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 t™SE«S,,!n?.d':«ract.on spectra; 
 
HARPER'S SCIENTIFIC MEMOIRS 
 
 EDITED BY 
 
 J. S. AMES, Ph.D. 
 
 PKOFESSOK OF PHYSICS IN JOHNS HOPKINS nNIVERSITI 
 
 II. 
 
 PRISMATIC AND DIFFRACTION SPECTRA 
 
Cornell University 
 Library 
 
 The original of tliis book is in 
 tlie Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924012330118 
 
PRISMATIC AND 
 
 DIFFRACTION SPECTRA 
 
 MEMOIES BY JOSEPH VON FRAUNHOFER 
 
 TRANSIATED AND EDITED 
 
 By J. S. AMES, Ph.D. 
 
 PROFESSOR OF FHTSIOS IN JOHNS HOPKINS HNIVEHSITY 
 
 NEW YORK AND LONDON 
 HARPER & BROTHERS PUBLISHERS 
 
 1898 
 
 "a 
 
A.m 1^'^' 
 
 HARPER'S SCIENTIFIC MEMOIRS. 
 
 EDITED BT 
 
 J. S. AMES, Ph.D., 
 
 PEOFRSSOE OP PUYSICS IN J0UN8 UOPJilNB UNIVEBSITT. 
 
 KO\r HEADY: 
 
 THE FREE EXPANSION OF GASES. Memoirs 
 by Gay-LuBsac, Joule, and Joule and Tliomson. 
 Editor, J. S. Amks, Ph.D., Johns Hopkins Uni- 
 versity. 
 
 PRISMATIC AND DIFFRACTION SPECTRA. 
 Memoirs by Joseph von Frauiihofer. Editor, 
 J. S. Amics, Ph.D., Johns llopliins University. 
 
 /.V PREPARATION: 
 RONTGUN RAYS. Memoirs by Rontgen, Stoljes, 
 
 and J. J. TliomsDU. Editoi-, Prof. GicouGii: P. 
 
 Baukke, University of Pennsylvania. 
 THE SECOND LAW OF THEllMOUYNAMICS. 
 
 Memoirs by Carnot, Claueine, and Thomson. Editor, 
 
 Prof. W. F. Magik, Princeton University. 
 
 ON THE PROPERTIES OP IONS. Memoirs by 
 Kohlraiisch and Hiltorf. Editor, Dr. H. M. Good- 
 win, Massachusetts Institute of Technology. 
 
 SOLUTIONS. Memoirs by Pfeffer, Van t'Hoff, Raoult. 
 Editor, Dr. H. C. Jonks, Johns Hopkins University. 
 
 ON THE LAWS OP GASES. Memoirs by Boyle, 
 Aniagat, Gay-Lussac. Editor, Prof. Caul Barub, 
 Brown University. 
 
 THE FARADAY AND ZEEMAN EFFECT. Me- 
 moirs by Faradav, Kerr, and Zeeman. Editor, Dr. 
 E. P. Lkwis, University of California. 
 
 WAVE THEORY OF LIGHT. Memoirs by Young 
 and Fresnel. Editor, Prof. Hbney Cuew, North- 
 western University. 
 
 MP-MOIRS CONCERNING THE LAW OF GRAV- 
 ITATION. Editor, Prof. A. S. Maokknzie, Bryn 
 Alawr College. 
 
 NEW YORK AND LONDON I 
 
 HARPER & BROTHERS, PUBLISHERS. 
 
 Copyright, 1898, by Haepeu & Beoihees. 
 
 Alt rights reserved. 
 
PREFACE 
 
 The spectrum of the sun was first observed, in 1666, by 
 ]N"ewton, who allowed light coming from a small round open- 
 ing in a shutter to pass through a glass prism. This spectrum 
 was most impure ; and a pure sp)ectrum was not obtained until, 
 in 1803, Wollaston repeated ISTewton's experiment, replacing the 
 round opening by a slit parallel to the edge of the prism. He 
 observed several dark lines crossing the spectrum, which limit- 
 ed, as he thought, the clifEercnt spectral colors. His descrip- 
 tion of this discovery is given at the end of this volume. 
 
 Working independently of Wollaston, Fraunhofer, in 1814, 
 rediscovered the lines in the solar spectrum, which now bear 
 his name. He at first used a slit and prism ; but, later, he dis- 
 covered that the same phenomena could be obtained by means 
 of gratings made up of wires or ruled on glass. The papers of 
 Fraunhofer in which he describes these results are printed in 
 full in this volume. The great merit of Fraunhofer's work is 
 the systematic, logical method by which he proceeds from in- 
 vestigation to investigation. 
 
 The most important contributions of Fraunhofer to the 
 science of Spectrum Analysis are : 
 
 1. The application of the objective prism to the study of 
 spectra of the sun, the stars, flames, etc. 
 
 2. The discovery of the principle of plane gratings. 
 
 3. The discussion of the effect upon spectra of 
 
 a. Periodic errors in the ruling of gratings. 
 
 b. The shape of the groove. 
 
 c. The relative widths of opaque and open spaces. 
 
 4. The first measurements of the wave-lengths of various 
 solar lines. 
 
PEEFACE 
 
 5. The discovery of the agreement in wave-length of lines in 
 the spectra of flames and of certain stars with those in the 
 solar spectrum. 
 
 All modern work in spectroscopy is based upon that of 
 Fraunhofer, and a brief bibliography of the most important 
 contributions is appended to this volume. 
 
GEI^EEAL CONTENTS 
 
 PAGE 
 
 Preface v 
 
 Determination of the Refractive and the Dispersive Power of Different 
 Kinds of Glass with Reference to the Perfecting of Achromatic 
 
 Telescopes 1 
 
 New Modification of Light by the Reciprocal Influence and Diffrac- 
 tion of the Rays, and the Laws of this Modification 11 
 
 Short Account of the Results of New Experiments on tlicLaws of Light, 
 
 and their Theory 39 
 
 Biographical Slcetch of Praunliofer 61 
 
 WoUaston's Discovery of the Fixed Lines 62 
 
 Bibliography 64 
 
 Index 67 
 
Detebmifatiok of the Refractive and the Dispersive 
 
 Power of Different Kinds of Glass, with Eeference 
 
 TO THE Perfecting of Achromatic Telescopes. 
 
 Denkscliriften der koniglicJien Akademie der Wissenschaften zu Mundien, V. , 
 
 pp. 193-326, 1817. 
 
 Schumaclier's Astronomische Abhandlungen, Heft II., pp. 13-45, 1838. 
 
 Edinburgh Philosophical Journal, IX., X., 1833, 1824. 
 
CONTENTS 
 
 Object and Method. {Omitted.) ''''™ 
 
 Fixed Bands in Flame- Spectra^ 3 
 
 Apparatus. (Omitted.) 
 
 Use of Sunlight 3 
 
 Discotei-y of Fixed Lines 4 
 
 Description and Discussion 5 
 
 Indices of Refraction for Different Lines. {Omitted.) 
 
 Achromatism. {Omitted.) 
 
 Spectra of Venus and Sirius 8 
 
 Spectrum of Electric Light and Flames 9 
 
[Introduction is omitted.'\ 
 
 It -vvoulcl be most advantageous if one could measure for 
 every kind of glass the dispersion for every color ; but the dif- 
 ferent colors in the spectrum have no definite limits, and so this 
 cannot be determined immediately from the color-image. The 
 uncertainty is so great that the experiments are useless. It 
 could be done more exactly if colored pieces of glass or colored 
 liquids could be found which would transmit light of only one 
 color — e.g., one which transmitted only blue, another only red, 
 etc. ; but I have not been so fortunate as to discover any such 
 substances. With all I tried, the white light which was trans- 
 mitted was broken up into all colors, the only difference being 
 that the particular color which the glass or the liquid had was 
 the strongest in the spectrum. Colored flames, also, which are 
 obtained by the combustion of alcohol, sulphur, etc., do not 
 give in their spectra homogeneous light which corresponds to 
 their color ; yet with these, as well as with oil and tallow light, 
 and in general with light of all flames, I found in the spectra a 
 bright, sharply defined streak in the region between the red 
 and the green, which is in exactly the same position in all the 
 spectra, and which will be most useful in what follows. This 
 bright band appears to be formed by rays which are not dis- 
 persed further by the prism, and are therefore homogeneous. 
 There is a similar streak in the green, which is, however, not 
 so well defined and is much more feeble, so that in some cases 
 it is recognized with difficulty ; on this account it cannot be 
 of much service. 
 
 [The experiments on the dis23ersion of various prisms are 
 omitted.'] 
 
 In order to determine more accurately the refraction of the 
 different colored beams, partly also to see if the action of the 
 refracting medium was the same on sunlight as on artificial 
 light, I devised an apparatus which could be used with sunlight, 
 
 3 
 
MEMOIRS ON 
 
 just as the one before described was with lamplight. This 
 was soon seen to be superfluous. 
 
 In the window-shutter of a darkened room I made a narrow 
 opening — about 15 seconds broad and 36 minutes high — and 
 through this I allowed sunlight to fall on a prism of flint-glass 
 which stood upon the theodolite described before. [The dimen- 
 sions are not given-l The theodolite was 34 feet from the win- 
 dow, and the angle of the prism was about 60°. The prism was 
 so placed in front of the objective of the theodolite-telescope 
 that the angle of incidence of the light was equal to the angle 
 at which the beam emerged. I wished to see if in the color- 
 image from sunlight there was a bright band similar to that ob- 
 served in the color-image of lamplight. But instead of this I 
 saw with the telescope an almost countless number of strong 
 and weak vertical lines, which are, however, darker than the 
 rest of the color-image ; some appeared to be almost perfectly 
 black. If the prism was turned so as to increase the angle of 
 incidence, these lines vanished ; they disappear also if the angle 
 of incidence is made smaller. For increased angle of incidence, 
 however, these lines become visible again if the telescope is 
 made shorter ; while, for a smaller angle of incidence, the eye- 
 piece must be drawn out considerably in order to make the lines 
 reappear. If the eye-piece was so placed that the lines in the 
 red portion of the color-image could be plainly seen, then, in 
 order to see the lines in the violet portion, it must be pushed in 
 slightly. If the opening through which the light entered was 
 made broader, the fine lines ceased to be clearly seen, and 
 vanished entirely if the opening was made 40 seconds wide. 
 If the opening was made 1 minute wide, even the broad lines 
 could not be seen plainly. The distances apart of the lines, 
 and all their relations to each other, remained unchanged, both 
 when the width of the opening in the window-shutter was al- 
 tered and when the distance of the theodolite from the opening 
 was changed. The prism could be of any kind of refractive 
 material, and its angle might be large or small ; yet the lines 
 remained always visible, and only in proportion to the size of 
 the color-image did they become stronger or weaker, and there- 
 fore were observed more easily or with more difficulty. 
 
 The relations of these lines and streaks among themselves 
 appeared to be the same with every refracting substance ; so 
 that, for instance, one particular band is found in every case 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 only in the blue; another is found only in the red; and one 
 can, therefore, at once recognize which line he is observing. 
 These lines can be recognized also in the spectra formed by 
 both the ordinary and the extraordinary rays of Iceland spar. 
 The strongest lines do not in any way mark the limits of the 
 various colors ; there is almost always the same color on both 
 sides of a line, and the passage from one color into another 
 cannot be noted. 
 
 With reference to these lines the color-image is as shown in 
 Fig. 5. It is, however, impossible to show on this scale all the 
 lines and their intensities. (The red end of the color-image is 
 in the neighborhood of A; the violet end is near I.) It is, how- 
 ever, impossible to set a definite limit at either end, although it 
 is easier at the red than at the violet. Direct sunlight, or sun- 
 light reflected by a mirror, seems to have its limits, on the one 
 hand, somewhere between G and H ; on the other, at B ; yet with 
 sunlight of great intensity the color-image becomes half again 
 as long. In order, however, to see this great spreading-out of 
 the spectrum, the light from the space between C and G must 
 be prevented from entering the eye, because the impression 
 which the light from the extremities of the color-image makes 
 upon the eye is very weak, and is destroyed by the rest of the 
 light. At A there is easily recognized a sharply defined line ; 
 yet this is not the limit of the red color, for it proceeds much 
 beyond. At a there are heaped together many lines which form 
 a band ; B is sharply defined and is of noticeable thickness. In 
 the space between B and there can be counted 9 very fine, 
 sharply defined lines. The line C is of considerable strength, 
 and, like B, is very black. In the space between and D there 
 can be counted 30 very fine lines ; but these (with two excep- 
 tions), like those between B and 0, can be plainly seen only 
 with strong magnification or with prisms which have great dis- 
 persion ; they are, moreover, very sharply defined. D consists of 
 two strong lines which are separated by a bright line. Between 
 D and E there can be counted some 84 lines of varying inten- 
 sities. E itself consists of several lines, of which the one in 
 the middle is somewhat stronger than the rest. Between E 
 and b are about 24 lines. At i there are 3 very strong lines, 
 two of which are separated by only a narrow bright line ; they 
 are among the strongest lines in the spectrum. In the space 
 between b and E there can be counted about 53 lines ; F is 
 
 5 
 
MEMOIRS ON 
 
 fairly strong. Between F and G there are about 185 lines of 
 different strengths. At G there are massed together many 
 lines, among which several are distinguished by their intensity. 
 In the space between G and H there are about 190 lines, whose 
 intensities differ greatly. The two bands at H are most re- 
 markable ; they are almost exactly equal, and each consists of 
 many lines; in the middle of each there is a strong line which 
 is very black. From H to I the lines are equally numerous. 
 In the space between B and H there can be counted, therefore, 
 about 574 lines, of which only the strong ones appear on the 
 drawing. The distances apart of the strongest lines were meas- 
 ured by the theodolite and transferred according to scale 
 directly to the drawing ; the weak lines, however, were drawn 
 in, without exact measurement, simply as they were seen in 
 the color-image. 
 
 I have convinced myself by many experiments and by vary- 
 ing the methods that these lines and bands are due to the nat- 
 ure of sunlight, and do not arise from diffraction, illusion, etc. 
 If light from a lamp is allowed to pass through the same nar- 
 row opening in the window-shutter, none of these lines are ob- 
 served, only the bright line E [referred to before], which, how- 
 ever, comes exactly in the same place as the line D (Fig. 5), so 
 that the indices of refraction of the rays D and E are the same. 
 The reason why the lines fade away, or even entirely vanish, 
 when the opening at the window is made too wide is not diffi- 
 cult to give. The stronger lines have a width of from five to 
 ten seconds ; so, if the opening of the window is not so narrow 
 that the light which passes through can be regarded as belong- 
 ing to one ray, or if the angular width of the opening is much 
 more than that of the line, the image of one and the same line 
 is repeated several times side by side, and consequently be- 
 comes indistinct, or vanishes entirely if the opening is made 
 too wide. The reason why the lines and bands are not seen 
 when the prism is turned, unless the telescope is made shorter 
 or longer, will be seen from the following considerations : 
 
 It is only when rays fall upon a prism in such a way that the 
 angle of incidence equals that of emergence that they proceed, 
 80 far as divergence is concerned, just as they fall upon the 
 prism; if the angle of incidence is greater, the rays, after re- 
 fraction through the prism, diverge from a more remote point ; 
 if the angle is smaller, the rays diverge from a nearer point. 
 
PRISMATIC AND DIFFKACTION SPECTRA 
 
 The reason is that the rays which pass through near the edge 
 of tlie prism have a shorter path through the prism to traverse 
 than those which pass through farther from the edge. This 
 does not change, it is true, the angle of the refracted rays ; but 
 the sides of the triangle for the emerging rays become greater 
 in the one case, less in the other. This diiference should van- 
 ish when the rays fall upon the prism parallel to each other, 
 which is in accord with experiment. Since the violet rays 
 through the objective of the theodolite telescope have a shorter 
 focal length than the red rays, it is evident why the eye-piece 
 must be displaced in order to see plainly the lines in the differ- 
 ent colors. 
 
 Since the lines and bands in the color-image have only a very 
 small width, it is evident that the apparatus must be most per- 
 fect in order to avoid all aberrations which could make the lines 
 indistinct or entirely scatter them. The faces of the prism 
 must therefore be perfectly plane. The glass to be used in 
 such prisms should be entirely free from waves and streaks ; 
 with English flint-glass, which is never free from streaks, only 
 the stronger lines are seen. Common glass and English crown- 
 glass contain many streaks, even if they are not visible to 
 the naked eye. If one does not possess a prism of perfect 
 flint-glass, it is better to choose a fluid which has a great disper- 
 sive power — e. g., aniseed oil — in order to see the lines ; yet in 
 this case the prismatic vessel must have faces which are per- 
 fectly plane parallel. With all prisms the faces should make 
 an angle of 90°, or nearly so, with the base ; this must be 
 placed horizontal, in front of the telescope, if the axis of the 
 latter is horizontal. The narrow opening through which the 
 light enters must be exactly vertical, etc. It is easy to under- 
 stand why the lines become indistinct if one or the other of 
 these precautions is neglected. 
 
 Since the lines and bands are seen in the color -image of 
 every refracting medium of uniform density, I have used them 
 in order to measure the refraction of a medium for each colored 
 ray ; and this could be done with great accuracy, because the 
 majority of the lines are sharply defined. Since with refract- 
 ing media which have feeble dispersion or with prisms of 
 small angles it is only with difficulty that the fine lines can be 
 recognized even with strong magnification, I selected in these 
 experiments, for all refracting media, the stronger lines, viz., 
 
 7 
 
MEMOIRS ON 
 
 B, 0, D, B, F, G, and H. The lines at 5 1 did not take, because 
 it is too near P; and I tried to come more in the middle be- 
 tween D and P. Since the eye-piece must be displaced in or- 
 der to see distinctly the lines in the difEerent colors, no large 
 arcs such as BH could be measured, only the small ones such as 
 BO, CD, etc. 
 
 [^Ten pages, containing descriptions of experiments on differ- 
 ent kinds of glass, are omitted.'] 
 
 On seeing the number of lines and bands in the spectrum of 
 sunlight, one can perhaps with difficulty avoid the conjecture 
 that difEraction at the narrow opening in the window-shutter 
 has something to do with these lines, although the experiments 
 which have been described do not in the least indicate this, but, 
 on the contrary, refute it. Partly in order to be perfectly 
 sure on this point, partly also in order to make further obser- 
 vations, I changed the experiment in the following manner : 
 
 If sunlight coming from a small round opening, 15 seconds in 
 diameter, in the window-shutter is allowed to fall upon a prism 
 placed in front of the theodolite telescope, it is clear that the 
 color-image which is seen through the telescope can have only 
 an inappreciable width, and therefore will form only a line ; in 
 a colored line, however, no fine cross - lines can be seen. In 
 order to see the many lines in this color-image, all that is nec- 
 essary is to make the spectrum broader without altering its 
 length in the least. I accomplished this by placing against the 
 objective a piece of glass which was plane on one .side and 
 curved on the other, so as to be a portion of a cylinder of 
 large diameter. The axis of the cylinder was placed parallel 
 to the base of the prism ; consequently, the length of the spec- 
 trum could not be changed, and only its breadth was increased. 
 With this arrangement I recognized again in the spectrum all 
 the lines exactly as they are seen when the light comes through 
 a long, narrow opening. 
 
 I applied this form of apparatus at night - time to observe 
 Venus directly, without making the light pass through a small 
 opening; and I discovered in the spectrum of this light the 
 same lines as those which appear in sunlight. Since, however, 
 the light from Venus is feeble in comparison with sunlight re- 
 flected from a mirror, the intensity of the violet and the ex- 
 treme red rays are very weak ; and on this account even the 
 stronger lines in both these colors are recognized only with 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 diflSculty, but in the other colors they are very easily distin- 
 guished. I have seen the lines J), E, b, P perfectly defined 
 (Fig. 5), and have even recognized that i consists of two lines, 
 one weak and one strong ; but the fact that the stronger one 
 itself consists of two I could not verify owing to lack of light. 
 For the same reason the other finer lines could not be distin- 
 guished satisfactorily. I have convinced myself by an approxi- 
 mate measurement of the arcs DE and EF that the light from 
 Venus is in this respect of the same nature as sunlight. 
 
 With this same apparatus I made observations also on the 
 light of some fixed stars of the first magnitude. Since, however, 
 the light of these stars is much weaker than that of Venus, it 
 is natural that the brightness of the spectrum should be much 
 less. In spite of this I have seen with certainty in the spec- 
 trum of Sirius three broad bands which appear to have no con- 
 nection with those of sunlight ; one of these bands is in the 
 green, two are in the blue. In the spectra of other fixed stars 
 of the first magnitude one can recognize bands ; yet these stars, 
 with respect to these bands, seem to differ among themselves. 
 Since the objective of the telescope has an aperture of only 13 
 lines*, it is clear that these observations can be repeated witia 
 much greater accuracy. I intend to repeat them with suitable 
 alterations, and with a larger objective, in order to induce, per- 
 haps, some skilled investigator to continue the experiments. 
 Such a continuation is all the more to be desired, because the 
 experiments would serve at the same time for the accurate com- 
 parison of the refraction of the light of the fixed stars with 
 that of sunlight. 
 
 The light of electricity is, with respect to these lines and 
 bands, markedly different from sunlight, and also from the 
 light of flames. Several lines are found in the spectrum of 
 this light; some are very bright, and among these one in the 
 green is almost dazzlingly bright in comparison with the rest of 
 the spectrum. There is another line in the orange which is 
 not quite so bright ; it appears to have the same color as the 
 bright line in the spectrum of lamplight. If, however, the 
 angle of refraction is measured, it is found that its light is 
 refracted much more — about as much as the yellow rays of 
 lamplight. Near the red end of the spectrum there is a line 
 
 [* 1 centimetre equals 4.43296 lines.] 
 9 
 
MEMOIES 
 
 which is not very bright; its light is refracted, so far as I 
 could be sure, exactly the same as that of the bright liue of 
 lamplight. In the rest of the spectrum four other lines can be 
 recognized easily.* 
 
 If lamplight is allowed to pass through a very narrow open- 
 ing of 15 to 30 seconds' width and then to fall upon a strongly 
 dispersive prism placed in front of a telescope, it is seen that 
 the reddish-yellow bright line of this spectrum consists of two 
 very fine bright lines which in intensity and distance apart are 
 like the two dark lines D (Fig. 5). But, regardless of the 
 width of the slit, if the point of the flame and the lower blue 
 end are covered, and so only the brightest portion of the flame 
 exposed, the reddish-yellow lines of the spectrum appear less 
 bright, and therefore are recognized with more difficulty. 
 These lines, consequently, seem to be formed mainly by the 
 light from the ends of the flame, especially by that from the 
 lower one. 
 
 In the spectrum of the light caused by the combustion of 
 hydrogen and alcohol, the reddish-green line is very bright in 
 comparison with the other portions. When sulphur is burned 
 it is seen with great difficulty. 
 
 I intend to repeat these experiments which have reference to 
 the perfecting of achromatic telescopes, using a new instru- 
 ment by means of which I hope to obtain at least twice the 
 accuracy. I shall be able also to make new experiments with 
 this instrument for which my present one is not adapted, and 
 which will be of interest perhaps for practical optics. 
 
 In all my experiments I could, owing to lack of time, pay at- 
 tention to only those matters which appeared to have a bearing 
 upon practical optics. I could either not touch other questions, 
 or at most not follow them very far. Since the path thus traced 
 in optical experiments seems to promise to lead to interesting 
 results, it is greatly to be desired that skilled investigators 
 should devote attention to it. 
 
 * Iq order to iise the electric light I placed two couductors one-half an 
 inch apart, one being joined to an electrical machine, the other to the earth, 
 and connected them with a fine glass fibre. The light then appeared to 
 pass continuously over the fibre, and the latter formed a fine luminous line. 
 
 10 
 
New Modification" of Light by the Mutual Influence 
 
 AND THE Diffraction of the Eats, and the Laws 
 
 OF THIS Modification. 
 
 Denkscliriften der koniglicTien Akademie der WissenscAaften zu Munchen, 
 
 1831, 1832, VIII., 1-76. 
 
 Schumacher'3 Aatronomiache Abhandlungen, II., 46-113, 1833. 
 
CONTENTS 
 
 PAGE 
 
 Introduction 13 
 
 Diffraction of Light through a Single Opening 14 
 
 Instruments 15 
 
 1. Narrow Slit 13 
 
 Spectra of tlie First Class 17 
 
 laws Deduced from Experiment 18 
 
 Discussion 19 
 
 3. Bound Opening 20 
 
 Laws and Discussion. {Omitted.) 
 Mutual Action of a Oreat Ifumber of Diffracted Beams. . . 21 
 
 Wire Gh-atings 22 
 
 Perfect Spectra of the Second Class 23 
 
 Discussion 34 
 
 Laws 26-27 
 
 Mutual Action of Two, Three, etc.. Diffracted Beams 31 
 
 Diffraction through Two, Three, etc., Slits 31-33 
 
 Laws 83 
 
 Discussion 84-35 
 
 Mutual Action of Beams Diffracted in Water and Otlier 
 
 Befracting Media. (Omitted.) 
 Mutual Action of Beams Diffracted by Reflection. (,Omitted.) 
 Mutual Action of Beams Diffracted through Round and 
 Quadrangular Openings. (Omitted.) 
 
 General Statements 86-38 
 
 Pnnciples of Interference 37-38 
 
New Modification of Light by the Mutual Influence 
 
 AND the Diffraction of the Eays, and the Laws 
 
 OF THIS Modification. 
 
 All experiments in which the eye of the investigator is 
 provided witli good optical instruments are distinguished, as is 
 well known, by a high degree of precision; and some of the 
 most important discoveries could not have been made without 
 these instruments. Up to the present time, in experiments on 
 diifraction there has been no instrument, except a magnifying- 
 glass, which could be used with profit; and this may perhaps 
 be one of the reasons why in this field of physical optics we are 
 so backward, and why we know so little of the laws of this 
 modification of light. Since at small angles of inclination re- 
 fraction and reflection of light are altered by diffraction, and 
 since in many other cases diffraction plays an important part, 
 which may often be unnoticed, it is most to be desired that 
 these laws should be exactly known ; and this is specially so be- 
 cause a knowledge of them makes the nature of light itself 
 better known at the same time. 
 
 If sunlight is admitted into a darkened room through a 
 small opening and falls upon a dark screen some distance away, 
 which has a narrow aperture, and if the light which passes 
 through this slit is allowed to fall upon a white surface or a 
 piece of ground-glass placed a short distance behind the screen, 
 one sees, as is well known, that the illuminated portion of the 
 white surface is larger than the narrow slit in the screen, and 
 that it has colored edges — in short, that the light through the 
 slit is inflected or diffracted. The narrower the openings, so 
 much the greater is the inflection. The shadow of every body 
 which is placed in a beam of sunlight entering a darkened 
 room through a small opening is bounded by fringes of color 
 which are, moreover, for any given distance of the surface on 
 which the shadow is received, of the same size for bodies of all 
 
 13 
 
MEMOIRS ON 
 
 kinds of matter. The shadow of a narrow object, such as a 
 hair, has, in addition to the outer fringes, others within the 
 shadow, which change with the tliickness of the hair, but in 
 other respects ai'e similar to the outer ones.* Since the colored 
 fringes are very small, and since most of the light is lost 
 through absorption at the surface on which the shadow is cast, 
 no great accuracy could be expected with the methods which 
 have been used up to this time to observe diffraction phenom- 
 ena ; and this is all the more true because by these methods 
 it is impossible to measure the angles of inflection of the light 
 which alone can make us acquainted with the laws of diffrac- 
 tion. Up to the present, these angles from which the path 
 of the diffracted light can be learned have been calculated from 
 the dimensions of the colored bands and their distance from 
 the diffracting body; but assumptions have been made which, 
 as we shall see, do not agree with the truth, and which, there- 
 fore, give false results. 
 
 The number of different optical phenomena has become in 
 our time so great that caution must be taken so as to avoid be- 
 ing deceived, and also to refer the phenomena always to the 
 simple laws. This is more necessary in the case of diffraction, 
 as we shall see, than in all the other phenomena. I shall, 
 therefore, report the experiments which I have made for the 
 determination of the laws of diffraction of light in an order 
 which is different from that in which I actually performed 
 them, by which procedure many experiments become super-, 
 fluous and a better understanding will be reached. 
 
 Diffraction of Light through a Single Opening. 
 
 In order to receive in the eye all the light diffracted through' 
 a narrow opening, and to see the phenomena strongly magni- 
 fied; still more, in order to directly measure the inflection of 
 the light, I placed in front of the objective of a theodolite-tele- 
 scope a screen in which there was a narrow vertical opening 
 which could be made wider or narrower by means of a screw. 
 By means of a heliostat I threw sunlight into a darkened room 
 
 * All tbat is known on the subject of diffraction may be found in Blot's 
 "Traite de Physique, Exp. et Math.," T. 4, p. 743; and in the Oottinger 
 Commentaren, Vol, IV., p. 49. 
 
 14 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 through a narrow slit so that it fell upon this screen, through 
 whose opening the light was therefore diffracted. I could then 
 observe through the telescope the phenomena produced by the 
 diffraction, magnified, and yet seen with sufficient brightness ; 
 and at the same time I could measure the angles of inflection 
 of the light by means of the tlieodolite. 
 
 The colors which are produced by the diffraction of light 
 through a single opening are arranged in an order similar to 
 that of the colors of Newton's rings, which are produced by the 
 contact of two slightly convex pieces of glass ; with this differ- 
 ence, that with the latter a black spot is seen in the centre, 
 while it is not with the former. Fig. III., Table I., will help the 
 description. If the telescope of the theodolite is so adjusted 
 that on removing the screen which has the diffraction-slit the 
 slit at the heliostat is focused on the micrometer cross-hairs, 
 and if then the screen — whose slit must be very narrow — is 
 placed in front of the objective, there will be Seen in the centre 
 of the field a white band L'L' ; and the cross-hairs will be in 
 the middle of this band at K. This band becomes yellow near 
 each side, and finally red. In the space L'L" there is a vivid 
 color- spectrum, which is indigo near L', then blue, green, 
 yellow, and near L" red. The color-spectrum in the space 
 L"L'" is much less intense than that in TJIj" ; the arrangement 
 of its colors is as follows : Near L" blue, then green, yellow, and 
 near L™ red. The spectrum in the space L™L'^ is still weaker 
 than the last ; near L™ it is green ; near L'^, red. There then 
 follow a great number of spectra which grow continually weaker 
 until they can be no longer distinguished, and then can be 
 seen only a horizontal strip of light which is, however, stretched 
 out through a great distance. The spectra just described are 
 exactly the same on the two sides of K — i. e. , they are symmet- 
 rical. The transitions from one color into another are not 
 sharply defined, but imperceptible, and the same thing is true 
 of the spectra. 
 
 The instrument with which I observed and measured the 
 angles is essentially a 12-inch repeating theodolite whose ver- 
 niers read to 4". In the middle of the circle and above it 
 there is a plane horizontal disk 6 inches in diameter which 
 turns on its axis, and whose centre lies exactly on the axis of 
 the theodolite. It has its own divisions, which read to 10". At 
 the middle of this disk is placed the screen through which the 
 
 15 
 
MEMOIRS ON 
 
 light is diffracted, and whicli therefore stands in the axis of the 
 theodolite, so that the corrections to the angles as measured, 
 which otherwise would have to be made, owing to the distance 
 of the diffracting body from the axis, are aot necessary. The 
 divisions marked on the disk serve to measure, if it is neces- 
 sary, the angle of incidence of the light, etc. Beyond the disk, 
 at a distance of 3^ inches* from the centre, the telescope begins. 
 Its objective has an aperture of r^O lines and a focal length of 
 16.9 inches, and it is clamped to the alidade of the I'i-inch 
 circle and suitably counterbalanced. The axis of the telescope 
 is parallel to the plane of the circle and accurately horizontal. 
 I used a magnifying power of 30 and 50. Tlie whole instru- 
 ment is isolated from the floor. In the prolongation of the 
 optical axis, 463^ inches from the middle of the theodolite, is 
 placed the heliostat, whose hour motion can be regulated by a 
 screw and a rod which is attached to it and which reaches to 
 the theodolite, so that one can at will increase or decrease the 
 intensity of the sunlight. The opening at the heliostat is ver- 
 tical, 2 inches long, and can be made wider or narrower. I 
 ordinarily used it with a width of only 0.01 to 0.0'i inch. 
 
 I measured the width of the opening in the screen by means 
 of an achromatic microscope which I devised for this purpose, 
 because this quantity must be known most exactly. At the 
 foot of this microscope there is a sliding-piece which can be 
 moved in one direction by a fine screw having nearly 88 turns 
 to a Paris inch ; the screen is so fastened to this sliding-piece 
 that its opening, which is to be measured, comes vertically 
 above the screw. There are cross-hairs in the eye-piece of the 
 microscope, which can be seen at the same time as the object 
 viewed. By means of the screw whicli moves the sliding piece, 
 first one edge and then the other of the object is made to coin- 
 cide with one edge of the cross-hair, and the position of the 
 screw is read each time. The difference in the readings is tlie 
 diameter of the object, in terms of the pitch of the screw, inde- 
 pendently of the construction of the optical parts of the micro- 
 scope, the magnification, etc. Since the Iiead of the screw is 
 divided by a vernier into 1000 parts, it is possible to measure 
 the diameter of a sharply defined object to at least 0.00002 of 
 an inch ; in many cases to 0.00001. I generally used an objec- 
 
 * [1 Paris inch = 2.70700 cm. = 1.06577 incJiea.] 
 10 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 tive with which the microscope magnifies the diameter of the 
 object 110 times. 
 
 Since it is impossible to find a fixed point of reference in the 
 color-spectrum arising from difEraction through a single nar- 
 row opening, I took, in order to measure the angles of deflec- 
 tion, the transition from one spectrum into another — that is, 
 L', L", L"', etc., or the red end of each spectrum. I measured 
 the distances L'L', L"L°, etc., repeating at least three times. 
 The halves of these are, therefore, the deflections from the 
 centre — that is, KL', KL", etc. I shall designate by U, L", 
 etc., the angles of these deflections. All spectra which are due 
 to difEraction through a single opening I shall call spectra of 
 the first class, merely to distinguish them from other kinds 
 which will be discussed later. The following table contains 
 the angles of inflection of light through openings of different 
 widths. I designate this width by y ; it is expressed always 
 in fractions of a Paris inch. I call the arithmetical mean of L', 
 
 ^, ^, etc., L. 
 2 3 
 
 No, 
 
 y 
 
 L' 
 
 L" 
 
 L"i 
 
 I.I' 
 
 L 
 
 L, 
 
 
 
 
 
 
 
 
 0.0000 
 
 1 
 
 0.11545 
 
 37". 58 
 
 1'1d".5 
 
 1' 53" 
 
 
 37". 66 
 
 210 
 
 2 
 
 0.06098 
 
 rii".o 
 
 2' 22'. 7 
 
 3' 31". 7 
 
 4' 44''. 7 
 
 I'll". 17 
 
 210 
 
 3 
 
 0.03690 
 
 l'57".l 
 
 3' 53". 3 
 
 5' 48". 3 
 
 
 1'56".6 
 
 209 
 
 i 
 
 0.02346 
 
 3' 4" 
 
 6' 7". 7 
 
 9' 16". 3 
 
 
 3' 4". 43 
 
 210 
 
 5 
 
 0.01237 
 
 5' 48". 6 
 
 11' 38" 
 
 17' 26". 6 
 
 23' 14". 7 
 
 6' 48". 7 
 
 209 
 
 6 
 
 0.01210 
 
 6' 
 
 12' 1" 
 
 18' 14" 
 
 24' 9" 
 
 6' 1".84 
 
 212 
 
 7 
 
 0.01020 
 
 6' 56" 
 
 13' 56" 
 
 20' 51" 
 
 
 6' 57". 3 
 
 206 
 
 8 
 
 0.00671 
 
 11' 6" 
 
 22' 12". 7 
 
 33' 14" 
 
 44' 35" 
 
 11' 6". 4 
 
 217 
 
 9 
 
 0.00642 
 
 11' 11" 
 
 22' 18" 
 
 33' 43" 
 
 44' 58" 
 
 11' 12". 2 
 
 209 
 
 10 
 
 0.00337 
 
 21' 3" 
 
 42' 16" 
 
 1° 4- 
 
 
 21' 10". 3 
 
 207 
 
 11 
 
 0.00308 
 
 23' 31" 
 
 47' 6" 
 
 1° 10' 43" 
 
 
 23' 32". 7 
 
 211 
 
 12 
 
 0.00218 
 
 33' 30" 
 
 JO 7' 40" 
 
 
 
 33-40" 
 
 213 
 
 13 
 
 0.00315 
 
 35' 24". 7 
 
 1° 10' 16" 
 
 
 
 35' 17" 
 
 220 
 
 li 
 
 0.00114 
 
 1° 4' 53" 
 
 
 
 
 1° i' 53" 
 
 215 
 
 The angles recorded in this table are all given exactly as I 
 observed them, without any corrections, and it is not difficult, 
 therefore, to determine the limits of accuracy. Since the 
 points of transition from one spectrum into another are not 
 sharply defined, recourse must be had, within certain limits, to 
 estimation. In long spectra — i.e., when the opening in the 
 screen is narrow — these limiting positions lie farther apart, and 
 the angles will not agree among themselves as well as in the 
 case of a large opening in the screen and small spectra. The 
 B 17 
 
MEMOIRS ON 
 
 relative accuracy is, however, nearly the same. Within the 
 limits of error, the following conclusions may be drawn from 
 the table : 
 
 With single openings of different tvidtlis the angles of in- 
 flection of the light are inversely 2)roportional to the tvidths of 
 the opening. 
 
 In light diffracted through a narroio opening the distances 
 from the centre to the red rags of the various spectra on both 
 sides form an arithmetical series in which the common differ- 
 ence is equal to the first term. 
 
 It will appear from later experiments that this law holds for 
 the other colored rays, and that it is true for the spectra which 
 are far from the axis as well. 
 
 In the general case, for any width of opening, measured in 
 fractions of a Paris inch and designated by y, where L', L", L'", 
 etc., are the arcs for radius 1, we have : 
 
 Ti_ 0.0000211 
 
 y 
 
 L"= 2 . 
 
 0.0000311 
 
 L-=3.Q-Q"°Q^^\etc. 
 
 In order to see whether the spectra which arise from dif- 
 fraction consist of homogeneous light, I fastened in front of 
 the eye-piece of the theodolite-telescope [i.e., bettveen the eye- 
 piece and the eye of the observer] a small flint-glass prism of 
 about 20°, in snch a manner that the axis of the prism was 
 horizontal and the edge pointed down. If, with an eye-piece 
 like this, one views a homogeneous spectrum such as is obtained 
 when a good prism is placed in front of the objective, the 
 cross-hairs of the eye-piece will be seen in every color. If, 
 however, there is no homogeneous light in the field of view, 
 the horizontal thread will disappear. The explanation is not 
 difficult. If the spectra produced by diffraction through a 
 single opening are brought into the fidld, no trace of the Irori- 
 zontal thread is seen in the first and second spectra ; in the 
 third it is just perceptible ; in the fourth it is more def- 
 inite, although still indistinct. This indistinctness becomes 
 
 18 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 gradually less in the succeeding spectra, so that far from the 
 middle of the field the horizontal thread can be seen fairly de- 
 fined. Accordingly, the spectra near the axis consist of non- 
 homogeneous light ; those farther away become more and more 
 homogeneous. 
 
 The lower horizontal red end of the first spectrum appears 
 blue when viewed through the prism ; the upper blue end of 
 this spectrum, however, appears red, which also proves that 
 this spectrum consists of non- homogeneous light; for in a 
 spectrum formed by a prism no blue light can be produced out 
 of red, nor red from blue. Since the light is refracted through 
 the eye-piece prism, and since rays are refracted differently — 
 e.g., the blue more than the red — it, therefore, happens that, 
 when there is in the field of view a homogeneous [i.e., pure] 
 spectrum, which without the prism would be horizontal, the 
 thread of the cross-hair which would have been horizontal is no 
 longer so, but is lower at the end where it points towards the 
 more refrangible rays, and higher at the other ; it, therefore, 
 has an inclined position which may be easily noticed. Since 
 in the spectra formed by diffraction those which are far from 
 the axis overlap, and since a portion of each spectrum en- 
 croaches upon the one which precedes and the one which 
 follows, as is apparent from the second of the above laws, the 
 inclined position of the cross-hair serves to convince one of 
 their existence and furnishes a method of counting them. For 
 if there are several overlapping spectra in the field of view, 
 there will be seen as many oblique cross - hairs as there are 
 spectra. I shall return to this matter later. 
 
 [The case is then discussed when the tivo halves of the screen 
 forming the slit are no longer in the same plane, hut one is dis- 
 placed normally with reference to the other.] 
 
 In all the above experiments the light at the heliostat fell 
 upon a narrow vertical opening, so that only one beam of 
 light entered, or, in other words, so that the light apparently 
 came from a luminous line. The reason for this is easily un- 
 derstood ; in every other case each beam would form its own 
 spectrum, and there would be as many of these overlapping as 
 there were beams. If, for instance, the light came from a lumi- 
 nous surface whose angular width was greater than that of 
 the spectra, it would be impossible to distinguish any spectra 
 through a narrow opening in the screen ; because the rays 
 
 19 
 
MEMOIRS ON 
 
 coming from the right-hand side of the luminous surface would 
 produce red in the same place where the rays from the left 
 side would produce bine, etc. ; and the light would be all con- 
 fused, and consequently white again. Since, however, light is 
 diffracted by every narrow opening, one might imagine that the 
 light falling upon the slit in the screen had already been mod- 
 ified by diffraction at the slit near the heliostat. Although 
 this doubt disappears, either by a consideration of the diam- 
 eter of the sun or on certain other grounds, nevertheless I 
 have investigated the subject experimentally. All that is 
 necessary is that the light should come as if from a luminous 
 line. I prepared, therefore, a lens, 2 inches long, ^ inch 
 wide, which was plane upon one side, and upon the other 
 was a portion of a cylinder of 0.66 inch diameter. [Par- 
 allel^ light falling upon this lens proceeds after refraction 
 as if it came from a line at a distance of 0.63 inch from 
 the lens. The opening at the heliostat was made -J inch wide, 
 and the cylindrical lens was placed in front of it. If the 
 path of the light through the lens is traced, it is seen that 
 no light passing around the edge of the slit at the heliostat 
 can fall upon the screen which is in front of the theodolite- 
 telescope, and consequently no diffracted light can reach it. 
 Using this cylindrical lens, both the spectra due to diffraction 
 through a small opening and their dimensions are exactly the 
 same as they were when the narrow slit was used at the heliostat. 
 By means of a screen which contains a long, narrow opening, 
 light is diffracted in one direction only ; by my screen this direc- 
 tion was horizontal, because the opening was vertical. A screen 
 containing an opening which is not narrow, but is, for instance, 
 as high as it is broad, will produce diffraction in a vertical di- 
 rection also. It is easily understood that in this case the in- 
 cident light must not come from a luminous line, because the 
 diffraction in a vertical direction would not be observed, for 
 the same reasons as I have given above. The light must come 
 through an opening at the heliostat, which is as broad as it is 
 high. I, therefore, allowed the light, as a rule, to pass through 
 a round opening 0.04 to 0.08 inch in diameter. If a round 
 opening is used, and if the screen with a long vertical opening 
 is placed in front of the theodolite-telescope, the spectra, as can 
 be easily predicted, have a very small height, but in a horizon- 
 tal direction they are exactly as they were when the light 
 
 30 
 
PEISMATIC AND DIFFEACTION SPECTRA 
 
 passed through a long vertical opening at the heliostat. There 
 is seen, therefore, only a horizontal line, in which the colors al- 
 ternate as described above, and wliich is narrower in proportion 
 as the round opening at the heliostat is made smaller. This 
 opening should not be made too small, however, because if the 
 light is to be diffracted in other directions also, there would 
 not be sufficient brightness. 
 
 If the light passes through a round opening at the heliostat, 
 and if there is placed in front of the theodolite-telescope a screen 
 containing a rectangular opening, which has perfectly straight 
 sides and sharp corners, and which is, e.g., as high as it is wide, 
 a colored cross will be seen in the telescope, in which the colors 
 alternate vertically as well as horizontally in the same way as 
 they did in light diffracted by a long, narrow opening. In the 
 corners of this colored cross there are seen still feebler color- 
 spectra, a, b, c, d. Table II., Fig 3. [This figtire is omiitecl] The 
 explanation of these spectra which are seen only in the corners 
 will be apparent from experiments which will be discussed fur- 
 ther on. The dimensions of the colors wliich form the cross are 
 the same as when a long, narrow opening of the same width is 
 
 , . Ti 0.0000311 Tii T 0.0000211 ^ - -, ^, 
 used : viz., ij = , L' =3. , etc., m both a 
 
 7 7 
 
 vertical and a horizontal direction. If the rectangular open- 
 ing in the screen is not as broad as it is high, the vertical 
 spectra of the cross have a different width from the horizontal 
 ones ; and the weak subsidiary spectra in the corners are al- 
 tered accordingly. By means of a screen, then, the width of 
 whose rectangular opening is less than its height, there is pro- 
 duced a colored cross whose vertical arm is composed of spec- 
 tra smaller than the horizontal ones, in the inverse ratio of the 
 height to the width. 
 
 [Diffraction through a circular opening is then discussed.] 
 
 Mutual Actioi^ of a Geeat Number of Diffeacted 
 
 Beams. 
 
 In order to make a great number of beams, diffracted ex- 
 actly alike, fall upon the whole surface of the theodolite-ob- 
 jective, I stretched upon a frame a great many wires of the 
 same thickness, parallel to each other and at the same dis- 
 tances apart ; the light was then diffracted through the inter- 
 
 21 
 
MEMOIRS ON 
 
 vening spaces. In order to be sure that the wires were exactly, 
 parallel and at equal distances from each other, I cut on two 
 opposite ends of a rectangular frame a fine screw-thread, which 
 had 169 turns, nearly, to a Paris inch ; I stretched the wires 
 in the spirals of this screw, and I could then be sure that they 
 were exactly parallel and at equal distances apart. 
 
 Through a vertical opening at the heliostat, 2 inches high and 
 0.01 inch wide, I directed an intense beam of sunlight upon the 
 objective of the theodolite-telescope, and placed the grating at 
 the middle of the theodolite -disk. The grating consisted of 
 about 260 parallel wires, which were 0.002021 inch thick and 
 whose edges were 0.003862 inch apart. I took care to see that 
 no light except that coming through the grating fell upon the 
 objective. Since the small openings between the threads dif- 
 fract the light, all the light which fell upon the objective was 
 diffracted to the same extent. I was most surprised to ob- 
 serve that the phenomena seen through the telescope when the 
 grating was used were entirely different from those observed 
 by diffraction through a single opening. The opening at the 
 heliostat is seen exactly as it would be through the telescope 
 if the grating were away ; and at some distance from this im- 
 age, on both sides, are seen a great number of colored spectra, 
 which are exactly like those seen through a good prism ; they 
 become longer the farther they are from the axis, but they de- 
 crease in intensity. Fig. 1, Table I., represents some of these 
 spectra. In A is seen the opening at the heliostat, colorless 
 and sharply defined, just as it would appear if the grating were 
 removed. On both sides of A the phenomena are perfectly 
 symmetrical. If the apparatus is well ma(^e, there is no light 
 in the space AH'. The first spectrum is in the space H'C' ; 
 ff is the violet end, C the red. There is no light in the space 
 C'H". The second spectrum is in the space H"0" ; it is twice 
 as long as the first, and the order of the colors is the same ; it 
 is somewhat less intense than the first. In the space between 
 C" and F^" comes the third spectrum ; a portion of its violet 
 rays, however, overlaps the red of the second, and the red of the 
 third overlaps the blue of the fourth. The intensity of the 
 third spectrum is again less than that of the second. Between 
 F" and D"' is the fourth spectrum, whose blue end overlaps the 
 third, and whose red end overlaps the fifth spectrum. Other 
 spectra follow, which become gradually weaker, and of which 
 
 22 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 13 on each side of A can be counted without difficulty if the 
 apparatus is perfected. One can convince himself easily of the 
 existence of a still greater number ; and the only reason why 
 they cannot be counted is because they become longer and 
 longer, and consequently overlap more and more. 
 
 If the eye-piece of the telescope is so focused that, if the' 
 grating were away, the opening at the heliostat would appear 
 perfectly sharp, there are seen in the spectra produced by the 
 grating the same lines and streaks which I discovered in the 
 spectrum of sunlight produced by a good prism.* This is of 
 special interest, because it makes it possible, as we shall see, to 
 determine with a great degree of accuracy the laws of this 
 modification of light produced by the mutual action of a great' 
 number of diffracted beams. In the drawing I have represent- 
 ed in each spectrum only the strongest of these lines, those 
 with which we shall have to do hereafter ; there is seen, how- 
 ever, especially in the longer spectra, a great number of lines, 
 exactly as with a prism. The relative intensity of the lines and 
 their arrangement are the same as with a prism. It is only 
 with reference to the relative spaces which in any one spec- 
 trum are occupied by different colors that there is a striking 
 difference between the spectra produced by the grating and the 
 prism. On this account, and because with some kinds of grat- 
 ings the spectra are very small, one must be well acquainted 
 with the Hues formed by a prism in order to know at once, 
 in spectra of every size, with which bands or lines he has to do. 
 This is all the more necessary because in the grating-sj)ectra 
 which are far from the axis the lines are superimposed. 
 
 I shall call these spectra which are produced by a grating of 
 parallel threads "perfect spectra of the second class," so as to 
 distinguish them from others which arise from the mutual ac- 
 tion of a smaller number of beams, and in which the bands and 
 lines are not seen. These spectra have different properties, and 
 I shall call them "imperfect spectra of the second class." 
 
 In order to vary the conditions of the phenomena as much as 
 possible, I made gratings of wires of different thicknesses and 
 
 * I have described them in a memoir printed in the DenkscUrifteii der k. 
 b. Akademie der WissenscJiaften for the year 1814-15, whioli bears the title, 
 "Determination of the refractive and dispersive power of different Itinds 
 of glass with reference to the peifecting of achromatic telescopes." [This 
 volume, page 3,] 
 
 23 
 
MEiMOIKS ON 
 
 with different spaces. For this purpose I made a fine screw on 
 which there were nearly 340 tnrns to the inch. I also drew 
 pai-allel straight lines at equal intervals on a piece of plane 
 glass covered with gold-foil, through which spectra were ob- 
 tained exactly as they were through wire gratings. 
 
 The size of the spectra of the second class, which are pro- 
 duced by a grating, does not depend upon the width of the 
 spaces nor upon the thickness of the wires, but only upon the 
 sum of the two, or, what is the same thing, upon the distance 
 apart of the centres of the spaces. The less this distance is, 
 the larger are the spectra. The finer, therefore, the screw in 
 whose grooves the thread is stretched, the larger is the spec- 
 trum. Consequently, for these spectra of the second class it 
 is entirely immaterial what the thickness of the wire or the 
 width of the openings is. A hair, silver wire, or gold wire 
 can be stretched in the screw-threads ; the kind of matter is of 
 no importance. Care must be taken, however, to have the 
 thread of uniform thickness, and particularly to have it 
 stretched straight in order that the openings may be of the 
 same width throughout their entire length. If wire is used, 
 great care must be taken in stretching it over the screws, be- 
 cause it bends so easily. It is difficult to use hairs, because 
 they rarely have a uniform thickness. 
 
 If the grooves of the screw upon which the threads are 
 wound are somewhat large — i.e., if the centres of the openings 
 lie far apart — the spectra are small, as noted above ; and con- 
 sequently all come in a small space. If with these coarse 
 grooves the wires are thick, and therefore the width of the 
 openings are correspondingly small, one can see that where the 
 perfect spectra of the second class cease — or, better, become 
 weaker — another kind of spectrum begins. These are much 
 longer ; and the lines and bands which occur in the prismatic 
 spectrum are not seen in them. They change only with the 
 width of the grating - openings, and behave like spectra of 
 the first class, which are produced by diffraction through a 
 single narrow opening ; and, therefore, I designate them by 
 L', L", etc. 
 
 We shall see that the spectra of the first class are visible 
 with nearly all perfect gratings regardless of whether the wires 
 are wound on fine or on coarse grooves. It often happens that 
 some of the spectra of the first class coincide with the spec- 
 
 34 
 
PRISMATIC AND DIFFEACTION SPECTEA 
 
 tra of the second class, and so modify their intensity. We 
 shall see the connection between these wonderful phenomena 
 from the experiments. 
 
 If, when a grating is used, the prism described above in the 
 case of diffraction through a single opening is placed, as there 
 described, in front of the eye-piece, we see that the perfect 
 spectra of the second class consist of homogeneous light, and 
 that beginning with the third, owing to the increase in their 
 length, they overlap at the places of transition from one spec- 
 trum into another. On account of the unequal refraction of 
 the different colored beams through the eye-piece prism, the 
 overlapping spectra will be in part separated and appear as is 
 shown in Fig. 4, Table II. \_This figure is omitted.] We see, 
 for instance, the red end of the third spectrum at C", and the 
 lines which belong to this color may be definitely recognized ; 
 likewise we see the violet end of the third spectrum at IT"', 
 and the lines belonging to it. The same thing is true of spec- 
 tra which lie farther from the axis. Since spectra become 
 longer the farther they are from the axis A, and since for an 
 eye -piece prism of definite angle the height C'd [the differ- 
 ence in refraction, i.e., the dispersion of C and Hhy the prisni] 
 is the same for all spectra, the slant of the upper and lower 
 edges of spectra far from the centre must be less steep than 
 that of those near the centre. As will be seen from the ob- 
 servations, glass has an action upon rays of difl:erent color dif- 
 ferent from that of a grating in air. This is the reason why 
 the lower and upper edges of the spectra viewed through the 
 prismatic eye -piece are seen to be non- rectilinear. The hor- 
 izontal cross -hair of the micrometer is seen well defined in 
 all perfect spectra of the second class, and may be used here 
 also to count the number of the spectra far from the centre, 
 which, on account of their great length and small inclination, 
 are distinguished with difficulty, even with the eye-piece prism. 
 
 If the light passes through a cylindrical lens at the heliostat, 
 the phenomena produced by the grating remain the same as 
 when the light passed through a narrow opening. 
 
 In the experiments which follow I have used the same system 
 of names for the different lines of the spectra as I did in the 
 prismatic spectrum, viz., 0, D, E, F, G, H,* For the first 
 
 * [A summary of ttie preceding paper is given in the note, wliioh is omitted.'] 
 
 35 
 
MEMOIRS ON 
 
 spectrum I shall use the symbols C^ D', E', etc. ; for the sec- 
 ond, C° D", E", etc. I shall call the thickness of the wire S, 
 and the width of an opening y. These quantities are given in 
 terms of a Paris inch. The arithmetical mean of, e. g., 0', C'Vg, 
 C'Va, etc., I call C ; that of D', D'Va, D"V3, etc., D, etc. By 
 means of the theodolite I have measuredj at least six times, the 
 angular distance of the two symmetrical spectra for each color, 
 or, more often, that of the lines named above. Since the spectrum 
 lines are sharply defined, great accuracy can be obtained with 
 perfect gratings. I give all the angles, exactly as I measured 
 them, without any correction. The gratimg was always placed 
 at the middle of the horizontal disk of the theodolite. All an- 
 gles, e. g., C^ D^ E', etc., are the simple distances from the 
 axis A. In the products (y + S)G, etc., I have used the sine of 
 the angles. However, with such small angles as these it is en- 
 tirely immaterial which is used, the sine or the arc. 
 
 Grating No. 
 
 1. 
 
 
 7 =0,000638 
 
 d =0.001324 
 
 B' = 44' 45" 
 
 E"i = l= 
 
 ' 43' 43'.7 
 
 C = 43' 43".3 
 
 E»'=3= 
 
 ' 16' 59".7 
 
 C" =1° 25' 25" 
 
 Fi = 
 
 31' 33".6 
 
 D' = 38' 19".8 
 
 F" =1"^ 
 
 ' 3' 10" 
 
 D" = l°16'38" 
 
 F'"=r 
 
 ' 34' 44" 
 
 D"'=r 55' 
 
 G' = 
 
 27' 57".3 
 
 Div=3°33' 14". 7 
 
 G" = 
 
 55' 51".7 
 
 EI = 34' 12".6 
 
 HI = 
 
 25' 42". 3 
 
 E" =1'= 8' 28".3 
 
 H" = 
 
 51' 31".7 
 
 B = 44' 45" 
 
 F = 
 
 31' 34".l 
 
 C = 42' 43". 4 
 
 G = 
 
 27' 56".o 
 
 D = 38' 19". 3 
 
 H = 
 
 35' 44" 
 
 E = 34' 14" 
 
 
 
 (y+S) B=0.00002o41 
 ly+S) 0=0.00003425 
 (7+«)D=0.00003176 
 (y+d) E=0.00001944 
 
 (r + ^)F=0.00001793 
 (y + 5) G=0. 00001587 
 (7 + 5)H=0.00001461 
 
 [In the following tables only the results are given.] 
 
 Grating No. 3. 
 
 7=0.001113 
 (y+S) B=0.00003541 
 iy+S) 0=0.00003436 
 (>-|-5)D=^0.00003177 
 (r +5) E -0.00001946 
 
 ^ =0.001817 
 (7 + 5) F=0. 00001 795 
 (7+5) G=0. 00001587 
 (y+S) H =0.00001464 
 
 36 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 Grating No. 3. 
 
 7=0.000972 a =0.001964 
 
 (y + 2) 0=0.00002435 {y + d) P=0.0000]J'88 
 
 (y + a)D=0.00003176 iy+S) 6=0.00001580 
 
 (y+5)E =0.00001943 [y + S) H=0.00001450 
 
 Grating No. 4. 
 
 7=0.000549 « =0.003359 
 
 (y + ^) B =0.00002543 (y+J) F=0.00001794 
 
 (y + 5) 0=0.00003436 (y + S) G=0.00001586 
 
 (7 + ^) D=0.00003178 (y+S) H=0.00001457 
 (7 + ^) E=0.00001947 
 
 Grating No. 5. 
 
 7=0.003863 5=0.003031 
 
 (7 + ^) 0=0.00002423 (y+S) F=0.00001786 
 
 (y + S) D=0.00003174 {y + S) G=0.00001578 
 
 (y + S) E=0.00001938 (y + 5) H=0. 00001420 
 
 Grating No. 6. 
 
 y =0.001036 5=0.006759 
 
 (y=5) C =0.00003422 (y+S) F=0.00001785 
 
 (y + S) D=0.0000317o (y + S) G=0.00001591 
 
 (7 + 5) E =0.00001942 (y + S) H=0.00001451 
 
 Grating No. 7. 
 
 y =0.00567 5=0.00610 
 
 (y + 5) B=0.00002174 (y+5) F=0.00001784 
 
 (y+5)E=0.00001940 
 
 Grating No. 8. 
 
 7=0.014256 5=0.003399 
 
 (y+5) D=0.00003174 
 
 Grating No. 9. 
 
 y =0.013470 5=0.006999 
 
 (y + 5) D =0.000031 73 
 
 Grating No. 10. 
 
 7=0.003878 5=0.033486 
 
 (7 + 5) D=0.00003173 
 
 A very minute change in the distance apart of the wires or 
 in the openings produces a proportionally great change in the 
 spectra ; therefore a small inequality in the distance apart of 
 the centres of the threads will cause a marked indistinctness 
 
 37 
 
MEMOIRS ON 
 
 in the lines of the spectra. However great may be the accuracy 
 of construction of the gratings, it has its limits ; and this is 
 the reason whj- even with fine gratings certain lines in some 
 spectra cannot be seen with such clearness as will permit their 
 position to be accurately observed. This was the case in grat- 
 ing Xo. 1 with line B" and the lines in the fifth and following 
 spectra ; in Xo. 2, with the line C and some others ; in No. 3, 
 with B', B", etc. The lines B and H are the hardest to see in 
 every spectrum and with every grating; because they lie near- 
 ly at the ends of the spectrum, and the intensity of their light 
 is small in comparison with that of the other lines of the 
 spectrum. 
 
 The grating with which the greatest number of spectra could 
 be measured with accuracy was No. 4. For some spectra I have 
 used the eye-piece prism in order to determine the position of 
 such lines as were covered by other spectra ; these are C"", C'^, 
 G"', H'", whicli are not visible except by means of the prism. 
 On account of this mutual overlapping only those lines can be 
 seen in the spectra far away from the axis which are contained 
 in the most intense portion ; this is in the neighborhood of 
 the line E. All the spectra observed with grating No. 4 have 
 peculiar properties ; namely, the spectra near E^' and E^'" be- 
 come weaker, E^'" cannot be seen, but those that follow are 
 again visible ; yet in each of these last a different color seems 
 to prevail. If we calculate the location of L' for a single open- 
 ing, making y = 0.000549 — i.e., the distance apart of the 
 wires of the grating — we find that this falls almost where W" 
 should be. AVe will see later that this is also the explanation 
 of the phenomenon described. 
 
 With grating No. 5 the fourth spectrum is almost three 
 times as bright as the third. The explanation of this is to be 
 sought in the fact that with this grating L" falls in the third 
 spectrum. 
 
 With grating No. 6 E^'" and E^'" cannot be seen. At each 
 of the E"s that follow a different color prevails, viz., by E'", 
 blue ; E-^ bright blue ; E^', green ; E^", yellow; and E'"", or- 
 ange. For this grating L' falls in the space where E^" and 
 E"" ought to be. The colors which are prominent in E"', etc., 
 are, with reference to their places, those which would be seen 
 in the second spectrum of the first class if the opening were 
 0.006759, which is the width of the openings of grating No. 6. 
 
 38 
 
PRISMATIC AND DIFFEACTION SPECTRA 
 
 With grating No. 7 the third spectrnm is only half as bright 
 as the second. 
 
 Since with grating No. 8 the first spectrum occupies a space 
 of about two minutes, the lines cannot be seen even if the 
 spectrum is magnified fifty times. In the third and fourth 
 spectra D was visible, but the other lines were not seen sharply 
 enough to allow of measurement. The fifth spectrum is almost 
 invisible ; the sixth is weak, the seventh is much less bright 
 than the sixth. With this grating one can distinguish most 
 plainly the spectra of the first class. In order to calculate 
 their positions and compare tliem with observations, the width 
 of the single opening must be taken as 2 instead of y with 
 this grating, in which the thickness of the wires is less than 
 the width of the openings ; and the same is true in all other 
 such cases. The explanation will appear from special experi- 
 ments which I have made on the question. 
 
 With grating ISTo. 9, also, the lines could not be seen in the 
 first spectrum. The third is almost invisible — there is scarce- 
 ly a faint trace of its existence ; similarly with the sixth and 
 ninth spectra. In the spaces where these spectra shou.ld fall, 
 L', L", etc., come; but in order to calculate their positions, S 
 must be taken in place of y for the width of the opening. 
 
 With grating No. 10 the lines could first be clearly seen in 
 the fourth spectrum. The eighth spectrum is less bright than 
 the tenth, and the ninth seems to be absent ; similarly the 
 eighteenth is apparently invisible. For this grating, also, L' 
 and L" fall in the spaces where the spectra are wanting. 
 
 From the close agreement of the values of (y+S) B, etc., 
 with diflrerent gratings, one can judge of the degree of pre- 
 cision, which is not unimportant. If any one has doubt as to 
 the possibility of such accuracy with reference to the quanti- 
 ties y and S, he need only realize that the method is to meas- 
 ure, say, 100 turns of the screw on which the threads are 
 wound, by means of the microscope described above, and to di- 
 vide the measured distance by the number of grooves taken ; 
 by which process y+S is often measured accurately to the sixth 
 decimal place. 
 
 The following laws are deduced at once from the experi- 
 ments with various gratings : 
 
 With two different gratings constructed of ivires of imiforin 
 thickness and having a coiistant width of opening, the size of the 
 
 39 
 
MEMOIRS ON 
 
 spectra which arise owing to the mutual action of a great number 
 of beams diffracted through the narrow openings, and their dis- 
 tances from the axis, vary inversely as the distance between the 
 centres of tivo openings, or, what is the same thing, as y + 1. 
 
 With perfect spectra of the second class the distances [from the 
 axis] of rays of the same color in different spectra form an 
 arithmetical series whose common diff'erence is equal to the first 
 term. 
 
 With a grating the thickness of whose wires and the width 
 of whose openings are expressed in fractions of a Paris inch, 
 
 -n_0. 0000 2541 pi _ 0.0000 2425 -p_0.00003175 
 
 r 
 
 +g y+S y+a 
 
 -p 0.00001943 -p 0.00001789 p 0.00001585 
 y+o y+o y+o 
 
 0.00001451 
 
 H=- 
 
 y+S 
 
 The relative spaces occupied by the different colors in any 
 one spectrum from a grating are remarkable. For instance, 
 the space CD is to the space GH nearly as 2 ; 1 ; while in a spec- 
 trum produced by a flint-glass prism of only 27° the ratio of 
 these spaces is almost 1 : 2, and with a prism of water nearly as 
 2 :3. 
 
 I have already called attention to the fact that in order to 
 see the lines in the spectra of the second class, the eye-piece 
 of the telescope must be accurately focused in such a way 
 that, if the grating were away, the vertical opening at the 
 heliostat would be clearly seen. A small displacement of the 
 eye-piece makes the lines indistinct or invisible. The rays, 
 therefore, after they are modified by the grating, diverge from 
 a point which is at the same distance from the grating as is the 
 opening at the heliostat. 
 
 If a grating is placed at a considerable distance in front of 
 the objective in such a manner that the rays falling upon the 
 telescope from the heliostat must pass through the grating, the 
 lines of the spectra appear, with the eye-piece in the position 
 described above, just as they would if the grating were close to 
 the objective ; the distances of the colored beams from the r.xis 
 
 30 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 are, however, found to be smaller. The reason for this may be 
 seen at once. [Bxplanation omitted.^ 
 
 If light is allowed to pass through two identical gratings at 
 the objective — i.e., if two identical gratings, one behind the 
 other, are placed in front of the telescope — the dimensions of 
 the spectra are the same as they would be with one of the grat- 
 ings. If two different gratings are used, the distances of the 
 spectra from the axis are what they would be if the finer of the 
 two gratings was placed by itself in front of the objective. 
 
 Mutual Action of Two, Three, Etc., Diffracted 
 Beams. 
 
 If by means of two screens whose edges are straight and ver- 
 tical the exposed surface of a grating is reduced to the interval 
 of one opening, and if, when placed in front of the telescope, 
 sunlight is allowed through this opening only, the spectra are 
 the same, of course, as those obtained by means of a single 
 narrow opening of the same width. The spectra are, there- 
 fore, of the first class, as represented by Fig. III., Table I. If 
 the two screens before the grating are moved back so that light 
 passes through two openings, and consequently two diffracted 
 beams fall upon the objective, there is seen through the tele- 
 scope a new sort of spectrum in the space which L'L' occupied 
 before, as is shown at M', M", etc., in Fig. II. I shall call 
 these spectra "imperfect spectra of the second class." With 
 reference to the colors and their order of occurrence, this space 
 M'M' is similar to L'L' in spectra of the first class ; the space 
 M'M" is like L'L", etc.; they are visible in that space only in 
 which, with a single opening, L'L' comes. Beyond this space 
 the spectra are exactly like those given by a single narrow 
 opening. Accordingly, if two diffracted beams fall upon the 
 objective, one sees the imperfect spectra of the second class 
 and the spectra of the first class at the same time. We shall 
 see below what relation there is between the dimensions of 
 these imperfect spectra of the second class and the width of 
 the openings, etc. I shall designate the red ends of these spec- 
 tra by M', M", M™, etc. 
 
 If the two screens in front of the grating are so placed as to 
 allow light to pass through three openings, the space M'M', 
 Fig. II., is divided into new spectra almost in the same manner 
 
 31 
 
MEMOIRS ON 
 
 as the space L'L' was before. These new spectra are similar to 
 the others in the order of their colors, and are present only 
 in the space !M'M'. I shall call these new spectra " sjiccfra of 
 the third class," and shall designate their red ends by N', N", 
 N™, etc. Beyond the space M'M' the spectra of the second 
 class appear almost exactly as they did when there were two 
 diffracted beams. However, with certain gratings their dis- 
 tances from the axis were changed slightly. The spectra of 
 the first class appear also as they did when there were two dif- 
 fracted beams. There are seen, then, in this case three differ- 
 ent kinds of spectra, viz., third class, imperfect second class, 
 and first class. The experiments described below will show 
 what relation exists between the dimensions of the spectra of 
 the third class and the width of the openings. 
 
 With four diffracted beams there are seen spectra of the 
 first class, the imperfect second class, and the third class ; but 
 the last are noticeably smaller than they were when there were 
 three diffracted beams. The spectra of the second class have 
 changed only slightly. 
 
 With five diffracted beams the spectra of the third class are 
 smaller than with four, while those of the second class have 
 changed only a little. With six diffracted beanrs the spectra 
 of the third class are smaller than with five ; with seven beams, 
 smaller than with six, etc., until they finally become so small 
 that they can be distinguished no longer, and there is seen 
 only a bright, colorless line which has the same appearance ex- 
 actly as the opening at the heliostat would have if the grating 
 were away. The spectra of the second class have in the mean 
 time, owing to the increase in the number of diffracted beams, 
 gradually changed both in their constitution and in their dis- 
 tances from the axis, and have approached more nearly in 
 every respect the perfect spectra of the second class. The 
 lines of the spectra become visible, however, and the light be- 
 comes homogeneous, only when a great number of equally dif- 
 fracted beams at equal distances apart mutually influence each 
 other. 
 
 In the following experiments, W, N", N'", etc., are, as I said 
 above, the red ends of each spectrum of the third class ; just 
 as M', M", etc., ai-e the red ends of each imperfect spectrum of 
 the second class. This method of writing symbols has also been 
 used in the spectra of the first class. What I said there also 
 
 32 
 
PEISMATIC AND DIFFRACTION SPECTRA 
 
 in regard to the accuracy of the angles holds true here. The 
 angles M', M", etc., are always the distances from the axis. 
 [Experiments omitted.] By careful consideration of the degree 
 of accuracy of the above experiments, it follows, within the lim- 
 its of error, that : 
 
 Using one and the same grating, tut a different nimiber of 
 openings, the dista?ices of the spectra of the third class from the 
 axis and their dimensions vary inversely as the number of dif- 
 fracted learns, i.e., as the number of grating openiiigs, begimmig 
 with three. 
 
 With different gratings and with the same number of openiiigs, 
 the distances of the spectra of the third class from the axis and 
 their dimensions vary inversely as y+8. 
 
 For spectra of the third class, the distances from the axis 
 form an arithmetical series whose common difference equals the 
 first term. 
 
 Further : 
 
 FOR THEEE BEAMS. 
 
 W = 
 
 0.0000208 
 3 (y+a) ' 
 
 N" = 2 
 
 0.0000208 
 3 (y+2) • 
 
 N' = 
 
 0.0000208 
 4 (y+2) •• 
 
 FOE FOUR BEAMS. 
 
 , 0.0000208 
 
 ]Sr"=:2 
 
 4(y+g) 
 
 N"' = 3 
 
 0.0000208 
 4 {y+B) ■ 
 
 W = 
 
 0.0000208 
 5 (y + g) ' 
 
 FOR FIVE BEAMS. 
 
 , 0.0000208 
 
 N" = 2 
 
 5 (y + g) 
 
 N"' = 3 
 
 0.0000208 
 5 ir+B) • 
 
 The space KM', Fig. II., Table I., which is seen when there 
 is mutual action of two difEracted beams, contains the spectra 
 of the third class if there are three beams, as I have stated 
 above ; therefore, with three, four, etc. , beams, M' can no 
 longer be seen ; and in these cases M" is the red end of the 
 first spectrum of the second class, a fact which must not be 
 overlooked when comparing perfect and imperfect spectra. 
 Since the spectra of the third class which are contained in the 
 space KM' become smaller as the number of beams which mut- 
 ually influence each other increases, and since the spectra be- 
 c 33 
 
MEMOIRS ON 
 
 come ultimately so small that they cannot be distinguished, 
 thus producing in K only a bright, colorless line, the space be- 
 tween K and M' must be without light ; because, with an in- 
 crease in the number of beams, the spectra of the second class 
 do not change their position and magnitude, comparatively. 
 
 With grating No. 9, M'^ is invisible because it falls nearly 
 at L'. Since in this grating y is greater than S, the latter 
 must be used instead of the former in calculating L^ Why this 
 is so will appear at once. In order to produce spectra of the 
 first class, one must have two edges lying close together, by 
 which the light is diffracted. It is not necessary that these 
 two edges should face each other ; they can also be turned re- 
 versed, provided only that they lie near enough, as is the case 
 with a narrow metal strip, a thread, or a wire. In these cases, 
 however^ the spectra of the first class cannot be seen plainly, 
 because they occur at the same places where non- diffracted 
 white light comes. By means of a telescope, however, one can 
 easily convince himself of their existence. For this purpose I 
 stretched a wire 0.02287 inch thick across the middle of an 
 opening in a screen, which was i inch wide, and placed it in 
 front of a telescope, with the thread vertical. The spectra 
 of the first class which must arise, owing to the width of the 
 opening in the screen — y=i inch — would be too small to notice, 
 and the opening at the heliostat must appear through the tele- 
 scope almost as if the screen were away ; if, however, the thread 
 stretched across the opening produces spectra, these must be 
 seen on either side of the opening at the heliostat ; this is ac- 
 tually the case. Owing to the width of the opening at the 
 heliostat, it is seen so brightly that the eye can scarcely bear 
 it ; and ou each side are seen spectra of the first class. On 
 account of the intensity of light in the middle, L' could not be 
 measured ; but the following two could be. I found L"=6' 16" 
 and L"'=9' 30". If we assume the above thickness of the wire as 
 the value of y, in order to calculate L" and L'", angles are ob- 
 tained which agree as closely with those observed as could be 
 expected under the circumstances.* In order, therefore, to 
 produce spectra of the first class, it is not necessary that the 
 edges which diffract the light should face each other ; they 
 
 * These experiments deserve to be continued, because, in some cases, 
 there are discrepancies which exceed the limits of probable error. 
 
 34 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 can be reversed, as is the case with a wire. With grating ISTo. 9 
 the edges of the wires are nearer than those of the intervening 
 spaces ; therefore, the former produce the spectra of the first 
 class. 
 
 The imperfect spectra of the second class are often modified 
 by the position of spectra of the first class ; and these modifi- 
 cations depend, besides, npon the increase or decrease in the 
 number of the beams which mutually interfere. The exact law 
 of these small changes cannot be deduced from the experi- 
 ments so far made, and other experiments are therefore neces- 
 sary. This much, however, can be seen from the above, that 
 with different gratings the distances of the imperfect spectra 
 of the second class, from the axis, and their dimensions, are 
 nearly inversely as y-(-S ; further, that with two beams M' is con- 
 siderably smaller than the differences M"— M', M™ — M", etc.; 
 and therefore, with reference to the succession of the distances 
 of the colored beams from the axis, these spectra are markedly 
 different both from those which arise from a round opening 
 and from those which come from a long, narrow opening. With 
 gratings where S is greater than y, it is not difficult to deduce 
 a law for the imperfect spectra of the second class — for instance, 
 with gratings No. 6 and No. 10. 
 
 The angles L', L", etc., cannot be determined with great 
 accuracy when there are two, three, etc., diffracted beams; 
 therefore no certain conclusion can be drawn from the varia- 
 tions in these angles with three, four, etc., diffracted beams in 
 the case of grating No. 10. One reason lies in the fact that it 
 is almost impossible to make three or four intervening openings 
 exactly equal, although the centres of the wires may be at equal 
 distances from each other. We know from the experiments 
 with one diffracted beam how great the variation in the distances 
 of the spectra is, if, with an opening already small, the width 
 changes even slightly ; therefore with three diffracted beams 
 the distances of the spectra of the first class from the axis may 
 easily be found to be different from what they are with two 
 beams, etc. This inequality [of the spaces] has much less in- 
 fluence upon spectra of the second and third class. 
 
MEMOIRS ON 
 MrTTiAL AcTio:s' of Beams Diffracted in Water and 
 
 OTHER EeFRACTING MeDIA. 
 
 [Experiments omitted. 1 
 
 The conclusion is : In different refracting media, with iden- 
 tical gratings, tlie sines of the angles of the diffracted beams vary 
 inversely as the indices of refraction. 
 
 Mutual Action of Beams Diffracted bt Reflection. 
 [Experiments omitted.l 
 
 Mutual Action of Beams Diffracted through Round 
 AND Quadrangular Openings. 
 
 [Experiments omitted.'] 
 
 When seen under a microscope the barbs of most birds' feath- 
 ers contain regularly arranged fine openings. If one looks 
 through the barbs at a brilliantly illuminated point which is 
 not too near, he can see, even with the naked eye, colored 
 spectra, which have a definite position. If such a feather is 
 placed in front of a telescope and light coming from a round 
 opening near a heliostat is allowed to pass through it, spectra 
 of the first and second class are seen. The spectra which were 
 seen with the naked eye were those of the first class, which are 
 very large but of feeble intensity ; and therefore, when seen 
 through the telescope, which magnifies greatly, they may be 
 easily overlooked, if attention is not paid to their distance 
 from the axis. 
 
 With some gratings made of parallel wires, one sees through 
 the telescope, beyond the space which is occupied by the length 
 of the spectra — that is, in the dark portion of the field — what 
 are apparently the wires of the grating itself, which is, however, 
 impossible, if one considers the path of the light ; one might 
 perhaps believe that this light is due to interval reflections at 
 the surfaces of the objective. But this is not the case ; for 
 the eye-piece can be pushed in or drawn out an inch, and the 
 lines still remain visible. These lines have also a definite col- 
 or ; namely, one is always a reddish yellow, the second is blue- 
 ish green, the third is again reddish yellow, etc. I shall re- 
 turn to this subject at another opportunity. 
 
 36 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 The phenomenon which is seen through a telescope wheni 
 light is allowed through an opening of the shape of an equi- 
 lateral triangle placed in front of the objective is also inter- 
 esting. 
 
 It may be surprising that so many phenomena could up to 
 this time have escaped the notice of investigators ; and that, for 
 instance, the simple law, that in diffraction through a single 
 opening the inflection of the rays varies inversely as the width 
 of the opening, was not only not found, but that results were 
 obtained differing widely from this. The explanation lies in 
 the mode of observation. One would fall into similar errors 
 if, for instance, he tried to determine the path of colored light 
 through glass lenses by intercepting and measuring this re- 
 fracted light at different distances. This mode of observation 
 is to blame for the fact that the phenomena of the mutual in- 
 fluence of beams of light have escaped the attention of inves- 
 tigators,* phenomena which must be known before the laws 
 of diffraction can be learned. For if light coming through 
 a grating is intercepted by a white surface or a piece of ground- 
 glass, one cannot see, even on a small scale, what is observed 
 through a telescope when used with the grating ; and in gen- 
 eral nothing is seen. 
 
 It is remarkable that the observed laws for the mutual 
 action and diilraction of beams can be deduced from the 
 principles of wave-motion ; that, from a knowledge merely ol 
 the angle of diffraction of the light and of the distances at 
 which the beams interfere, the magnitude of a vibration of 
 light, for every color, can be expressed by means of an ex- 
 tremely simple equation, and that these determinations, under 
 the most varying conditions, agree to a high degree of accura- 
 cy ; further, that these same principles furnish an explanation 
 of the cause of the origin of the lines and bands which are 
 seen in a prismatic spectrum, etc, On another occasion I shall 
 make known the theory of interference and diffraction of 
 beams of light. 
 
 The phenomena of interference and diffraction of light are, 
 
 * T. Young had already observed that the colored fringes which are 
 seen in the interior of the shadow of a hair vanish if one edge is covered ; 
 so that the beams of light going by both edges must combine to produce 
 the interior color-bands. 
 
 37 
 
PEISMATIC AND DIFFRACTION STECTRA 
 
 as we see from the laws deduced, infinite in nnmber ; and all 
 that was previously known amounts to only a few special cases. 
 The theory will also make us acquainted with these phenom- 
 ena which can be subjected to no new investigation following 
 the path which I have taken.* 
 
 I cannot repeat too often that all apparatus to be used in 
 these experiments must be perfect to a high degree ; and one 
 can judge of the degree of this perfection from the ratio of the 
 dimensions of the grating to the dimensions of the spectra, etc. 
 An inequality or imperfection, apparently unimportant, can 
 produce a great indistinctness or oven the entire vanishing of 
 the phenomena ; therefore, one must consider well everything 
 that can be of injurious influence. More than with all other 
 optical phenomena, one must be on one's guard in these ex- 
 periments against optical illusions. 
 
 It will be reward enough for me if, by the publication of the 
 present experiments, I have directed the attention of investi- 
 gators to this subject, which still promises much for physical 
 optics and appears to open a new field. 
 
 * Among these are the color -fringes which are seen in the shadow of 
 a single edge of a body ; also the phenomena which Herr Hofrath Meyer 
 observed long ago and described in tlio Qottinger Commentarcn, Vol. IV., 
 p. 49. 
 
 
Short Account of the Results of New Experiments on 
 THE Laws of Light^ and their Theory. 
 
 Gilbert's Annalen der Physik, Band 74, p. 337-378. Edinburgh Journal of 
 Science, VII., VIII., 1837, 1828. 
 
CONTENTS 
 
 PAGE 
 
 Introduction 41 
 
 Sketch of Previous Work on Oratings 41 
 
 Ruling of Glass Oratings 44 
 
 Normal Incidence. Exact Law 45-47 
 
 Efl'ect of S/uipe of Groove 47 
 
 Oblique Incidence. Exact Law 48-51 
 
 Laws Deduced from Principles of Interference 51 
 
 Spectra Obtained by Beflection 54 
 
 Effect of Unevennesses 55 
 
 Effect of Periodic Errors 56 
 
 Spectra of Flames 58 
 
 Spectra of the Moon and the Fixed Stars 58 
 
 New Apparatus 59 
 
Short Account of the Results of New Experiments on 
 THE Laws of Light, and their Theory. 
 
 Read in the Mathematical-Physical Section of the Academy, June 14, 1823. 
 
 I PUBLISHED a year ago, in a memoir which is printed in the 
 eighth volume of the DenkseJiriften of the Royal Bavarian 
 Academy of Sciences, an account of some new experiments 
 concerning diffraction of light and those phenomena which oc- 
 cur owing to the mutual action of diffracted beams of light ; 
 and the laws which can be deduced from these experiments 
 were also developed. Guided by these deductions, I have 
 continued these experiments since then ; and what follows is 
 an account of those of my results which are suited for commu- 
 nication in a brief description. I must, however, assume as 
 known the larger portion of what the above-mentioned memoir 
 contains on this subject. 
 
 [Resume of previous papers is omitted.l 
 
 In this memoir I shall designate by B, 0, ... H colored 
 rays of different kinds : B is a red ray which lies near the end 
 of the spectrum ; C is deeper in the red ; D is orange-colored ; 
 E, green ; F, blue ; G, indigo ; H, violet. In every spectrum 
 of sunlight which consists of perfectly homogeneous light there 
 are found in the places named fixed lines or streaks which are 
 distinguished from the other countless lines of the spectrum 
 either by their intensity or by their position.* 
 
 The angles from the axis through which the rays B, C, etc., 
 are deflected by the grating I designate by B', G', etc., in the 
 first spectrum, which is nearest the axis ; by B'', C", etc, in 
 the second ; by B"', C", etc., in the third from the axis, etc. 
 From the experiments which are described in detail in my 
 
 * [A long note giving the conditions for securing a pure prismatic spectrum 
 is omitted.'] 
 
 41 
 
MEMOIRS ON 
 
 second memoir, it follows that, with all gratings, if y denotes 
 the width of a single grating space, and S the width of a single 
 wire, expressed in fractions of a Paris inch, the arcs of these 
 angles are as follows, the radius being taken equal to 1: 
 
 ■gi_ 0.00002541 ^i_ 0.00002425 di_0^ 
 
 00002175 
 
 y+S y+5 y+S 
 
 ■gi^ 0.00001943 p_ 0.00001789 Qi-^ 
 
 00001585 
 
 y+S y+S y+S 
 
 Further, that 
 
 -g-i_ 0.00001451 
 
 y+S 
 
 B" =2 B', C" =2 C, etc. 
 B"'=3 B', C'"=3 0\ etc. 
 Etc. 
 
 The numerator in these general expressions is a number 
 which is absolutely constant for each definite colored ray, but 
 different for different rays, however varied the cases are, and 
 which refers, as is easily seen, to a definite absolute scale ; in 
 this case to the Paris inch. If for each colored ray this num- 
 ber is designated by w, and if the angle of deflection of one 
 and the same ray in the first spectrum is designated by ■&', in 
 the second by S", in the third by 3"°, etc., then, 
 
 ^'=.-^; 3"=-?^, etc. 
 y+8 y+S 
 
 And if, further, v denotes the number which gives the order 
 of the spectrum (for the axis v = ; for the first spectrum 
 r=l; for the second, )'=2, etc. ; and it can never be a fraction) ; 
 and if, for the sake of brevity, we call the sum of the width 
 of one grating opening and of one line of the grating, or y + ^, 
 equal to e, we have as a general formula 
 
 (I.) r'= 
 
 E 
 
 According to the results of the previous experiments (and as 
 is shown by the general formula (I.) which is derived from 
 them), the angles of deflection of the same colored beams in 
 
 43 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 the series of spectra formed by the grating are in the ratio of 
 the numbers 0, 1, 2, 3, etc. Tlie experiments from which 
 these results are deduced gave, however, such small angles that 
 for them the sine, tangent, and arc do not sensibly differ. 
 With my finest grating, where £=0.001952 inch, D' was equal 
 to 38' 19". 3. If the angles were larger, that is, if the gratings 
 were many times finer, one might think it probable, from cer- 
 tain considerations, that the arcs themselves do not have the 
 relations given above, but that some trigonometrical function 
 of them does. In accordance with the theory which will be 
 discussed later, the sities of the angles should have the given 
 relation if the light falls normally upon the grating. Partly in 
 order to verify this directly by experiment, partly because the 
 laws of this modification of light caa be deduced with more ac- 
 curacy from larger spectra, and conclusions as to the theory of 
 these phenomena can be drawn with more certainty, it was great- 
 ly to be desired, it seemed to me, that gratings should be made 
 much finer than those which I used in my earlier experiments. 
 The distances apart of the lines or wires of such fine gratings 
 must, however, be exactly equal to such a high degree that the 
 fixed lines of the spectra can be seen ; otherwise the distances 
 of the colors from the axis cannot be measured. 
 
 It will not be considered possible by any one who is ac- 
 quainted with the difficulties of the work to prepare a screw 
 much finer than that which I made for my earlier experiments. 
 "With a special apparatus I succeeded iu scratching parallel 
 lines upon a piece of plane glass, covered with gold-foil, which 
 were at such distances from each other that c was equal to 
 0.00114 inch. If one tries to scratch lines closer together than 
 this, no gold is left on the glass, and there are, consequently, no 
 apertures. The spectra produced by such a grating, where 
 £=0.00114, are much larger than those obtained before, and 
 the fixed lines were plainly seen in them ; but the results ob- 
 tained were still far from being able to decide the question at 
 issue. 
 
 It is entirely immaterial in a grating which is to be used 
 for these experiments whether the threads out of which it con- 
 sists are opaque, translucent, or transparent. A grating of 
 glass fibres, for instance, produces these phenomena as well as 
 one made out of metal wires. I covered, therefore, one side of 
 a piece of plane glass with a layer of grease so thin that it 
 
 43 
 
MEMOIRS ON 
 
 could scarcely be recognized by the eye alone ; in this grease I 
 scratched parallel lines which were only half as far apart as the 
 finest of those ruled on the gold - foil. With this grating I 
 obtained spectra in which the fixed lines could be plainly seen, 
 and which were therefore suited for measurements of the dis- 
 tances from the axis. In no layer of grease or varnish is it 
 possible to rule finer parallel lines than these, which shall be at 
 equal intervals. 
 
 It was only by means of the diamond that I succeeded in 
 producing finer gratings. A machine specially made for the 
 purpose enabled me, by using a diamond-point, to rule lines in 
 the surface of a piece of plane glass which were almost per- 
 fectly parallel. If one is so fortunate as to find a good diamond- 
 point, lines can be ruled with this machine which are so close 
 together that they cannot be distinguished by the strongest 
 compound microscope. It is, however, not enough to be able 
 to rule in a given space a great number of lines which shall 
 still be separate from each other ; these lines must be ruled so 
 accurately at equal distances apart that the variation shall not 
 amount at the most to the one-hundredth of this distance. By 
 means of my machine I have obtained a grating in which 
 E^O.0001333 inch, and whose lines are so evenly spaced that 
 the fixed lines of the first and second spectra obtained with it 
 can be plainly seen.* 
 
 * By means of my machine one can rule parallel lines which are sepa- 
 rated by spaces as wide as themselves, and which are so close together that 
 3300 of them lie in a Paris inch ; but I have not yet succeeded in making 
 their distances from each other so exactly equal that in this distance, which 
 is 0.00003125 inch, errors of one part in a hundred— i.e., of 0.00000031— 
 are not present; and perhaps this would not be possible for the hand of 
 man, whatever machine is used. Since no use can be made of 100 or 200 
 parallel lines, and since with such fine gratings there must be several thou- 
 sand lines in order to produce intense perfect spectra, it is evident that it 
 was largely a question of fortune, with £=0.0001323, to find a diamond- 
 point which could rule several thousand such fine lines without changing. 
 So far, I have succeeded in making only one grating as fine as this. If 
 the diamond-point changes during the ruling, the previous work is useless. 
 Without one's intending it, the point often makes stronger or weaker lines. 
 Even with the most powerful microscope one cannot be sure whether the 
 point is suited to rule proper lines. A diamond which appears less pointed 
 than anotlier often rules the finer lines ; and therefore a suitable point can 
 be found by experiment only. What renders the matter more difficult is 
 that a slight change in the inclination or in the position of the diamond, 
 
PEISMATIC AND DIFFRACTION SPECTRA 
 
 By means of this grating spectra are obtained which are 
 as long as those obtained from large prisms ; and even in the 
 first spectrum the D line (in the orange) can be seen practi- 
 cally double, so that the space between can be measured. And 
 since with this grating D', for instance, equals 10° 14', the law 
 of modification of the light produced by it can be deduced 
 with great accuracy. 
 
 When the light fell normally upon the grating in which £ = 
 0.0001223, 1 obtained 
 
 C =11° 25' 20" F' = 8° 26' 6" 
 
 C"=23°19'42" F" = 17° 3' 34" 
 
 D' =10° 14' 31" G' = T 27' 19" 
 
 D"=20° 49' 44" G"=15° 3' 9" 
 
 E' = 9° 9' H'= 6° 52' 36" 
 E"=18° 32' 34" 
 
 The angles are so large that the arcs, sines, and tangents 
 are sensibly different. Since the instrument with which the 
 angles are measured gives, without repeating the observation, 
 readings accurate to 4", one can easily decide how trustworthy 
 the readings are. 
 
 The third spectrum, the fourth, and the following were seen 
 satisfactorily in these experiments with this grating ; but the 
 fixed lines in the various colors could not be recognized with 
 sufficient precision to have their distances from the axis meas- 
 ured as accurately as in the first and second.* 
 
 with refeience lo the plane of the glass often seriously influences the 
 strength of tlie lines. Since every line must be drawn separately and with 
 the greatest care, one can easily understand how much time and patience 
 is required in order to rule a few thousand lines with sufficient accuracy. 
 
 * However great the accuracy of the ruling with reference to the dis- 
 tances apart of the lines of the grating, it naturally has its limits, and perfect 
 accuracy cannot be expected ; a statement which is true of everything made 
 by the hand of man. The amount of the displacement or blurring of 
 the fixed lines of the different spectra which would be produced by a small 
 inequality in the intervals of the parallel lines of a grating, can be de- 
 duced from the equation (I.) & = — . For it follows from it that 
 
 <© = — cZj-j- ; consequently an equality which amounts to only one-hun- 
 dredth of the very small distance e {i.e., (f£=0. 00000133 inches) will pro- 
 
 45 
 
MEMOIRS ON 
 
 The measnrements given for the first and second spectras 
 are sufficient, however, to allow one to decide upon the law of 
 this modification. 
 
 Since the distance between the parallel lines, ruled on the 
 glass grating, as I shall call it, must be known most accurately, 
 and since these lines are seen with great difficulty even with 
 the strongest microscope, and in any case cannot be counted, 
 I try to rule the first and last line of the grating somewhat 
 stronger than the others, and I measure their distance apart by 
 means of a microscopic apparatus prepared for the purpose. 
 The ruling-machine counts the lines as they are ruled ; and so 
 I know how many there are in the ruled space ; e.g., in the 
 grating just discussed there are 3G(Jl lines. Therefore, from 
 a knowledge of the distance of the first line from the last, 
 the distance between the centres of two — that is, c — can be 
 determined to a high degree of accuracy. The ratio, too, 
 of the thickness of a scratch to the width of the opening be- 
 tween two lines can be very closely determined. If the lines 
 were so wide that one touched the other, and consequently 
 there was no aperture between, no light could be regularly re- 
 flected from the ruled surface ; it would be scattered as from 
 a ground surface. If the apertures were as wide as the 
 scratches, the ruled surface could reflect only half as much 
 light as an unruled surface of the same size. The ratio, there- 
 fore, of the light regularly reflected from the ruled glass sur- 
 face to that which is reflected by an unruled glass surface of 
 the same size is the same as that of the width of the aperture 
 between two scratches to the width of the lines [i.e., to e].* 
 It need scarcely be noted that in the experiments made in this 
 
 duce a displacement of the fixed line D, in the first spectrum, of 6' 5"; in 
 the second, of 13' 10" ; in the third, of 18' 15", etc. This is the reason why 
 the fixed lines may be well defined in the first and second spectra, and yet 
 not be so in the third, fourth, etc. Whoever has to do with small mag- 
 nitudes, not merely in numbers, but in experiments, will know liow to es- 
 timate this accuracy, and will have an idea as to the difficulty with which 
 it is obtained. 
 
 * Even if the amount of the reflected light could be accurately measured, 
 this conclusion must be regarded as only approximately true for reasons to 
 be discussed later. With gratings for which e is still smaller than this it 
 would be less true. In the experiments described in this paper the deter- 
 mination of this ratio is of no importance whatever ; the magnitude of £ is 
 alone of interest. 
 
 46 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 way care naust be taken to have no light reflected from the 
 second surface of the glass. 
 
 Using another grating, where e was equal to 0.0005919 inch, 
 I obtained, with light at normal incidence, 
 
 C = 2° 20' 57" E^ =9° 28' 3" 
 
 D' = 2° 6' 30" F' =1° M' 19" 
 
 D" = 4° 13' 7" F" =3° 28' 45" 
 
 D'"= 6° 20' 7" F"' =5° 13' 23" 
 
 D'^= 8° 27' 43" F'^ =6° 58' 18" 
 
 D^' =10° 35' 53" G' =1° 32' 22" 
 
 E' = 1° 53' 7" G" =3° 4' 57" 
 
 E" = 3° 46' 17" G"' =4° 37' 30" 
 
 E"'= 5° 39' 50" H' =1°25' 
 
 E'^ = 7° 33' 41" H" =2° 50' 11" 
 
 All the observations, with both glass gratings, can be ex- 
 pressed very approximately by the equation 
 
 (II.) sinS(y)=— • 
 
 If the light is incident normally, therefore, the sines of the dis- 
 tances of a colored ray from the axis in the different consecu- 
 tive spectra are in the ratio of the numbers 0, 1, 2, 3, 4, etc.* 
 
 The glass grating, £=0.0005919, has the remarkable property 
 that its spectra on one side the axis are more than twice as in- 
 tense as those on the other. The scratches of this grating are 
 visible under a microscope, but it is impossible to distinguish 
 
 * If it were not tlie sines, but tbe angles, of deflection of a colored ray in 
 thedifferent spectra which had the given ratio, then with the finer grating, 
 wliere Di=10° 14' 31", D" should equal 20° 29' 2" ; according to experi- 
 ment, however, D"=20°49'44" — that is, is 20 minutes greater. Conse- 
 quently, the sines of the angles have the given relation. Calculation leads 
 to a difference in the seconds, which, although small, is larger than can be 
 ascribed to an error of observation. Whether this difference is to be 
 ascribed lo a slight imperfection in the grating, or whether it lies in the 
 nature of the phenomena, can be decided only by a series of experiments 
 with different fine gratings. I give in the table the angles exactly as they 
 were observed, not allowing myself any correction whatever. I determined 
 these angles very often, and always by repeating six times ; yet I obtained 
 angles for the bright colors which agree nearly always to within one sec- 
 ond; notwithstanding which, small constant errors could cause the differ- 
 ences in the seconds which are mentioned above. 
 
 47 
 
MEMOIRS ON 
 
 in them any sjiocial form. I sonijlit tbo oxplanntion in the 
 idea that, on ruling tho lines, the diiimond-jioint had snch a 
 position with reference to tho piano glass that ono edgo of each 
 scratch was sharp, tho other not so well defined ; and 1 think 
 that this hypothesis is confirmed by tho following experiment; 
 On a piece of plane glass, over which there was a thin layer of 
 grease, I ruled parallel lines in such a way that with every lino 
 the grease on one side was sharply defined, on the other less so; 
 and I obtained phenomena, in fact, through this grating which 
 Avere like those seen through tho glass grating mentioned. 
 
 If the incident light docs not fall perpendicularly upon tho 
 grating, but is in the plane perpendicular to the lines of the 
 grating, and iiicllued to the normal to the grating, the action is 
 as if for this incident light the distance apart of the parallel 
 lines — that is, e — was smaller than when tho incidonco was nor- 
 mal, in tho ratio of the radius to the cosine of the angle of in- 
 cidence. The distances of the spectra from the axis (5) must 
 therefore become greater as the angle of incidence increases ; 
 because (as equation (II.) shows) tho sines of this distance in- 
 crease in tho same ratio as t decreases. If we designate, there- 
 fore, by (7 the angle of incidence — i.e., the angle between the 
 incident beam and tho normal to the grating — wo might think 
 
 we could safely conclude from equation (II.) — i.e., sin d^'^— — 
 
 — that the following is true : sin (5)" = . But from the 
 
 ^ ' t.cos a 
 
 theory of these phenomena, which will be disC|US8ed later, it 
 
 may be predicted that in this case tho spectra on the two sides 
 
 of the axis will be no longer symmetrical ; that therefore, e.g., 
 
 D' must be larger on one side of the axis than upon the otlicr. 
 
 This is confirmed by experiment, as appears below. With 
 
 gratings in which c is not very small, the diilerenoo is not 
 
 marked, it is true ;* it is, however, exceptionally largo with the 
 
 grating in which £=0.0001323 inch. For instance, with this. 
 
 for (7 = 55°, D' on the one side of tho axis equals 15° C, and 
 
 on tho other, D'=30° 33'. 
 
 * In fact, witli coarse gratings, if a is not very large, ono can use the ex- 
 pression sin 9<''= — ■ witli sufflcient accuracy, as I did in my memoir 
 
 A New Modification , etc. We shall, however, find below an exact ex- 
 pression whicli is equally simple. 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 If in tlie theory of spectra of the first class the non-symmet- 
 rical ones, which consist of non-homogeneous light, and which 
 contain no fixed lines,* are of importance, the non-syminetrical 
 qjedra of the second class are of immensely greater theoretical 
 interest, because they show the fixed lines ; and therefore the 
 laws of this modification of light can be exactly deduced, and 
 the theory of these phenomena can be most closely verified. f 
 I give here the results of numerous experiments on the colored 
 rays D and F. In order to indicate on which side of the axis 
 S lies — the angle measuring the distance of the colored ray from 
 the axis — I mark with —I, —II, . . ., those spectra which lie 
 upon that side of the axis on which the incident light is in- 
 clined towards the face of the grating ; and with +1, +11, . . ., 
 the spectra on the opposite side, where the inclined incident 
 beam makes obtuse angles with the grating, so that D"', D"*"' or 
 D"", D"*"", .... mean the opposite positions of D in the first 
 or second spectrum, etc. By <r is to be understood the angle of 
 incidence in the sense described above — i.e., the angle included 
 between the incident ray and the normal to the grating. 
 
 EXPERIMEKTS WITH THE GLASS GKATIN-G £ = 0.0001223. 
 
 <7=55° 
 
 D-'=15° 6' 36" F- =13° 44' 40" 
 
 D+' =30° 33' 10" F+' =19° 58' 54" 
 
 D-"=27° 23' 18" F-" = 23° 16' 50" 
 
 <7=50° 
 
 D-' =13° 58' 12" F-' =11° 43' 53" 
 
 1)+' =20° 42' 51" F+' -=15° 53' 10" 
 
 D-"=25° 46' 20" F-"=21° 47' 36" 
 
 ff=45° 
 
 D-' =13° 2' 3?" F-' =10° 54' 55" 
 
 D+' =17° 14' 14" F+i =13° 37' 38" 
 
 D-"=24° 25' 30" F-"=20° 33' 39" 
 
 * Kew Modification of Light, etc. 
 
 •)■ A simple hypotbesis caa be easily devised lo satisfy all simple laws. 
 For instance, the laws of refractiou and reflection can be deduced from a 
 great number of Iiypotheses. It is, therefore, good fortune if a new law is 
 found which is apparently very complicated, because it has at least the 
 advantage of limiting more closely the field of the hypotheses concerning 
 light. 
 
 D 49 
 
MEMOIRS ON 
 
 D-' =13° 17' 34" F-' =10° 15' 29" 
 
 D+'=15° 8' 52" F+'z=12° 8' 12" 
 
 D-" = 23° 18' 54" F-"=19° 3:2' 57" 
 
 = 30° 
 
 D-' =11° 13' 33" F-' = 9° 18' 36" 
 
 D+' =13° 40' 30" F+" =10° 17' 34" 
 
 D-"=31° 43' 5" F-"=1S° 4' 35" 
 
 D+"=38° 50' 5" F+"=33° 30' 10" 
 
 (7=30° 
 
 D-' =10° 33' 2" F-' = 8° 44' 10" 
 
 D+' =11° 19' 33" F+' = 9° ]5' 33" 
 
 D-"=30° 46' 54" F-"=17° 13' 45" 
 
 D+"=34° 14' 30" , F+" = 19° 37' 
 
 In these experiments, ■wlicn measuring the first angle, the instrument 
 could not be used in such a way as to allow repetition. Those first angles 
 are, therefore, in the seconds, somewhat less exact than when the light has 
 normal incidence. Since, however, the differences between the two sides 
 of the axis amount to several degrees, a few seconds do not affect the 
 matter. 
 
 In all the experiments of this kind D~' and D+' are different, as 
 is seen ; similarly with F"' and F+' ; and the same was trite of the 
 other colored rays, for which I have not given the observations. 
 If the light is not incident normally, therefore, the spectra pro- 
 duced by the grating are no longer symmetrical on the two 
 sides of the axis ; and the difference in their positions is so 
 marked when the angle of incidence is great that it could be 
 detected even if it were only one-hundredth part as much. It 
 would be, however, extremely difficult for the most clear-sight- 
 ed physicist to deduce a law for these phenomena directly 
 from the experimental results. 
 
 Let T denote the angle made with the plane of the grating by 
 a colored beam after diffraction (with normally incident light, 
 therefore the complement of 3), and y a straight line drawn 
 perpendicular to the plane of the grating from the micrometer- 
 thi'cads of the observing-telescopo.* All of my observations can 
 
 * If a ia the distance from the grating to the micrometer-thread (and 
 therefore to the place where the image of the phenomenon is formed), 
 y=a sin T. [a is measured along the beam of light.} 
 
 50 
 
PEISMATIC AND DIFFRACTION SPECTRA 
 
 then be expressed, with the accnracy obtainable in experiments 
 of this kind, by the following formula : 
 
 (III )tan-r(^-)= ^^^'~(^-^^^'^-"")']-^^^' + ^'~^"^^"^^'^'-^^^] 
 ^ ^ ^ ^ 2«/(£.sin(T±cio) 
 
 I have deduced this equation, without any approximation, 
 from the principles of Interference which were proposed in 
 1803 by Dr. Thomas Young, and afterwards fully Justified by 
 the painstaking labors of Arago and Fresnel. In this formula 
 0) denotes the length of a ligM-wave. Although this quantity is 
 extremely small, we can deduce it with a high degree of accuracy 
 from the experiments which are described in my memoir, New 
 Modification of Liglit, etc. ; and the results of which for the dif- 
 ferent colored rays are given in general formulae on page 30. 
 From the experiments with glass gratings we learn this quantity 
 so exactly that, for the bright colors, hardly one-thousandth 
 portion of oi can be uncertain. From the experiments with the 
 finer gratings we obtain, by means of the angles for the first 
 spectrum with normal incidence of the light, if (Cw) denotes 
 the length of a light-wave for the ray C, (Dw) for the ray D, 
 etc., 
 
 (Cw) =0.00002422 
 (Dw) =0.00002175 
 (Ew) =0.00001945 
 (Fw) =0.00001794 
 (Go,) =0.00001587 
 (Hu) =0.00001464 
 
 in fractions of a Paris inch.* 
 
 [Reduced to ceniimetres, this gnes for D the wave - length 0.00005888 cm. 
 1 Paris 2nc7t=3, 70700 cm.] 
 
 * The fixed line B, near the red end, could not be seen well enough, owing 
 to the great width of the image, to allow its position to be determined ac- 
 curately. I shall try to make a greater number of fine gratings, in order to 
 determine more accurately, where it is possible, the value of u for the dif- 
 ferent colored rays ; yet this value is now known sufficiently closely to de- 
 cide whether the theory is confirmed by the experiments. If the values of 
 (Dw), (Ew), etc., are deduced from the experiments with the coarse glass 
 gratings, they are found to be somewhat greater in the eighth decimal 
 place than those given by the finer gratings ; this small difference simply 
 points to a less exact determination of e, which is more accurately known 
 
 51 
 
MEMOIRS OX 
 
 It will strike one from equation (III.) that the value of t de- 
 pends somewhat upon y — i.e., upon the distance at which the 
 image of this phenomenon is formed; that therefore, according 
 to the principles of interference, this light thus modified does 
 nob proceed exactly in a straight line, but in a curved one. The 
 equation of this curved line, developed without any approxi- 
 mation, is 
 
 (IV.) .r='[4f=-4(£.sin<r±ia,)']=4/(£.sin<7±ru)' 
 -|-[e'' — (t-sinffivo))'] (e. sine ±10)).'' 
 
 * 
 
 Since these phenomena can be observed only with a telescope, 
 which must have great power if the distances are to be meas- 
 ured with some accuracy, and therefore cannot be very short, 
 y is always large in comparison with u and e. With my instru- 
 ment, the distance of the micrometer-threads from the grating 
 is 21.43 inches. It would be only when y is not very large in 
 comparison with w that the value of r could vary with that of 
 y; but if in equation (III.) y is put one-half as great as it act- 
 ually was in my experiments, and then twice or three times as 
 great, the same value of r is always obtained, f As the equa- 
 tion shows, the value of e^ — (t.sin irii'w)" vanishes, then, in com- 
 
 witli the finer gratings. I do not need to recall tlie fact that the accuracy 
 of the determination of the value of e, however great it is by the help of the 
 means which I use, has its limits. I hope to increase it still more in the 
 future. 
 
 * Equations (III.) and (IV.) are developed for the case when the incident 
 rays may be regarded as parallel. It the distance of the source of light 
 were not great in comparison with e, instead of e . sin a in these equations 
 
 one would have to write . . , where 3 is defined by the equation 
 
 cos J/3 '^ J 1 
 
 sin S=— . In this last equation a denotes the distance of the source 
 
 a 
 
 of light from the grating. 
 
 t I measured these angles also with a telescope of 4-inch focal length ; 
 but, as was to be expected from the equation, no other changes were found 
 than those which must be ascribed to the diminished power ; they were 
 sometimes positive, sometimes negative. If a curvature of the modified 
 light were noticeable, it might be in the case when the distance of the 
 source of light is not so great ; but in that case the experiments are subject 
 to many difiiculties, and demand a different apparatus, whicli must be per- 
 fect to a high degree. 
 
 53 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 parison with iy' ; and so it can be neglected. We therefore 
 have, approximately, 
 
 , , , , v'[e'— (t.sinffi™)'] 
 tana; r(±') = — ^ '-^, 
 
 ° t.smirdzrw 
 
 ,,, , , , , f .sin (Tztrio 
 or (v.) cos rl±''= • 
 
 This equation represents the experiments on page 49, with im- 
 symmetrical spectra, as closely as does equation (III.). In both 
 equations the sign + gives the position of the colored ravs on 
 one side of the axis in the difEerent spectra ; the — sign, those 
 on the opposite side. In making comparisons, it must not be 
 forgotten that in the experiments the angular distances from 
 the axis are measured, but that r expresses the angles measured 
 from the plane of the grating. It is scarcely necessarv to re- 
 mark that in the special cases when, for instance, the above 
 equation is used for the ray C, instead of w. (Cw) is to be intro- 
 duced ; for the ray D, (Dw), etc. In these cases I designate 
 for the ray C the corresponding - by (Cr) ; that for D, by (D-), 
 etc. Equation (V.) becomes, accordingh', in these cases, 
 
 cos(Cr)(±"="^"^'^f"<^'"); 
 cos(D.)'^"= "^'"'^-"^H etc. 
 
 If the incidence of the rays upon the grating is normal, 
 sin (7=0, and equation (V.) becomes 
 
 cos -(±"'= . 
 
 £ 
 
 Since in this case cos r=sin^. this is the equation (II.) de- 
 duced directly from the experiments on page i7; therefore those 
 experiments also confirm the theory. 
 
 In any otJier medium than air I denote the index of refrac- 
 tion, e.g., of the ray C by (C;i), of the ray D by (D«), etc. It 
 follows at once from the experiments on light difEracted in dif- 
 ferent media* that in the above equation (Cw) is to be replaced 
 
 , (Co,) _, , (D<.) , 
 
 ^y(c^'^'-'^y(W)'^*"- 
 
 * Xew Modification of Light, etc., p. 36. 
 o3 
 
MEMOIRS ON 
 
 If the unruled surface of a glass grating is covered with 
 ilach resin varnish, which has nearly the same refracting power 
 as the glass, then, as is well known, no light will be reflected 
 from this side into the interior of the glass, and only the ruled 
 surface of the glass reflects light. If light from an apparently 
 very narrow opening in the window-shutter is incident upon the 
 grating, and if, in the manner described, the light reflected from 
 tlie ruled surface reaches the objective of the telescope, the phe- 
 nomena are exactly the same as if the light, at the same inclina- 
 tion, had been transmitted through the grating — viz., unsyni- 
 metrical spectra of the second class arc seen. The intensity of 
 these spectra is also great enough to allow the distances of the 
 different fixed lines to be determined with considerable accu- 
 racy. I have made a great many experiments on these spectra 
 arising from reflection at different angles of incidence, the de- 
 tails of which I pass over. Equation (V.) represents all the 
 results as satisfactorily as was to be expected. By the develop- 
 ment, from the principles of interference, of the formula for the 
 phenomena due to reflection, the same expression is obtained as 
 for transmitted light — viz., without approximations, equation 
 (III.). In this way, also, the theory is confirmed by experiment. 
 
 It is most remarkable that for a certain angle of incidence a 
 part of one spectrum arising from reflection consists of com- 
 pletely polarized light. This angle of incidence is very different 
 for the different spectra, and, still more notably, even for the 
 different colors of one and the same spectrum. With the glass 
 grating £=0.0001223, (Er)+' is polarized — i. e., the green part of 
 the first spectrum, if (r=49° ; (E-)*+"', or the green part of the 
 second spectrum on the same side, if (7=40° ; finally, {Eirf"^, or 
 the green part of the first spectrum on the opposite side of the 
 axis, if (7=69°. If (Ery+'' is completely polarized, the other 
 colors of this spectrum are not completely so. With (Er)<+"' 
 this is less the case ; and a can be sensibly changed while this 
 color remains polarized. For no angle of incidence is (Er)~' as 
 completely polarized as is (Er)'+". With a grating in which t 
 is greater than in this one, the angles of incidence must be en- 
 tirely different if the above-mentioned spectra are to be polar- 
 ized.* 
 
 * It would be premature to wish to deduce the law for this phenomenon 
 from a small number of observations. This can be done with certainty , 
 
 54 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 It is seen from equation (V.) that, if £<(E.sin a-±vw), 
 cos r'^t^J^i^ which is impossible. With normal incidence £ must 
 be greater than >>(o, if t'") is to be visible — i.e., possible. If e is 
 less than w, no colored beam is any longer visible, however the 
 light is incident; and there remains only the white light in the 
 axis — viz., cos r*'''=sin a-. This holds true for both transmitted 
 and reflected beams, because the equations are the same for both. 
 If E=o), r™ would be 90°. If, therefore, a grating were made in 
 which the distance apart of the centres of two of the parallel 
 lines is smaller than w, no spectrum at all would be seen, only 
 the white beam at the axis. 
 
 "We cannot believe that the polishing, which is done ar- 
 tificially upon glass, etc., is mathematically perfect. If the 
 polish consists of unevennesses, which, in reference to their 
 distances apart, are smaller than w, they are of no detriment 
 to either transmitted or reflected light,- and no colors of any 
 kind could be produced by them. Further, there would be no 
 means of making these inequalities visible.* If the small ine- 
 qualities had an action on the light — e.g., by reflection accord- 
 ing to the known laws — the rays would be scattered most irreg- 
 ularly, because the radii of curvature of these small uneven- 
 nesses must be very small, and any regular reflection would be 
 impossible. If a reflecting surface consists of unevennesses 
 whose distances apart are smaller than w, no spectrum is pos- 
 sible, as has been said ; and light can be reflected only along 
 the axis. For this ray v=0; in which case equation (V.) gives 
 the ordinary laiu of reflection — viz., cos r^'^r^sin o-. This law 
 follows, therefore, from interference, without the need of as- 
 only from a large number of gratings with which f is widely different. 
 Since in these experiments it is not necessary for the fixed lines of the spectra 
 to be plainly seen, gratings can be made inwliich £ is sensibly smaller tlinn 
 In the finest ones which I have used up to this time. It is not improbable 
 that the principles of interference will lead perhaps to a theory of the po- 
 larization of light. This is neither the place nor the time (at present) for 
 me to communicate my opinions on this matter. Fortunately, other exper- 
 iments of another kind are possible, which seem to have bearing upon 
 this question ; yet they are of a most delicate nature, as are the greater 
 part of all the experiments on this subject. 
 
 * We can conclude from this what it is possible for one to see through a 
 microscope. A microscopic object — e. g., one whose diameter is equal to u, 
 and which consists of two portions — cannot be recognized as consisting of 
 two parts. This shows us the limits of the power of a microscope. 
 
 55 
 
MEMOIRS ON 
 
 Sliming a repelling force perpondicnlar to the reflecting plane.* 
 The fact that at greater angles of incidenee more light is 
 reflected than at smaller ones follows jnst as sinijily and is in 
 aecord witli experiment. It is remarkable that aeeording to 
 the extxct formula (III.), at distances from the reflecting sur- 
 face which are not great in comparison with lo—i.c, at very 
 short distances — the angle of reflection can bo markedly dif- 
 ferent from the angle of incidence. One can easily see by an 
 accurate consideration of this equation that at distances which 
 permit one to make exact observations this dilTeronce is too 
 small to bo thought of ; therefore, tho ordinary experiments 
 for the determination of the law of reflection can prove noth- 
 ing against its deduction from the theory of interference. 
 
 It is seen, as a result of all the experiments with tho differ- 
 ent gratings, that the distances of the spectra from the axis 
 increase as the grating-space — that is, c — becomes smaller ; and 
 that, if the spectra are to bo homogeneous, this r must remain 
 constant throughout the whole grating. If these spaces are 
 unequal, the larger e's will produce small spectra, tho smaller t "s 
 large ones, which mingle with each according to the degree of 
 the irregularity. If the irregularity is very great, not even het- 
 erogeneous colors will be seen ; and the light must be white 
 in tho whole region, as experiment shows is tho case. It is, 
 nevertheless, interesting to know what phenomena would arise 
 if the grating-spaces were luicqunl in a regular 'manner — i.e., if 
 the inequality of the distances, whatever it is, is repeated at 
 regular intervals. To this end I covered several pieces of 
 plane glass with gold-foil, and upon them I ruled parallel linos 
 whose distances apart were unequal, but unequal in various 
 regular ways. I can give here in brief only a few of tho 
 results of these experiments, which must, besides, be continued 
 further. The spectra which are seen with a telescope through 
 this kind of a grating consist of homogeneous light ; and their 
 flxed lines are recognized most plainly, so that their distances 
 from the axis can be accurately measured. If the grating- 
 sjDaces of a grating with periodic inequalities are denoted by 
 e', e", etc., and if one of tho identical portions, each of which 
 
 * [A long note follows in wJiicJt Fraunlwfer upholds tlm wave-theory iigainat 
 Us rivdls. Be says it afcoiints for reguhir refraction, the colors of thin plates 
 and of mother -of -pearl, reflection from a rough surface, etc.] 
 
 56 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 contains unequal t's, is expressed by s'+e"+e"'+ . . . +£", 
 tlien the results of the experiments are, that with normal inci- 
 dence the distances of the different spectra from the axis are 
 expressed by the following equation : 
 
 sin S<''=^ 
 
 £ +E +£ + . . . +£ 
 
 In whatever manner the e's follow each other in the portion 
 which contains the unequal parts and which is represented by 
 the division of the equation, even if some of them are equals 
 the equation remains always the same, provided only that these 
 portions cannot be themselves subdivided into smaller identical 
 portions in which the e's succeed each other in the same man- 
 ner and same sense. This phenomenon, arising from gratings 
 with periodic errors, is remarkable on account of the relative 
 intensities of the different spectra, concerning which, however, 
 no general statement can be made in a few words and without 
 a figure. With some gratings of this kind, several spectra, or 
 parts of them, may be entirely wanting, or may have such a 
 feeble intensity that they can be observed with difficulty, while 
 the following ones again are very intense. This has the great 
 advantage, that in this case the fixed lines of those spectra can 
 be observed which cannot be seen with gratings whose grating- 
 spaces, £, are equal, because they are covered by the neighbor- 
 ing spectra. For instance, with no grating having equal e's 
 can C" and F^" be seen ; but with a grating which has periodic 
 errors, such that each portion consists of three e's differing 
 from each other in the ratio 35 : 33 : 42, C", D^", E^", F'"' may 
 be seen so plainly that their distances from the axis can be 
 safely measured. For with such a grating the tenth and 
 eleventh spectra are almost entirely absent. With this grating 
 I saw even E^'''^, and saw it so plainly that its distance from 
 the axis could be measured. The relation between the inten- 
 sities of the different spectra depends upon the relation between 
 the e's which follow each other in any one portion, and this is 
 in many cases very complicated.* Similar gratings with peri- 
 
 *One Cfin conclude from the experiments mentioned, as well as from 
 others, that many of these phenomena are so complicated — at least, in all 
 likelihood — that they cannot well be described in a few words ; and I am 
 for tills reason forced to leave untouched much that might be of interest. 
 The further one goes in these experiments, so much the wider becomes the 
 
 57 
 
MEMOIRS OX 
 
 odic ineqnalities are obtained if two different gratings — i.e., two 
 in each of which t is constant, but larger in one than in the 
 other — are placed with their ruled faces together so that their 
 lines are exactly parallel. 
 
 \A paffe concerning gratings with concentric circular rulings 
 is here omitted.] 
 
 Addexduii Coxcerxixg the Spectea of Flajtes, Moon 
 AXD Star Light, axd the Electric Light. 
 
 As is well known, the prismatic color-spectrum of the light 
 coming from aflame {lamplight) does not show the dark fixed 
 lines which are present in the spectruni of sunlight; instead of 
 them there is in the orange a bright line which is prominent 
 above tlie rest of the spectrum, is double, and is at the same 
 place where in sunlight the double line D is found. The 
 sj)ectrum obtained from the light of a flame which is blown 
 with a llast-tube contains several prominent bright lines. Of 
 still greater interest for optical experiments is the fact that, by 
 skilful blowing of the flame, the light of the front half of the 
 flame can be dispersed no further by the prism, and, conse- 
 quently, is simple homogeneous light. This light has, so far 
 as I have investigated it, the same ref rangibili ty as the D ray 
 of sunlight. Simple homogeneous light which proceeds in all 
 directions is, for known reasons, very difiieult to produce, and 
 can never be obtained with prisms directly ; therefore this 
 flame is of great use in many experiments. 
 
 By means of the large electrical machine of the physical 
 cabinet of the Ro^-al Academy, I obtained a spectrum of the 
 electric light, in which I recognized a greater number of bright 
 lines than I had seen before with weaker light. I deter- 
 mined the relative positions and intensities of the brightest of 
 these. 
 
 The light of the moon gave me a spectrum which showed in 
 
 field which offers itself for now investigations. It is greatly to be regretted 
 that they can be repeated so seldom by any one, owing to the fact that Ihey 
 demand very large, and, in part, expensive apparatus, and also a great deal 
 of time. Tlie fact that the sky must be most favorable makes one lose 
 more time than would be believed, perhaps ; which I feel all the more be- 
 cause the demands of business leave me only a few definite days in the 
 month which are free for these investigations. 
 
 58 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 the brightest colors the same fixed lines as did sunlight, and in 
 exactly the same places. 
 
 To observe the i:pectra of the ligM of the fixed stars, and at the 
 same time to determine tlie refrangihiUty of this light, I prepared 
 a short time ago a suitable apparatus specially adapted to this 
 end, the telescope belonging to it having an objective of 4 inches' 
 aperture. With it I have obtained many interesting results, 
 although the experiments are still far from being completed. 
 The flint-glass prism of this instrument has an angle of 37° iO', 
 and has the same diameter as the objective. The angle which 
 the incident ray makes with the ray emerging from the prism 
 is about 36°, so that, if the refrangibilitv of the light of one 
 star were to differ only slightly from that of anotlier, the dif- 
 ference could be very easily detected. In order to measure 
 with certainty this difference, in ease such is found, I added a 
 second smaller telescope, which is fastened to the larger one, 
 and cuts it at an angle of about 26° — i.e., at the angle which 
 the ray emerging from the prism makes with the incident ray. 
 Two observers are needed : one observes the arrival of the star 
 at the cross-hairs of the smaller telescope, which views the star 
 directly, not through the prism ; the other observes, through 
 the larger telescope, the arrival of a portion of the spectrum of 
 the same star. This larger instrtimeut has for this purpose a 
 micrometer-screw, whose movable edge is so placed by the ob- 
 server, by means of the screw, that at the instant when the 
 star passes the cross-hair of the smaller telescope, viewed di- 
 rectly without the prism, one of the fixed lines of the spectrum 
 coincides with the edge in the larger telescope. The microm- 
 eter is left unchanged, and the instrument is then pointed at 
 another star, concerning which one wishes to know if its light 
 has the same refrangibility. If. at the instant when this star 
 passes the cross-hair of the smaller telescope, the same color of 
 the spectrum or the same fixed line arrives at the edge of the 
 micrometer in the larger instrument, the refrangibility of the 
 two kinds of light are the same. Since two observers are nec- 
 essary for these experiments, Herr Soldner had the kindness to 
 make them with me. These experiments are, however, to be 
 regarded as only just begun; and I must make some important 
 modifications in the instrument in order to obtain still greater 
 accuracy and to save time in the observations. 
 
 Up to the present we have found no fixed star whose light, 
 
 59 
 
MEMOIRS ON 
 
 so far as its refrangiiility is concerned, is sensibly difEerent 
 from that of the planets. When the fixed lines of the spectra 
 are seen plainly, one can be certain with this instrument to 10 
 seconds ; and when the fixed lines cannot be seen, one can still 
 be certaia for the orange light to ^ minute. Since the total 
 refraction through the prism is 26°, a difference amounting to 
 ■g-jig-j- of the whole refraction could still be noticed with this in- 
 strument, a difference which even with the horizontal refrac- 
 tion in the atmosphere did not amount to:^ second. Up to this 
 time, as is well known, some astronomers have doubted whether 
 the refraction tables for different stars should not be some- 
 what different ; therefore this doubt seems to be removed by 
 the experiment noted. The continuation of this investigation 
 will lead us, I hope, to more complete knowledge. 
 
 In order to see the. fixed lines of the different stars (with this 
 large instrument) the air must be most favorable — a condition 
 which happens rarely to a sufficient extent. The spectra of 
 the light from Mars and Venus contain the same fixed lines as 
 does sunlight, and in exactly the same places, at least so far as 
 the lines D, E, Zi,*and F are concerned, whose relative posi- 
 tions can be exactly determined. In the spectrum of the light 
 from Sirius I could not distinguish fixed lines in the orange 
 and yellow ; in the green, however, there is seen a very strong 
 streak ; and in the blue there are two other unusually strong 
 streaks, which seem to be unlike any of the lines of planetary 
 light. We. have determined their positions with the microm- 
 eter. Castor gives a spectrum which is like that of Sirius ; the 
 streak in the green, in spite of the weak light, was intense 
 enough for me to be able to measure it ; and I found it in ex- 
 actly the same place as it was with Sirius. I could also dis- 
 tinguish the streaks in the blue ; but the light was too feeble 
 to allow of measurement. In the spectrum of P.ollux I recog- 
 nized many fixed lines which resembled those of Venus ; but all 
 were weak. I saw the D line quite plainly, in exactly the same 
 position as with planetary light. Capella gives a spectrum in 
 which, at the places D and S, the same fixed lines are seen as 
 in sunlight. The spectrum of Betelgeiix [a Orionis] contains 
 countless fixed lines which, with a good atmosphere, are sharply 
 
 * The line b lies in tlie green, between E and F ; it consists of three 
 strong lines, two of which are nearer than the third. See previous papers. 
 
 60 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 defined ; and, although at first sight it seems to have no resem- 
 blance to the spectrum of Venus, yet similar lines are found 
 in the spectrum of this fixed star in exactly the places where 
 with sunlight D and h come. Some lines can be distinguished 
 in the spectrum of Procyon; but they are seen with difficulty, 
 and so indistinctly that their positions cannot be determined 
 with certainty. I think I saw a line at the position D in the 
 orange. 
 
 Munich, July 14, 1833. 
 
 Joseph Feaunhofer was born in Straubing, near Munich, 
 March 6, 1787, and died in Munich, June 7, 1826. His father 
 was a master glass-workman, and at the age of twelve he was 
 apprenticed to a glass-polisher in Munich. In 1806 he became 
 the optician in an optical-mechanical institute in Benediktbeu- 
 ern. While there he invented new methods, machines, and 
 measuring instruments to perfect the construction of achro- 
 matic lenses. In the course of this work he was led to the dis- 
 covery of the lines in the solar spectrum which bear his name. 
 With the aid of a prismatic-objective telescope he studied the 
 spectra of the moon, the planets, and some of the stars. These 
 results were presented to the Eoyal Academy of Sciences of 
 Bavaria in 1814 and 1815, and were published in 1817, imme- 
 diately after which he was elected a Member of the Academy. 
 He returned to Munich to live in 1819, where he was engaged 
 in the manufacture of optical instruments. In 1831 he pub- 
 lished his experiments on diffraction through one or more 
 openings, and on the spectra obtained by gratings. In 1823 
 this paper was continued by further experiments with glass 
 gratings and by measurements of the wave-length of various 
 solar lines. In 1825 appeared his memoir on halos, mock-suns, 
 and allied phenomena. In the later years of his life he was ap- 
 pointed Eoyal Professor, and received numerous honors both 
 from Bavaria and from foreign lands. He was buried in a 
 plot of land given by the city of Munich for the purpose. His 
 tomb bears the simple inscription, " Approximavit sidera." 
 
A Method of Examining Eefbactite and Dispersive 
 Powers by Prismatic Eeflection. 
 
 By "WILLIAM HYDE WOLLASTON, M.D., F.R.S. 
 Read June 34, 1802. PhiloaopMcal Transactions, 1803. 
 
 [J. method is described wliich is based upon the principle of 
 total reflectioji; and the results of experimetits upon various solids 
 and liquids are give?i. Then folloivs a brief discussion of the 
 number of distinct colours in the solar spectrum. The author's 
 ideas are based upon thefolloiving experiment.'\ 
 
 If a beam of daylight be admitted into a dark room by a 
 crevice -^ of an inch broad, and received by the eye at a dis- 
 tance of 10 or 12 feet, through a prism of flint-glass, free from 
 veins, held near the eye, the beam is seen to be separated into 
 the four following colours only — red, yellowish green, blue, and 
 violet, in the proportions represented in Pig. 3. [^Omitted.'^ 
 
 The line A that bounds the red side of the spectrum is 
 somewhat confused, which seems in part owing to want of 
 power in the eye to converge red light. The line B, between 
 red and green, in a certain position of the prism, is perfectly 
 distinct ; so also are Dand E, the two limits of violet. Bat 0, 
 the limit of green and blue, is not so clearly marked as the 
 rest, and there are also on each side of this limit other distinct 
 dark lines — f and g — either of which, in an imperfect experi- 
 ment, might be mistaken for the boundary of these colours. 
 
 The position of the prism in which the colours are most clear- 
 ly divided is when the incident light makes about equal angles 
 with two of its sides. I then found that the spaces AB, BO, 
 CD, DE, occupied by them, were nearly as the numbers 16, 
 23, 36, 25. 
 
 Since the properties of these colours to each other have been 
 supposed by Dr. Blair to vary according to the medium by 
 
 63 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 which they are produced, I have compared with this appear- 
 ance the coloured images caused by prismatic vessels containing 
 substances supposed by him to diiier most in this respect, such 
 as strong but colourless nitric acid, rectified oil of turpentine, 
 very pale oil of sassafras, and Canada balsam, also nearly colour- 
 less. With each of these I have found the same arrangement 
 of these four colours, and, in similar positions of the prisms, as 
 nearly as I could judge, the same proportions of them. 
 
 But when the inclination of any prism is altered so as to in- 
 crease the dispersion of the colours, the proportions of them to 
 each other are then also changed, so that the spaces AC and 
 CE, instead of being as before, .39 and 61, may be found altered 
 as far as 42 and 58.* 
 
 By candlelight a different set of appearances may be distin- 
 guished. When a very narrow line of the blue light at the 
 lower part of the flame is examined alone, in the same manner, 
 through a prism, the spectrum, instead of appearing a series of 
 lights of different hues contiguous, may be seen divided into 
 five images at a distance from each other. The first is broad 
 red, terminated by a bright line of yellow ; the second and 
 third are both green ; the fourth and fifth are blue, the last of 
 which appears to correspond with the division of blue and vio- 
 let in the solar spectrum or the line D of Fig. 3. 
 
 When the object viewed is a blue line of electric light I have 
 found the spectrum to be also separated into several images, 
 but the phenomena are somewhat different from the preceding. 
 It is, however, needless to describe minutely appearances which 
 vary according to the brilliancy of the light, and which I can- 
 not undertake to explain. 
 
 WoLLASTON was born in Norfolkshire, August 6, 1766, and 
 died in London, December 22, 1828. He discovered the two 
 elements palladium and rhodium, and invented a process for 
 rendering platinum malleable. He is best known, perhaps, for 
 his invention of the various instruments named after him — the 
 reflecting goniometer, the cryophorus, a microscopic doublet. 
 
 * lA note on the existence of the infra-red and the ultra-violet spectra.'\ 
 
BIBLIOGRAPHY 
 
 Spectroscopic Appahatus. 
 
 Miclielson. Interference Methods. 
 
 Philosophical Magazine, (5), XXXI., 338-346, 1891; XXXIV., 
 280-299, 1892. 
 
 Astronomy and Astro-Physics, XL, 884-903, 1892. 
 Hale. Spectrolieliograpli. 
 
 Astronomy and Astro-Physics, XI., 407-417, 1892 ; XII., 241- 
 2r.7, 1893. 
 Pickering. Objective Piism. 
 
 Astronomy and Astro-Physics, XL, 199-303, 1892. 
 Hale and Wadswortli. Objective Pri-^m. 
 
 Aslrophysical Journal, IV., 54-79, 1896. 
 Wadswortli. Spectroscopes of Various Forms. 
 
 AstrophysicalJournal, I., 11. , III., IV., 1895, 1896. 
 
 SOLAB SpECTHUM. 
 
 Poggendorll's Annalen, OX., CXI., CXIIL, 1860, 
 
 Kirclihoff und Hansen. 
 1861. 
 
 Philosophical Marjaaine, (4), XX., 89, 1860. 
 Angstrom. Reclierclies sur le Spectre Solaire, Up.siila, 1868. 
 Rowland. Aslrophysical Journal, I.-VL, 1895-1897. 
 Higgs. AstrophysicalJournal, VII., 86, 1898. 
 
 Stellak Spectka. 
 
 See Sclieincr, " Spectralanalyse der Gestirnc," Braunscliweig, 1888. 
 English Translation by Frost, Boston, 1894. 
 
 Spectra of the Elements. 
 
 See Scheiner, " Spectralanalyse.'' 
 
 See Kiiyser, '' Spectralanalyse," Winkelmann's Handbuch der Physilc, II. 
 
 See Watts, "Index of Spectra," Manchester. 
 
 Inpra-Red Spectra. 
 
 H. Becquerel. Annates Chimigue et Physique, (5), XXX., 1-144, 1883. 
 Langley. Philosophical Magazine, (5), XVIL, XXL, XXIL, XXVI., 
 
 1884^1888. 
 American Journal of Science, XXVIL, XXXL, XXXII, , 
 XXXVI. , 1884-1888. 
 64 
 
PRISMATIC AND DIFFRACTION SPECTRA 
 
 Abne}'. Philosopldcal Transactions, p. 457, 1886. 
 Lewis. Astrophysical Journal, II., 1-25, 106-109, 1895. 
 Rubens and Nichols. Wiedemann's Anmlen, LX., (3), 418-46.3, 1897. 
 Physical Review, IV., 314-323, 1897. 
 
 TJltba- Violet Spectka. 
 
 Schumann. Anzeige der Wiener Akademie, XL, 1895. 
 AstrophysicalJournal, III., 220, 387, 1896. 
 
 Standard "Wave-Lengths. 
 
 Rowland. Pliilosopliical Magazine, (5), XXXVI., 49-73, 1893. 
 Astronomy and A.^tro-Physics, XII., 821-346, 1893. 
 Michelson. Memoires du Bureau International des Poids et 2fesures, XL, 
 
 1894. 
 Bell. PMlosopMcal Magazine, (5), XXV., 345, 850, 1888. 
 
 Origin op Fraunhopek Lises. 
 
 KirchhofF. Abliandlungen der Berliner Akademie, 1861. 
 
 PoggendorfE's Annalen, CIX., 2T5, 1860. 
 
 Philosophical Magazine, (4), XX. , 1860. 
 Rowland. Johns Hopkins f niversil}' Circulars, 10, 1891. 
 Janssen. Comptes Rendus, 56, 1860 ; 60, 1864 ; 63, 1866 ; 78, 1874 ; 101, 
 1885 ; 103, 1886 ; 106, 1888 ; 107, 1888 ; 108, 1889. 
 
 DiPPRACTiON Gratings akd their Adjustment. 
 
 Rowland. Gratings in Theory and Practice. 
 
 Astronomy and Astro-Physics, XII., 129-149, 1893. 
 
 Philosophical Magazine, (5), XXXV., 397, 1893. 
 
 Concave Gratings for Optical Purposes. 
 
 American Journal of Science, (3), XXVI., 1883. 
 
 Philosophical Magazine, (5), XVL, 197, 1883. 
 Rayleigh. " Wave-Theory of Light." Encyclopedia Britannica. 
 
 Manufacture and Theor3f of Diffraction Gratings. 
 
 Philosophical Magazine, (4), XL VII., 1874. 
 Kayser. " Spectralanalyse." Winkelmann, Eandbuch der PhysiJc, Band 
 
 II., Abth. I., 403-413. 1894. 
 Wadsworth. The Modern Spectroscope. 
 
 AstropJiysical Journal, I., II., III., 1895, 1896. 
 Ames. Concave Grating in Theory and Practice. 
 
 Philosophical Magazine, (5), XXVII. , 1889. 
 
 Astronomy and Astro-Physics, XL, 28-42, 1892. 
 
INDEX 
 
 a Ovionis, Spectrum of, 60. 
 
 Capella, Spectrum of, 60. 
 Castor, Spectrum of, 60. 
 Cylindrical Lens, Use of, 8, 20, 35. 
 
 D 
 
 D Line in Flame Spectrum, 3 ; in 
 Solar Spectrum, 6 ; in Venus, 
 etc., 9, 59. 
 
 Diffraction, Laws of. Deduced from 
 Wave-Theory, 51 ; in Water, etc., 
 36, 53 ; by Reflection, 36, 54. 
 
 Diffraction through a Narrow Open- 
 ing, 13, 14; through a Round Open- 
 ing, 21 ; through a Square Open- 
 ing, 21 ; tlirough Gratings, 21 ; 
 through Two, Three, etc., Narrow 
 Openings, 31 ; around an Edge, 
 38 ; around a Hair, 14, 34, 37. 
 
 Feather, Diffraction by, 86. 
 Fixed Stars, Spectra of, 9, 60. 
 Flames, Spectrum of, 3, 10, 58, 63. 
 
 G 
 
 Grating, Reflectinff, 54 ; Conditions 
 for a Perfect, 35 ; Difficulties in 
 Ruling, 44 ; Normal Incidence, 47 ; 
 Oblique Incidence, 48. 
 
 Grating Space, Measurement of, 29, 
 46 ; Inequality of, 27, 35, 45. 
 
 Grating Spectra, Properties of, 22, 
 29. 
 
 Gratings, Glass, 44 ; Wire, 21 ; Rul- 
 ings on Gold-Foil, etc., 24, 43. 
 Groove, Elleot of Shape of, 48. 
 
 H 
 
 Homogeneous Spectra, Test for, 18, 
 35. 
 
 Interference, Principles of, 51. 
 Irrationality of Prismatic Spectra, 
 8. 
 
 Lines, Spectrum, B, C, D, etc., 5, 
 43 ; Discovery of, 3, 4. 
 
 M 
 
 Mars, Spectrum of, 60. 
 Micrometer, Description of, 16. 
 Microscopic Vision, Limits of, 55. 
 Moon, Spectrum of, 58. 
 Mother-of- Pearl, Colors of, 56. 
 
 N 
 Newton's Rings, 56. 
 
 Oblique Incidence on Gratings, 48. 
 Overlapping Spectra, 19, 22, 29, 35. 
 
 Periodic Errors of Gratings, 56. 
 Planets, Spectra of, 8, 60. 
 Polarization from Gratings, 54. 
 Pollux, Spectrum of, 60. 
 Prismatic Eye-Piece, 18; Objective, 4. 
 
INDEX 
 
 Prismatic Spectrum, 5. 
 
 Prisms, Imperfect, 7. 
 
 Procyon, Spectrum of, 61. 
 
 Pure Spectrum, Conditions for, 7, 41. 
 
 R 
 
 Reflection, Law of, f>5. 
 Reflection-Grating, 54. 
 Refraction, Law of, 56. 
 Ruling Gratings, Difficulties of, 44. 
 Ruling-Machine, Description of, 44. 
 
 S 
 
 Shape of Groove ; Effect on Grating 
 Spectra, 48. 
 
 Sirius, Spectrum of, 9, 60. 
 
 Spectra of the First Class, 17, 34 ; 
 of the Second Class, Perfect, 33, 
 29,42,45,47; of the Second Class, 
 Imperfect, 31 ; of the Third Class, 
 32, 33. 
 
 Spectroscope, 4. 
 
 Spectrum, Solar, Discovery of, 4, 63; 
 of Flames, 3, 10, 58, 63 ; of Venus 
 and Planets, 8, 60; of Fixed Stars, 
 9, 60; of Electric Discharge, 9, 58. 
 
 Stellar Spectra, Apparatus for, 8, 59. 
 
 Telescope Used, Description of, 4, 15. 
 
 V 
 Venus, Spectrum of, 8. 
 
 W 
 
 Wave-Lengths of Light, 51. 
 Wave-Theory, 37, 51, 56. 
 
 Young, T., 37, 51. 
 
 THE END 
 
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STANDARDS IN NATURAL SCIENCE 
 
 COMPARATIVE ZOOLOGY 
 
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