
 reproduction, the person will appear to be seated on a chair 
 the seat of which is inclined, in the case where the objective 
 has the position A. 
 
 If the person is standing (fig. 8, pi. I.), the objective ought 
 to have its axis horizontal and on a level, D C', with his 
 shoulders, a. It will be necessary to lower the stand which 
 carries the objective D, so that the image, h a c, of the person 
 may fall on about the middle of the ground -glass, in order to 
 have the space, h c, above the head nearly equal to the space, 
 d c, beneath the feet. By proceeding in this way the image 
 cannot be at all deformed. 
 
 Few photographers operate in this way, but incline the axis 
 of their objective so that the image is thereby deformed. To 
 keep the axis of the objective on a level with the loins in re- 
 producing a person in the standing position is contrary to the 
 laws of perspective, he always having then, in the photograph, 
 his neck too short. It is better, then, to do as we have stated 
 above. We may add that if the objective has a long focus, a 
 slight inclination of its axis produces, as in the case of views, 
 no very evident deformation of the image. 
 
 Reproduction of Landscapes. — For this kind of photo- 
 graphy, the single objective, which we have already described, 
 the triplet , and the orthoscopic , answer the best, because it is 
 
152 
 
 PHOTOGRAPHIC OPTICS. 
 
 often requisite to employ large diaphragms on account of the 
 little photographic power of green, the prevailing colour in 
 landscapes. 
 
 As landscapes do not present straight lines, the operator 
 may incline the axis of his apparatus upwards or downwards 
 without causing perceptible deformation in the image. This 
 is all that it is necessary to say here concerning this kind 
 of photographic reproduction. 
 
 Architectural reproductions. — If the building be very 
 near, and if persons are not required to be seen in the proof, 
 the doublets of Mr. Ross (p. 133) and of M. Steinheil (p. 130), 
 and the globe-lens (p. 124), are the most suitable for the purpose. 
 If the building be not so near, and particularly if persons are 
 desired in the proof, then the triplet (p. 141) is to be preferred, 
 seeing that it allows of the employment of larger diaphragms, 
 and consequently of a shorter exposure to the light. The 
 single objective and the orthoscopie do not answer at all, on 
 account of the distortion (p. 96) which they produce in the 
 image. 
 
 The essential point in the reproduction of a building, C B A 
 (fig. 9, pi. I.), is to keep the camera, D E, perfectly hori- 
 zontal. Most usually in this case the image of the summit, A, 
 of the building fails outside the ground-glass of the camera ; 
 but to obviate this inconvenience, the wooden slide carrying 
 the objective, H, must be elevated until the image, cba, of the 
 building occupies the desired place on the ground-glass. 
 
 If, instead of proceeding in this way, the objective were 
 pointed upwards, the vertical lines of the building would 
 then incline towards each other, as shown in fig. 10, pi. I. 
 Such a course of procedure must be avoided. 
 
 If in the reproduction of a building we are in a high position, 
 the slide carrying the objective must be lowered, and not the 
 axis of the objective declined ; else the same want of paral- 
 lelism of the vertical straight lines is produced, but in the 
 opposite direction to that in the case just now considered. 
 
 It is true that, by proceeding in the way described, part of 
 
THE EMPLOYMENT OF PHOTOGRAPHIC OBJECTIVES. 153 
 
 the building is always deficient in sharpness (the summit A, 
 for instance, as shown in fig. 9, pi. 1), and it is so for the 
 reason, that, by raising the objective H, so that its axis, B b, 
 is higher than that of the axis, o o', of the camera, we make 
 it serve for a dimension of the focal plane greater than that 
 for which it was constructed. For b o increases in the ratio 
 of B A ; whence it follows that the more lofty the building, 
 the less sharp will its summit, A, be. But better sacrifice 
 the sharpness of this part of the image than obtain those un- 
 fortunate distortions in which the houses are seen falling 
 towards the street, towers leaning, &c., and which cause the 
 photographic art and the objectives to be unjustly accused 
 of deforming the images — a reproach only merited by the 
 operator ignorant of the precepts of optics. 
 
 As regards the want of sharpness in the summit of a 
 building, it can in many cases be partly avoided by placing 
 ourselves with the apparatus as far off as possible, and entirely 
 avoided by placing the apparatus at a height equal to half 
 the total height of the building. 
 
 Reproduction of Engravings, Drawings, Maps, 
 Pictures, Photographic Proofs, Sco . — For this purpose, 
 the same objectives are employed as those for taking build- 
 ings. To keep the camera horizontal, the face of the 
 engraving exactly vertical, the point of intersection of 
 the diagonals drawn between the opposite angles of the map, 
 picture, &c., exactly in the axis of the objective, which is 
 seen by the image then covering the ground-glass symmetri- 
 cally — these are all the optical instructions for this kind of 
 photography. 
 
 The objective is to be reversed if an enlarged reproduction 
 has to be obtained, that is, the lens which ordinarily faces the 
 ground-glass is in this case to be towards the object to be 
 reproduced. For this purpose, the triplet and the orthoscopic 
 are to be employed in preference, because of their large 
 aperture, which allows of a short exposure as compared with 
 that of the non-aplanatic objectives mentioned at p. 75. 
 
154 
 
 PHOTOGRAPHIC OPTICS. 
 
 Ill reproducing a drawing or a photograph of the same 
 size as or larger than the original, it is advisable to use an 
 objective of longer focus than is theoretically necessary, 
 because when the distance between the object and the objective 
 is too short there is great difficulty in illuminating the object 
 properly. Thus, triplets and orthoscopies of 10 or 12 inches 
 focal length ought not to be emploj^ed for reproductions, 
 identical in size with the object to be reproduced, of more 
 than about 6 by 8 inches. It is otherwise when the repro- 
 duction is smaller than the object. 
 
 In the case of reproductions, particularly those of daguer- 
 reotypes and photographs on glass which reflect light, a large 
 disc of black velvet with the same aperture as, and in close 
 contact with, the objective, is interposed between them. This 
 is to prevent the image of the object receiving that of the 
 objective by reflection from the polished surface of the object 
 to be reproduced. 
 
( 155 ) 
 
 BOOK II. 
 
 APPARATUS FOR ENLARGEMENTS. 
 
 The future of photography rests in the practical solution of 
 the amplification of small photographic images. In fact, with 
 the optical means actually at our disposal, we can produce 
 with certainty a small proof — the size of a card picture, for 
 example — of absolute sharpness, both at the centre and margins. 
 
 If we effect the enlargement of this proof with a perfect 
 apparatus, we shall obtain from it a proof of plate size, double 
 plate, entire sheet, and of even 1 metre high, with an extreme 
 perfection, such, that any objective, employed directly, 
 cannot produce one either so beautiful or so fine. The author 
 of this work has, in fact, proofs of the size of the photographic 
 sheet (44 centimetres by 57) so sharp, that in the opinion of 
 opticians of the highest merit, such as Messrs. Secretan, Eoss, 
 and Dallmeyer, nothing can be produced so fine by the use 
 of large objectives. 
 
 All the importance, therefore, of this part of our work will 
 be perceived. We shall divide it into chapters, wherein we 
 shall separately examine : — 
 
 1. The production of the negative intended for enlarge- 
 ment. 
 
 2. The amplification of the negative (enlarging apparatus). 
 
156 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTER I. 
 
 ON THE NEGATIVE INTENDED FOR ENLARGEMENT. 
 
 In this chapter we have to examine : — 
 
 1st. The optical apparatus for producing the negative. 
 
 2nd. The photographic process to he followed for obtaining 
 the negative. 
 
 Section I. — The optical apparatus suitable for producing a very 
 small perfect negative. 
 
 Influence of the focal length of the Objective. — If a 
 
 camera furnished with an objective be directed on a man who is 
 walking away, his image on the ground-glass becomes smaller 
 and smaller, while, on the other hand, it is necessary to bring 
 the ground-glass constantly nearer to the objective, in order 
 that his image may remain sharply defined. There is, how- 
 ever, this to be remarked, that if the man be very close to the 
 objective, (which to fix our ideas we shall suppose to have a 
 focal length of 30 centimetres) for example, 3 or 4 metres from 
 it, the movement to be communicated to the ground-glass is 
 then very considerable, and that, in proportion as the man 
 moves off, a point is soon reached when on the' contrary this 
 movement becomes absolutely nothing. Then the distance 
 which separates the man from the objective is such that his 
 image is formed at the principal focus of the objective. 
 
 Experience shows that if an object be situated at a distance 
 of a hundred times the focal length of the lens, its image is 
 then formed at the principal focus of the lens, the same as that 
 of all objects' situated further away. A perusal of pages 85, 
 et seq ., will clearly demonstrate this fact. Therefore, in order 
 
ON THE NEGATIVE INTENDED FOR ENLARGEMENT. 157 
 
 to produce a good negative, the object must be very dis- 
 tant. But how is this to be reconciled with the short length 
 of glass studios, or, in the case of views, with the short 
 distance which always separates us from the foregrounds? 
 Evidently by making use of objectives of very short focus * 
 It is true, the image will be in this case very small, but 
 it will be sharp at all points. 
 
 It is, in fact, necessary to be thoroughly impressed with the 
 principle that an objective of very short focus has the property 
 of giving equally sharp images of objects at different distances 
 away, provided these are at a distance from the objective at 
 least equal to 100 times its focal length. For portraits, there- 
 fore, the best objectives are the smallest. Let us now see the 
 influence of the diameter of objectives on the sharpness of 
 images and the truthfulness of perspective. 
 
 Influence of the diameter of the Objective. — An 
 objective which has a very large diameter as compared with 
 its focal length, produces images not only of very unequal 
 sharpness at their centre and at their margins, but also faulty 
 as to the perspective. The latter point will be understood 
 when it is considered that every point of the objective has a 
 different view of the object to be reproduced, and that the 
 image of this object is made up of an infinity of different 
 superposed images, one of them being formed by every point 
 of the surface of the objective. Therefore objectives of large 
 diameter always deform the reproduced object. It is precisely 
 for this reason that all objectives which have more than two 
 inches aperture do not give by any means such sharp images 
 as would be obtained by enlarging a very small negative. An 
 objective of three inches, much more one of four, five, or six 
 inches, never gives images sharp over all the surface of its focal 
 plane. On the contrary, an objective of one inch, or even of 
 two inches, gives an image sharp and truthful (without de- 
 
 * We do not mean by objectives of very short focus objectives with very 
 large diameter relatively to their focal length, as is usually meant, but 
 very small ordinary objectives. 
 
158 
 
 PHOTOGRAPHIC OPTICS. 
 
 formity), because in this case the diameter is too small in 
 relation to tbe distance which separates the objective from 
 the object to be reproduced. Many photographers, therefore, 
 are already giving up .objectives of five and six inches, 
 and the number of those doing so will increase much 
 more as the use of the apparatus for enlarging becomes more 
 extended. 
 
 If the dimension be made less than this, as the enlarge- 
 ment required for a given size of paper is more considerable, 
 the least defects of the glass or of the collodion him become 
 very apparent. 
 
 Apparatus suitable for Portrait-Negatives.— The ap- 
 paratus most suitable for these are the carte-de-visite objectives, 
 by proceeding in the way we have indicated at page 150. 
 
 Apparatus suitable for Landscape-Negatives. — The 
 best size for a negative for enlarging, in the case of views as 
 well as of portraits, being that of the carte-de-visite , small 
 objectives are preferable to large ones. 
 
 Messrs. Eoss and Dallmeyer, the celebrated English opti- 
 cians, construct small triplets, which have only three or four 
 inches focal length, and which give proofs of carte-de-visite size 
 of an absolute sharpness at the margins as well as at the 
 centre. If the foregrounds are situated more than about 
 twenty-five feet from the objective, and if this is never in- 
 tended to be used but for negatives destined for enlargements, 
 it should then be mounted on a small camera without sliding 
 movement , and in which the ground-glass is fixed, as in the 
 self-acting camera of M. Bertsch, which we describe below. 
 We must never forget the recommendations laid down at pages 
 151, et seq. 
 
 Self-acting Camera of M. Bertsch. — M. Bertsch has 
 constructed small cameras, specially intended for landscape- 
 negatives, in which no focussing is necessary, in virtue of the 
 principle already given (page 157). Fig. 74 is an exact draw- 
 ing of it. Eaised on its stand at the distance of ten feet, it 
 takes in an angle of about 23° — an angle much smaller, how- 
 
ON THE NEGATIVE INTENDED FOR ENLARGEMENT. 159 
 
 ever, than that which would be taken in by a triplet. The 
 lens, G, which M. Bertsch uses, is a single objective of 
 the old construction (p. 119). 
 
 A is a cubical box of brass, carrying the quadrangular 
 appendages I and L, in- 
 tended to render it rigid. 
 
 C is a spirit-level, and B 
 a sight which serves for 
 placing the landscape in 
 the best position on the 
 frame M. As much of 
 the landscape as is in- 
 cluded in the frame B 
 will be reproduced oh Fl £- 74 * 
 
 the sensitised glass placed in the frame M. E is a spring- 
 shutter with an elastic spring, which holds the glass closely 
 against the corner pieces of the frame. The glasses used by 
 M. Bertsch are eight centimetres square. He has also con- 
 structed, on the same principle, self-acting portrait-cameras, 
 in which the single is replaced by the double combination. 
 
 Section II . — The Photographic Process. 
 
 The Glass. — Thin glass should be selected, 2 millimetres 
 thick at the most, and as uniform in thickness as possible, be- 
 cause the heat of the sun, condensed by the semi- transparency 
 of the image, very quickly causes plate-glass to break in pieces, 
 while blown- glass will stand this strong heat much better. 
 Small bubbles and other defects of the glass (such as inequa- 
 lity of the surface) have no influence on the perfection of 
 the enlarged image. The thickness of the glass has a great 
 effect upon that accident to which the glass is liable, of 
 breaking under the influence of the solar ,rays ; the thicker 
 it is, the less likely is it to stand their heat. In this respect 
 
160 
 
 PHOTOGRAPHIC OPTICS. 
 
 it is like plate-glass. There is, besides, another inconvenience 
 in nsing thick glasses, which is, that they alter the path of the 
 convergent rays which pass through them, and that in this case 
 it is necessary, with unfailing attention, to keep the solar rays 
 in a constant direction, or else the outlines of the image will be 
 doubled, particularly at their margins. With thin glass this 
 defect is not appreciable. 
 
 The Process. — The only process which is suitable for 
 negatives intended for enlargements is the collodion process. 
 What is necessary, in fact, for such a negative, is great trans- 
 parency, of which one can scarcely have any correct idea until 
 after having seen negatives made by experienced operators. 
 The dry collodion and the albumen processes have not given 
 such good results as the wet collodion process. Nevertheless, 
 these ought to succeed when properly employed, as well as 
 the wet collodion process. 
 
 This transparency of the negative, to which we cannot too 
 much call the attention of the reader, and to which we shall 
 again have occasion to call it, is necessary for several reasons. 
 In the first place, in the apparatus for enlarging, the solar light 
 ought freely to traverse the negative, else there will be ex- 
 treme heating of the glass, and consequent fracture. Secondly, 
 several images are found superposed on the paper, the optical 
 apparatus acting, firstly, by the light transmitted , then by that 
 emitted, by every point of the negative. Lastly, all the 
 sharply-defined outlines of the negative are found doubled on 
 the enlarged proof, phenomena of diffraction being produced, 
 to which we shall by-and-by return. 
 
 Now, to obtain this extreme transparency of the negative, 
 and, above all, a complete absence of fogging (which has the 
 bad effect of requiring an exposure double and triple of that 
 which would be necessary if it were not fogged), there must 
 necessarily be a well-prepared collodion, silver bath, and 
 developer. 
 
 All collodions, silver baths, and iron developers are good 
 if they produce good results in the ordinary process. To give 
 
ON THE NEGATIVE INTENDED FOR ENLARGEMENT. 161 
 
 formulae here would be of no use. But the following is the 
 mode of operating, which is of more importance : — 
 
 The glass covered with sensitised collodion is exposed in the 
 camera a little longer than usual. It is easy to understand the 
 object of this longer exposure. If a just sufficient exposure 
 were given, the iron would only bring out the details in the 
 shadows after some time, during which the blacks would have 
 acquired too great an intensity ; whereas, by giving a longer 
 exposure, the image at once appears in the shadows as well as 
 in the lights. The negative is then, after exposure in the 
 camera, carried to the dark room, and the glass is removed from 
 the frame. A considerable quantity of iron is taken in a lipped 
 glass, and a trough full of water placed ready to hand. The 
 iron is poured over the negative, covering it very abundantly 
 so as to remove all the nitrate of silver which is on the film. 
 In a word, to give thorough expression to our meaning, the 
 negative is washed with the iron. The image appears, and the 
 moment the details in the shadows come out, the glass is 
 plunged into water, washed, and fixed with cyanide of potas- 
 sium. 
 
 All the skill consists in operating very quickly. First, flood 
 the negative with iron, and just before fogging has had time 
 to appear (most usually five or six seconds after having applied 
 the iron), at once arrest the action by a copious stream of water, 
 and fix with cyanide (not with hyposulphite). 
 
 The dry negative examined by daylight ought barely to allow 
 the details in the shadows to be seen : the blacks ought to be 
 so feeble, that one could read through them, and even observe 
 the most delicate objects ; otherwise the enlargement will never 
 be perfect. Above all, avoid fogging. It is often preferable 
 to produce a negative too intense (provided it be not fogged) 
 than one too faint. For there is a simple and easy method of 
 lessening the intensity of negatives, which is also applicable to 
 old negatives provided they have not been varnished. This is 
 the method : — 
 
 The negative is first wetted with distilled water : if the 
 
 M 
 
162 PHOTOGRAPHIC OPTICS. 
 
 film lias a tendency to separate, previously varnish, its edges 
 with a brush dipped in a solution of caoutchouc in benzole. 
 Then dip the negative in a solution of one gramme of 
 sublimed perchloride of iron in 100 grammes of distilled water, 
 for a time varying from some seconds to several minutes. The 
 chloride of iron attacks the image, but only at its most intense 
 parts. Wash the negative in water, dip it in a weak solution of 
 cyanide of potassium, and wash again with water. The inten- 
 sity of the negative will be found to be diminished. If it be 
 too much so, then it has been left too long in the chloride of 
 iron ; if it be too little, repeat (even several times) the same 
 treatment. 
 
 No varnish, not even gum, can be applied to the negative ; 
 varnish and gum, on getting heated, would entirely spoil the 
 image. This point is of extreme importance. Besides, the 
 varnish partly destroys the fineness of the image ; an assertion 
 which appears paradoxical, but which most accurate experi- 
 ments enable us to make. 
 
 For the rapid process with nitro-glucose (proofs by develop- 
 ment), a good ordinary negative (but not fogged) gives excel- 
 lent results ; this process generally giving proofs in which the 
 contrast of the blacks and the whites is less than with 
 albumenised paper. Even varnished negatives — which have 
 not been made expressly for enlargement, and which would 
 require with ordinary albumenised paper a very considerable 
 exposure to the sun’s rays — can be used for enlargement by the 
 development-process. 
 
DESCRIPTION OF THE APPARATUS FOR ENLARGEMENTS, 163 
 
 CHAPTER IL 
 
 HISTORY AND SUMMARY DESCRIPTION OF THE APPARATUS FOR 
 ENLARGEMENTS. 
 
 The object of apparatus for enlargement is to produce 
 proofs of a large size from a very small negative — of carte-de- 
 visite size, for example — with a uniform sharpness all over their 
 surface, which cannot be obtained without its employment. 
 The sun being the source of the most intense light we possess, 
 it is usually by means of the rays of this body that we work ; 
 in this chapter we shall only treat of the apparatus used with 
 this light. 
 
 Two methods naturally present themselves by which to 
 throw an enlarged image of a negative on a surface sensitive 
 to light and capable of retaining it. One is to illuminate the 
 negative by the direct rays of the sun ; the other, to illuminate 
 it by these rays first concentrated by a lens. A lively discus- 
 sion has taken place between several savants as to the supe- 
 riority of one method over the other— a discussion which will 
 engage our attention in the next chapter. 
 
 Section I. — Woodward's Apparatus and its Modifications. 
 
 This apparatus (fig. 75), often described under the name of 
 the American solar camera, is composed essentially of a large 
 lens, I (fig. 75), called the condenser , at the principal focus of 
 •which an achromatic objective, L, is fixed. A mirror, AB, 
 throws the solar rays, r r, on the condenser, I ; and the negative, 
 
 m 2 
 
164 
 
 PHOTOGRAPHIC OPTICS. 
 
 J, moveable by means of a rack, K, is placed between the two 
 lenses at a distance which varies with that of the screen on 
 which the image is to be formed. 
 
 Fig. 75. 
 
 Such is the apparatus as a whole. Let ns now pass to its 
 details. 
 
 The condenser is 8 inches in diameter, but may be larger; 
 if possible, 50 centimetres in diameter. The reason of this is 
 very simple : the larger this lens is, the more light it collects, 
 and the more quickly, consequently, is the positive printed. 
 
 Its focal length should not be less than twice its diameter, 
 nor more than three times. 
 
 The objective, intended to be placed at L, should be cor- 
 rected for its chemical focus. Its place is a little in advance 
 of the focus, /, of the condenser. An ordinary objective, single 
 or double, serves for this purpose, but the greatest care must 
 be taken that the lens of the objective which faces the ground- 
 glass, as ordinarily used, now faces the negative, J. 
 
 The negative should be moveable in the direction of the 
 axis of the optical system ; consequently, the apparatus should 
 be specially constructed with this object. This is the use of 
 the rack K. 
 
 The most usual form of the solar camera is that of a large 
 square box, EFGH. The adjustible mirror, which we have 
 described at page 12, is attached to the apparatus, at the ex- 
 tremities of which are the condenser, I, and the enlarging 
 lens, L. 
 
DESCRIPTION OF TIIE APPARATUS FOR ENLARGEMENTS. 165 
 
 Tlie management of the apparatus is very simple. It is 
 sufficient to place the part EHBAof the solar camera in an 
 opening in a darkened window ; to communicate, by means of 
 the adjusting screws B and D, the movements necessary for 
 keeping the solar rays alwa} 7 s reflected in the same direction, 
 If; to properly adjust the negative, J, so that its enlarged 
 image is sharply formed on a screen, placed at a distance and 
 perpendicular to the optical axis of the apparatus; and, lastly, 
 to substitute for the screen a sheet of sensitive paper, or some 
 other photographic surface. 
 
 Modifications introduced into the Solar Camera of 
 
 Woodward. — Each time that the screws for moving the 
 mirror were touched, the apparatus was shaken, and a corre- 
 sponding movement imparted to the image, the more consider- 
 able according as the enlargement was greater. Besides, the 
 wind, or the least agitation of air, is sufficient to shake the 
 apparatus, and in this way destroy the sharpness of the image. 
 
 M. Wothly, photographer, of Aix-la-Chapelle, introduced the 
 first modification in Woodward’s apparatus, by detaching the 
 mirror from the apparatus. He formed it (fig. 7, pi. III.) of 
 a large mirror, A, turning on pivots between two uprights, 
 B and D. A weight attached to the upper part of the mirror 
 tended to move it in one direction, but it was maintained in 
 the other by a cord, a, which passed into the dark room, and 
 over a pulley worked by an endless screw. Two cords, b 
 and c, communicated to the mirror its second movement about 
 its vertical axis, which was supported by the tripod C. 
 
 The situation of the mirror was towards the north, the 
 silvered part of the mirror, A, looking towards the south over 
 the roof of a small building slightly elevated. The reflecting 
 instrument was therefore placed some metres away from the 
 apparatus (and in the open air), as we explained, page 15. 
 The solar camera, properly so called, was composed of a con- 
 denser, A (fig. 6, pi. III.), to which M. Wothly gave 10, 14, 
 18, 24, 30, and even 36 inches diameter, and the plano-convex 
 form. This lens had a focal length equal to about one and 
 
16*6 
 
 PHOTOGRAPHIC OPTICS. 
 
 a half times its diameter. It was mounted in an iron ring 
 made fast to three iron rods, B, C, D, equi-distant from each 
 other, and perpendicular to the plane of the lens. On these 
 iron-rods was fixed, in a permanent manner, the objective F, 
 at the focus of the condenser. The holder of the negative, E, 
 is moved between the objective and the condenser, by means 
 of an endless screw, not represented in the figure. The appa- 
 ratus was entirely j>i iron, and was enclosed in a wooden box. 
 
 M. Hermagis, a French optician, who has made himself 
 famous by the large number of excellent objectives which he 
 has sent out, also introduced a modification of the primitive 
 apparatus of Woodward. His adjustible mirror was detached 
 from the apparatus, and was very nearly the same as that we 
 ourselves use in our dyalitic apparatus. But the mirror, in- 
 stead of being suspended about its centre of gravity, which is 
 necessary to produce stability, was suspended at its lower part 
 by an arc attached to the side of the mirror. The whole weight 
 of the mirror, therefore, rested on a point, so that its flexion 
 was considerable, and had the inevitable consequence of altering 
 the parallelism of reflected solar rays. This was a great defect. 
 
 At a certain distance from the adjustible mirror the solar 
 camera was placed. This was identical with that of Wood- 
 ward, except that the frame for the negative received in his 
 arrangement two movements by means of adjusting screws, 
 the object of which was to fix the central part of the negative 
 in the axis of the optical apparatus. Moreover, M. Hermagis 
 introduced between the negative to be enlarged and the con- 
 denser a moveable ground-glass. It was thus possible to work 
 with either diffused light or the direct rays of the sun, accord- 
 ing as the ground-glass was interposed or withdrawn. Lastly, 
 the solar camera was connected with the adjustible mirror by a 
 cloth cylinder, in order to shut out the daylight which might 
 enter obliquely through the interval between them. 
 
 Solar Cameras without a Reflector. — Since the origin of 
 enlarging processes, several persons, under the false impres- 
 sion that the mirror caused much of the light to be lost (in 
 
DESCRIPTION OF THE APPARATUS FOR ENLARGEMENTS. 167 
 
 reality, not an eighth of it is lost), directed their apparatus 
 towards the sun, mounting all the parts on a single piece of 
 wood or iron. 
 
 The first apparatus of this kind was described in England 
 in 1863 by Mr. Stuart, the arrangement adopted by him being 
 the following : — 
 
 The condenser, fixed in a very long box, is followed by the 
 negative and the objective, precisely as in the American 
 apparatus. On the box is fixed a cone, at the bottom of 
 which is the frame on which the sensitive paper is stretched. 
 Mr. Stuart places two of these apparatuses side by side, protects 
 them from the wind, and makes them move with the sun by 
 means of two movements, one horizontal, the other vertical. 
 
 Solar Camera of M. Liebert. — M. Liebert, of France, 
 has produced an apparatus based on the same principle, but 
 he does not protect it from the wind, under the belief that, 
 the negative, the objective, and the image being connected 
 together, and the wind or the shaking of the ground making 
 all move together, the image remains motionless. This at 
 first appears very true, but such an arrangement is fatal to 
 the sharpness of the proof. For, in order that it should be 
 correct, it would be necessary that the sun itself moved in 
 the same way, whereas it remains motionless ; and therefore, 
 on the least wind or the slightest movement of the ground, 
 all the outlines of the image are seen to be doubled , by which 
 defect all fineness in the enlarged proof is lost. 
 
 To understand thoroughly this effect, it must not be for- 
 gotten that the sun is a fixed luminous point, and that if the 
 optical apparatus happens to move when its axis is directed 
 towards this point, the axis is deranged and the summit of 
 the luminous cone falls more or less on the outer part of the 
 objective instead of on its centre. There results from this a 
 displacement of the image, because the image formed by the 
 central part of the objective and that formed by its margin do 
 not coincide, and are the farther from doing so in proportion 
 as the radii of curvature of the surfaces of the lens are 
 
168 
 
 PHOTOGRAPHIC OPTICS. 
 
 shorter. (There would he no displacement of the image if 
 the radii of curvature were equal to infinity.) This displace- 
 ment of the image is not very apparent, and it is this probably 
 which has led M. Liebert into error. But it is, nevertheless, 
 easy to convince oneself of the fact if the ordinary negative be 
 replaced by one having two very fine threads stretched over 
 it and crossing each other. If the point in the enlarged 
 image where these threads cross be marked with a pencil, it 
 will be seen to be displaced (often to the extent of a milli- 
 metre) if the apparatus happen to be shaken. 
 
 This experiment can easily be made with an apparatus 
 working with a reflector. Select in the enlarged image a 
 point very sharply defined, and mark its place with the point 
 of a pencil. Disturb the position of the reflector, and you will 
 see the point displaced, only to a small extent it is true, but 
 still sufficiently to destroy all the sharpness of the image. 
 
 M. Liebert’s apparatus, as well as instruments having a 
 reflector, ought, therefore, to be protected from the wind and 
 from any movement of the ground on which it rests, or else, 
 although condenser, negative, and screen may be fixed in 
 a common box, the enlarged image will lose its sharpness. 
 It is the same also with all imaginable apparatus, and to 
 attempt to make it otherwise would be uselessly to deny a 
 mathematical truth. 
 
 Fig. 4, plate III., shows M. Liebert’s apparatus-. A rect- 
 angular box, A B, carries at its upper part the condenser, a, 
 which is of crown-glass, plano-convex or concavo-convex, and 
 of very short focal length. The frame for the negative, b , 
 moves, as in the American apparatus, between the objective, 
 c, placed at the principal focus of the condenser, and the con- 
 denser. To the box is fastened a cone, D C, at the base of 
 which the enlarged image of the negative is formed. A 
 bellows arrangement, C B, intermediate between the cone and 
 the optical part, permits of a variable length being given to 
 the apparatus, according to the size of the enlargement. This 
 adjustment is effected by the screw g. 
 
DESCRIPTION OF THE APPARATUS FOR ENLARGEMENTS. 169 
 
 The whole of the apparatus is supported on a foot, H, 
 susceptible of two movements, one in azimuth by the screw e, 
 the other vertical by the screw /. But the centre of gravity 
 of the apparatus being placed above the point of suspension 
 causes very great instability, so that the least wind makes the 
 solar camera oscillate about its centre of suspension. To 
 avoid this, it would have been necessary to adopt the plan 
 used in heavy astronomical telescopes, namely, to suspend the 
 apparatus from a point above its centre of gravity, between 
 two uprights, as represented in fig. 5, plate III. Then the 
 equilibrium would have been stable, according to the rules 
 laid down in mechanics. The base, LM, of the apparatus 
 should have been very heavy and of large diameter, as shown 
 in our figure. The two movements, the one in azimuth and 
 the other vertical, are effected by the handles N and 0. 
 
 Lastly, the greatest fault of this apparatus lies in the short 
 length which is obliged to be given to it to render it manage- 
 able, and which can only be effected by giving a very short 
 focal length to both the condenser and the objective. The 
 condenser no longer gives a cone of solar rays terminated at 
 its summit by a well-defined image of the sun, because of 
 the considerable spherical and chromatic aberrations. The 
 objective which has a small diameter does not include a 
 sufficient angle ; its margins are covered by some of the solar 
 rays coming from the condenser. This produces the phe- 
 nomena of diffraction, which have the effect of doubling all 
 the sharply defined outlines of the image — an effect which we 
 shall examine more in detail afterwards. 
 
 On the other hand, the apparatus arranged on this system 
 works easily in winter, and does not require a special method 
 offsetting up ; a point of some advantage in large towns. 
 
 We may add that, carrying the most rigid economy into 
 the construction of this apparatus, its inventor has been able 
 to render the price accessible to photographers on a small 
 scale, which aids in spreading the taste for enlargements. 
 
170 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTER III. 
 
 THEORY OF THE FORMATION OF THE ENLARGED IMAGE IN 
 woodward’s APPARATUS. 
 
 Much discussion took place in 1860 and 1861 at the meet- 
 ings of the French Society of Photography, relative to the 
 theory of Woodward’s apparatus and on the imperfections 
 possessed by it. 
 
 We shall now analyse the principal points of this discussion, 
 which we extract from the Bulletin de la Societe Frangaise de 
 Photograjphie. 
 
 Theory of M. Claudet. — -According to M. Claude t (Bull. 
 Soc. Frang . de Phot ., 1860, pp. 249, et seg .), who first brought 
 forward this theory, the solar camera realises the following 
 conditions : 
 
 1st. The objective acts, in enlarging the negative, by its 
 central part, as determined by the diameter of the solar 
 image formed at the focus of the condenser. The image of 
 the sun being nearly a point at the focus of the condenser 
 (and exactly so if the condenser be no more than 8 inches 
 in diameter), it follows that the enlarging objective is, 
 through this fact, reduced to a very small fraction of its 
 aperture. 
 
 2nd. All the light proceeding from the Condenser which 
 traverses the negative and then the objective is useful for 
 imprinting the enlarged image of the negative projected on 
 a surface sensitive to light. 
 
 3rd. The objective acts, in enlarging the image, according 
 to the law of conjugate foci. 
 
woodward’s apparatus. 
 
 171 
 
 Observations of M. Bertsch. — M. Bertsch contends that 
 the system of illumination by means of convergent light 
 cannot give sharp images in the enlarged proof. Let ns 
 examine the value of his arguments. 
 
 In the first place, M. Bertsch says (Bull. Soc. Franp. Phot., 
 1860, pp. 63, et seq.), the non-achromatic lens of large diameter 
 employed as condenser does not give a cone of light of which 
 any section whatever — that, for example, where the negative 
 for enlargement is — represents a circle equally illuminated. 
 This circle is formed by concentric rings composed of rays 
 of unequal refrangibility, the red only being visible at the 
 circumference. Now, these differently coloured rings being 
 unequally refrangible by the objective, the image, though 
 sharp on the negative, cannot be so on the enlarged screen. 
 
 This observation is true, and it would be necessary, in order 
 to avoid the defect pointed out by M. Bertsch, to employ an 
 achromatic condensing lens. However, a more profound 
 examination of M. Bertsch’s observation proves that the 
 section of the cone of light where the negative is, may, in 
 reality, be considered (except the edges) as a circle of 
 white light, for, if it seem otherwise to the eye, it is not 
 so for photographic substances which are only sensitive to the 
 blue and indigo rays. The most incontestable proof which 
 could be furnished of this fact consists in effecting the en- 
 largement of a network formed of very fine lines traced on a 
 plate of glass, with an ordinary solar camera, in the first place, 
 and then with it when achromatised by means of a blue 
 solution of ammoniacal chloride of copper, as we have pointed 
 out at page 7 7. The image of the network in the first case, 
 and that in the second, although unequally sharp in appear- 
 ance, are equally so in reality on the enlarged proofs. 
 
 This experiment, which the author of this work has made 
 many times before competent persons, proves on the best 
 evidence that it is not necessary to achromatise the condenser 
 of the solar camera, because the enlarged image has not to 
 be sharp on the screen, but only on the photographic proof. 
 
172 
 
 PHOTOGRAPHIC OPTICS. 
 
 The second observation of M. Bertsch is not, it seems to ns, 
 better founded. We shall let him speak for himself : — “ Not 
 to complicate the question, and to confine ourselves within 
 the practical limits of superficial enlargements of five or six 
 times, we shall admit that the convergent rays which emerge 
 from the collecting lens are of white light. On examining 
 these rays after having interposed in their path a plate of 
 glass with parallel sides, we perceive that the caustic curves 
 which limit the focus stretch out very far, and that at the 
 same time the field of light changes in aspect. We have 
 before us a phenomenon of interference. From the centre, 
 where the refraction is nothing, to the circumference, where 
 it is at its maximum, the pencils fall on the glass with 
 very different incidences, so that on their emergence the 
 ratio of their sine of refraction to that of their incidence is 
 changed. They now move less nearly pjarallel and intei> 
 fere with each other before reaching the focus. The final 
 result is a fresh disturbance of the equality of the illumi- 
 nation, which is further complicated by the circumstance 
 that the glass which bears the negative never has parallel 
 faces. 
 
 “ It is sufficient to substitute a microscopic object for the 
 transparent glass, to observe the effect of this new cause of 
 disturbance. 
 
 “ Blurs of diffraction will form on all the outlines ; the 
 details will be vague, and the lines spread out, thickened, and 
 multiplied.” 
 
 We make avowal, with all humility, of never having our- 
 selves perceived that, on placing a sheet of glass with parallel 
 surfaces in the course of a luminous cone, a phenomenon of 
 interference was produced, the result of which was the pro- 
 duction of double lines in the outlines of the enlarged image. 
 In the Newtonian telescope — a form of instrument still very 
 common — a concave mirror throws a cone of convergent 
 luminous rays on a prism: now, this prism is evidently a 
 plate of glass not having parallel surfaces, so that there should 
 
woodward’s apparatus. 
 
 173 
 
 be a production of interferences in the image, and conse- 
 quently imperfection in its sharpness. We think no astronomer 
 or optician has ever suspected or perceived it. 
 
 We have many a time made the experiment of substituting 
 for the network formed of very fine lines drawn with a 
 diamond on a sheet of glass, a network formed of fine platinum 
 wires stretched across a frame ; but never, when employing 
 comparatively these two networks in the solar camera, have 
 we perceived the disturbance which, according to M. Bertsch , 
 the interposition of the plate of glass ought to have produced 
 in the enlarged image of the lines. 
 
 We have certainly observed the multiple lines which occur 
 about the sharply terminated outlines of the enlarged image, 
 but we shall show, further on, under what circumstances they 
 occur. 
 
 To obviate the defects of Woodward’s solar camera, which 
 we have just pointed out, M. Bertsch substitutes {Bull. Soc. Frang. 
 Phot., 1860, p. 67), for Woodward’s single condenser, two 
 lenses of the same kind of glass, the first, o. (fig. 7 6), convergent, 
 the second, B, divergent, 
 and placed at such a dis- 
 tance from the first that 
 the solar rays emerge 
 from the system in the 
 direction or', parallel to 
 each other and to the 
 principal axis. In this 
 way M. Bertsch says the solar rays will fall normally on the 
 negative to be enlarged, and, therefore, there will no longer 
 be any blurs of diffraction. 
 
 That such a system gives a cylinder of rays very nearly 
 parallel is correct, but a section of this cylinder is a circle 
 much more heterogeneous and unequal, as a field of illumi- 
 nation, than that taken in the cone emerging from a single 
 convergent lens. For the chromatic aberration is in this case 
 much more considerable than in the system of Woodward. 
 
174 
 
 PHOTOGRAPHIC OPTICS. 
 
 We believe that M. Bertschh as not sent out apparatus with two 
 lenses (at least we have never met with one), and we know 
 that he has replaced this double condenser by the simple 
 rays of the sun, which illuminate the negative normally to its 
 surface. In these conditions the illumination is evidently 
 perfect, but insufficient as regards intensity; a question which 
 we shall examine, however, when treating of M. Bertsch’s 
 apparatus used with parallel light. 
 
 M. A. Thouret’s Observations. — ( Bull Soc. Frang . Phot., 
 1860, p. 285). Without wishing to examine the influence of 
 the non-achromatism of the condenser, and of the passage 
 of this convergent light, pc and pc (fig. 77), through the 
 
 p cp , of solar rays proceeding from the condenser. For, says 
 M. Thouret, any point, a , of this negative also sends a cone 
 of rays, LaM, to the whole surface of the lens LM; there- 
 fore, the lens, in enlarging this point, acts in two ways; 
 firstly, by the solar ray which traverses it, and, secondly, by 
 the rays emitted by this point. 
 
 To this M. Claudet replies {Bull. Soc. Frang. Phot., 1861, 
 p. 7), that the argument would have weight if the negative 
 arrested the solar light. But it is very transparent, there- 
 fore the relation between the light transmitted and that emitted 
 is such that the latter has no influence (through want of 
 intensity) on the sharpness of the image, and, therefore, that 
 the enlarging lens, L M, may be considered as acting by its 
 centre only. Experience, as we shall presently show, proves 
 that M. Claudet was right. 
 
 Theory of M. Foucault. — These are, in the main, the 
 
 Fig. 77. 
 
 negative, N o , this author 
 contends that the enlarged 
 image of the negative will 
 be wanting in sharpness, 
 because the enlarging lens 
 is not limited to its central 
 part, as determined by the 
 summit, c, of the cone, 
 
woodward’s apparatus. 
 
 175 
 
 principal observations made on tbe solar camera. It is clear, 
 beyond doubt, that the true place of the enlarging lens was 
 that of the summit of the cone of convergent rays. When 
 the discussion (which lasted several months) was terminated, 
 M. Foucault, the distinguished physicist, spoke in his turn, 
 and gave a clear and plain account of the theory of the solar 
 camera, with which we ourselves fully agree (Bull. Soc. Frang . 
 Phot., 1861, pp. 14-16). 
 
 “After attentively listening to the explanations advanced 
 by M. Anthony Thouret, I think I noticed that the discussion 
 entirely rested on a confusion of words. 
 
 “ The small image which, in Woodward’s apparatus, it is 
 requisite to cause to fall on the enlarging lens, has never 
 been taken, as M. Thouret supposes, for an image of the 
 negative to be reproduced ; it is a real image of the sun, 
 formed by the union of all the rays received by the condenser. 
 This condition being satisfied, it is right to maintain that the 
 enlarging lens acts as if it were stopped down to the diameter 
 of the solar image. 
 
 “In fact, let the condenser be C (fig. 12, pi. I.), the 
 enlarging lens L, and the screen E, placed at a distance cor- 
 responding to the conjugate focus of the plane N, where the 
 negative is to be placed. In the apparatus thus arranged, 
 and with the negative absent, it is evident that the whole of 
 the light spread over the screen is composed of the same rays, 
 which, at the position of the enlarging lens, are grouped so 
 as to form an image of the sun. This image, therefore, con- 
 tains in its small extent all the light which, farther on, is 
 spread over the surface of the screen. It follows from this 
 that the entire zone of the enlarging glass which exceeds the 
 solar image could be covered up by a diaphragm, without 
 in any way altering the effect, and without cutting off a 
 single ray. 
 
 “Now let a negative be placed in the plane N ; the glass 
 which supports it having faces sensibly parallel, the general 
 course of the rays will not be changed; the solar image will 
 
176 
 
 PHOTOGRAPHIC OPTICS. 
 
 continue to be formed on the enlarging lens; but many of 
 tbe rays, in their passage through the different points of the 
 negative, will undergo a partial and varied extinction, the 
 effect of which will be reproduced at points similarly disposed 
 on the screen. It is in this way that an enlarged image of the 
 negative is formed solely by the partial and local extinctions 
 that it causes, without in any way modifying the geometrical 
 path of the persistent rays. 
 
 “ There is, therefore, good reason for asserting that, in the 
 formation of the enlarged image, the region only of the objec- 
 tive occupied by the solar image has any effective influence, 
 that the external zone gives passage to but an insignificant 
 proportion of diffused rays, and that, consequently, the lens 
 cannot by spherical aberration give a wrong direction to the 
 useful rays. 
 
 “ If it be said that, to obtain the best results, it is indispen- 
 sable to receive the focus of the condenser on the enlarging 
 lens, it is another question altogether. All that is to be 
 concluded from the preceding explanations is, that everywhere 
 where the bundle of illuminating rays forms itself into an 
 image of the source of light, it may be considered as passing 
 through a diaphragm of the same form and the same extent 
 as this image. From this simple consideration it is easy to 
 foresee the part reserved to the various portions of the en- 
 larging lens, according as the solar image is formed at the 
 position of the optical centre, before it or behind it. 
 
 “ By making the focus of the solar rays fall on the enlarging 
 lens, it results that only one and the same portion of this lens 
 is affected in the formation of the entire image of the negative, 
 which is not in general a condition favourable to equality of 
 effect.* Under 'pretext of avoiding spherical aberration , the more 
 serious inconvenience is fallen into , which consists in a diminution 
 of the field of good definition. This is a fault inherent in the 
 arrangement claimed by Mr. Woodward, and which does not 
 
 * See pnge 89 and fig. 48. 
 
woodward’s apparatus. 
 
 177 
 
 allow of its being considered as a complete solution of the 
 problem of optical enlargement. 
 
 “ It would be preferable, in my opinion, to make tbe solar 
 image, I (fig. 11, pi. I.), fall beyond tbe enlarging lens, L, on 
 tbe condition of giving to it tbe form of a meniscus, of 
 w r hich tbe concavity is turned towards tbe solar focus. There 
 would thus be obtained a system which would act in the 
 opposite way to tbe old form of camera of Wollaston, adopted 
 by Daguerre. 
 
 “ This arrangement, based on tbe employment of a single 
 glass, ought, even now, to give tolerably good results ; but 
 new resources would still be found in tbe employment of 
 combined glasses.” 
 
 This preliminary examination having been made, the reader 
 will have formed some idea of the theory of the formation of 
 the image in Woodward’s apparatus ; and we shall now, in 
 our turn, examine the theory, and point out its principal 
 defects. 
 
 CHAPTEE IV. 
 
 IMPERFECTIONS OF WOODWARD’S APPARATUS. 
 
 Blurs of Diffraction produced by the Circle of Aber- 
 ration of the Condenser. — When the condenser of the Ame- 
 rican apparatus has only a small diameter (for example, one of 
 8 inches) and a rather great focal length (three or four times 
 its diameter, for example), it may then be considered as true 
 that all solar rays emerging from the lens converge towards 
 
178 
 
 PHOTOGRAPHIC OPTICS. 
 
 a single point, and that there is formed at its focus a sharp 
 image of the sun. If, now, the angle (fig. 78) included by the 
 enlarging objective, M,* is greater than the angle, 0, of 
 
 the cone of solar 
 rays, the whole 
 of the rays strik- 
 ing the conden- 
 ser are nowhere 
 arrested in their 
 course, and the 
 enlargement of 
 the photogra- 
 phic negative is 
 made with an 
 admirable sharpness. But in all solar cameras actually made 
 this condition is not fulfilled, the objective not including a 
 sufficient angle ;j* and this causes, in the enlarged image, 
 blurs of diffraction, which are particularly observed when an 
 enlarged image is imprinted on paper sensitive to light: 
 multiple lines are seen to be formed around all the sharply 
 marked outlines of the negative, the trace of which is re- 
 cognised in the finished proof. 
 
 Many persons attribute the doubled outlines of the image 
 to a vibration of the ground by a passing carriage, or else to 
 a displacement of the cone of solar lays, resulting from the 
 imperfection with which the rays of the sun reflected into 
 the apparatus are kept in a constant direction. Such, how- 
 ever, is not the fact ; for if it were one of the parts of the 
 apparatus which became deranged — the negative, for example, 
 or the frame which holds the sensitised paper — the multiple 
 lines ought evidently to affect all the outlines in a direction 
 
 * We are supposing here the case in which a double objective is used as 
 the enlarging lens, the single objective giving, for this purpose, not nearly 
 such satisfactory results. 
 
 f The two lenses forming the objective being too distant from each 
 other. 
 
 Fig. 78. 
 
IMPERFECTIONS OF WOODWARD’S APPARATUS. 179 
 
 contrary to the displacement. Now, generally, towards the 
 centre of the image the blurs of diffraction are not perceived ; 
 it is especially towards the margins that they are produced. 
 
 As to the second hypothesis : when excessive care is taken 
 in managing the reflecting mirror, and even when this is 
 replaced by a heliostat, set and constructed with the greatest 
 precision, blurs of diffraction are produced, and therefore this 
 is not their cause. 
 
 With any solar camera whatever, it is easy to produce, at 
 will , blurs of diffraction in the following manner. Place 
 before the enlarging objective, and nearly in contact with its 
 surface (which faces the negative to be enlarged) , a diaphragm, 
 the aperture of which is a little too small to allow the solar 
 rays emanating from the condensing lens to pass. The enlarged 
 image of the negative appears very sharp upon the screen, 
 but if we proceed to print this image, in a few moments we 
 observe blurs of diffraction produced — particularly if the 
 negative presents well-defined lines — around which multiple 
 lines are formed, which destroy all the sharpness of the 
 outlines of these parts of the proof. By making a negative of 
 the black characters of a book and enlarging them, these blurs 
 of diffraction may be particularly well observed. 
 
 The blurs of diffraction will also be observed, and the 
 enlarged image of a negative, PQ (fig. 78), with minute 
 details, will not be sharply defined, if the margins, r r, of the 
 cone, L 0 I/, of solar rays fall on the brass ring which forms 
 the mounting of the objective, M. It is known that if solar 
 ra}^s fall on a convergent lens in the direction of its axis, they 
 will all converge towards the focus, o ; that a section of this 
 cone, P Q, is a white circle bounded by a red circumference, 
 which is due to the non-achromatism of the lens, L. If these 
 red rays do not pass freely through the enlarging objective, 
 but fall on the mounting, as represented in the figure, though 
 these rays may be quite useless for impressing the image, and 
 though the enlarged image may be very sharp to the eye, 
 still there will be produced, during the printing of the image, 
 
 n 2 
 
180 
 
 PHOTOGRAPHIC OPTICS, 
 
 double lines round its sharply marked outlines. This expe^ 
 riment we have made hundreds of times in the open country, 
 on very firm ground, far from all roads and all disturbances, 
 with the solar rays reflected by a heliostat of extraordinary 
 precision, obtained from the celebrated house of Ertel and Son 
 of Munich, and set with special care. These blurs are not 
 produced at all in the circumstances which we have previously 
 enumerated, and of which we are about to treat more fully. 
 
 With the primitive apparatus of Woodward, the plano- 
 convex condenser of which is no more than 8 inches in 
 diameter, the blurs of diffraction are not found to appear, 
 and what is most extraordinary is that they only appear when, 
 in order to operate more quickly, the diameter of the condenser 
 is increased, the magnifying objective remaining the same. 
 We worked in 1861 with a condenser of 6 inches in diameter, 
 but it required several hours to produce, on chloride-of-silver 
 paper, enlargements of 40 centimetres by 50. In 1862 we 
 applied to M. Sautter, engineer and director of the manufacture 
 of instruments for French lighthouses, who made for us, for 
 our experiments, two convergent lenses, of 13 and of 20 
 inches diameter, with a focal length two-and-a-half times this 
 diameter. It was a surprising fact, that these two lenses,' 
 employed with the same negative and the same magnifying 
 objective, never gave enlarged proofs nearly so sharp as 
 the small primitive apparatus, the condenser of which was 
 only 6 inches in diameter. Our first idea was to achromatise 
 these lenses by the interposition of a vessel containing a solu- 
 tion of ammoniacal chloride of copper between the reflecting 
 mirror and the condenser, which arrests the red, yellow, and 
 orange rays ; but the results were not changed. 
 
 These experiments were repeated a great number of times, 
 and gave us, before long, evident proof that large condensers 
 should never have been employed for solar cameras, and that 
 it was not by any means their achromatic defect which was 
 the cause of the want of sharpness (the doubled lines) which 
 they produced in the enlarged image. 
 
IMPERFECTIONS OF WOODWARD’S APPARATUS. 181 
 
 A visit to MM. Ghemar Brothers, in 1864, in their magnifi- 
 cent studio for enlarging, in the Chaussee de Charleroi, 
 Brussels, furnished us with a new proof of the correctness of 
 our observations. These gentlemen possessed two of M. 
 Wothly’s apparatus, one of which had a condenser of 9 inches, 
 and the other a condenser of 24 inches diameter. Relatively 
 to the surface of the condenser, the first was much more rapid 
 than the second, but often gave rise to blurs of diffraction from 
 which the second was free. An attentive examination caused 
 us to see that the first apparatus (the condenser of which was 
 9 inches) sent its entire cone of emergent rays to the objective, 
 and as its focal length was very short , the red margins of the 
 cone impinged, as represented in fig. 78, against the edges of 
 the mounting of the objective, which was the ordinary por- 
 trait combination. 
 
 In the other, the negative holder, P Q (fig. 79), was per- 
 forated by an aperture very nearly 18 
 centimetres square, and the cone, L / 
 
 L', of solar rays was thus reduced to 
 only a part, o f o', of its section. In 
 other words, the edges of this negative- 
 holder greatly lessened the extent of 
 the condenser. This caused the appa- 
 ratus to have little power, but it also 
 caused the absence of blurs of diffrac- 
 tion, since the emergent cone of solar rays now passed freely 
 through the enlarging objective. 
 
 An attentive examination of most enlarging apparatus 
 constructed in Prance, as well as in Germany and elsewhere, 
 soon led us to perceive that the enlarging objective generally 
 had too great a focal length, and such that the negative was 
 too near the condenser, arresting (as represented in fig. 79) 
 a part of the solar rays sent out by the latter ; hence the 
 little power of all these apparatus, which required and which 
 still require several hours for printing, on chloride-of-silver 
 paper, a proof 55 centimetres high by 45 broad. 
 
182 PHOTOGRAPHIC OPTICS. 
 
 If, on the contrary, the whole surface, L / L' (fig. 79), of 
 the condenser is ntilised, by giving to the enlarging objective 
 a shorter focal length, and such that the negative is placed in 
 the cone of convergent rays, so that the red which bounds 
 it falls on the margins of the objective, then the blurs of 
 diffraction appear during the printing ©f the proof, parti- 
 cularly if this be of large size ; a result due to the fact that the 
 margins of the cone do not freely traverse the objective. The 
 proofs are then deficient in the sharply defined outlines which 
 constitute the beauty of a proof, particularly of a view, and 
 these proofs most frequently require much touching up. 
 
 From what precedes, every intelligent reader will under- 
 stand that which we ourselves have comprehended, namely, 
 that it was necessary to give up in the condenser a short focal 
 length, and to give to it, L L' (fig. 80), a very considerable 
 
 Fig. 80. 
 
 one, L M, at least five or six times its diameter, if this dia- 
 meter be more than 14 inches. But then the objective, M, 
 ought also to have a great focal length itself; for the negative, 
 P, must be very far away from it, if its whole surface is to be 
 illuminated. The enlarged image must then be projected a 
 distance of several metres, and, in employing under such con- 
 ditions a condenser 19 inches in diameter, the camera that 
 would be necessary for a proof one metre square would be 
 12 metres long. It will be seen, therefore, that this system, 
 which, on the whole, would be the best in all respects, cannot 
 be employed in the conditions under which most photo- 
 graphers are placed. 
 
 In order to avoid this inconvenient length, we had made, 
 towards the end of 1863, some negative lenses, N N' (fig. 81), 
 
IMPERFECTIONS OF WOODWARD’S APPARATUS. 183 
 
 which, placed in the path of the cone, L / L\ of solar rays 
 emanating from the condenser, L L', increased the focal length 
 
 Fig. 81. 
 
 from/ to /'. The objective, M,* had a great diameter, oo, in 
 relation to its focal length, and such that it conld be brought 
 near the negative, P Q, so as to throw the image to a shorter 
 distance. This apparatus, however, did not produce a good 
 result. An attentive examination led us to see that the 
 spherical aberration (and not the chromatic) of the system 
 L L', NF, was very considerable, and that it was impossible 
 to accurately limit the bundle, a, of emergent rays, by a 
 diaphragm, D, even by achromatising the system by a vessel 
 of ammoniacal chloride of copper. It was at this period that 
 we had systems of condensers made completely free from this 
 aberration, which have ever since given us proofs of remark- 
 able sharpness. 
 
 The cause of the doubled lines in the solar camera with one 
 condenser, appears therefore to us to be due to the great 
 spherical aberration of these condensers. When, in fact, 
 it is considered that these lenses of plano-convex form 
 are 30 and 36 inches in diameter, and that their focal length 
 is generally less than twice their diameter, and often only 
 once and a half their diameter, an exact idea can easily be 
 formed of the great value of the circle of aberration, the dia- 
 meter of which increases with, the cube of the aperture (see 
 
 * The objective had the form of Kamsden’s eye-pieces in telescopes of 
 large field called comet-finders. 
 
184 
 
 PHOTOGRAPHIC OPTICS. 
 
 p. 66). What follows from this, even on artificially achroma- 
 tising such a condenser (whether we suppose it so or inter- 
 pose a vessel of ammoniacal chloride of copper)? That 
 the enlarging objective, even when we give it a considerable 
 diameter, always arrests a certain part of the rays emergent 
 from the condenser, particularly those which emerge from the 
 margin, on account of the large diameter of the circle of 
 aberration ; and even should the objective be placed where 
 the circle of aberration is the least — a condition which can 
 hardly be realized in practice — still this phenomenon would 
 be produced. 
 
 On the contrary, with a condenser free from spherical aberra- 
 tion (through the addition of a divergent lens of suitable curva- 
 tures), these blurs of diffraction are no longer produced, the rays 
 emergent from the condenser all now cutting the axis at the 
 same point, and thus passing freely through the enlarging 
 objective without being arrested by the sides of its mounting. 
 
 The principal defect of the solar camera, as first constructed 
 by its inventor, arises, therefore, not from its want of achroma- 
 tism, but from this rather, that, if we suppose incident rays 
 of one order only — those which affect chloride-of-silver paper, 
 namely the blue and the violet — they cut the axis at different 
 points, and thus there is produced at the focus of the con- 
 denser an image of the sun surrounded by a round aureola, 
 the diameter of which increases as the focal length of the 
 condenser is shortened. 
 
 We can conceive (but not execute in practice) a single 
 enlarging objective (achromatic, however, otherwise it would 
 have a chemical focus) which would include all the rays 
 emergent from the condenser, designed by M. Leon Foucault, 
 as represented in fig. 11, pi. I. But up to the present time 
 single objectives, as enlarging lenses, have not given good 
 results. Generally the field of the enlarged image is curved 
 — that is, it is deficient in sharpness at the edges — and 
 further, the distortion of the image is the greater, according as 
 these objectives have a shorter focal length. 
 
IMPERFECTIONS OF WOODWARD’S APPARATUS. 185 
 
 As for the doublet-system of Petzval * (the ordinary double 
 objective), tbe angle included by it being greater, and its field 
 flatter, it gives, when employed in tbe solar camera, better 
 results than tbe single objective. But if it be placed in tbe 
 axis of a condenser, of which tbe circle of spherical aberra- 
 tion is considerable, even if tbe first, N (fig. 78), of the two 
 lenses (that facing tbe negative) should include all tbe rays 
 emergent from tbe condenser, these rays would only in part 
 strike tbe second lens, o. Tbe experiment is very easily 
 made, and then on tbe centre of tbe first lens of the doublet, 
 tbe circle of light will be seen surrounded by red ; and 
 on tbe second, which faces tbe screen, tbe image of the 
 
 Fig. 82. 
 
 sun surrounded by blue — of which a part (that emerging 
 from the margins of the condenser) is arrested by the* mounting 
 of tbe objective. And therefore this objective, particularly 
 when modified as we have described it further on, only gives 
 satisfactory results on tbe condition of being associated with 
 a condenser of which tbe circle of aberration is of slight 
 diameter. 
 
 To thoroughly understand how it is that the form of the 
 objective cannot be made to bend to necessity, it must not be 
 
 * The triplet of Dallmeyer, and still more the globe-lens, is inferior for 
 this purpose. 
 
186 
 
 PHOTOGRAPHIC OPTICS. 
 
 forgotten that the best size for the negative being given, there 
 exists between the distance from the negative, P Q, to the 
 optical centre, C, of the enlarging objective, and the distance 
 from this point?, C, to the screen, N M, on which the enlarged 
 image of the negative is projected, a fixed relation (that of 
 the conjugate foci) which thus determines the enlargement, 
 that is, the ratio of the size of the negative to that of its 
 enlarged image — of P Q to N M. 
 
 Illuminating this negative, P Q, by diffused light, or by 
 convergent solar light, the distances from P Q to C, and from 
 N M to C, remain invariable. Now, if it is wished to illumi- 
 nate the negative, P Q, by convergent light by means of con- 
 densers, L, L' or L", the focal lengths of these condensers must 
 be such that the angle of the cone P C Q remains always 
 exactly the same, whatever may be the diameter of the con- 
 denser. 
 
 It will consequently be seen that with a small condenser, 
 L", or a very large one, L, the results ought to be identical as 
 to sharpness, and in the ratio of L 2 to L ' 2 as to rapidity. 
 But if L" has a small diameter, its circle of aberration will be 
 small and may therefore be less in diameter than the en- 
 larging objective, C ; if it is considerable, its circle of aber- 
 ration, which increases as the cube of its aperture, becomes 
 greater in diameter than the objective ; and hence blurs of 
 diffraction are produced. 
 
 It would, therefore, be necessary to enlarge the diameter of 
 the amplifying objective, C, whilst preserving its focal length, 
 P C, and this in proportion as the condenser becomes larger. 
 Now, every one knows that this is not practicable, and that 
 there exists between the diameter of an objective and its 
 focal length a relation learnt by calculation and experience 
 which the optician must perforce observe. 
 
 If it is impossible to make enlarging objectives for large 
 condensers with short focal lengths, it is, on the other hand, 
 possible to make large condensers, the emergent ra}^s from 
 which are jp radically and really all in the condition required by 
 
IMPERFECTIONS OF WOODWARD’S APPARATUS. 187 
 
 figure 82. It is sufficient for this to destroy their circle of 
 spherical aberration by destroying this aberration itself. Then, 
 the size of the negative remaining fixed, the objective which 
 enlarges it remains also fixed, whatever may be the diameter 
 of the condenser. 
 
 Imperfections of the Objective. — The observation 
 pointed out by M. Thouret, and of which we have spoken at 
 p. 174, though refuted by M. Claudet, is not the less true in 
 practice. The negative, if it is very transparent, certainly 
 allows nearly ail the solar light falling on it pass through. 
 But very often the negative is less transparent than it 
 ought to be, and the sun, through the interposition of slight 
 clouds, often gives, particularly in our climates, less light than 
 usual. Thus a given point in the negative is reproduced by 
 the objective in two ways — firstly, by the solar light which 
 traverses it ; and secondly, by that which it gives out. The 
 more intense the negative, and the weaker the light of the 
 sun, the more this is true. In the first case, the objective acts 
 by one point of its surface, and in the second by all its sur- 
 face, and these two images are neither concordant, nor equally 
 sharp, particularly at the margins of the image. 
 
 Any one who possesses an ordinary solar camera can easily 
 satisfy himself of this. Focus on the screen a very sharp 
 negative. You will remark that if a cloud veils the sun the 
 margins of the image want sharpness (which sharpness in- 
 creases by diaphragming the enlarging objective), and that, 
 according as the sun gets clear of clouds, the sharpness at the 
 margins considerably increases and remains the same with 
 or without diaphragms on the enlarging objective. On 
 placing a ground-glass between the condenser and the negative 
 the image loses in sharpness at its margins ; on withdrawing 
 the ground-glass, the image not only becomes brighter, but 
 much sharper. 
 
 This demonstrates that the objective (we speak here of the 
 ordinary double lens) does not act in the solar camera as usual. 
 For in the solar camera each point of the negative to be 
 
188 
 
 PHOTOGRAPHIC OPTICS. 
 
 enlarged may be considered as traversed by a single pencil of 
 solar light; therefore an infinitely small fraction of the 
 enlarging objective forms the image of this point on the screen. 
 Ordinarily a point of the plane to be reproduced sends to 
 the objective a bundle of light, of which the entire aperture 
 of the objective is the base and the point the summit: con- 
 sequently it is the entire objective, or at least the part of 
 its surface that the diaphragm does not cover from the point, 
 which forms the image of that point. The two cases are very 
 different, and therefore an objective, although excellent as 
 the enlarging objective of a solar camera, may be of no value 
 as an ordinary objective, and conversely. # 
 
 The necessity that exists for leaving the objective with a dia- 
 meter as large as possible, in order to give passage to all the 
 rays emerging from the margins and from the centre of the 
 condenser, has, as M. Bertsch and M. Thouret have very 
 properly observed, the effect of fogging the proof, because the 
 rays emitted by the points of the sky, bordering on the sun, 
 pass through the objective like the solar rays themselves. 
 Experience has taught us that in the ordinary solar camera 
 this defect is of very little importance in very clear weather, 
 when the sun shines with his full brightness, and the negative 
 to be enlarged is very transparent. But if the sky is cloudy, 
 if the sun is veiled by light clouds, or if the negative is a 
 little too intense, the whites of the enlarged image are 
 always discoloured by the diffused light thrown out by the 
 objective. If the objective be diaphragmed, diffraction is 
 produced, which destroys the sharpness of the image (that 
 is, with the ordinary systems of condensers). 
 
 This is why, in the construction of the solar camera, we 
 have abandoned the form of the double lens and adopted another 
 (based, however, on the data of M. Petzval) of which M (fig. 
 78, p. 178) is an accurate representation. 
 
 This objective has a form such that the image of the nega- 
 
 * This is why the triplet, the orthoscope, the globe-lens, &c., are all very 
 inferior to Petzval' s combination, even with equality of aperture. 
 
IMPERFECTIONS OF WOODWARD^ APPARATUS. 189 
 
 tive is equally sharp, whether illumined by solar or diffused 
 light. Further, to avoid the diffused light of which we 
 were just now speaking, and which has the effect of fogging 
 the enlarged image, the lens, o, facing the screen, is just large 
 enough to let the image of the sun pass, and intercepts all 
 light coming from the points of the sky bordering on this body. 
 
 Suspension of the Negative. — The third imperfection of 
 Woodward’s solar camera consisted in the way in which the 
 negative was placed in the cone of solar rays. Jt was fixed in 
 a square or rectangular frame, and was traversed by the rays 
 of the sun, which heated it in proportion to the density of the 
 negative. The margins of the negative remaining cold (for 
 most often only the central part of the negative was traversed 
 by the solar rays), it became unequally expanded, and frac- 
 tured in consequence. 
 
 This imperfection, like the two others, was of little import- 
 ance in the original American solar camera, the condenser 
 of which was only eight inches in diameter, and in which, 
 therefore, the heating of the negative was not considerable. 
 But it was otherwise when large lenses came into use ; and 
 nine out of ten negatives broke when the condenser had a 
 diameter of from 19 to 24 inches. M. Delessert, who had a 
 solar camera of which the condenser, 80 centimetres in diameter, 
 broke all the negatives, w T as obliged to keep them cool by 
 directing on them a strong current of air produced by a ven- 
 tilator. M. Yerbecke, of Louvain, without knowing the 
 remedy of M. Delessert, found it out for himself, and also 
 employed it ; but he made use of organ-bellows instead of a 
 ventilator. 
 
 By suspending the negative so that it is heated equally all 
 over its surface, this inconvenience is avoided. We shall de- 
 scribe this mode of suspension in the following chapter. 
 
190 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTEE V. 
 
 THE DYALITIC APPARATUS.* 
 
 Differences between it and the ordinary Solar Ca- 
 mera. — The dyalitic apparatus — a name which we have given 
 it because of its analogy in form with the dyalitic telescope-— 
 differs from Woodward’s solar camera in the three following 
 points : — 
 
 1st. The condenser is corrected for spherical aberration, so 
 that, taking only one order of incident rays into consideration, 
 all the rays emerging from the condenser cut the axis at the 
 same point : this prevents the blurs of diffraction. 
 
 2 ndly. The negative is suspended in the apparatus in such a 
 way that it no longer breaks under the heat of the solar rays. 
 
 3 rdly. The objective has a peculiar form, better suited for 
 enlargement than that of the single or the double com- 
 bination, the enlarged image being sharper and free from 
 mistiness. 
 
 Summary description of the Dyalitic Apparatus. — 
 The adjustable mirror (figs. 1, 2, 5, pi. II.) is composed of a 
 finely polished and perfectly silvered glass, supported by a 
 framework of iron or wood, which prevents it bending. This 
 glass is a little larger than the diameter of the condenser, and 
 two-and-a-half times as long. The axis which supports it 
 passes through its reflecting plane perpendicularly to its 
 length in such a way as to render its equilibrium stable. The 
 glass can take all imaginable positions about this axis by 
 means of a toothed wheel fixed on its axis of rotation, this 
 
 * Vide tome X. du Bull. Soc. Fr. de Phot. — ‘ Mdmoire sur un nouvel 
 appareil dyalitique pour agrandissements photographiques.' 
 
THE DYALITIC APPARATUS. 
 
 191 
 
 wheel being governed by an endless screw, the rod of which 
 passes into the dark room in which is the optical apparatus. 
 The axis which supports the mirror turns between two hori- 
 zontal arms attached to a disc revolving in a vertical plane, 
 and also receiving its motion from inside. The mirror can 
 therefore take, in relation to the sun, all the positions neces- 
 sary for sending his reflected rays horizontally into the optical 
 apparatus. 
 
 The reflector is fixed in the shutter of a room, suitably 
 darkened, in front of the solar camera. 
 
 The optical apparatus (fig. 4, pi. II.) is composed of a box, 
 on the front of which is fixed the condenser, the diameter of 
 which is 19, 14, or 8 inches, according to the power it is 
 wished to have. This condenser is bi-convex ; the face turned 
 inwards being nearly plane, and that turned outwards very 
 convex. Its curvatures are such as to reduce its spherical 
 aberration to the minimum. At a distance from this lens, 
 equal to its diameter, is a concavo-convex lens, the con- 
 cave side of which faces the condenser. The diameter of 
 this negative lens is a little more than half that of the con- 
 denser; its thickness is very slight— only 6 or 8 millimetres— 
 in order to absorb as little light as possible. The effect of 
 this lens is to completely correct the spherical aberration 
 of the condenser, so that the cone of solar rays emerging 
 from the negative lens has a single point of the axis for its 
 summit. 
 
 These are the numerical data of this combination, expressed 
 in terms of the semi -diameter of the condenser, taken as unity. 
 
 Thickness at the centre .. 0T96 
 Focal length 4-015 
 
 0-067 
 
 1st surface R = 2-645-1 
 2nd surface R' = 21*639) 
 
 3rd surface R" = I'OSBl Thickness at the edges 
 4th surface R'" = 1*234 / 6 
 
 Distance between the two lenses .. 2-0075 
 Focal length of the combination . . 4-617 
 Index of refraction (blue) .. .. 1*543 
 
 In the path of the cone of solar rays is the negative. This 
 
192 
 
 PHOTOGRAPHIC OPTICS. 
 
 can be moved in the direction of the optical axis so as to be 
 moved towards or away from the condenser. 
 
 At the focus of the illuminating system is the amplifying 
 objective , which has a common axis with the condenser and 
 the correcting negative lens. This objective has the external 
 form of Ramsden’s eye-pieces placed on pocket telescopes, but 
 it is constructed on the principles of M. Petzvals doublet. 
 It is completely free from spherical aberration along its axis 
 and from chemical focus. 
 
 The diameter of the two lenses which form it is different, the 
 largest lens being towards the negative. The object of this 
 difference is to prevent the objective throwing over the sen- 
 sitive paper, by diffusion, some of the light coming, not from 
 the direct solar rays, but from the points of the sky bordering 
 on the sun. An objective, the two lenses of 'which had the 
 same diameter, but of which that facing the enlarged image 
 was furnished with a diaphragm, would effect the same 
 object. 
 
 The author of this work has had constructed several of these 
 objectives having different diameters and focal lengths ; but all 
 these objectives still include an angle, sCtf (fig. 82 , p. 185 ), 
 greater than the angle of divergence, ACL, of the cone of 
 solar rays emergent from the condenser. Theoretically, it 
 would be sufficient if the angle included by the objective were 
 equal to (but in no case smaller than) the angle of divergence 
 of the cone of solar rays ; but then the objective ought to be 
 placed immoveably in the apparatus, or else, in advancing it 
 towards the condenser, the edges of the solar cone would fall 
 on the margins of the objective, and the sharpness of the 
 enlarged image would be injured by the production of blurs 
 of diffraction. Great inconveniences would result from this in 
 practice, because the place of the negative (the dimension of 
 which is variable) in the cone of solar rays is exactly deter- 
 mined by the diameter, p q, P Q, p' f (fig. 82 ), of the section 
 which corresponds to the largest dimension of the negative, in 
 order to profit by all the solar light emanating from the illu- 
 
THE DYAL1TIC APPARATUS. 
 
 193 
 
 minating system. The place of the negative being thus deter- 
 mined, it would be necessary that the focal length of the objec- 
 tive should be just that necessary for throwing the enlarged 
 image sharply on a screen of which the dimension is deter- 
 mined by the. sizes of paper made use of in photography. Now, 
 as these conditions do not occur one time in a thousand, it 
 would be necessary to make the negative itself moveable, as 
 Woodward does. But in advancing the negative towards the 
 condenser all the light is lost which falls outside its surface ; 
 and in advancing it towards the objective the image is con- 
 fined to the part of the negative traversed by the solar rays. 
 
 The angle of divergence of the amplifying objective, its 
 focal length, and the dimension of the negative, ought there- 
 fore to be in relation with the angle of divergence of the cone 
 of solar rays, and, in order to permit of the amplifying objec- 
 tive being moved some centimetres on the axis of the appa- 
 ratus — a condition indispensable for varying its distance from 
 the negative — a much more considerable diameter is given to 
 that one of the lenses forming it which faces the negative, in 
 order to increase the angle which it includes, and thus to 
 prevent the edges of the solar cone striking against the edges 
 of the mounting. 
 
 The angle of divergence of the three sizes of the dyalitic 
 apparatus determined by that of the condensers, which are 8, 
 14, and 19 inches, being equal for all three; further, having 
 chosen centimetres by 9 as the size of the negative, the 
 size called carte-de-visite ; and lastly, having supposed that 
 the linear enlargements would be limited to between 4 and 12 
 times, we have proved by calculation, confirmed by experi- 
 ment, that the objective which answers best for the enlarge- 
 ment in the conditions enumerated above is the following :* — 
 
 * When the condenser is only eight inches in diameter, the amplifying 
 objective may have a less diameter, the red circle which surrounds the cone 
 of convergent solar rays being less. These are the dimensions adopted for 
 this objective — which we shall name by the letter A, in order to distinguish 
 it from the others, which we indicate by B, C, &c. : — ■ 
 
 0 
 
194 
 
 PHOTOGRAPHIC OPTICS. 
 
 Millimetres. 
 
 Diameter of the lenses opposite the negative . . . . 63 
 
 „ „ „ enlarged image 45 
 
 Distance between the two lenses . . 85 
 
 Focal length of the combination * * 150 
 
 This objective is called B. 
 
 It happens very frequently that the negative, although 
 formed on a glass of by 9 centimetres, is smaller than this. 
 This happens particularly when only a part of the negative 
 has to be reproduced. It is then necessary to reduce the 
 negative to the part indicated by cutting it. The place of 
 the negative in the cone of solar rays is then brought consider- 
 ably nearer to the focus of the condenser, so that the objective * 
 can no longer be conveniently employed. For this purpose, 
 we have had constructed a second form indicated by the letter 
 C, the two lenses of which have the same diameter, namely, 
 63 and 45 millimetres, but which are brought much closer 
 together, and have a focal length of only 12 centimetres. 
 
 This objective includes, therefore, a still more considerable 
 angle than does the objective B ; it could also serve, therefore, 
 to enlarge negatives of centimetres by 9, and it would 
 throw their enlarged image to a much shorter distance than B 
 does, but the image would then be less sharp at its edges. 
 The objective C is specially suitable, therefore, for negatives 
 of at least 4 centimetres by 5, and of at most 5 by 6. The 
 objective B is, on the contrary, suitable for the enlargement 
 of negatives of at least 5 centimetres by 6, and of at most 
 6 by 8. 
 
 Lastly, if negatives larger still, and included between 7 
 centimetres by 10 and 12 by 15, are to be enlarged, we have 
 
 Millimetres. 
 
 Diameter of the lenses facing the negative . . . . 60 
 
 „ „ „ enlarged image . . 40 
 
 Distance between the two lenses 55 
 
 Focal length of the combination 114 
 
 * Reckoned along the axis from the principal focal plane to the tangent 
 plane of the lens facing the focal plane. 
 
THE DYALITIC APPARATUS. 
 
 195 
 
 a fourth form, named D, of which these are the dimen- 
 sions : — 
 
 Millimetres. 
 
 Diameter of the leases facing the negative .. 81 
 
 „ „ „ enlarged image . . 50 
 
 Distance between the two lenses 110 
 
 Focal length of the combination . . . . . . ...183 
 
 If it were required to enlarge still greater negatives, forms 
 could easily be constructed on analogous data. 
 
 It is clear thai, since the place of the objective along the axis 
 of the apparatus varies, the space, x x' and a (fig. 4, pi. II.), 
 covered by the solar rays is variable. In the position indi- 
 cated by fig. 4, pi. II., it is very small at a , and the central 
 part only of this lens is traversed by the solar r&ys. To avoid 
 the diffused light which the points immediately bordering on 
 the sun send through the outer part of this lens, diaphragms 
 are employed. Their diameter necessarily varies according to 
 the position of the objective, and it is necessary to avoid using 
 them too small, or the magnified image will exhibit blurs 
 of diffraction. Generally, with a very active solar light, 
 these diaphragms are unnecessary ; but if the sun is slightly 
 clouded, they are indispensable ( vide p. 187). 
 
 This, then, is the description of the dyalitic apparatus, at 
 least from a purely scientific point of view. It remains for us 
 to give a description of this apparatus in its practical aspect ; 
 and this will assist the reader in setting up other arrange- 
 ments.* 
 
 * Before commencing to do so, we may be permitted to insist on some 
 experiments, which we have many times repeated, with the object of assuring 
 ourselves if the different improvements made by us in the primitive solar 
 camera of Woodward are really useful. We shall here only occupy ourselves 
 with the introduction of the negative correcting lens, and of the amplifying 
 objective, setting aside the mechanical improvements as of less importance. 
 
 A question we have often had addressed to us is this : — “ Do you believe 
 that the negative lens is really quite indispensable, and that it is not enough 
 for the condenser to have such curvatures as to reduce its spherical aberration 
 to the minimum ? ” 
 
 And again : — 44 Does not the ordinary double lens,, as constructed by good 
 
 0 2 
 
196 
 
 PHOTOGRAPHIC OPTICS. 
 
 opticians, serve to magnify the image better than, or at least quite as well as, 
 the objective which you. employ — an objective in which you so greatly in- 
 crease the front glass — a circumstance certainly increasing the angle included 
 by the objective, and rendering the field flat, but which enormously in- 
 creases the astigmation ? ” (vide p. 139.) 
 
 Here is our reply : — • 
 
 Certainly, by substituting for the old plano-convex condensers, with short 
 focal length (they are' still in' use at present), a condenser with a focal length 
 three times its diameter, and by giving it suitable spherical surfaces, the 
 blurs of diffraction in the enlarged image, which have the effect of destroying 
 its sharpness ( vide p. 178), can, up to a certain point, be avoided. But this 
 is only true on the condition that the condenser does not exceed 8 or 10 
 inches in diameter, the negative to be enlarged being, of carte-de- visit e size. 
 Thus ft is that on removing the negative correcting lens from the dyalitic 
 apparatus, the condenser of which is 8 inches, results are obtained not 
 sensibly different from those obtained with the correcting lens, which is 
 explained by the small diameter of the lateral circle of aberration of a lens 
 of 8 inches, having 16 or 20 inches focal length. But the results are very 
 different if a condenser is used of 14, and above all of 19 inches diameter. 
 If the negative lens is removed from this apparatus, the image does not 
 to appearance , lose in sharpness, but when the image is printed blurs of 
 diffraction are always observed : these, on the contrary, are never seen with 
 the apparatus when the negative lens is in place, in which case the images 
 are of remarkable sharpness, particularly striking when a successive and 
 increasing series of enlargements are compared. The appearance of these 
 proofs causes those who see them to say that the fineness increases with 
 the enlargement. It is very different with the common solar cameras, 
 which all produce sufficiently good results in the slight enlargements, but 
 utterly bad in the great enlargements. 
 
 This result is explained by the considerable circle of aberration of large 
 condensers. Whenever the correcting lens is taken out of the apparatus, 
 particularly if the condenser is 19 inches in diameter, there is an in- 
 surmountable difficulty in placing the objective in such a way as that 
 the inside of its mounting does not receive some of the sun's light, an 
 evident proof of the irregular path of the solar rays through the ob- 
 jective. And even in the position of the objective in which this defect 
 is the least apparent (that of the least circle of aberration), the sharply 
 marked outlines of the image are seen to be doubled during the printing of 
 the proof. 
 
 All the summer of 1864 we had two apparatus exactly the same, of 19 
 inches (only that one had its correcting lens suppressed), standing side by 
 side, and capable of working simultaneously. Whenever we received a visit 
 from an amateur or from a scientific man, we caused the two apparatuses 
 to operate on identical negatives, and the dyalitic apparatus always gave 
 the sharper results. The only exception was when the negative was not 
 
THE DYALITIC APPARATUS. 
 
 197 
 
 fine, and had not very sharply marked lines : there was then, however, no 
 means of making a regular determination. 
 
 It rests therefore positively beyond question in science that the conver- 
 gent illumination in photographic enlargements must be free from spherical 
 aberration, as otherwise double lines always appear, unless the value of the 
 aberration be an extremely small fraction of the diameter of the objective, 
 which is only the case if the condenser, with proper curvatures, is less than 
 10 inches in diameter, and that its focal length is more than two-and-a-half 
 times its diameter. 
 
 Indeed, even if the condensing combination should be free from spherical 
 aberration, good results as to sharpness would not be constantly obtained, 
 if the ordinary double lenses were made use of, particularly those called in 
 commerce “ quarter and sixth ” We know perfectly that by very greatly 
 increasing that one of the lenses of Petzval’s doublet which, employed 
 under ordinary circumstances, faces the ground-glass, we preserve all the 
 astigmation arising from the oblique position of the two lenses in relation 
 to the incident rays. But observe that a considerable and profound diffe- 
 rence exists between the objective as we employ it and as it is employed in 
 the usual camera. In the latter case every point of the object to be re- 
 produced sends to the objective a bundle of light, the angle of which is de- 
 termined by the aperture of the objective and the distance of the radiating 
 point. The astigmation, therefore, arises from the obliquity only of the radia- 
 ting point, and if the lens of the doublet facing the ground-glass transmits 
 to the focal plane all the rays emergent from the first the astigmation will 
 certainly be intolerable. But there is nothing like this here. In fact, it 
 is necessary to fully consider that every point of the negative is traversed 
 by a single solar ray , which, on reaching the objective, passes through it. 
 You can, therefore, cover with impunity such part of the surface of the 
 objective as you may wish, by an opaque screen, without producing any 
 confusion in the points of the image not cut off by the screen. It is 
 sufficient, therefore, for the objective to be perfect, that it be quite free 
 from both chromatic and spherical aberrations, along its axis , and that its 
 focal length for oblique pencils be equal to that for axial pencils. Neither 
 aberration of thickness nor astigmation is possible in this case, and the 
 most evident proof of this we can give is, that the objective we make use 
 of as the amplifying objective — though possessing these two imperfections 
 to a considerable degree if we make use of it to obtain proofs with the 
 camera obscura— gives, in enlarging, images in which the straight lines are 
 rigorously preserved, and in which not a trace of astigmation is to be 
 discovered. 
 
198 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTER VI. 
 
 DESCRIPTION AND SETTING-UP* OF THE DYALITIC APPARATUS, AND 
 IN GENERAL OF ALL APPARATUS FOR ENLARGEMENTS. 
 
 The premises intended for the Apparatus. — The first 
 condition for the proper setting-up of apparatus for enlarg- 
 ments, of whatever nature they may be, is to choose a place, 
 the floor of which is as far as possible protected from the 
 vibrations of the ground. If the building is solidly con- 
 structed, the passage of carriages does not at all interfere with 
 the sharpness of the proof. Thus, the author of this work has 
 seen the dyalitic apparatus in operation at the establishments 
 of M. Franck de Villecholle, Rue Vivienne, Paris, and of M. 
 Alexandre Ken, Boulevard Montmartre, Paris — places where 
 the continual passage of vehicles is undoubted — but where the 
 solidity of the buildings is such as to preserve the apparatus 
 from the vibrations of the ground. 
 
 The place of operations ought to be 5 metres long, if it is 
 desired to work with sheets of paper 120 centimetres high, a 
 size very considerable, and one sufficient for the majority of 
 professional photographers. The flooring ought to be ren- 
 dered as unyielding as possible before fixing the apparatus 
 upon it. If the flooring is altogether deficient in firmness, 
 have twx> pieces of timber, F and H, 20 centimetres thick by 
 35 broad, let into the wall, in the way represented in fig. 83, 
 and rest upon them all the parts of the apparatus. These 
 two pieces of timber must not be in contact with the floor, but 
 
 * Plates II. and III. represent, with great accuracy, the summer and 
 winter arrangement of the apparatus No. 3. They are drawn to the 
 scale of 5 centimetres to the metre. 
 
APPARATUS FOR ENLARGEMENTS. 
 
 199 
 
 3 or 4 centimetres above it. We can then walk about the 
 place without any fear of causing any movement of the pieces 
 of the apparatus ; otherwise we must avoid doing so as much 
 as possible. 
 
 The wall A (fig. 83), which is perpendicular to the length of 
 
 the camera, ought to face the south as nearly as possible, and 
 receive the adjustible mirror. At least this arrangement is the 
 most favourable, for the sun is then available all day long, if 
 neighbouring objects form no obstacle. Moreover, when the 
 aspect is towards the south-east, the mirror is not long enough 
 in the afternoon, particularly in winter, and when towards the 
 south-west, it is not long enough in the morning. It is therefore 
 necessary to give the adjustible mirror and the apparatus as 
 much as possible a north and south aspect, the mirror being 
 towards the south. 
 
 The general disposition of the setting up of a solar chamber 
 (whatever its plan may be) is represented in fig. 83. A is 
 the darkened window exposed to the south in which the 
 
200 
 
 PHOTOGRAPHIC OPTICS. 
 
 adjustible mirror, B, is inserted, and opposite this is the solar 
 camera, C, on a stand, D E. The enlarged image of the nega- 
 tive is projected on a frame, L M. Let ns now pass to details. 
 
 Description of the Adjustible Mirror. — When the 
 mirror is of large size it is well for it to he mounted entirely 
 in iron. This is, at least, the plan we have adopted after a long 
 experience. For the adjustible mirror to he well constructed 
 three conditions must he fulfilled. It must present a stable 
 equilibrium such as to resist the action of the wind ; the centre 
 of motion must correspond to the centre of figure or he 
 symmetrical with it, in order that the mechanical force re- 
 quired to move it he the least possible ; and thirdly, the glass 
 must he supported by a framework which prevents it bending. 
 The last point in particular is of great importance, if it is 
 wished to obtain a round image of the sun at the focus of the 
 condenser instead of an elongated image, such as is obtained 
 if the mirror in consequence of flexion is curved instead of 
 being plane. These conditions are rigorously fulfilled in the 
 form of adjustible mirror we have adopted, and of which fig. 1, 
 pi. II., is a representation. 
 
 The glass, AB, is rectangular, or, rather, octagonal, the 
 corners being cut off. The iron frame on which it rests is 
 shown separately in fig. 2. This frame, which can also be 
 made of good and well-seasoned oak, carries four projecting 
 pieces of iron, C D E F, between which the glass is placed on 
 the well-levelled surface of the frame, and by which the glass 
 is prevented from sliding off the frame when it is in a ver- 
 tical position. 
 
 Four other catches, of which the extremities are bent at 
 right angles, can be adopted to glasses of any thickness what- 
 ever between 5 and 10 millimetres. These catches are fixed 
 to the iron frame by screws of the same metal. The two 
 bars, O and N, give great solidity to the frame. 
 
 The support, G H (fig. 2, pi. II.), is of cast-iron, and is 
 screwed to the frame in such a way that the silvered part of 
 the glass passes exactly through the axis of the pivots Gr and 
 
APPARATUS FOR ENLARGEMENTS. 
 
 201 
 
 H, as is seen in the figure. This support has pivots, G and H, 
 at its extremities, on one of which, H, is fixed the toothed 
 wheel, I, of bronze. In order to make the frame and wheel , I, 
 quite solid , a screw fixes the wheel to the support. This is indis- 
 pensable, for else the wheel, which, as we shall see directly, 
 receives its motion from a pinion, might turn without carrying 
 the frame with it. And it is accordingly quite indispensable 
 to ascertain if this takes place, for if it does a second screw 
 must be employed. 
 
 As we said at first, a wooden frame may be substituted for 
 the iron frame, and instead of making the endless screw work 
 the pinion directly, another wheel may be employed, as shown 
 in fig. 3, pi. II., in such a way that the endless screw, m, acts 
 on the pinion, n , and this on the large wheel, o, placed on the 
 axis of the frame which bears the mirror. In this case 
 the movement is slower ; but it is necessary to be careful to 
 fix the circle, o, on the frame, B, by a screw, a, for else the 
 frame, B, would turn freely about its axis. 
 
 SU V X (fig. 1, pi. II.) is a frame of cast-iron turned in a 
 iathe on both its faces, and presenting a large, ledged aperture, 
 X X, in which turns the annular disc, Z Y, toothed at its cir- 
 cumference. The cast-iron frame has holes at its four angles 
 by which it may be fixed to the shutter of the dark room. 
 The two arms, ah, c d, are fixed on the ring, Y Z, by six 
 rivets, and the latter, toothed through its whole circum- 
 ference, and receiving its motion from a pinion, X, carries 
 along with it also the two arms at the extremities of 
 which are the sockets into which the pivots of the frame of 
 the mirror fit, as will be at once understood on looking at 
 the figure. 
 
 Lastly, an iron rod, R e, traverses the ring, Y Z, and the 
 base of the arm h a. It is terminated inside the dark room by 
 a brass knob, R, and at its other end by an endless screw, e. 
 
 When the adjustible mirror is completely mounted, as it is 
 seen in fig. 1, pi. II., it is necessary to prevent the extremities 
 of the iron frame, A B, from striking against anything, the 
 
202 
 
 PHOTOGRAPHIC OPTICS. 
 
 effect of which would be to twist the end of the rod, R e, which 
 bears the endless screw. Then, on turning the knob, R, great 
 resistance would be experienced during one half a rotation, and 
 great facility during the other. The bent extremity, e, of this 
 rod is easily straightened in the position where a notable 
 resistance is found on turning the knob, R, by pressing 
 strongly but gradually on the lower part of the iron frame 
 carrying the glass, which causes torsion of the rod in the 
 opposite direction. But in all cases it is necessary to act 
 with precaution if we wish not to deteriorate this part of the 
 instrument. 
 
 The sockets which terminate the arms ought to be tight, 
 but not too much so, in order that the pivots on which the 
 frame of the mirror turns do not experience too much resist- 
 ance. 
 
 In order to avoid the loss of motion which always occurs 
 between the endless screw and the toothed circle, I, a weight 
 of from 2 to 4 kilogrammes may be suspended from the lower 
 part of the mirror ; but in the majority of cases this is not 
 indispensable if the different parts of the adjustible mirror are 
 well adjusted. The adjustible mirror ought evidently to be 
 kept in order like other machines, by dismounting it occa- 
 sionally in order to oil it, and remove any rust which may 
 have formed on it. The toothed circle in particular must be 
 kept well oiled. 
 
 The glass ought to be thoroughly well silvered, and painted 
 beneath. For further security, tinfoil, such as is wrapped 
 about chocolate, may be pasted on the painted surface, which 
 will preserve the silvering still better than the oil-paint which 
 covers it. 
 
 The margins of the glass ought to he covered up with hlach paper , 
 fastened on with paste, for otherwise it frequently happens 
 that coloured lines (rainbow colours) are seen in the enlarged 
 image, arising from the dispersion of the solar rays by the 
 edges of the glass. 
 
 The glass itself ought to be cleaned every eight days with 
 
APPARATUS FOR ENLARGEMENTS. 203 
 
 alcohol and a cloth covered with tripoli, and every morning 
 with a dry cloth. In the course of the day it is necessary to 
 frequently remove the dust blown over it by the wind with a 
 long-haired brush, otherwise the printing of the enlarged 
 image might require a much longer time. 
 
 Lastly, the glass ought to be sheltered from the rain, or else 
 it would become covered by the end of some months with 
 yellow stains in the silvering, which would cause the expense 
 of a fresh silvering of the glass.* 
 
 The management of the adjustible mirror is extremely easy. 
 As the sun advances from east to west, and as further he 
 continues to ascend from his rising until noon, and then 
 descends till he sets, it is necessary to communicate two 
 movements, the one to the handle L (fig. 5, pi. II.), which has 
 the effect of bringing the longer side of the glass into the 
 plane of the solar rays, the other to the knob, P. which gives 
 the glass the inclination suitable for reflecting the solar rays 
 horizontally, and perpendicularly to the surface of the frame, 
 KC. 
 
 A cylinder of reflected solar rays which entirely fills the 
 opening KC is thus obtained. We shall see afterwards how 
 the solar rays are kept reflected in an absolutely constant 
 direction. 
 
 Setting up of the Adjustible Mirror. — The setting up of 
 the adjustible mirror is extremely simple, j* Choose a window, 
 A X (fig. 5, pi. TI.), of the apartment, the glazed part of which 
 descends as nearly as possible to the floor, and substitute for 
 the casement a strong deal-board, two inches thick, in which 
 you contrive a ledged aperture of one centimetre, into which 
 the cast-iron frame of the adjustible mirror exactly fits. Four 
 small wedges then suffice to hold it so that it cannot fall into 
 
 * Done very well in Brussels, at Nyssens and Co., looking-glass makers, 
 Laeken. 
 
 t It is represented with very great accuracy in pi. II., fig. 5, showing, 
 reduced to a twentieth, the adjustible mirror No. 3 ; fig. 4, the optical ap- 
 paratus ; and figs. 6, 7, and 8, the proof frame. 
 
204 
 
 PHOTOGRAPHIC OPTICS. 
 
 the room.* To the outside of the board attach the wooden flap, 
 B F, moving on a hinge, J. This flap, covered with thin zinc, 
 ought to be a third longer than the mirror, and a third broader, 
 and the hinge is to be only a few centimetres above the upper 
 part, D, of the opening. A cord, G H I Q, enables the flap, 
 to be raised so that it may not in any way impede the move- 
 ment of the mirror . — ( Vide fig. 10, pi. II.) Two small side- 
 flaps, E, E (figs. 9 and 10, pi. II.), shut in at the sides the 
 space about the adjustible mirror, which may be left open 
 below. These small flaps, which are shown closed in fig. 9 
 and open in fig. 10, are moved by cords. 
 
 Fig. 5 shows the position of the mirror, S R, when the flaps 
 are closed, a position in which the glass faces the ground in- 
 stead of the sky, as when using the light from it. This position 
 is obtained by turning the handle L until the axis of the mirror 
 is horizontal. In this way the adjustible mirror need not be 
 taken in to protect it from the rain. The board, AX (fig. 5, 
 pi. II.), ought to be level with the adjacent wall outside, 
 Z Y, unless it is as broad as the mirror is long, and presents a 
 length below the opening equal to half that of the mirror. 
 For if an obstacle were to be there, it might prevent the 
 motion of the mirror. 
 
 An important condition , when setting up the adjustible mirror, 
 is to place it as near as possible to the floor, and perfectly 
 vertical. Generally the lower part, C, of the opening ought 
 to be 80 centimetres from the floor, X — the handle L being at 
 the upper part of the opening (either to the right or left). If 
 for any cause we are obliged to place it more than 80 centi- 
 metres from the floor, it is then preferable to have the handle 
 L at the lower part, O. The frame of the adjustible mirror 
 being square, the handle can be brought at will either below 
 or above, and to the right or the left, of the iron frame. 
 
 * Fig. 5, pi. II., represents the adjustible mirror, KC, inserted into 
 another wooden frame, D N, moveable on the hinges, N O. By this means 
 (vide pi. III.) the adjustible mirror can be inclined, which is indispensable in 
 winter. 
 
APPARATUS FOR ENLARGEMENTS. 
 
 205 
 
 If the apparatus is placed on beams as we have figured it at 
 page 199, then the height of the lower part of the cast-iron 
 frame of the adjustible mirror ought to be 80 centimetres 
 above the upper part of the beams. 
 
 Description of the Solar Camera. — We have already 
 described the dyalitic solar camera and the American solar 
 camera from a scientific point of view. We shall now describe 
 them from a purely practical point of view, without, how- 
 ever, dwelling on the latter. But this has to be constructed 
 in the same manner as the former, save that the double con- 
 denser is to be replaced by a simple condenser, the negative 
 holder with moveable rods by an ordinary, ledged, negative 
 holder, and the amplifying objective by the ordinary double 
 lens : apart from this, everything remains the same as to the 
 way of using it, setting it up, &c. 
 
 Fig. 4, pi. II., shows the dyalitic solar camera in section. 
 The large condenser, A 1 B 1 , is fixed at the front end, its more 
 convex face being turned outwards. The correcting lens, C 1 D 1 , 
 is placed in the middle, its convex side being turned towards 
 the objective M. The wooden frame, H 1 1 1 , is moveable along 
 the length of the camera. It is moved by a rack movement, 
 G 1 , and fixed by a screw which is at the side of the milled 
 head working the rack, G l . Lastly, the objective, M 1 , is also 
 placed on a piece of wood moveable in the same direction, and 
 capable of being fixed in the same manner. The apparatus is 
 indeed so simple that it is at once understood by inspecting 
 the figure. We have only to say that if the moveable frames 
 work a little too stiffly, it is only necessary to move out a 
 little one of the thick pieces of wood between which they slide. 
 These pieces of wood are fixed by means of screws to the 
 bottom of the solar camera, but are nevertheless easily move- 
 able the diameter of the screws being less than that of the 
 holes which give passage to them. 
 
 It is indispensable that all the spherical surfaces which form, 
 to the number of 12, the optical system, have a common axis. 
 This is the business of the maker ; but if this work, in itself 
 
206 
 
 PHOTOGRAPHIC OPTICS. 
 
 very long and difficult, were not done with the care and 
 attention which it merits, great difficulty would he caused in 
 printing the magnified image with sharpness and without 
 double lines appearing on all its outlines. 
 
 The box, O l P 1 Q 1 R 1 , which forms the solar camera, is 
 usually closed at the sides by wooden doors, but we have 
 found it more convenient to do away with these doors on the 
 side of the handle L (fig. 5). Thus, if this handle is on the 
 right of the circular opening which gives passage to the solar 
 rays, then do away with the doors to the right of the appa- 
 ratus. This arrangement is more convenient because with it 
 the interior of the solar camera can always be seen, which 
 oherwise can only be done by opening the doors, and this is 
 troublesome. 
 
 In order to prevent light passing through these open doors 
 into the dark room, and especially in order not to fatigue the 
 eyes, we replace these doors by green glasses , which slide be- 
 tween two grooves, MN, OP (fig. 11, pi. II.), placed parallel 
 to the length of the solar camera above and below. (Green, 
 as we know, does not affect ehloride-of-silver paper.) 
 
 To the end P 1 Q 1 (fig. 4) of the solar camera we have attached 
 a board, Q R ( vide fig. 11), having at its central part a hole, X, 
 1 6 centimetres square. Two small-grooved pieces of wood are 
 placed horizontally above and below this opening. This 
 opening can be closed by a green glass, Z, and a ground-glass, 
 Y, of the same size. The green glass slides to the left, the 
 ground-glass to the right. Further, the board can be moved, 
 as a whole, up and down between two vertical grooves, S T, 
 U Y, by means of a cord, a , which passes over a pulley fixed 
 to the ceiling, and the end of which is brought near the ad- 
 justible mirror, within reach of the operator who is managing 
 it. Its object is to prevent the light which illuminates the 
 interior of the solar camera from reaching the enlarged proof 
 through the intervals which exist between the objective- 
 holder and the sides of the solar camera. This frame, R Q 
 (fig. 11, pi. II,), must be capable of being raised and lowered 
 
APPARATUS FOR ENLARGEMENTS. 
 
 207 
 
 in order that the rack movements may be got at. The green 
 glass, Z, is of very great use in arresting the photogenic power 
 of the solar light, in such a way that the image of the negative 
 may be visible to the eye without being active on the sensi- 
 tised paper, the utility of which will be better comprehended 
 presently. Lastly, the ground- glass serves to throw a white 
 and diffused light on the enlarged proof already printed, while 
 it arrests the image of the negative on its ground surface. 
 
 Every apparatus ought to receive this addition, the great 
 utility of which we have recognised in practice. We have 
 also caused to be added to the frame carrying the objective an 
 iron plate having a circular aperture exactly the size of the 
 objective. This is in order to prevent the summit of the cone 
 of rays setting fire to this board when it is displaced from the 
 axis of the apparatus.* 
 
 Setting up of the Solar Camera. — Eig. 4, pi. II., exhibits 
 the solar camera placed on a stand opposite the adjustible 
 mirror. The distance between them ought to be 20 centi- 
 metres, the interval being covered up by a black curtain , except on 
 the side of the handle. The knob, P (fig. 5), commanding 
 the endless screw, T U, is, moreover, always brought to the 
 side of the handle, L, an arrangement always practicable. 
 
 The solar camera ought to be placed horizontally on. its stand, 
 as ascertained by means of a spirit-level, S', placed on its 
 top ; and it is necessary to take the greatest care to have the 
 centre of the aperture, K C, of the adjustible mirror, and the 
 centre of the condenser, A 1 B l , on the same horizontal axis. 
 This is at once seen when , the apparatus being horizontal, the solar 
 rays are reflected on to the front lens. This should be completely 
 covered , at the same time that the apex, a , of the cone of solar rays 
 emergent from the condenser passes through the objective. 
 
 * We look upon these improvements as so essential that we have given 
 orders to the manufacturers of our apparatus to do away from this day 
 forward with the side doors, and to add the different pieces of which we 
 have just spoken, leaving to those who get the apparatus the care of 
 procuring the green glasses, the carriage of which without breakage would 
 be difficult. 
 
208 PHOTOGRAPHIC OPTICS. 
 
 The stand of the apparatus ought to be very simple and 
 very solid, as it is seen in the figure on page 199. B eject 
 without any hesitation the use of stands capable of being 
 raised or lowered by rack movements, as deficient in the 
 stability necessary for an enlargement apparatus. At the 
 utmost put four strong iron screws on the bottom of the stand 
 to steady it, but still nine times out of ten the adjustment of 
 the apparatus can be made by a good carpenter without these 
 screws, and this is better. Besides, the stand being firmly fixed 
 on the ground , and terminated at its upper part by a tab'e 
 having exactly the size of the bottom of the solar camera, the 
 latter can always receive the slight displacement necessary for 
 its final adjustment : and it is then to be fixed to the stand. 
 
 The Negative-Holder. — The support for the negatives 
 (fig. 12, pi. II.) is formed of a wooden or metal frame, ABCD, 
 which fits exactly into the moveable case, H l I 1 (fig. 4, pi, II.), 
 and from which it can be readily taken out. Four grooves are 
 made in the frame, in which four clamps, bevelled off at their 
 lower end and which serve to hold the negative, slide with 
 facility. If they do not, the grooves should be enlarged with 
 a file. The clamps can be fixed by pressure-screws, shown 
 in the figure. 
 
 The upper clamp, G, having a small pin at its lower end 
 against which rests the metallic spring i m, is always pressed 
 downwards. The spring, i m, is very weak, and just strong 
 enough to keep the negative motionless when the frame is 
 taken out, the two side-clamps being open. This spring can 
 also act on negatives of different sizes by means of a pressure- 
 screw fixed at its insertion, i. When the screw- is loosened, 
 which sets the spring free, the negative is then placed between 
 the two clamps, H and G ; the lower one, H, only being fixed. 
 The spring is then pressed by the finger, while the pressure- 
 screw, i, is tightened. The spring thus acts on the pin, G, and 
 causes it to press against the negative. The consequence of 
 this is, that if the heat expands the negative, this pushes up the 
 pin ; so that if the latter were fixed the negative would break in 
 
APPARATUS FOR ENLARGEMENTS. 
 
 209 
 
 pieces. The great point, therefore, for avoiding the fracture of 
 the negatives under the influence of the great heat of the cone 
 of concentrated solar rays, is not to press upon it by any 
 other means than by the action of a spring. 
 
 As to the two side-clamps, we scarcely ever use them. Still 
 they may serve to keep the negative in the plane of the 
 frame. But these clamps must not be fixed firmly by tighten- 
 ing too much the pressure-screws which govern them ; and, 
 above all , they must never be allowed to bear too hard against 
 the negative. 
 
 The spring, im, might be done away with, and replaced 
 advantageously by a leaden weight of 200 grammes, fastened 
 at G to the upper clamp, which in this way would bear 
 sufficiently upon the negative to keep it fixed. M. 
 Damry, of Liege, employs this method, and never breaks a 
 negative. 
 
 The negatives which are to be inserted between the clamps 
 of the negative-holder ought previously to be cut with a good 
 diamond,* and accurately limited to the part to be enlarged, by 
 cutting away all those parts which are not to appear in the 
 enlarged proof. 
 
 The best enlargements are made from negatives of carte-de- 
 visite size (vide p. 193). If you want a full-length figure, then 
 make the negative of carte-de-visite size ; if you want a half- 
 length figure life-size, take your negative on a half- plate, so 
 that the half figure occupies a space on it a little smaller than 
 a carte-de-visite — just like the vignetted busts that are made 
 of card size — and cut away all the rest. 
 
 Description of the Proof-Frame . — The frame for the 
 proofs ought to be constructed of such dimensions as that it 
 corresponds to the sizes of the sheets usually made. That 
 which we have used for the last four years is exceedingly 
 
 * If the edge of the negative is not cleanly cut with the diamond, a 
 crack is often formed, though invisible to the eye, which, by extending 
 under the influence of the heat of the solar rays, brings about the de- 
 struction of the negative. 
 
210 
 
 PHOTOGKAPHIC OPTICS. 
 
 simple, and allows of being made to suit three sizes, 
 namely — 
 
 The photographic sheet . . . . 45 by 59 centimetres. 
 
 The double sheet 59 by 90 „ 
 
 The double elephant size 80 by 105 „ 
 
 We stretch these sheets on boards a centimetre thick, 
 having the following dimensions — 
 
 50 by 60 centimetres. 
 
 60 by 95 
 
 85 by 110 
 
 Plate II. (figs. 6, 7, and 8) exhibits the frame * completely 
 mounted. A 2 B 2 , C 2 D 2 , are the two uprights of wood con- 
 nected by the cross-pieces, as shown in the figure. A frames 
 F 2 G 2 H 2 I 2 , is attached to the two uprights, presenting two 
 ledges, F 2 G 2 and J 2 M 2 (see also fig. 8), one centimetre deep : 
 (the same arrangement is presented at the lower part of the 
 frame). Between these ledges are introduced the boards, 85 
 by 110 centimetres and 95 by 60 centimetres. There are two 
 slots, I 2 Y 2 , on its vertical sides, K 2 J 2 , M 2 L, 2 which give pas- 
 sage to the screws Y 2 and X 2 , by means of which it is fixed to 
 the uprights. The frame can therefore be raised or lowered 
 to the extent of some centimetres, so that it is easy to make 
 the height of the middle of this frame from .the floor corre- 
 spond exactly with that of the objective of the solar camera. 
 This should be done once for all. 
 
 The breadth, G 2 F 2 , of the frame being greater than that of 
 the boards, these can slide a little to the right or left, which 
 is necessary in order to accurately adjust the sensitive paper. 
 This adjustment being made, the board is solidly fixed by 
 small brass or wooden screws. Lastly, into the lower ledges, 
 J 2 M 2 , L 2 K 2 , a board, 0 2 N 2 , is introduced, 95 by 60 centi- 
 metres externally, but having a ledged aperture, P 2 Q 2 R 2 , 
 
 This frame is represented in these figures one-twentieth of its size. 
 
APPARATUS FOR ENLARGEMENTS. 
 
 211 
 
 S 2 , and receiving in its tnrn the boards of sheet size (50 by 
 60 cent.) 
 
 The light wooden boards which receive the sensitised paper 
 are 14 millimetres thick, but are bevelled off at top and bottom 
 so as to be only 1 centimetre thick, which is the thickness of 
 the ledge of the frame. This bevelling permits the wedges 
 which serve to fix the board to hold it firmly. 
 
 The board, of the size 50 by 60 centimetres, is formed 
 entirely of wood, but the two others, of 60 by 95 and of 85 by 
 110, are formed of a light wooden frame fastened on a cross, 
 and the whole covered by a sheet of brown paper, which is 
 glued on while wet in order that it may become tense on 
 drying (fig. 7, pi. II.) 
 
 The frame ought to be accompanied by boards on which 
 sheets of white paper are stretched, which serve for the focus- 
 sing of the image. 
 
 There ought to be twelve boards of the size 50 by 60 centi- 
 metres, six of the size 60 by 95 cent., and six of the size 85 
 by 110 cent., kept in a grooved box of white wood, with a 
 thin coating of black paint outside. 
 
 If it is wished to make sizes still larger than 60 by 95 
 cent., the frame is turned round the other way, and a very 
 large drawing-board is attached to the two uprights, on which 
 the paper is stretched, as will be afterwards explained. 
 
 The sensitised papers,* either albumenised or prepared with 
 nitroglucose, after they are thoroughly dry , are stretched over the 
 frames and fastened with drawing-pins. It is not necessary 
 to attach importance to the folds which remain in the paper, 
 particularly in the case of portraits, or to take minute care to 
 avoid them. We content ourselves usually with attaching the 
 paper by ten drawing-pins, three above, three below, and two 
 at each side. The paper is first fastened at the top, then 
 gently stretched and fixed at the bottom by drawing-pins. 
 
 * We do not treat in this work of the preparation of the papers, which 
 is identical with that of the papers which are used for ordinary proofs. 
 
 P 2 
 
212 
 
 PHOTOGRAPHIC OPTICS. 
 
 Then the sides are fixed. This operation hardly takes a 
 minute. The hoards covered with their sensitised paper are 
 put into the grooved box, by which means they can be easily 
 conveyed from place to place. 
 
 If it is wished to make use of only one board, for example, 
 in the case of the very large sizes, the image is first brought 
 to a focus on the large board of which we have spoken. Then 
 the cone of solar light emerging from the objective is inter- 
 cepted by sliding across it the green-glass; and lastly, illumined 
 by this green light, which has no action on the sensitive paper 
 while it renders the image visible on the board, the paper is 
 fixed in its proper place. 
 
 Setting-up of the Proof Frame. — The frame for the 
 proofs ought to move exactly in the direction of the length of 
 the solar camera on two pieces of wood or iron. It is indis- 
 pensable that the geometrical centre of the frame is situated 
 in the prolongation of the optical axis, Y a (figs. 4 and 5), of 
 the solar camera. Then place under the castors, Z 2 , on which 
 the frame rests, two flat pieces of wood, or better still, have 
 two grooves hollowed out of the floor exactly parallel with the 
 length of the solar camera, in which the castors will run. A 
 screw, Y 2 , placed in front of the frame, enables it to be fixed 
 in its place. To do this it is sufficient for the screw merely 
 to touch the floor. 
 
 It is almost needless to add that it is necessary in this 
 setting up of the frame to take care that the plane, cb (fig. 8), 
 of the boards is perpendicular to the direction of the grooves, 
 and quite vertical. 
 
MANAGEMENT OF ENLARGING APPARATUS. 
 
 213 
 
 CHAPTER VII. 
 
 THE MANAGEMENT OF THE ENLARGING APPARATUS. 
 
 All being arranged as we have said — the lenses and tbe 
 mirror well cleaned with alcohol and a dry cloth, dust re- 
 moved, &c., everything, in a word, being ready for use — 
 the instrument is worked as follows. Merely for the sake of 
 clearness, we shall still divide this description according to 
 the several pieces which form the apparatus. 
 
 Management of the Adjustible Mirror — (figs. 4, 5, and 
 6, pi. II.) — Since the rays of the sun strike full on the 
 adjustible mirror, it is necessary to cause them to be reflected 
 along r r upon the condenser A 1 B 1 , and to cross exactly at the 
 centre, a , of the objective M l . This is very easily accom- 
 plished by successively turning the handle, L, and the knob, 
 P, which govern the movements of the mirror. An assistant, 
 remaining constantly by the adjustible mirror, ought to keep 
 the rays reflected in this direction. There are two ways of 
 doing this : the one by never removing the eye from the lens, 
 xx, of the objective which faces the negative, and on the 
 margins of which no red light ought ever to be seen (vide 
 pp. 179, et seqq.); the other — much more practicable and, 
 above all, much more exact — is the following : — 
 
 The cone b a C, emergent from the enlarging lens, forms on 
 the frame a luminous disc bordered by a red circle, b ef 
 (fig. 6). Make sure, by looking at the lens a, that the image 
 of the sun is quite in the centre, and then at once place in the 
 red circle three drawing-pins, g, /, e. 
 
 The operator at the adjustible mirror keeps the red circle 
 always on these three drawing-pins, by communicating a 
 
214 
 
 PHOTOGRAPHIC OPTICS. 
 
 motion to the handle and knob every twenty seconds, and it 
 is on the precision with which he guides the mirror to attain 
 this end that the fineness of the image in great part depends. 
 This, however, ought only to he done after the focussing of the 
 image. 
 
 When the operation is finished a rapid movement must be 
 communicated to the handle L in the opposite direction to that 
 of the course of the sun , in order to withdraw the sun’s rays 
 from the apparatus. Or else, if the enlargement of other 
 negatives has to be continued, the green glass is slid between 
 the enlarging lens and the magnified image, the board which 
 bears the printed proof removed, the green glass opened 
 again, &c., while the operator continues guiding his mirror. 
 
 Adjustment of the Negative. — Place firstly the cut 
 negative between the clamps of the negative holder, as has 
 been mentioned at p. 208. To do this the negative-holder 
 ought not to be removed from its frame. First open the green 
 glasses which close the apparatus, place the negative reversed 
 between the upper and lower clamps, the layer of collodion 
 being towards the enlarging lens , and then move the frame into 
 the cone of solar rays, using for this purpose the knob G 1 
 (fig. 4), which acts upon the rack fixed on the floor of the 
 apparatus. Cause the negative holder to move in such a way 
 that the red margin of the disc of light that you see on the nega- 
 tive by looking at it from behind falls nearly on the edges H 1 and 
 I 1 (fig. 4), of the negative , but in all cases positively touches its 
 angles . For the more light there is external to the negative, 
 the more time the enlargement will take. This is precisely 
 why you should cut away from the negative all which need not 
 be in the enlarged proof ; and it is a matter of the greatest 
 importance. Without this your enlargements would take 
 much more time than is necessary. 
 
 The negative then being in position, you make the screw 
 which fixes the rack, the wedges, &c., all quite tight, so that 
 nothing may get displaced should a vehicle pass : for otherwise all 
 the outlines will be doubled in the proof. The same recom- 
 
MANAGEMENT OF ENLARGING APPARATUS. 
 
 215 
 
 mendation holds good for the objective and for the frame 
 which carries the enlarged proof. 
 
 We shall speak presently of the focnssing. But let us 
 mention now, that after the focussing it is always necessary 
 to return to the negative in order to place it quite in the 
 middle of the cone of solar rays, and so that the vertical lines 
 in it fall quite parallel to the edge of the sensitised paper ; 
 or else, when the proof is finished, it will be necessary to 
 remove a not inconsiderable part of it with the scissors. This, 
 however, is very easily done, the negative being very readily 
 moved between the upper and lower clamps. This done, the 
 two lateral clamps may then, but not before, be made to 
 lightly touch the negative. 
 
 Adjustment of the Lens and the Frame. — Focussing 
 the enlarged Image. — If the negative is of carte-de-visite 
 size, the lens which accompanies the dyalitic apparatus will 
 be suitable for its enlargement.* (See our remarks on this 
 subject at p. 193.) 
 
 If the size of the sensitised paper which is to hold the 
 enlarged image of the negative is 45 centimetres by 59, slide 
 the frame 1 metre from the lens, and double and treble that 
 distance for sheets of double or treble that size. 
 
 Focus the enlarged image by approaching or withdrawing the 
 lens from the negative, choosing for this purpose what seems 
 to be the sharpest part of the negative. If the enlarged image 
 is seen to be larger than the size of the paper, approach the 
 frame to the solar camera, and if it is too small withdraw 
 the frame, regulating the focus anew with the objective, and 
 repeat these operations until the perfectly sharp image is 
 of the size of the paper ; then make the frame fast by the 
 screw Y 2 (fig. 8). The red circle surrounding the cone of 
 light will then fall near the margins of the paper, and under 
 
 * In our apparatus with a condenser of from 8 to 14 inches in diameter 
 there is only one amplifying objective, suited for enlarging negatives of 
 carte-de-visite size. That with a condenser of 19 inches possesses a second 
 objective which can be used to enlarge smaller negatives. 
 
216 • PHOTOGRAPHIC OPTICS. 
 
 these conditions the printing of the image on the sensitised 
 paper will he very rapid. 
 
 A point of great importance is so to regulate the position 
 of the lens as that the red circle surrounding the solar cone 
 in the apparatus never falls on the edges, x and x, of the 
 mounting of the lens M l , * or else ( vide p. 178) there will he 
 blurs of diffraction. As to the diaphragm carried by the 
 objective, see what we remarked at p. 195. 
 
 Everything being thus arranged, close up the green* 
 glasses of the apparatus; slide the green glass between the 
 enlarging lens and the magnified image ; substitute the sensi- 
 tised paper for the white screen on which you have focussed ; 
 take away the green glass, and allow the light to act. By 
 sliding the ground-glass between the objective and the en- 
 larged image every five minutes, you can watch the progress of 
 the image and arrest it at the desired moment, which is iden- 
 tical with that in the printing of a positive on paper from 
 an ordinary negative. Then interpose the green glass, take 
 away the sensitised paper, &c. Do not forget to see that the 
 assistant always guides the mirror so that the red circle keeps 
 its place on the drawing-pins fixed on the frame. 
 
 # If this occurred it would be necessary to slide the objective backwards 
 (away from the enlarged image) until the red is just included within the 
 surface of the lens x\ x, focussing with the negative itself, which we should 
 be obliged to displace. But this never happens when the negative is of 
 the carte-de-visite size. 
 
SETTING UP OF ENLARGING APPARATUS IN WINTER. 217 
 
 CHAPTER VIII. 
 
 * 
 
 THE SETTING UP OF THE ENLARGING APPARATUS IN WINTER. 
 
 Alterations to be made in the setting up of the 
 pieces constituting the Apparatus. — In our northern 
 climates the length of the reflector of the adjustible mirror 
 ought to he at least 50 times the diameter of the condenser, in 
 order to reflect the rays of the sun on the 31st of December 
 over all the surface of the condenser. With the length which 
 we have given to it, from the end of September (and. up to 
 March) the condenser is not all covered by the reflected rays 
 of the sun; and accordingly, instead of a round disc being 
 seen on the proof frame, there is only a rectangle cut by arcs 
 of a circle, while the sides of this rectangle, vertical at noon, 
 are inclined morning and evening. Hence the necessity of 
 adopting in winter a special arrangement, and nevertheless a 
 very easy one, if we confine ourselves to enlargements not 
 exceeding the size of the photographic sheet or double sheet.* 
 
 It is extremely easy to adapt to the winter arrangement all 
 the pieces of the apparatus which we have already described, 
 and represented in pi. II. Plate III. shows, on the same scale 
 of 5 centimetres to the metre, the arrangement of the apparatus 
 in winter. 
 
 Begin by inclining the adjustible mirror forward as repre- 
 sented in the plate, fcnd in such a way that two triangular 
 pieces of wood, having exactly the dimensions indicated in the 
 figure, hermetically close the openings at the side. The upper 
 part of the mirror is fixed by a strong piece of iron, and closed 
 up with a black cloth. On the foot which served to support the 
 
 * The adaptation of the heliostat to the apparatus allows of our working 
 in winter the same as in summer. (See the ensuing chapters.) 
 
2.18 
 
 PHOTOGRAPHIC OPTICS. 
 
 apparatus a second one is to be placed, of the dimensions re- 
 presented in tbe figure • (multiplied by 20), and the object of 
 which is to bring the axis of the apparatus into the axis of the 
 circular aperture of the adjustible mirror. Lastly, the proof- 
 frame itself has also to be modified by adding to' it two 
 wooden thbes, AD, BO (fig. 3, pi. III.), about its uprights, 
 which can be raised and lowered at pleasure, and be fixed by 
 a screw, N. The proof-board holders, represented by A B C D, 
 is fixed on the inclined cross-bar F G, so that the frame in 
 plate III. differs from that in plate II. only by the piece 
 FENG, the dimensions of which must be closely adhered 
 to, particularly thoser elating to the inclination. The manage- 
 ment of the apparatus is identical with that of the horizontal 
 apparatus, except that the frame has not only to be shifted 
 backwards or forwards to focus the image, but more than that, 
 the wooden tubes must be raised or lowered in order to bring 
 the centre of the proof-boards into the optical axis. 
 
 CHAPTER IX. 
 
 SETTING UP OF THE MOVEABLE DYALITIC APPARATUS. 
 
 Description of the Apparatus. — A single inspection 
 of fig. 1, pi. III., will enable the reader to understand the 
 working of the apparatus. 
 
 * ir(p\p is a rightangled triangle in which mp = T64 metres, ir <p = T74 
 metres, (p\p = 0‘57 metres ; which is first to be drawn on the wall, and to 
 which the supplementary foot is to be applied in order to see if it really 
 has the desired inclination. 
 
SETTING UP MOVEABLE DYALITIC APPARATUS. 219 
 
 The adjustible mirror, ABD, is fixed by means of strong 
 cross-bars to the solar camera proper, in continuation of which 
 is a bellows-arrangement, E F, and a wooden cone, F G, termi- 
 nated by a dark -frame, G H, of which the back is white, and 
 which can be removed from the cone. A groove, in which a 
 Bristol-board works, permits of the sensitised paper being 
 withdrawn from the action of the light when it is in the 
 frame. Ify means of a handle, L, the bellows can be drawn 
 out or shortened ; and the whole apparatus is borne on a foot. 
 The other pieces are identical with those we have already 
 described. 
 
 Management of the Apparatus. — First set the appa- 
 ratus * in such a way that the rays of the sun falling on the 
 adjustible mirror are reflected into the enlarging lens, K, and 
 to do this you will naturally make use of the guiding screws 
 attached to the adjustible mirror. Move the negative-holder, 
 J, into its proper place (vide p. 214) ; adjust the lens, K ( vide 
 p. 215) by lengthening or shortening the cone, E G (the doors 
 of which being open permit of the enlarged image being seen 
 projected on the white ground of the frame G H) ; then, when 
 the focussing is completed, slide the green-glasses over the 
 apparatus (not represented in the figure) ; close also the door 
 of the cone, FGH; keep the direction of the reflected solar 
 rays constant by continually looking at the objective, K ; and 
 remove the frame, GH, into which you put the sensitised 
 paper. 
 
 To do this, open the dark frame like a book ; pass a very 
 slightly damp sponge over the back of the sensitised sheet ; lay 
 it on the bottom of the dark-frame, and allow it to dry, which 
 
 * By placing the apparatus in the open air, the mirror is always long 
 enough, even on the 31st of December, to completely cover the condenser 
 with solar rays, which is not the case with the immoveable apparatus ( vide 
 p. 217). For this purpose, it is enough for the apparatus to make a more or 
 less wide angle with the vertical plane passing through the sun at the 
 time of operating. When the proof is finished, the apparatus is set aside 
 so as to preserve this angle. 
 
220 
 
 PHOTOGRAPHIC OPTICS. 
 
 will occupy only a few minutes. Then introduce the Bristol 
 board by which the sensitised paper is withdrawn from the 
 action of the light, and place the dark-frame in the apparatus. 
 
 It is necessary to have several frames, in order not to lose 
 time ; for the paper ought to be dry, so as to be tense like 
 the head of a drum (although folds do not sensibly distort 
 the image). 
 
 CHAPTER X. 
 
 APPLICATION OF THE HELI0STAT TO ENLARGING APPARATUS. 
 
 The necessity which exists of continually moving the govern- 
 ing screws of the adjustible mirror in order to keep the 
 reflected solar rays in a constant direction, has made many 
 persons seek for some means of performing this operation by 
 means of clock-work. But to effect this the axes of the several 
 parts of the adjustible mirror must turn with a determinate 
 velocity, and occupy positions assigned to them by the laws 
 which regulate the motion of the earth about its axis. Such 
 instruments bear the name of heliostats. An accurate know- 
 ledge of astronomy and mechanics is indispensable to any one 
 who wishes to use heliostats ; for without such a knowledge 
 no one can succeed in setting them correctly, and making 
 them work with the precision of which they are capable. 
 
 Three forms of heliostats* are suitable for photographic 
 enlargements ; and all three have their advantages and their 
 imperfections, which we shall point out in describing them. 
 
 * The other forms do not carry mirrors of large size. 
 
APPLICATION OF THE HELIOSTAT. 
 
 221 
 
 August’s Heliostat.— Imagine a mirror mounted in the 
 way seen in' fig. 2, pi. II., with its axis, G H, passing through 
 the plane of its reflecting surface, and exactly coincident with 
 the earth’s axis, and turning about this axis with a velocity 
 equal to half the sun’s angular velocity round the earth — that 
 is, making a complete revolution in forty-eight hours — and 
 you have August’s heliostat, which is necessarily of very great 
 accuracy because of its simplicity. 
 
 The sun being in the plane of the equator, a plane perpen- 
 dicular to the axis of rotation of the mirror (as on the 21st of 
 March) at any hour of the day, it is possible to give the 
 mirror such a position as that the reflected pencil may be 
 horizontal, and in the plane of the prime vertical, a position 
 which the reflected pencil will preserve all day long. 
 
 But the day following, the sun having approached the pole 
 by a quantity 8, the reflected pencil if made horizontal will 
 lie in a different plane from that of the prime vertical, or 
 if taken in this plane will make an angle with the horizon 
 equal to S. The apparatus for enlargement has therefore to 
 be moved every day, and this is very inconvenient. More- 
 over, the length of the mirror, inconsiderable in the morning 
 if the reflected ray is towards the east, will be too short after 
 two or three o’clock in the afternoon. 
 
 This heliostat, then, can only be practically useful in the 
 hands of an experienced astronomer, and in a country where 
 the sun mounts high enough in the heavens to enable us to 
 be content to make use of the apparatus for a part of the day 
 only. 
 
 The Heliostat of M. Leon Foucault.*— Let us leave the 
 inventor to describe the instrument himself : — “ What is a 
 heliostat? It is a reflector which moves by itself (see the 
 figure). In it the mirror, which is not less than 80 centi- 
 metres by 40, is attached to a mechanism which has to move 
 it slowly all day long in such a way as to make allowance for 
 
 Bull. Soc. Franc. Phot. 1862, p. 287. 
 
222 
 
 PHOTOGRAPHIC OPTICS. 
 
 the apparent motion of the sun, and reflect the light received 
 from it in an unvarying direction. 
 
 “ The sun, as you know, follows a path which varies inces- 
 santly in different countries and at different periods of the 
 
 Fig. 84. 
 
 year. A perfect heliostat ought strictly, like that which we 
 owe to M. Silhermann, to meet all the contingencies of the 
 problem ; it ought to work in all latitudes and in all seasons, 
 and to send the reflected rays in any direction whatever at 
 the will of the operator. I have not thought it necessary 
 to treat the question in a manner so general. I have taken for 
 granted that this machine set up as a fixture would never make 
 
APPLICATION OF THE HELIOSTAT. 
 
 223 
 
 part of a travelling stock ; and have left out of consideration 
 the complication of varying latitudes. I have likewise supposed 
 that in your experiments the bundle of solar rays would pre- 
 serve a nearly horizontal direction ; and have limited its 
 available inclination to the small extent which is fully suffi- 
 cient for the necessities of the centering and adjustment of 
 the optical apparatus. 
 
 “ Thus reduced to its essential elements, the apparatus is 
 formed of the following parts : — 
 
 A mirror, M (vide fig. 84), free to .move in all directions 
 about its centre, and solidly borne on a vertical column, P ; 
 
 “ A clock, H, regulated by the escapement and the pen- 
 dulum of the metronome ; 
 
 “ A horary, A, parallelly inclined to the earth’s axis ; 
 
 “ And a guiding-rod, F G, mounted on an arc of declina- 
 tion, D, and attached by a moveable joint to the rod perpen- 
 dicular to the mirror. 
 
 “ The first thing in placing the heliostat is to make the 
 table horizontal by the aid of a spirit-level, and to turn it 
 round so as to place the horary axis very nearly in the plane of 
 the meridian — that is, in the vertical plane through the sun 
 at noon. Then the day of the month is to be looked for on 
 the declination arc, and brought round and fixed opposite 
 to the index; and the dial, R, set very nearly to the time. 
 In this approximate position a line of solar light is seen passing 
 through the sight fixed on the diameter of the declination-arc, 
 and forming an image on the opposite plate on which two 
 engraved lines cross each other at a right angle. To give the 
 heliostat its exact position, nothing remains but to bring 
 the image on the point where the lines cross ; for this purpose 
 the movement of the entire instrument on its central pivot is 
 combined with that of the sundial. Lastly, the clock is set 
 going, and the catch is pressed down which puts the dial in 
 train with the wheelwork. The instrument is known to be 
 well placed by the small image continuing to rest on the 
 point of crossing of the lines. 
 
224 
 
 PHOTOGRAPHIC OPTICS. 
 
 “If now it is wished to cast its light in a determinate 
 direction, the pinion which moves the column P is turned, 
 and the reflected rays are made to follow the direction of the 
 line which passes through the centre of motion of the mirror 
 and the middle, L, of the guiding rod. 
 
 “ It is easy to understand why the mirror has an elongated 
 form. It is always necessary in order to send the sun’s rays 
 horizontally into our houses to incline the mirror more or 
 less, which considerably foreshortens its reflecting surface ; 
 and for this, allowance has to be made in the length of the 
 mirror. Besides having this elongated form, the mirror must 
 be able to set itself in the plane of reflection ; and it is for 
 this reason that it turns on agate planes, and that it is 
 attached to the guiding-rod by a groove fixed parallel to 
 the back of the frame. 
 
 “ All these conditions which it was necessary to fulfil have 
 been perfectly included by M. Dubosq. This large machine 
 works with the accuracy of a mathematical instrument. In 
 its execution M. Dubosq has found occasion to introduce into 
 it the improvement of a spring concealed in the column of the 
 mirror which assists it in surmounting difficulties which do 
 not occur in practice, but which would not have failed to give 
 occasion for adverse criticism. This is an improvement 
 which I thoroughly appreciate, and which would give a high 
 conception of the practical sense of the maker had we not 
 many times already had opportunity of forming in this respect 
 a very decided opinion.” 
 
 The heliostat of M. Foucault works with great accuracy if 
 the direction of the reflected rays is from the south to the 
 north or differs little from it. Otherwise the least irregularity 
 in the clock’s movement or in the setting of the instrument 
 in position may give rise to great disturbance in the direction 
 of the reflected rays. But it is always easy to place the 
 apparatus nearly in the direction of the meridian. 
 
 In winter the mirror of M. Foucault’s heliostat is much too 
 short to fully cover a lens 14 inches in diameter with reflected 
 
APPLICATION OF THE HELIOSTAT. 
 
 225 
 
 rays ; and it is only from April 1st to September 1st that this 
 can be done. 
 
 Finally, if the process lasts some time, the image of the snn 
 at the focus of the condenser is apt to get slowly displaced, 
 and there is no provision for readjusting the mirror by which 
 to correct the position of this image while the heliostat is in 
 action ; consequently, the process has to be interrupted. To 
 render the instrument thoroughly efficient, it would be neces- 
 sary to adapt to the axis and to the declination-arc two 
 adjusting screw’s, by means of which the error might be 
 corrected without having to stop the clock-work. 
 
 Fahrenheit’s Heliostat, modified by M. V. Monek- 
 hoven.— This heliostat has the advantage over that of M. 
 Foucault of being far simpler, and of thereby having a much 
 more regular motion. Further, it can be as well made use of 
 on December 21st, the time at which the sun is at its lowest, 
 as on June 21st, when the sun is at its highest, and this in 
 any part of the world. On the other hand, it is requisite that 
 the optical apparatus be placed in the plane of the meridian, 
 and inclined to the horizon at an angle equal to the latitude 
 of the place ; and to do this is often both inconvenient and 
 difficult, though when once accomplished, it always re- 
 mains so. 
 
 For the rest, the following is a full description of all the 
 parts which form the heliostat. The table N (fig. 85), is of 
 turned and polished iron. It is supported on three screws, 
 one of which is seen at 0, and presents at its centre a conical 
 part, about which turns the piece L M, capable of being made 
 fast to it by tightening the screw a. To render the table 
 horizontal, a good spirit-level, 15 cent, long, is applied to its 
 upper surface, in the direction of two of the screws, and one 
 of them turned until the air-bubble comes to the middle. The 
 spirit-level is then turned round, at right angles to its first 
 position (the position of the piece, L M, being shifted for this 
 purpose), and by means of the third screw, the air-bubble 
 again brought to the middle. The table is then horizontal. 
 
 Q 
 
226 
 
 PHOTOGRAPHIC OPTICS. 
 
 Frequently the screws, on which the table rests, are sup- 
 pressed, and the piece, L M, fixed to the table, — the he- 
 
 liostat in this case being mounted on one foot with the 
 optical enlarging apparatus. Then, the spirit-level must be 
 
 placed on the table alongside the piece, L M, and the table 
 rendered horizontal by means of the screws attached under 
 the foot of the entire apparatus. 
 
 The support, J K L M, is of iron. The arc, J K, necessary 
 
APPLICATION OF THE HELIOSTAT. 
 
 227 
 
 for the adjustment for latitude , is moveable, but is fixed by the 
 maker to the latitude for which the instrument is required. 
 No attempt, therefore, must ever be made to move this arc, 
 JK; on the contrary, it must be preserved from all displace- 
 ment.* 
 
 To the piece, JKLM, is fixed the arm-rest in which the 
 axis, A, turns, as the figure sufficiently explains. 
 
 The axis, A, is of steel, fixed by a screw’ to the arm-rest, 
 P Q, and rests upon the brass screw, B, which serves to bring 
 the several pieces into position. The screw, B, is made fast 
 by a side-screw. The parts of the axis touching the bearings 
 must be kept always well oiled. 
 
 The toothed circle , C, is fastened to the axis by a screw, of 
 which the thread runs the reverse way, in order that it may 
 not get loose by the rotatory movement of the axis* This screw 
 also should be securely fastened. The wheel, C, is divided 
 into 360 teeth, and must he kept clean by means of a brush 
 passed over it every day in the direction of the length of its 
 teeth. 
 
 The horary circle, I), divided into hours from six in the 
 morning to six in the evening, then into parts of twenty 
 minutes each, and lastly, into others of four minutes each, is 
 fixed on the axis by an hexagonal nut which can be tightened 
 by the hand. The index, E, slightly moveable, serves to in- 
 dicate the time on the horary circle, and has, for this object, 
 a line engraved with a diamond on its upper part. 
 
 The collar , I, works in a groove cut in the axis, A, and can 
 be made one piece with the axis by tightening the screw I, or 
 be left to turn freely about the axis day loosening the screw 
 I, which must be handled gently and never screwed up very 
 tight. This collar terminates at its lower part in a rod, 
 constantly pressed towards the letter J by a spiral spring. 
 
 * It is easy to verify if the axis, A, is inclined to the table (previously 
 rendered horizontal) at an angle equal to that of the latitude of the place. 
 For it to be so, the mirror, S R, being placed horizontal, the index, P, 
 ought to point to 90 3 — l. 
 
 Q 2 
 
228 
 
 PHOTOGRAPHIC OPTICS. 
 
 A screw, J, therefore, fixed on an arm-rest, which is attached 
 to the immoveable part of the heliostat and which also carries 
 the spiral spring, enables the collar to be moved in one 
 direction or the other (and consequently the axis, A, if the 
 screw I is fast) by very small degrees at a time. After having 
 used this part of the apparatus frequently, the rod which 
 works between the adjusting screw and the spring may get 
 caught against one of the two brass supports which carry 
 them. The screw J must then be turned until the rod reaches 
 the middle, and the axis, A, turned with the hand. The 
 rod is brought exactly into the direction of the screw J and 
 the spring by the screw B. But this is always done by the 
 maker. 
 
 The arm-rest , P Q, is of irorf At one end it carries a counter- 
 poise, Q, which serves to balance it about the axis, A; and 
 at the other an index, P, and an adjusting screw, T U, of 
 which we shall speak presently. 
 
 The mirror , S R, is octagonal, of finely silvered glass. It is 
 mounted in a frame of polished ebony, and has at its two 
 extremities two pivots of polished brass of exactly the same 
 diameter, and with their imaginary axis passing through the 
 reflecting surface of the mirror, and at right angles to the in- 
 dex XZ and to the axis A. These pivots revolve on the 
 arm-rest P Q on Y- shaped bearings, and are kept in place 
 by plates of brass. 
 
 The declination-circle , P, is fixed on one of the pivots and 
 divided into half degrees. When the zero of the graduation 
 is brought opposite the index, the surface of the mirror is 
 exactly perpendicular to the axis A* — an adjustment made 
 
 * This adjustment is made thus (fig. 2, pi. IY.) : — The zero of the 
 circle having been brought opposite the iudex — which is easily done with 
 the adjusting screw T — and the screw Y being fast (fig. 85), place the 
 point of a needle D (fig. 2, pi. IY.) in such a way that it touches the lower 
 part of the mirror. Then turn the mirror, B 0, gently round its axis A, so 
 that the part B may come round to the needle, which ought still to touch 
 the mirror. If it does not, correct half the difference by shifting the needle 
 
APPLICATION OF THE HELIOSTAT. 
 
 229 
 
 by the maker, and which mnst never be deranged in dis- 
 mounting or shifting the index. In the position of the circle 
 shown in fig. 85, the circle must be read to the right of the 
 zero (fig. 1, plate IV.), in winter (from September 21st to 
 March 21st), and to the left of the zero in summer (from 
 March 21st to September 21st). 
 
 The index (fig. 1, pi. IV.) is formed of a moveable plate of 
 brass, which can be applied to the division, of the circle, oi 
 removed from it by pressing on the lower part. A single 
 line traced on its upper surface serves to indicate the division 
 of the declination-circle ; and as the half and even the quarter 
 of each of them, corresponding to i or -1 of a degree (15 or 7 h 
 minutes of an arc) can be very well estimated, this amply 
 suffices for the adjustment of the instrument. It is necessary, 
 however, to be well practised in reading the circle, or better 
 still, to get assistance from some one accustomed to this kind 
 of readings, which besides requires to be done but once for all. 
 
 The bar , U T, consists of a slide-rod, capable of forming 
 one piece with the mirror by tightening the screw V. An 
 adjusting screw, T, attached to the arm P Q, allows, when the 
 screw V is fast, of the mirror being moved very small dis- 
 tances at a time. 
 
 The two sights , X, Z, are squares of brass-plate, placed at 
 the sides of the wooden mounting of the mirror, each being 
 pierced by a small hole. Further, the sight X bears on its 
 surface, facing the opposite sight, two lines perpendicular to 
 each other, traced with a diamond, one being parallel to the 
 surface of the mirror. 
 
 When the sights, X, Z, are brought in a line with the sun, 
 
 and the other half by the adjusting screw T (fig. 85), and repeat this opera- 
 tion until, on turning the mirror upon its axis, both its upper and its lower 
 parts just come into contact with the point of the needle as they present 
 to it. Then correct the index by moving it until the line which is 
 marked on it exactly coincides with the line 0 of the graduation traced 
 on the circle. This operation is performed with the greatest exactitude 
 by the maker before delivering the instrument, and if the index has not 
 been touched we may be certain of its correct position. 
 
230 
 
 PHOTOGRAPHIC OPTICS. 
 
 a thread of sunlight is seen proceeding from the aperture in 
 the sight Z, and falling on that of the sight X, where it 
 forms an image of the sun. In performing this operation we are 
 guided by the shadow of the sight Z, which ought to fall parallel 
 to the wooden mounting of the mirror. The hand is besides held 
 behind the sight X, in order to bring the shadow of the other 
 sight more easily upon the first. 
 
 The clock-work, G-, is enclosed in a brass box, is wound up 
 by the key b , goes 10 hours, and communicates its motion to 
 the wheel C by its pinion H. 
 
 The clock-work is fixed to the immoveable part of the helio- 
 stat by four screws, but by slightly loosening the two inferior 
 screws and lowering the clock-work, the pinion PI is thrown 
 out of gear. The pinion, PI, can at pleasure be put in 
 train with the clock-work or be rendered independent of 
 it, by tightening or opening the nut PI. If it is unscrewed, 
 the axis, A, can be slowly turned, and then the pinion is 
 seen to revolve rapidly. If it is screwed up, the clock- 
 work immediately acts on the toothed-wheel, C, so as to 
 make it perform a complete revolution in 24 hours. Care 
 must always be taken not to lose the nut II and the pinion, 
 which are liable, if the axis, A, is too frequently turned 
 round, to get detached. It is accordingly well to hold the 
 nut between the fore-finger and thumb, either to keep it open 
 or to screw it up. Keep also the open part of the box under 
 the key b, covered by a brass plate so as to prevent dust from 
 getting into the box. 
 
 Management of the Heliostat. — Wind up the clock- 
 work, loosen the screws Y, I, H, take hold of the mirror at R, 
 and give it its proper direction, about which we shall speak 
 farther on ; when this is very nearly effected, tighten the screws 
 Y and I, and adjust the mirror by the screws T and J to 
 give it its correct position ; then immediately close the nut PI 
 and loosen the screw I, and the mirror will obey the clock- 
 work. 
 
 Setting the Heliostat. — Make the table, X, horizontal in 
 
APPLICATION OF THE HELIOSTAT. 
 
 231 
 
 the way described at p. 225. Keep the screws a, Y, I and H 
 loose, after having wound up the clock-work. 
 
 Begin by rendering the mirror horizontal by applying 
 the spirit-level to its surface in the direction XZ, tighten the 
 screw Y, and complete the adjustment with the screw T. 
 Then applying the level to it in the direction of the pivots 
 (and at right angles to X Z) tighten the screw I and complete 
 the adjustment with the screw J. Go through the two ad- 
 justments again, without loosening the screws Y and I, making 
 use of the screws T and J only. 
 
 Having thus rendered the mirror quite horizontal, see if 
 the line xii of the horary circle, D, is quite in juxtaposition 
 with the line marked on the index E, and if it is not so, 
 move the index and the circle, D, cautiously, so that these 
 two lines become a prolongation one of the other — but with- 
 out the index, E, touching the circle, D, otherwise a dis- 
 placement of this index might take place in turning the 
 axis, A. Now loosen the screws Y and I. 
 
 Find out from an astronomical almanac the declination of 
 the sun on the day on which you are working, and, taking 
 the mirror in the right hand at R, communicate to it such 
 a motion as to very nearly bring the indicated degree of the 
 circle, P, opposite the index. Tighten the screw Y, and 
 turn the screw T until the index exactly marks the declina- 
 tion of the sun at the time. 
 
 Taking now the mirror in the hand at R, and noting on 
 your watch the true time * make the index indicate this time 
 
 * The true or apparent time is the time marked by the sundial, and not 
 the time marked by the ordinary clock, which is mean time. The difference 
 between the mean time and the true time constitutes the equation of 
 time. 
 
 To set a heliostat well, a knowledge of the exact time (to within a minute) 
 is indispensable, and should be carefully attended to. Throughout the 
 United Kingdom, at all railway stations, Greenwich meantime is always 
 adopted for civil convenience, although obviously that time does not truly 
 indicate mean time in other localities situated east or west of Greenwich. 
 In any place, therefore, where a heliostat is to be arranged for the day, it 
 
232 
 
 PHOTOGRAPHIC OPTICS. 
 
 on the circle, D, by communicating a rotatory motion to the 
 axis A. When this is very nearly effected let go the mirror 
 and tighten the screw I. Then turn the entire instrument 
 round on its pivot, a — taking it by the screw B, and without 
 stirring the table, N — until you see the thread of solar rays 
 emerging from the aperture of the sight Z and falling on the centre 
 of the sight X. Then tighten the screw a and the heliostat is 
 set. A much easier means of setting the heliostat is pointed 
 out farther on. 
 
 If now, in succession , you open the screw I and close the 
 screw H, you will see the image of the sun remain motion- 
 less for hours together at the centre of the sight X, and it is 
 only when this is the case that the heliostat is accurately set. It 
 must never be made use of until its working has been thus 
 
 will be very easy to calculate the true or apparent time by the following 
 data : — 
 
 1st. The exact longitude of the spot to within fifteen seconds must be 
 accurately ascertained. This can easily be got from the Ordnance 
 maps. 
 
 2nd. Greenwich mean time must be known ; and this, to within a few 
 seconds, can be ascertained at the nearest railway station. 
 
 3rd. An astronomical almanac (Dietrichsen and Hannay’s is very conve- 
 nient and cheap), containing the equation of time, declination of the sun , &c., 
 for every day of the y ear, is required. 
 
 With these data known, suppose it is wished to arrange a properly set-up 
 heliostat at Liverpool for a day’s work, say at nine o’clock on the 1st of 
 October, 1867. The longitude of Liverpool is three degrees west of Green- 
 wich ; the true time at that place is, therefore, exactly twelve minutes later 
 than London time. First ascertain accurately nine o’clock by Greenwich 
 mean time, deduct from that twelve minutes for difference of west longitude, 
 then turn to the almanac for the equation of time for that day, which 
 happens to show minus ten minutes fourteen seconds. In other words, the 
 sun is faster or passes the meridian sooner than the mean time indicates. 
 This difference must therefore be added to the mean in order to get the 
 true time. Thus 9 hrs. — 12 min. + 10 min. 14 sec. = 8 hrs. 58' 14", 
 which is the time at which the horary circle of the heliostat is to be set for 
 that day at Liverpool. And so for any other place, taking care, however, 
 to note that a divergence from Greenwich time must be added when the 
 place is east longitude, and that every 15' of longitude is equivalent to one 
 minute of time. 
 
HELIOSTAT WITH ENLARGING APPARATUS. 
 
 233 
 
 verified. When the heliostat is set, the table N and the 
 pieces LM, KJ, JM, being left in position, all the other 
 parts may be dismounted and taken away. To do this, open 
 the nuts which hold the circles C and D ; lower the clock- 
 work; open the collar I, by removing the screws which 
 close it round the axis ; and open and remove the upper half 
 of the bearing in which the upper part of the axis works. 
 The mirror, the arm-rest, and the axis can then be removed, 
 without the heliostat having to be reset when they are 
 replaced. 
 
 To take out the mirror alone, the screws Y and T are 
 first taken out and then those which hold the mirror in the 
 arm-rest P Q, the index P is turned outwards, and the mirror 
 removed. 
 
 CHAPTEE XT. 
 
 SETTING UP THE HELIOSTAT WITH THE ENLARGING APPARATUS. 
 
 Three ways of setting up the heliostat may be adopted : — - 
 
 IsL The most simple consists in inclining the enlarging 
 apparatus so that its optical axis coincides with the axis of the 
 heliostat. 
 
 2nd. The second consists in rendering the reflected rays 
 horizontal by means of a second mirror, and in any direction 
 whatever. 
 
 3rd. The third in rendering the reflected solar rays hori- 
 zontal by a mirror inclined at 45° to the axis of the heliostat, 
 in such a way as to reflect them from the east to the west, or 
 from the west to the east. 
 
234 
 
 PHOTOGRAPHIC OPTICS. 
 
 Section I. — Apparatus inclined to the Horizon. 
 
 Description of the Apparatus. — Fig. 4, pi. IV., repre- 
 sents this arrangement very accurately, including the wooden 
 shed which serves to protect the instrument from the rain. 
 
 This apparatus ought to he set up in the open air on a plat- 
 form or a terrace, or in a garden or a window balcony ; * but 
 in every case the floor must be made quite firm, &c. The 
 apparatus is composed of parts quite distinct from each 
 other. 
 
 ls£. The heliostat proper. It is similar in every respect to 
 that of which we have already given the description (pp. 225, 
 et seq .), and of which fig. 85 gives a true representation, 
 with this difference only, that the three screws of the table 
 are suppressed ; that the table is fixed immovably on the base 
 of the foot A B (fig. 4, pi. IV.), from which no attempt even 
 must he made to move it for fear of deranging its adjustment ; and 
 that the pieces LM and J K (fig. 85) are made fast — for the 
 
 * Look, at true noon-time , at the direction of the shadow of the vertical 
 cross-bar of the window. If this shadow falls to the left, F G, put the 
 apparatus to either the window B or A ; if the shadow falls to the right, 
 H I, put the apparatus either to 0 or B ; and if the shadow is perpendicular 
 to the wall, select the window B. But the window alwa,ys ought to open 
 on a level with the balcony outside and with the floor of the room. 
 
 
HELIOSTAT WITH ENLARGING APPARATUS. 
 
 235 
 
 maker accurately adjusts the heliostat so that its axis rigor 
 ously coincides with the axis of the optical apparatus. To 
 effect this adjustment the maker takes out the lenses of the 
 apparatus, and replaces them by circular discs of metal, having 
 at the centre a concentric aperture five centimetres across. He 
 takes out the axis of the heliostat, and slides in its place a 
 cylinder of wood two metres in length. He brings in this 
 way the axis of the heliostat and the apertures in the discs all 
 in a line with the cylinder of wood, and this done, he makes 
 all the parts immovable. It is therefore necessary to be care- 
 ful not to derange them. Above all, do not remove the table 
 C (fig. 85) from the foot to which it is attached, and do not 
 derange either the piece L M or the arc J K. But you can 
 remove the mirror, the axis A, the clockwork, &c., provided, 
 and this is essential, the fixed part of the heliostat remains so. 
 
 2nd. The foot , D E C U A (fig. 4, pi. IV.), of which D E 
 makes an angle with A B just equal to that of the latitude 
 of- the place for which the heliostat is constructed. It is 
 necessary, once that the apparatus is put up and adjusted, 
 to fix it firmly to the sides of the shed by lintels of wood and 
 its part A B to the floor, in order to prevent it from oscillating 
 or moving. Two screws, one of which is seen at C, serve to 
 render the foot horizontal in the direction of the length of the 
 apparatus, and in a direction at right angles to this. 
 
 The optical apparatus , H I, which is in everything like the 
 apparatus represented by fig. 1, pi. III., and worked in exactly 
 the same way ( vide p. 219). 
 
 The shed which shelters the instrument is drawn in the 
 figure, just one-twentieth * of its real size, for the apparatus of 
 which the condenser is fourteen inches in diameter, and for a 
 
 * For the apparatus of which the condenser is only eight inches in dia- 
 meter take three-fifths of the measurements which refer to the apparatus 
 of which the condenser is fourteen inches in diameter. As for the appa- 
 ratus of which the condenser is nineteen inches in diameter, it is not con- 
 structed in this way because of the height to which the building would go, 
 and of the difficulty there would be in managing it. 
 
236 
 
 PHOTOGRAPHIC OPTICS. 
 
 latitude of 45°. But if tlie latitude varies, the height of the 
 shed varies, as well as its length. As for its width, that 
 remains unaltered. Here are, however, the exact numbers 
 relating to fig. 5, pi. TV. : — 
 
 Latitude. 
 
 LV 
 
 Metres. 
 
 LK 
 
 Metres. 
 
 OP 
 
 Metres. 
 
 30° 
 
 2 
 
 2-50 
 
 3*0 
 
 40° 
 
 2 
 
 3-0 
 
 2'50 
 
 50° 
 
 2 
 
 3-25 
 
 2*25 
 
 60° 
 
 o 
 
 A 
 
 3-50 
 
 2-25 
 
 OM= 0-80; OS = 0'80 ; EM = 150; 1 
 
 TU = 1. 
 
 This shed is made of one-inch hoards and is ‘previously 
 directed towards the sun, which at true noon-time ought not to 
 cast a shadow on its longest sides (0 P, fig. 5, pi. IV.) In front 
 it opens, as shown in fig. 5, the two side-doors and the flap 
 being analogous to those in fig. 9, pi. II. 
 
 The door is placed at the bottom of the side L K (fig. 4), 
 and ought to he from 2 to 2*50 metres high and 1 metre 
 across. 
 
 Setting the Apparatus. — Nothing is easier than setting 
 the apparatus. Firstly, it is placed in a direction from south 
 to north (the heliostat to the south), and in doing this the 
 place of the sun at the true noon-time is the guide. 
 
 Place on the table N a spirit-level close to and parallel to 
 the piece L M (fig. 85) ; then in front of the heliostat arrange 
 a plumb-line formed of a string two metres long and two 
 millimetres thick, to which you suspend a weight (of half a 
 kilogramme), plunged in a small bucket of water so as to 
 render it less moveable.* Dispose the plumb-line in such a 
 
 * Fig. 6, pi. IV., represents the arrangement. A B, A C, A D, is a tripod 
 (a pair of steps will do also), E G the plumb-line, and H the bucket. A 
 wooden triangle, A (fig. 7, pi. IV.), attached to the optical apparatus, B, 
 and carrying the plumb-line, a b , will also do. 
 
HELIOSTAT WITH ENLARGING APPARATUS. 
 
 237 
 
 way that its lower part is at a very small distance from the 
 screw B (fig. 85) of the heliostat. Now carefully set your 
 watch to the true time as described at p. 231, and at the true 
 noon-time precisely move the entire instrument from right to 
 left or from left to right, so that the shadow of the plumb-line 
 divides the screw B (fig. 85), the circle D, the axis A, and the 
 case of the optical apparatus, into two quite equal parts. 
 
 A second person at the screws which are found at 0 (fig. 4, 
 pi. IY.) at the back of the foot, A B, turns them so that the 
 spirit-level placed on the table N (fig. 85) against the piece 
 L M indicates the horizontality of the table. It is necessary 
 to commence this operation some minutes before noon, to re- 
 move the mirror XB, to operate gradually and to stop 
 precisely at the true noon-time, beginning again the next day. 
 
 This operation, performed with care , is more than sufficient 
 to set the heliostat very accurately, but the wind may often 
 interfere with it. Always take great care that the plumb-line 
 is as near as possible to the instrument, without, however, 
 letting the bucket touch the foot of it. The nearer the plumb- 
 line is, the sharper does its shadow appear. 
 
 Another way of setting the heliostat is the following, which 
 must likewise be performed as near noon as possible. 
 
 The point xii of the horary circle being placed as has been 
 described at p. 231, put the circle P (fig. 85) at the sun’s 
 declination, and the circle D at the true time. Then at once 
 move the entire instrument with its foot, A B (fig. 4, pi. IY.), 
 until you see the image of the sun form at X (fig. 85). You 
 are to proceed as directed at p. 231, substituting the move- 
 ment of the entire instrument for the movement of the single 
 piece L M. But always keep the table horizontal by the foot- 
 screws. The operation must besides be performed several 
 times successively, as has been mentioned at p. 231, line 11, 
 et seq.; and it must then be tried if the instrument is well 
 set by making the clock-work act on the toothed circle 0, 
 in order to see if the sights remain constantly in the direction 
 of the sun, in which case the image of the sun remains 
 
238 
 
 PHOTOGRAPHIC OPTICS. 
 
 motionless for hours together at the centre of the sight X 
 (vide p. 232). 
 
 This done, the instrument is set once for all, and you should 
 fix the foot to the ground by screws or load it with blocks of 
 stone, in order to render it quite firm. It is always well to 
 place the apparatus on a well-hardened piece of ground, on a 
 thoroughly firm flooring, on a foundation of masonry sur- 
 mounted by a large flat stone, or on something of this kind. 
 
 Management of the Apparatus. — The management of 
 the apparatus is exactly like that of the ordinary apparatus, 
 of which we have spoken in the instructions at p. 218, ei seq ., 
 and which is seen in fig. 1, pi. III. Only let us remark, if 
 the operator desires to enlarge negatives to sizes exceeding 
 the photographic sheet — the size which the apparatus allows 
 of — he will throw the image on to a large board placed at the 
 upper part of the shed in a suitable position. 
 
 Whatever may be the time and the sun’s declination — 
 which have only to be considered on the days when the 
 apparatus is set — we commence by loosening the screws Y, I, 
 and H of the heliostat (fig. 85), and then, holding the mirror 
 at R whilst looking at the centre of the enlarging lens % we 
 direct the solar rays upon it. When we have brought them 
 very nearly on to it, we tighten the screws Y and I, and finish 
 the adjustment with the screws T and J. This being 
 effected, we tighten the nut H and loosen the screw I ; and 
 then the heliostat, obedient to the clock-work, keeps the image 
 of the sun for hours together at the centre of the enlarging 
 lens, provided that it has been correctly set, and that the appa- 
 ratus from that moment has remained exactly in its place. 
 But if the sun’s image, getting slowly displaced, comes to 
 touch the margin of the objective, rectify it by loosening the 
 nut H, tightening the screw I, and touching the screws I and J. 
 The rectification made, screw up the nut H, and loosen the 
 screw I. All this is done in some seconds, without sensibly 
 checking the motion of the apparatus. Of course, first of all, 
 the clock-work has to be wound up. 
 
239 
 
 HELIOSTAT WITH ENLARGING APPARATUS. 
 
 When it is wished to terminate the operation, the nnt H 
 and the screws I and Y are loosened, and the part, S, of the 
 mirror brought against the arc of the circle K ; then leaving 
 all in this state, the shutters which preserve the heliostat 
 from dust and rain are closed. 
 
 The opening in the shed which gives passage to the heliostat 
 should be capable of being closed by easily moved curtains, 
 which shut out the heliostat from the interior of the shed. 
 When the reflected solar light is directed by the heliostat into 
 the apparatus, the curtains are opened in order to see into the 
 optical apparatus. Protect the foot of the apparatus, even 
 the part situated under the heliostat, from the heat of the 
 sun’s rays by covering it with a cloth lined with wadding or 
 
 hay* 
 
 Section II . — Apparatus with the heliostat of two mirrors. 
 
 Application of the Heliostat to apparatus , with 
 ordinary adjustible mirror. — All enlarging apparatus, both 
 on our system and on the old system of Woodward, can have 
 the heliostat applied to them, if in front of the adjustible 
 mirror there is a clear space of one metre and a half in all 
 directions. 
 
 To thoroughly comprehend how these apparatus are placed, 
 it is necessary to bear fully in mind the principle that the 
 heliostat figured at p. 226 keeps the sun’s rays reflected in 
 the direction of the prolongation of the axis A. If now a 
 second mirror is employed to reflect the rays again in any 
 direction whatever, they will still be given off motionless, 
 since they are first made so by the heliostat itself. There is, 
 it is true, the loss of a tenth of the light by the employment of 
 a second mirror, but, on the other hand, there is the advantage 
 of dispensing with the assistant placed in charge of the ordi- 
 nary adjustible mirror. This system has moreover been 
 employed since January 1st, 1864, by M. Damry of Liege 
 and M. Yerbeke of Louvain with complete success. Their 
 
240 
 
 PHOTOGRAPHIC OPTICS. 
 
 enlarging apparatus is horizontal, and they employ the 
 heliostat, so simple and easy to work, represented by fig. 85. 
 The diameter of the condensers of their apparatus is nineteen 
 inches. 
 
 In all parts of Europe, and above all in the north, this way 
 of mounting the heliostat is very convenient, particularly if 
 the direction of the enlarging apparatus, already set up at 
 the time of applying the heliostat to it, instead of being from 
 south to north, makes a considerable angle (an angle of 45°, for 
 example), with this direction, and is rather from east to west 
 or from west to east. A wall facing the east, the south-east, 
 the west, or the south-w*est, is more favourable than a wall 
 towards the direct south. Nevertheless, if, following the 
 instructions which always accompany all enlarging appa- 
 ratus, the setting towards the south should have been chosen, 
 it would be well, previous to the operations for mounting the 
 heliostat which we are about to indicate, to shift the apparatus 
 from this direction, placing it across the room in line with the 
 south-east or south-west, at the same time moving into this 
 r direction the adjustible mirror also. All this, as we shall soon 
 see, is for the purpose of preventing the shadow of the ordi- 
 nary adjustible mirror in summer time from covering any part 
 of the mirror of the heliostat. 
 
 Operations preliminary to the Setting np the Helio- 
 stat. — Fig. 4, pi. Y., gives a clear idea of the operations 
 preliminary to mounting the heliostat. Let A be our adjust- 
 ible mirror, from which the mirror itself has been removed and 
 replaced by a rod of wood turned in a lathe, and resting on 
 the bearings a and 5, which terminate the iron arms. Suspend 
 from the middle of this rod a plumb-line, which will touch the 
 ground at c. Suspend another plumb-line, E F, a metre or two 
 in front of the first, and, precisely at true noon-time, move 
 this line until its shadow, F C, passes exactly through the 
 point C. Trace on the ground the straight line C F, which 
 will evidently be the direction of the meridian. If now BF 
 makes with C F an angle equal to the latitude of the place, it 
 
241 
 
 HELIOSTAT WITH ENLARGING APPARATUS. 
 
 is clear that this line exactly represents the axis, A, of our 
 heliostat which has itself also to be in the plane of the 
 meridian, making with CF an angle, F, equal to the latitude of 
 the place. 
 
 If the height B C is from 1*50 to 2 metres, the heliostat 
 will then be easily applied, because there will be a sufficient 
 distance between the heliostat and the adjustible mirror. 
 
 The preliminary operation consists therefore in setting up 
 the plumb-lines B C and C F, so as to get the straight line C F, 
 which represents the meridian, or north-and-south line. 
 
 Application of the Heliostat.— Now, on a packing case 
 or temporary wooden stand, some centimetres high, mount 
 the heliostat so that its axis, A (fig. 85), is projected along the 
 straight line 0 F, and set it by means of the sun just as we 
 have described at p. 234, et seq. When the heliostat is fully 
 in position and working, loosen the screw V very gently, depress 
 the part R of the mirror until the circle P just indicates the 
 number . of degrees and parts of a degree of the sun’s de- 
 clination as given in an astronomical almanac for the date of 
 the day on which we operate. Then tighten the screw V, and 
 properly adjust the circle by means of the screw T. 
 
 The sun’s rays are now reflected in the direction of the axis 
 of the heliostat, and if the instrument is set up in a proper 
 position — that is, if the axis of the heliostat coincides with 
 the imaginary straight line B F — all the rays reflected by the 
 mirror of the heliostat will be seen to fall on B. To see this 
 better, paste white paper over the entire surface of the mirror 
 of the heliostat, exceptirfg its centre, where you leave an 
 open circular space five centimetres in diameter. (The centre 
 of the mirror is the point which divides into two equal parts 
 the straight line which joins the two pivots). 
 
 In working with a mirror thus covered up, you will see the 
 reflected image of the sun by interposing a white card in 
 the course of the reflected pencil in the neighbourhood of the 
 adjustible mirror. This solar image ought to fall exactly on 
 the- point B, and if it does not do so we must try to make it 
 
 R 
 
242 
 
 PHOTOGRAPHIC OPTICS. 
 
 do so within some centimetres, by moving the heliostat and 
 resetting it. Then, replace the provisional foot by a small 
 mass of masonry of the same height resting on the ground, and 
 bounded at top by a very smooth and quite horizontal stone 
 surface, about one metre square. Upon this rest your heliostat, 
 recommence the setting, place the mirror of the adjustible 
 mirror horizontal, reflect the already reflected solar rays into 
 the enlarging apparatus, and see if the condenser of this 
 apparatus is fully covered by the solar light ; if this is not the 
 case your heliostat still does not send the solar light into the 
 apparatus properly. 
 
 There is a simple and easy means of moving your heliostat, 
 so that its reflected rays may take a perfectly right direction. 
 
 Have a small flat wooden rule, A B (fig. 3, pi. IV.), made, 
 fifteen centimetres long, and with a sight at each end analo- 
 gous to those, X, Z (fig. 85), placed on the sides of the mirror ; 
 and fix this rule by a screw, C, to the side of the mirror. 
 When you have lowered the mirror until the circle P just 
 indicates the given number of degrees of declination — when, in 
 a word, the sun’s rays are reflected on to the adjustible mirror 
 1 — make the rule, A B, rotate gently about its centre, C, until 
 the. solar rays, entering by the sight B, just form a round 
 image on the sight A, the place of which you mark by a 
 metallic point. If the heliostat is in action and is well set, 
 the sun’s image on the sight A will remain motionless, as well 
 as that at the focus of the condenser of the enlarging apparatus. 
 If this condenser is not fully covered by the sun’s rays, it is 
 because a part of the light reflected by the heliostat falls to 
 one side of the adjustible mirror. You can now shift your 
 heliostat without disturbing its setting by seeing that the 
 sun’s image, during the shifting, always falls on the same place 
 on the sight A. You could in this way move the heliostat 
 where you liked, on condition that the mirror is moved by the 
 clockwork. 
 
 The heliostat once in right position, keep the adjustible 
 mirror quite still, and if the reflected pencil does not remain 
 
HELIOSTAT WITH ENLARGING APPARATUS. 
 
 243 
 
 quite motionless, rectify it exactly in the way described at 
 p. 238, line 30 et seq. But it will remain motionless if it has 
 been set exactly to the right time, and if the declination has 
 been carefully read off. 
 
 Once the apparatus is in position, it is protected from the 
 rain by covering it with a small wooden case, which may be 
 constructed according to the operator’s taste. 
 
 After this, to make use of the apparatus, it suffices to direct 
 the sun’s rays into the enlarging apparatus just as we have 
 described at p. 237. 
 
 Fig. 5 (pi. V)* represents the most favourable arrangement 
 in setting up this apparatus when from want of the necessary 
 space under the adjustible mirror a wooden shed is obliged to 
 be erected on a terrace or in a garden. In this case the optical 
 apparatus is directed along the line C D (from east to west), 
 and the heliostat, A, is placed at a corner of the building. 
 The length, C D, of the building is five metres, and its breadth 
 two, and the height, F G, of the floor from the ground one and 
 a half metre. 
 
 Section III. — Another disposition of the Apparatus with the 
 Heliostat of two Mirrors. 
 
 Description of the Apparatus. — This apparatus, repre- 
 sented in fig. 8, pi. 1Y., is in the main exactly similar to the 
 preceding, with this difference, that the second mirror, instead 
 of being between the heliostat and the condenser, is behind 
 the condenser itself. It is more easily set, but requires a 
 building, if not erected expressly for it, at least adapted to it, 
 such as a room with a window balcony, &c. j 
 
 * Only the draughtsman has wrongly placed the heliostat, A, which 
 ought to be in front of the post I, and not behind it. 
 
 f Supposing it to be the room in fig. 86, the apparatus will be placed at 
 the window 0 if the shadow of the vertical bar of the window is along H I 
 at true noon-time ; and at the window A if this shadow is along F G, but 
 in this case the maker must be told to change the box K O (fig. 8, pi. IV.) 
 to the other side, and to alter the position of the reflector from along C E 
 to along B D. 
 
244 
 
 PHOTOGRAPHIC OPTICS. 
 
 In other respects, it exactly resembles the apparatus de- 
 scribed at pp. 225, et seq., and is set in the same way : there- 
 fore the reader, after having made himself acquainted with 
 the detailed description of the heliostat which we have given 
 at pp. 225, et seq ., ought also to study pp. 233, et seq., for 
 we shall pass rapidly over the details of the mounting of this 
 apparatus. 
 
 The following is a description of the apparatus (fig. 8, 
 
 Pl- IV.):- 
 
 The heliostat is exactly like that which we have described 
 at pp. 225, et seq. (fig. 85), save that the three screws of the 
 table are in it suppressed, and also the movement of the piece 
 M L about the screw a and that of the arc K J. This heliostat 
 therefore is fixed immoveably on a cast-iron foot, Q E (fig. 8, 
 pl. IY.), which carries at its end K two adjusting screws 
 serving to make the table of the heliostat horizontal, just as in 
 the apparatus described at pp. 234, et seq. The stand S, fixed 
 also immoveably on the iron foot Q E, carries a cubical 
 box, C E G, made of very thick oak. 1 n this box is the con- 
 densing lens H, the axis of which coincides rigorously with 
 that of the heliostat. The side of wood opposite presents a 
 circular hole five centimetres in diameter, which also coincides 
 with this axis, and which enables the apparatus to be very 
 accurately adjusted. This is how the maker proceeds for 
 this purpose. He fastens the heliostat on the cast-iron foot,, 
 renders the table quite horizontal — so made as that the axis of 
 the heliostat forms with the table an angle exactly equal to the 
 latitude of the place for which the heliostat is intended— 
 and then fixes the pieces M L and K J (fig. 85) with strong 
 irremovable screws. He next removes the axis A from the 
 heliostat, replaces it by a very accurately turned cylinder of 
 wood two metres long, and then, removing the glass, I J, and 
 replacing the condenser by a circular card with a hole in 
 -its centre also circular, he fixes the stand S (fig. 8, pl. TV.) 
 on to the cast-iron foot when the two apertures (that in the 
 card and that pierced in the opposite side) are exactly 
 
HELIOSTAT WITH ENLARGING APPARATUS. 
 
 245 
 
 obstructed by tbe wooden cylinder. The axis of the cubical 
 box thus becomes exactly coincident with the axis of the 
 heliostat ; but for this to be perfectly so in relation to the other 
 parts of the optical apparatus, extreme care must be taken to 
 give it a true cubical form. The heliostat , therefore , must never 
 he removed from the foot Q R, nor any attempt he made to shift the 
 stand S and, the cubical hox. This is of great importance. 
 
 The negative lens U is fixed in the side E D of the cube ; 
 the negative holder, Y, and the enlarging lens, X, being in a 
 separate box, K 0, of which the axis, at right angles to the axis 
 of the heliostat, is horizontal. Before setting the apparatus, 
 this hox , K 0, as well as the condenser , H, and the glass , I J, must 
 he removed , and the condenser replaced by the card having a 
 concentric aperture of which we have spoken above. 
 
 Setting the Apparatus. — For the rest, the apparatus is 
 set exactly in the way we have given at p. 236, both by the 
 plumb-line in the first place, and then more precisely by 
 making use of the true time marked by the horary circle, 
 and of the declination of the sun on the day when the appa- 
 ratus is set. 
 
 When the mirror obeys the sun very accurately, keeping its 
 image motionless on the sight X (p. 232), the adjustment of the 
 mirror J I must be proceeded with, and, before doing so, the 
 box K P be adjusted, after having fixed the foot Q R solidly 
 to the ground either by loading it with blocks of stone or by 
 screwing it to the ground with bolts. 
 
 Set the heliostat going, and reflect the sun’s rays on to the 
 card H in such a way that you see a circular line of light 
 round the hole made in the side C D of the wooden cube. 
 Then tighten the screws of the heliostat, and see at the end of 
 half an hour if the sun’s rays reflected through the aperture 
 in the card keep their place well — as they will do with 
 surprising exactness if the heliostat is well set. And, if they 
 do not, examine well whether you have not forgotten to 
 tighten one of the screws of the heliostat, or have badly put 
 the clock-work in train, or done some such thing ; and then 
 
246 
 
 PHOTOGRAPHIC OPTICS. 
 
 begin, again the setting itself, not forgetting that quite the 
 exact time is necessary for this object. 
 
 But when the reflected solar rays remain qnite motionless 
 on the aperture in the side C D, introduce the lens H, and 
 cover it with the circular card which limits it to its central 
 part. Then introduce the mirror I J, previously well cleaned, 
 between the corner-pieces which serve to keep it in the diagonal 
 of the cube, and see if the round image of the aperture H is 
 cast exactly on the middle of the enlarging lens — without, 
 of course, at any time stopping the motion of the heliostat. 
 
 If this is not the case, the position of the mirror I J must 
 be corrected with extreme care by shifting the corner-pieces of 
 wood, which are made expressly for this end. This must be 
 done without jerks or jolts, which might derange the apparatus 
 (this is why it is necessary first to fix its foot to the ground), 
 and without stopping the motion of the heliostat. "When at last 
 this adjustment is made, put on the flap CDEB. 
 
 Management of the Apparatus. — The apparatus is now 
 ready for use. And to use it, it is sufficient at any hour of the 
 day, and on any day in the year whatever, to direct the sun’s 
 rays into the apparatus until the image of the sun is formed 
 at the centre of the objective exactly as we have described at 
 p. 8. As to the management of the parts constituting the 
 optical apparatus, it is in everything similar to that of the 
 horizontal apparatus, a description of which we have given at 
 p. 238, and to this the reader must refer. The negative to be 
 enlarged is placed at Y in the cone of solar rays ; the objective 
 X serves for focussing ; and the green glass Y serves for a 
 shutter. Green glasses slide in the grooves K L, P 0, &c. 
 
 Site of the Apparatus. — The shed which has to protect 
 the apparatus may be made of either wood or masonry. Figs. 
 1 and 2, in pi. V., give a very accurate representation of it, 
 one-twentieth of the actual size. 
 
 The following is its description : — 
 
 AC DB a wooden building of which the length, A C, is 
 5 metres, the breadth at AB, 14 metre, and at CD, 3 to 34 
 
HELIOSTAT WITH ENLARGING APPARATUS. 247 
 
 metres, the height, 0 D, 2 h metres, and the height, 0 Z, of 
 the roof, 1 metre — the sides CD, AB being placed exactly 
 in the line of the meridian,* and the side A C at right angles 
 to them. The opening, abed, which gives passage to the 
 heliostat, G L, has' for its dimensions : — 
 
 ab = 2 metres. 
 be — li metre. 
 
 This opening is closed by lateral shutters, HI, K J, moving 
 on hinges, and a wooden flap, P, lined with zinc, the play of 
 which is analogous to that represented in pi. XV., fig. 5. 
 
 EF is a straight line parallel to AC, which represents the 
 axis of the optical apparatus, G. On this axis is the proof- 
 frame, MN, the construction of which exactly corresponds 
 with the drawing in fig. 6, pi. II., save that the centre of 
 figure of this frame must be kept at the height, from the ground, 
 of the enlarging objective of the apparatus. 
 
 The side B D should make an angle of at least 1 5 degrees 
 with the sides A B, DC ; for if this side were parallel to the 
 opposite side, A 0, of the shed, the image projected by the ap- 
 paratus, L, would fall on this side. If, however, it is wished 
 to form the part ABCD rectangular, the sides CD, A B, 
 instead of being in the plane of the meridian, will then have 
 to make with it an angle of some degrees. The apparatus will 
 then be placed as represented in fig. 3.f 
 
 In all cases the aperture ab cd is closed by moveable cur- 
 tains which envelope the cubical oaken box and the stand of 
 the apparatus, and which ought to open readily, so that the 
 moment the sun’s rays from the heliostat are sent into the 
 optical apparatus they can be observed by the person who 
 directs the heliostat. 
 
 ' On this point see what we have said at p. 236. 
 
 f In this ease, the wall 0 B will now run in the direction of the shadow of 
 the plumb-line at one o’clock in the afternoon. The dimensions of this room 
 will he — B 0 = 3 metres ; AB = 4 metres ; the opening D E, &c., the same 
 as that in figs. 1 and 2. 
 
248 
 
 PHOTOGRAPHIC OPTICS. 
 
 CHAPTER XII. 
 
 THE PARALLEL SOLAR LIGHT APPARATUS OP M. BERTSCH.* 
 
 M. Bertsch finds in Woodward’s apparatus the defects which 
 we have pointed out, and, to avoid them, he has constructed 
 a small apparatus in which the condenser is suppressed, the 
 negative being traversed by the direct rays of the sun. 
 Fig. 87 represents the apparatus. The mirror, B, receives two 
 
 Fig. 87. 
 
 movements by means of a milled head D and a screw C, so 
 as to bring the sun’s rays S into the axis of the instrument. 
 This moveable mirror is fixed in the shutter of a well-darkened 
 
 * A minute comparison has been made by the author of this work 
 between the small-sized apparatus of Woodward (the condenser of which 
 is no more than four inches in diameter) and M. Bertsch’s apparatus, with 
 the object of convincing himself whether in reality parallel light was to be 
 preferred to convergent light for illuminating the negative to be enlarged. 
 This comparison has made it evident that if the enlarging lens of Wood- 
 ward’s apparatus is constructed on the principles we have stated in speak- 
 
SOLAR LIGHT APPARATUS OF M. BERTSCH. 
 
 249 
 
 room. The negative, which cannot be more than eight centi- 
 metres in the side, is fastened in a frame E, and introduced 
 through a slit, O. The two achromatic lenses H and I, 
 capable of being approached to or drawn back from the nega- 
 tive by means of the rack M, form the image on a screen 
 
 mg of this objective, no difference in the results can be perceived in- the 
 enlarged images furnished by the two apparatus. 
 
 M. Bertsch’s apparatus, compared — and always with extreme care and in 
 a great nnmber of experiments — with the dyalitic; apparatus, of which the 
 diameter of the condenser was not less than twenty inches, has not given 
 better results, but the contrary, the considerable time required by this 
 apparatus (that of M. Bertsch) for printing the proof tending to bring a 
 certain haziness into the image in consequence of the inevitable motions of 
 the ground, and the parts which support the apparatus. But in making 
 these experiments, as soon as the optical image had made a slight impres- 
 sion on the photographic surfaces sufficient for judging of the sharpness of 
 the image, they were arrested ; and we were thus able to convince ourselves 
 that the convergent light, properly employed, gives as good results as 
 parallel light, besides possessing the advantage of an infinitely greater 
 intensity. 
 
 This intensity, which M. Bertsch endeavours to dispute (Bareswill et 
 Davanne, Ghimie Photographique) by asserting that the thickness of the 
 condensers absorbs a very large quantity of the incident light, thus taking 
 from large condensers the advantage which their surface would lead us to 
 expect, is such that M. Bertsch’s apparatus requires forty times more time 
 to print a proof of a negative than Woodward’s apparatus, of which the 
 condenser is nineteen inches across. The truth is that the intensity of 
 the light given by the condensers is approximatively proportional to the 
 squares of their diameters, which the law of absorption, stated at page 7, 
 sufficiently explains. 
 
 The little intensity given by M. Bertsch’s apparatus has caused this 
 writer to print from the negative to be enlarged a small positive by trans- 
 parency, and then to enlarge this to a negative from which positive proofs 
 can then be taken in the pressure-frame. We shall presently speak of 
 this method, which is hardly practicable, and which, above all, gives proofs 
 infinitely less sharp than the method of direct enlargement of the negative 
 on to the positive on paper. 
 
 Upon the whole, the apparatus (M. Bertsch’s) gives proofs of great 
 sharpness, most undoubtedly; but, according to us, this is due, not to 
 the parallelism of the solar rays which illuminate the negative, but to the 
 absence of all aberration in its illumination, the injurious effects of which 
 aberration we have pointed out when speaking of the theory of Woodward’s 
 apparatus. 
 
250 
 
 PHOTOGRAPHIC OPTICS. 
 
 at a suitable distance. A diaphragm, K, which is at the end 
 of the instrument, and placed at the principal focus of the 
 objective H I, cuts off the diffused light. 
 
 This diaphragm, K, represented separately at K', carries' a 
 moveable plate pierced with two holes, m and n, the first open, 
 the other closed by a yellow glass, which allows of the photo- 
 genic action of the apparatus being arrested at any desired 
 moment. 
 
 The apparatus of M. Bertsch would be better, in a mechanical 
 point of view, if the adjustible mirror were separated from the 
 optical apparatus ; for the wind, or a movement of the hand, 
 causes the mirror to vibrate, and consequently also the optical 
 apparatus, and often in this way destroys the sharpness of the 
 enlarged image. 
 
 CHAPTER XIII. 
 
 INDIRECT ENLARGEMENT BY THE SUN OR BY DIFFUSED LIGHT. 
 
 Inferiority of this method over the direct method. — 
 
 As we have just said, many persons, arguing from the frequent 
 absence of the sun in northern climates, and the necessity 
 under which the photographer by profession often finds him- 
 self of having to employ old negatives the intensity of which 
 is too great for them to be enlarged by the solar camera, prefer 
 to reproduce this negative as a positive by transparency, the 
 intensity of which they regulate at pleasure, and which they 
 next enlarge to a negative, from which they then print off 
 as many positives on paper as they desire. 
 
 Evidently much of the sharpness of the original negative is 
 
INDIRECT ENLARGEMENT BY THE SUN, ETC. 251 
 
 lost, for if the positive is taken from it by contact with dry 
 collodion or at a distance by means of the camera, sharpness 
 is at once lost by this operation (but less so in working at a dis- 
 tance by means of the camera than by contact). Secondly, in the 
 act of enlarging this positive into a large negative, sharp- 
 ness is further lost, particularly if diffused light is employed 
 — (see p. 187, lines 22, et seq .) To this we may add, that in 
 the enlarged negative the spots and defects of the original 
 negative, of the positive, and lastly of this negative itself, are 
 united. It is therefore very difficult to obtain with this 
 method enlarged positive proofs which have not to be exten- 
 sively touched up. 
 
 However, this method can be employed in winter when the 
 absence of the sun renders it indispensable. It is carried 
 out in two ways, either by means of the enlarging appa- 
 ratus itself, which affords the most convenient disposition for 
 this purpose, or by means of a camera and a good ordinary 
 objective. 
 
 Conversion of the original Negative into a Positive 
 by transparency. — The adjustible mirror of the apparatus, 
 and the apparatus itself, being disposed in the way we have 
 described, the mirror is so placed that it reflects the diffused 
 light coming from the zenith on to the negative, which is put 
 in the ordinary manner into the negative holder. If there is 
 sun, the sun-light is directed into the apparatus, placing 
 between the condenser and the negative to be enlarged and 
 ten centimetres from the latter, a finely-ground glass or a 
 sheet of oiled paper. The objective is to be reversed — that is, 
 the lens of least diameter must face the negative to be 
 enlarged. Moreover, the smallest diaphragm accompanying 
 it must be put on. Lastly, apply to the objective the cir- 
 cular aperture of a small quarter-plate camera, and reproduce 
 from the negative to be enlarged a small positive by trans- 
 parency which should be at the most of the size of eight centi- 
 metres by six, whatever the dimension of the original negative 
 (which we suppose, however, larger than eight cent, by six). 
 
252 
 
 PHOTOGRAPHIC OPTICS. 
 
 For tlie rest, this positive should present all the characters of 
 a negative intended for enlarging, that is, intensity and an 
 absence of fogging. 
 
 The enlarging apparatus, however, can just as well be 
 dispensed with, and the original negative placed against a 
 window and be reproduced of carte-de-visite size by means of 
 a good ordinary objective (the triplet suits best) and a camera ; 
 but in general the employment of the enlarging apparatus 
 is more convenient, because the mirror permits of the light of 
 the sky upon which it is projected being reflected on to the 
 negative. 
 
 The method which consists in applying a dry collodion plate 
 over the negative in an ordinary pressure-frame, and obtaining 
 thus, after its development, a positive by transparency, is not 
 at all so good as the preceding, inasmuch as the surfaces 
 are liable to rub and not to come completely together on 
 account of want of flatness ; and lastly, because we are not 
 able to give to the positive the dimension the most advan- 
 tageous, which is that of the carte de msite. 
 
 Enlargement of the Positive by means of the enlarg- 
 ing apparatus. — Place it as you would do a negative in 
 the enlarging apparatus, employing the magnifying lens no 
 longer in a reversed position as directed above, but in its 
 normal position, represented in fig. 4, pi. II. 
 
 Make use either of diffused light or of sunlight ; with the 
 latter, in order to lessen the excessive power of the illumina- 
 tion, interpose between the condenser and the mirror two, 
 three, or even four deep-blue glasses, which will absorb a great 
 part of it. Never interpose, as some persons advise, a ground- 
 glass between the condenser and the positive to be enlarged. 
 But if you do so, you must furnish the enlarging lens with the 
 smallest of its diaphragms ; whereas with sunlight transmitted 
 through blue glasses you can employ larger diaphragms, and 
 even the largest of all, without affecting the sharpness of the 
 enlarged image.* 
 
 * P. 187 will make this intelligible to the reader. 
 
INDIRECT ENLARGEMENT BY THE SUN, ETC. 
 
 253 
 
 The image of the positive to be enlarged should be thrown 
 on the sensitised collodion surface either dry or moist. Waxed 
 paper may also be used, but the time of the operation is much 
 longer, and is too long when we are working without sun. 
 
 It is well, particularly when we are working with moist 
 collodion, to attach a conical bellows to the enlarging lens and 
 the holder of the glass bearing the collodion- surface, in order 
 to preserve this from all light but that proceeding from the 
 positive to be enlarged. 
 
 The focussing of the enlarged image is effected with much 
 greater sharpness by sunlight than by diffused light ; and the 
 rapidity in printing is necessarily much greater. Most 
 frequently, after having interposed the blue glasses we have 
 spoken of, the time of exposure is, so to speak, instantaneous, 
 while with diffused light it is always several minutes. We 
 here suppose the employment of moist collodion ; dry collodion, 
 and waxed paper especially, requiring a much longer time. 
 The enlarged negative obtained then serves for taking posi- 
 tives on paper by the ordinary method. 
 
 Enlargement of the Positive by the Camera Obscura, 
 — Place the positive to be enlarged quite vertically up against 
 a fully exposed window, and if the sun comes on this window 
 place the positive over a ground-glass, leaving between the 
 two glasses a space of one centimetre, in order that the grain 
 of the ground-glass may not come out in the enlarged negative. 
 
 It is well, in order to prevent reflections of light in the 
 camera, to place round the positive a strip of black paper 
 twenty centimetres wide, or better, to place the positive in a 
 wooden frame made for the purpose, the edges of which are 
 joined to those of the camera by a piece of some black material, 
 which keeps out all light that has not traversed the said 
 negative. 
 
 Now put a triplet of fifteen or twenty centimetres’ focal 
 length on a camera with bellows-movement, of a size adapted 
 to that of the enlarged negative you desire to obtain, and of 
 a suitable length; and so arrange that the centre of the 
 
254 
 
 PHOTOGRAPHIC OPTICS. 
 
 positive to be enlarged may be situated in the optical axis 
 of the triplet and its surface quite perpendicular to this 
 axis. Reverse the triplet in its mounting , so that the largest lens 
 faces the positive to be enlarged, and then focus by draw- 
 ing back the ground-glass from the objective, at the same 
 time that you so regulate the distance of the latter from 
 the positive as to get its enlarged image sharp over a surface 
 of given size. 
 
 The rest of the operations are performed in the usual way of 
 using moist collodion. 
 
 This method, which is a very old one, has given very good 
 results in the hands of M. Verneuil, the French photographer, 
 who in the course of the year 1865 laid before a meeting 
 of the Societe Frangaise de Photographie very fine enlarged 
 proofs obtained by this process. 
 
 CHAPTER XIV. 
 
 .APPLICATION OF ARTIFICIAL LIGHT TO ENLARGING APPARATUS. 
 
 Necessity of a Light of very great brilliancy within 
 a very small surface. — If a great quantity of light were 
 sufficient for illuminating the negative in the enlarging 
 apparatus, this could easily be obtained from flames of very 
 large surface. But the cone of rays emergent from the 
 condenser of the optical apparatus must have a very small, 
 summit for its surface, because the enlarging lens situated at 
 the summit of this cone has itself only a small surface. Fur- 
 ther, if the summit of the cone of light strikes the edges of the 
 mounting of the enlarging lens, there is, as we have explained 
 
APPLICATION OF ARTIFICIAL LIGHT, ETC. 525 
 
 on p. 177, et seq a production of diffraction-blurs in tbe 
 enlarged image. A friend of ours, M. A. Neyt, of Ghent, 
 made on this point some very conclusive experiments, using 
 both the electric light and the Drummond light as a source 
 of light in a magnificent solar microscope by Hartnack, with 
 convergent light or with parallel light (so extolled by 
 M. Bertsch) ; and he found that whenever the luminous spot 
 had too large a surface, and that consequently its image 
 fell on the edges of the enlarging objectives, diffraction-blurs 
 were produced in the magnified image, by the employment of 
 parallel light as well as by that of convergent light, even when 
 using condensers which were achromatic, such as that of the 
 microscope which he employed. 
 
 blames therefore which possess considerable photogenic 
 power, like those of cyanogen, Way’s electric mercury-lamp, 
 white Bengal lights of arsenic, antimony, nitrate of magnesia, 
 petroleum lamps, and even magnesium-wire lamps, do not 
 serve for photographic enlargement. 
 
 The flames of very small surface which are especially suit 
 able are, the electric light produced between carbon-points, 
 and the Drummond light, in which a compact cylinder of 
 magnesia is substituted for the lime cylinder. 
 
 The electric light ought to be produced by fifty of Bunsen’s 
 elements, large size, and the electric lamp be of very perfect 
 make, so as to keep the luminous point well in the axis of the 
 optical apparatus. For if this point came to be displaced, not 
 only would the enlarged image be to a very small extent dis- 
 placed by the thickness of the lenses which form the enlarg- 
 ing objective, but diffraction-blurs might be produced; and 
 these are two circumstances that would affect the sharpness 
 of the magnified image. 
 
 The best forms of electric lamp are M. Serrin’s and M. Leon 
 Foucault’s, particularly the latter, which can be procured at 
 M. Dubosq’s, philosophical -instrument maker, Paris, who, we 
 believe, is entrusted by the inventor with the manufacture of 
 this lamp. 
 
256 
 
 PHOTOGRAPHIC OPTICS. 
 
 Every one knows the Drummond light : a pointed lime 
 cylinder, the extremity of which is made white hot by an in- 
 flamed jet of oxy-hydrogen gas,, so as to give a spot of very in- 
 tense light. If a cylinder of compact magnesia (obtained by 
 calcination of nitrate of magnesia in covered crucibles) is sub- 
 stituted for the lime cylinder, the point of light, without being 
 more brilliant to the eye, is much more photogenic — a result 
 which is probably caused by the particles of magnesia giving 
 to the flame the properties of that of burning magnesium itself. 
 
 Instead of compact magnesia, Prof. Carlevaris of Genoa 
 makes use of light magnesia, and applies this light with 
 success to one of our eight-inch enlarging apparatus. He 
 assures me that he has thus made enlarged proofs one metre 
 square in less than one minute. Probably on moist iodised 
 paper, and after development, in the way practised in Paris 
 by M. Numablanc with the electric light, they could be taken 
 in a much shorter time. 
 
 Lastly, there is one method, surpassing all the others, 
 which consists in throwing oxy-hydrogen gas under a strong 
 pressure (of at least one metre of water) by means of a 
 .platinum blow-pipe, so as to obtain a jet four or five centi- 
 metres long upon the point of one of the small parallelopipeds 
 of hard charcoal which are used in the electric lamp, moist- 
 ened with chloride of magnesium. It is the most powerful of 
 all lights in a photographic point of view, and the most 
 economic. This luminous point, just as that of the electric 
 lamp, should be maintained with care in the optical axis of 
 the enlarging apparatus, in order to prevent the enlarged 
 image being deficient in sharpness, as we have said above. 
 
 Disposition of the Optical Apparatus. — If a parabolic 
 reflector were made use of to throw the light from the illu- 
 minating point upon the condenser of the apparatus, the image 
 of the support of the point would be visible in the form of a 
 shadow over the enlarged image. 
 
 In fact, stick a wafer, a (fig. 14, pi. I.), on the condenser, 
 L, of an enlarging apparatus or of a solar microscope, and 
 
APPLICATION OF ARTIFICIAL LIGHT, ETC. 
 
 257 
 
 the image of the wafer — invisible at the focus, /, of the con- 
 denser — will become very distinctly visible in front of, b , or 
 behind, c, this focus. Now the support of the luminous point 
 cutting off a portion of the parallel rays reflected by the para- 
 bolic mirror, produces here the same effect of an opaque screen 
 as the wafer. 
 
 The following is an arrangement which, if it collects less 
 light upon the condenser than the parabolic reflector, is 
 exempt from the defect which we have just recognised in it. 
 
 Let ABC (fig. 13, pi. I.) be a spherical glass mirror with 
 parallel surfaces, of which one, ABC, is silvered. Let B I 
 be the axis of the mirror, and D its centre of curvature, where 
 we place the luminous point D. Let EG be a plano-convex 
 flint-glass lens on the same axis, IB, of which the diameter is 
 the same as that of the mirror, A C, and the focal length, F D, 
 exactly equal to B B, the radius of the mirror A C. 
 
 Every ray of light, DA, emanating from the luminous 
 point, D, and striking the mirror, A C, returns along A D, 
 and, continuing its way, strikes the lens, E G, from which it 
 emerges parallel to the axis. In the same way, every ray, 
 DE, which emanates from the luminous point, D, and which 
 strikes the lens, emerges parallel to the former and to the axis. 
 In this way, the support, D K, is not visible at all on the 
 enlarged image. 
 
 The following are the numerical data of this arrangement, in 
 which we make use of flint-glass of which the index is 1*6 
 instead of crown-glass of 1*5 index, in order to avoid too great 
 a thickness of the lens E G-, which should have a focal length 
 as short as possible, and equal to the radius, BD, of the 
 mirror, ABC. B is the radius of the mirror A C, fx its thick- 
 ness, D its diameter, and R' the radius of curvature of the 
 lens, E G (the other face being plane). 
 
 D 
 
 R 
 
 A* 
 
 R' 
 
 216 millimetres 
 
 25 centimetres 
 
 4 millimetres 
 
 15 centimetres. 
 
 380 „ 
 
 45 „ 
 
 6 
 
 27 
 
 513 
 
 60 „ 
 
 8 
 
 36 
 
 s 
 
258 
 
 PHOTOGRAPHIC OPTICS. 
 
 These data are sufficient for any optician to construct similar 
 apparatus at the desire of the reader. They accord, besides, 
 with the sizes of condensers most in use, which are 19 inches 
 (513 millimetres), 14 inches (380 millimetres), and 8 inches 
 (216 millimetres). 
 
 This apparatus is set up in the axis itself of the enlarging 
 apparatus, the optical part of which, LM, and the manage- 
 ment remain in every respect the same as in our description 
 of these apparatus. The diameter of the lens, E G, ought 
 to be equal to that of the condenser, L, which moreover is 
 placed as near as possible to this lens. 
 
 Choice of the Photographic Process. — The luminosity 
 of the artificial light being infinitely less intense than that of 
 the sun, the application of this artificial light to enlarging 
 by the ordinary processes with albumenised or chloride- 
 of-silver paper cannot be thought of; for it would then 
 be necessary to continue the printing of the image for 
 whole days. Paper prepared with nitro-glucose,* a process 
 which we have described in the Bulletin de la Societe Frangaise 
 de Photographie, for 1865, p. 143, requires about an hour’s 
 exposure for a size of enlarged image fifty centimetres by 
 sixty. Paper prepared with iodide of potassium and arrow- 
 root, sensitised in an aceto-nitrate of silver bath, and employed 
 immediately, and consequently moist, gives by development 
 proofs in ten or twelve minutes, but much less fine in tone 
 than those obtained with nitro-glucose paper. 
 
 M. Yilette j obtains very fine positive proofs from a small 
 negative by projecting the enlarged image on a surface of 
 collodion, which he then transfers to paper. He makes use 
 of artificial light (the Drummond light), and an optical appa- 
 ratus similar to that we have described above and constructed 
 by M. Dubosq of Paris. The time of exposure is one minute 
 for an enlarged proof sixty centimetres by fifty. 
 
 * It can be obtained in Paris, at Romain Talbot’s, 50 Rue d’Enghien. 
 f Bull. Soc. Fr. de Phot, for 1865, p. 149. 
 
APPLICATION OF ARTIFICIAL LIGHT, ETC. 
 
 259 
 
 Unfortunately the process of transferring the collodion film 
 on to paper requires very great practice. But the proofs pro- 
 duced by M. Yilette, which we have seen, are of a beautiful 
 black tone, imitating that of an engraving, and of necessity 
 very fine, because the optical apparatus is very perfect. 
 
 We have only to add, in conclusion, that the application 
 of artificial light to enlargements is particularly advantageous 
 for enlarging small positives by transparency into large 
 negatives in the way we have described in the preceding 
 chapter. 
 
 THE END. 
 
 ONDON : PRINTED BY W. CI-OWES AND SONS, STAMFORD STREET , 
 AND CHARING CROSS. 
 
Pl.t.