A TREATISE ON THE ANALYSIS OF SPECTRA CAMBRIDGE UNIVERSITY PRESS C. F. CLAY, MANAGER LONDON : FETTER LANE, E.C. 4 LONDON: H. K. LEWIS AND CO., LTD., 136, Gower Street, W.C. 1 LONDON : WHELDON AND WESLEY, LTD., 28, Essex Street, Strand, W.C. 2 NEW YORK : THE MACMILLAN CO. BOMBAY ^ CALCUTTA V MACMILLAN AND CO., LTD. MADRAS ) TORONTO : THE MACMILLAN CO. OF CANADA, LTD. TOKYO : MARUZEN-K A.BUSHIKI-KAISHA ALL RIGHTS RESERVKD A TREATISE ON THE ANALYSIS OF SPECTRA BASED ON AN ESSAY TO WHICH THE ADAMS PRIZE WAS AWARDED IN 1921 BY W. M. HICKS, Sc.D., F.R.8. EMERITUS PROFESSOR OF PHYSICS IN THE UNIVERSITY OF SHEFFIELD FORMERLY FELLOW OF ST JOHN'S COLLEGE, CAMBRIDGE CAMBRIDGE AT THE UNIVERSITY PRESS 1922 .***'** * * ***..'** * . PREFACE THE greater part of the present treatise was submitted as an essay for the Adams Prize for the years 1919-21. The award has rendered it possible to meet the present excessive costs of publication. The author desires to thank the Royal Academy of Science of Stockholm for their permission to reprint Rydberg's tables, and Messrs Meggers and Peters for similar permission to reprint their new I.A. tables of reduction of wave lengths to vacuum. He takes this occasion specially to acknowledge the great debt he owes to his friend Professor Milner for his acute criticism, his valuable suggestions and the great care he has taken in reading the proof sheets. W. M. H. February, 1922. ABBREVIATIONS USED IN THE TEXT The series of papers by the author a critical study of spectral series in the Trans- actions of the Royal Society are indicated by numbers in square brackets. Thus [i] Trans. Roy. Soc. 210 A, 55 (read Dec. 9, 1909). The alkalies, H, He. [n] 212 A, 33 (read Mar. 7, 1912). The p and s sequences. [m] 213 A, 323 (read June 26, 1913). The atomic weight term. [iv] 217 A, 361 (read June 1, 1916). Structure of spark spectra. [v] 220 A, 335 (read June 23, 1919). The monatomic gases. O - C denotes observed less calculated values. M.P. Melting point. W.N. Wave number. Z.P. Zeeman pattern, see p. 92. K.R. Kayser and Runge. E.V. Eder and Valenta. E.H. Exner and Haschek. p, q are used to denote proportion of possible error, so that p z <\. There is never any confusion with its use for the p sequence. / is often used to denote a fraction, also without confusion with its use as denoting the / sequence. v is used to denote the separations of the S, P series. . . 124 Oun data from S, P series . . . . . . 127 Satellite separations 134 Displacement 137 Isotopes 142 Atomic numbers . . 146 CHAPTER VII. LINKAGES Links and linkages . . 149 Occurrency curves ' . .151 Regularities . 154 Sounding . 162 CHAPTER VIII. THE p AND s SEQUENCES General distinctions between p, s, d, f sequents . . 165 General relations of p l , p 2 , p 3 . . . . ,.167 Dependence on atomic volume . . . . .170 The s sequence 177 CHAPTER IX. THE d AND / SEQUENCES General features of d, f sequences . . . .180 Laws of constitution of mantissae . . . . . 182 Application to determine value of N . . ... 189 CHAPTER X. THE MONATOMIC GASES Two types . . . . . . . I . 198 The blue spectra of A, Kr, X, Ra.Em. . . . .199 The red spectra of A, Ne . ' . . ... % 205 CHAPTER XI. MISCELLANEOUS Series in Sn, Sb ' .,' . 214 A congery in II (a) . . 217 B . . . . . ; J' . 220 L ....;... 221 8 (1), D (1) in Group III . . < j . . 226 APPENDIX Table I. Reductions to vacuo . . . . . 234 Table II. Rydberg's table of N/(m + /x) 2 . . . 236 Table III. Data of series lines 240 Table IV. Formulae constants . . . . .315 Table V. D mantissae . . - . . . .320 INDEX 323 INTRODUCTION WHEN the atom or molecule of an element is excited to light emission, the light in general is found to consist of a number of superposed waves of definite frequencies peculiar to the element and to the mode of excitation. The method of analysing the light by observation produces a number of narrow lines each produced by light of the same frequency and it is usual to refer to these as "lines" and to the whole congery of lines or frequencies as the spectrum of the element. This spectrum must depend in some way on the constitution of the atom and be determinable by it. Conversely if we knew the process by which radiation is produced, and transmitted to the aether, it would be possible to get some definite information as to the constitution of atoms. These spectra are indeed documents containing implicitly the description of this constitution or special possible configurations within it; but they are written in an as yet unknown language and unknown script. Their decipherment has made as yet little progress although the mass of data at disposal is immense. The first requisite is a comparative study of relations existing between lines of the same element and between the spectra of different elements. We know that in certain groups of the periodic table, the spectra contain sets of lines whose frequencies can clearly be arranged in a series form, and that certain relations hold between some of these series. But of the laws which govern these series, their dependence on the element, and the relationship of series lines to other lines in the spectrum, we know next to nothing. In the majority of the elements indeed not even series have yet been detected. It is much to be desired that a larger number of in- vestigators should be drawn to this study an indispensable preliminary to any further progress although not so exhilarating as the making of theories or as interesting as experimental work. The object of the present treatise is to present, as a more or less connected whole, the knowledge already obtained, and thus to provide an introduction to the subject for those desirous of entering on its study, as well as a book of reference for data for those working in it. For this purpose the data are studied in a purely objective manner, without any preconceived opinions based on theories as to the cause or manner of production. The frame of mind in which they will be considered is to be one in which suggestions from explanatory theories not yet established will be looked into, but deductions presented as facts will be met with closed ears. For instance the question of the con- stancy or otherwise of Rydberg's constant will be considered simply and solely on observational grounds. The devotees of a theory unconsciously incline to ignore pikestaffs when they point the " wrong " way and grasp at straws pointing the "right" way. This does not mean that all suppositions are to be avoided but they will be such as arise immediately from the comparative study of the H. A. S. 2 INTRODUCTION data, and they will be tested on this basis. In decipherment indeed this is the only proceeding possible. A comparison of a few data suggests relations and these relations have then to be tested on all the data at disposal. In the early days of such decipherment this means a patient consideration and a laborious dis- entanglement of a mass of details. This is not easy for a reader to follow or to grasp by a summary reading. Moreover the nature of the evidence must be cumulative and this requires the assembly of a large number of examples affording apparent support to a given supposition. A considerable number of these must naturally be due to chance coincidence, and the discovery later that a certain number are so is apt to destroy reliance on the agreement of the others. It is, however, the number and nature of the agreements which must influence belief in the existence of a certain effect. The scope of the treatise thus excludes the consideration of spectroscopic technique, of theories of spectroscopic effects, and indeed of the effects produced by physical conditions except in just so far as they are capable of throwing light on the immediate question of line relationships. Thus in Chapter V their de- scription and discussion are strictly limited by this consideration. Even the discussion of the Zeeman effect which receives the most elaboration is thus restricted. The author had hoped to be able to include the properties of band spectra, but he has reluctantly been compelled to omit its consideration. Also, the new region opened up by X-ray spectra is not referred to. At present their relations to the other line emission spectra are little known. They would require either a complete presentation or none at all. The Appendices consist of tables of data which it is hoped will be found useful by investigators in this region. Amongst such a mass of numbers, many in- volving complicated computations, it is impossible to expect that no errors are present. The author can only hope that the great care applied to them has resulted in reducing such cases of error to a few only. The wave length data given are those which have appeared to him in each case to be the most reliable, and references to the sources are given. This carries with it the misfortune that the early investigators who have produced the data on which our present know- ledge is based are rarely mentioned. It is a fatality common to all pioneers. Fortunately complete references to these down to the dates of publication (1910, 1912) are given in Bde. v, vi of Kayser's Handbuch, which every spectroscopist will possess. CHAPTER I DATA 1. From the point of view of the physicist a knowledge of the exact value of the wave length of a spectral line is a matter of secondary importance compared with that of the exact relations to one another of the complex of lines which go to form the spectrum of a given element. A true map rather than a correct scale is his desideratum. Probably for a long time to come the chief importance of a knowledge of the true value of a wave length or of the length of the metre in terms of a given wave length will he in its metrological aspect, as a means of testing whether our standards of length vary with age or not. Apart from this, however, it is still a matter of interest. Its attainment has been a scientific goal since the times of Young and Fraunhofer, a century ago. The problem .is one of extreme difficulty and has only quite recently been placed on a secure basis. The progressive success in the attack forms one of the finest monuments of scientific achievement in its union of insight and invention with careful and painstaking labour of the highest order. It is one in which scientific men of all the leading nations have taken part. In the Bakerian lecture before the Royal Society in 1801, Thomas Young gave estimates based on his wave theory of Newton's rings of the order of magnitude of the wave lengths of different parts of the continuous spectrum. His value for the red end was -0000256 inch, a value which we should now call 6000 angstrom units. Twenty years later Fraunhofer had developed the grating and was able to deal with definite lines and measure them. His value for the wave length of the D lines of sodium, expressed in our present units, was 5887-7 angstroms. When Angstrom took up the problem he thought that his measurements were correct to the fourth significant figure and consequently adopted as the unit of measurement 10~ 8 cm. or a tenth metre which involved the decimal point being placed after the fourth significant figure when dealing with visible light. This has been universally adopted as the unit and is known as the angstrom unit. Often, however, when a wave length is only approximately known to a few angstroms, or when merely a small region of the spectrum is referred to, a unit of one-millionth of a mm., or 10~ 7 cm., is used. After Kayser this is written /*/x, in analogy with the custom of using p for one- thousandth of a mm. Thus a line 589 JJL^ will represent a region about 5 A.u. on either side of 5890 A.U. The attack on the problem of determining the true scale may be divided into four periods connected respectively with the names of Fraunhofer, Angstrom, Rowland, and Michelson, the first three marked by successive mechanical im- provements in the gratings used, and the last by the application of a new method. 4 ANALYSIS OF SPECTRA [CH. Of these the measurements of Rowland and of Michelson alone are of importance for modern work. But it may be interesting to exhibit the increasing degree of accuracy attained by giving the values adopted for the D 1 line* of sodium by the different observers. They are Fraunhofer (1821-2-3) ... 5887-7 Angstrom (1864-9) ... 5895-13 Rowland (1887-93) . . . 5896-156 at 20 C. and 760 mm. Michelson (1887-93) ... 5895-932f at 15. The great increase in the accuracy of 'the value adopted by Rowland was due to the mechanical improvement in the ruling of gratings brought about by him. From a series of most careful measurements of the D lines of sodium carried out by Bell on several of Rowland's best plane gratings, combined with some- what arbitrarily weighted measures by other observers, Rowland arrived at the above value for the D l line. To compare it with the later measure of Michel- son it should be reduced to that in air at 15 C. viz. 5896-129. The introduction of Michelson' s method rendered possible measurements with a degree of accuracy up to then regarded as unattainable. In 1895 1 he published the results of work carried out in Paris with the collaboration of M. Benoit. They found the mean of three very closely concordant determinations on the cadmium red line to be expressible in either of the following ways: Im = 1553163-5A or A = 6438-4722 A.U., the light being measured in air at 20 C. and 760 mm. pressure. No correction was, however, applied for the effect of water vapour in the atmosphere. In order to test the reliability of this value and so to get confidence in its adoption Fabry, Perot and Benoit undertook to redetermine its value, using Michelson' s method. Their result (1907) gave Im = 1553163-99A, A = 6438-4696 x 10~ 8 cm. at 15 C. on the H scale and 760 mm. pressure. Applying an estimate (necessarily rough) for the water vapour effect and reducing to the same temperature they found that Michelson's measurements gave A = 6438-4700, in remarkable agree- ment. It may be regarded as certain that the absolute value of a wave length of light in terms of the cm. has now been obtained within less than 1 in 10 7 . Reduced to the scale of Fabry and Benoit' s value, their value for the sodium D l line is 5895-930. Relative measurements. 2. The great importance of the accurate measurement of wave lengths led Rowland to devote himself to this problem. By his improvements in the * The D 19 D z of Na are in modern notation Na P 2 (1), Na P l (1). t By Fabry and Perot, based on Michelson's value of the red Cd line. j Mem. du bureau internat. des poids et mesures, 11 (1895); see also C.R 116, 790 (1893); J.dePhys. (3), 3, 5 (1894). G.R. 144, 1082 (1907); J. de Phys. (4), 7, 169. i] DATA 5 mechanical construction of gratings, by his invention of the concave grating, and by his introduction of the method of coincidences he inaugurated a new epoch in spectroscopic measurements. He crowned these achievements by publishing a complete system of accurately measured lines to serve as standards for the determination of other lines by interpolation. Unfortunately he chose to base it on lines in the solar spectrum, overlooking the necessary Doppler displacements produced by solar rotation and other effects. By the method of coincidences he first obtained the ratios of the wave lengths of about 15 lines in the visible spectrum afterwards extending into the ultra-violet by the use of spectra of orders up to the 4th and even the 8th. He published his first tables (referred to in a list published later as a preliminary table) in 1887* containing solar lines from 7671 to 3169 and based on a value for D l = 5896-080, which was Bell's result at that time. In 1889f he published a portion of a final list of solar standards based on further measurements with the scale increased by 1 in 80,000 to bring the D line into agreement with the later value 5896-156 referred to above. The complete set was publishedf in the years 1895-7 under the title Preliminary Table of solar spectrum wave lengths. In the interval in 1893 he published another table involving both solar lines and metallic arc spectra. Here the solar lines differ slightly from those of the other tables ||. The accuracy of these lists was enormously in advance of any previously in use, and they were adopted at once by all spectroscopic observers. All spectra measured down to within the last few years are based on Rowland's standards. He himself was of opinion that his method gave an absolutely correct map, subject only to observation errors. It has since been found that this is not justified, and that errors in some cases of -02 A. occur in them. That errors existed was first proved by Fabry and Perot 1{. They measured accurately by means of their interferometer the wave lengths of 33 solar lines between 6500 and 4600 and compared them with the corresponding measures of Rowland. If both were correct the ratios of all the corresponding measures should be a constant. This was not at all found to be the case. The ratio of Rowland to Fabry and Perot showed a periodic variation, fluctuating between 1-0000381 and 1-0000286. Fig. 1 is a copy of a diagram given by them to indicate these fluctuations. Eberhard** showed that when a similar comparison was made with a list which M tiller and Kempf had made in Potsdam a similar irregularity was apparent. 3. This result raised the question as to the suitability of the concave grating and the coincidence method, a question definitely answered in the negative by Kayserft- A detailed description of his work lies outside the scope of this book. * On the relative wave lengths of the lines of the solar spectrum, Amer. Journ. Sci. (3), 33, 182; Phil. Mag. (5), 22, 257. t Table of standard wave lengths, Phil Mag. (5), 27, 479. J Astro. J. 1-6. A new table of standard wave lengths, Astron. and Astro-Phys. 12, 321 ; Phil Mag. (5), 36, 49. || For discussion and comparison of these different tables, see Hartmann, Astro. J. 18, 167 ( 1903). If Ann. de Chim. et de Phys. (7), 25, 98; Astro. J. 15, 270 (1902). ** Astro. J. 17, 141 (1903). ft Ib - 19 > 157 (1904). ANALYSIS OF SPECTRA [CH. It is sufficient to say that by using two of Rowland's large gratings and measuring a certain set of lines by the method of coincidences based on Fabry's lines at AA 5302, 5434 he obtained different results from the two gratings. Although the observation errors in a large number of published spectra based on Rowland's standards exceed the limits of accuracy of the latter, it was clearly desirable to obtain the means of correcting the standards themselves, as well as if possible of correcting the values for spectra based on them. The latter problem is, however, impracticable, for observers as a rule do not state the standards to which their individual measures are related. Fabry and Perot's observations give the results for a small range only in the visible spectrum and their curve will serve at least to make the readings for the untested standards within that region more correct even if not exact. It is clear from the curve that there is no definite unique scale for Rowland's standards. In Fabry and Perot's region the ratios fluctuate between 1-0000381 1-0000350 1-0000300 450 650 and 1-0000286. Hartmann* has proposed so to define the scale that the correc- tions to the standards shall be as small as possible, and has suggested that the Rowland scale shall be taken as that corresponding to the mean of the above ratios, or 1-000034 in other words the scale shall be 1-000034 that of the Cd red line. He has given a table of corrections on this basis for the region in question. But as Kayser, with justice, points out, the corrections in other spectra can never be determined, and it is preferable to refer all future measurements to the Cd scale. Meanwhile until all spectra have been again measured in the new units we can only be satisfied to reduce the measures on the old Rowland scale to the international (see below) as accurately as possible. Kayserf has attempted to meet this want by forming a table, and a curve of correction, for lines based as far as possible on iron lines and a few other metals given by Row- land which have since been measured by interferometer methods. Having regard to the now attainable degree of accuracy, this state of things is manifestly undesirable. The pioneers in providing a better system * Astro. J. 18, 167(1903). f Handbuch, 6, 890 (1912). i] DATA 7 were Fabry and his co-workers Perot, Benoit, and Buisson. The question of the provision of a completely new system was considered at the first meeting of the International Union for solar research. At their second meeting at Oxford (1905) the following decisions were arrived at: (1) The wave length of a suitable spectroscopic line shall be taken as the primary standard of wave length. The number which defines the wave length of this line shall be fixed permanently and thereby define the unit in which all wave lengths are to be measured. This unit shall differ as little as possible from 10~ 10 metre and shall be called the angstrom. (2) Secondary standards are required at distances not greater than 50 ang- strom units. These secondary standards should be referred to the primary standard by means of an interferometer method. The source of light should be obtained by means of an electric arc of from 6 to 10 amps. The repetition of the Michelson and Benoit experiment for the absolute determination of the red line of cadmium in terms of the metre was then taken up and carried out by Benoit, Fabry and Perot with the results given above. At the third meeting of the Union at Meudon (1907) it was then possible to decide definitely that this primary standard should be that of the red line of Cd and that its wave length should be taken to be 64384696 angstroms : in other words as far as is known at present the angstrom is 10~ 8 cm. Should a more accurate determination of the wave length be made later, this measure will remain un- altered, but the magnitude of the angstrom will be modified in accordance. 4. In 1908 Fabry and Buisson* published a set of standards between 6494 and 2373 on iron lines with a few from Ni, Mn and Si to fill spaces where good iron lines are wanting. At the fourth meeting of the Union at Mt Wilson in 1910 a preliminary set of secondary standards extending from 6494 to 4282, based on the means of values obtained by three independent measurements, viz. Fabry and Buisson at Marseilles, Eversheim at Bonn and Pfund at Baltimore, was agreed to and published. In this list the individual measurements agreed very closely with one another, in only a few cases were there differences amounting to so much as -005 I.A. This list was extended at the meeting at Bonn in 1913 down to A = 3370 and up to A - 6750. About the same time as the official publication of the first list of secondary standards Kayserf published a list of tertiary iron standards made by observa- tions with a concave grating based on the new secondary standards. In carrying out the work he was led to the conclusion that the secondary standards did not form a consistent set and he proposed small changes in many of them, some of the changes even considerably exceeding the differences between the values by the three original observers. The International Union as a body seem to have had little trust in the ac- curacy of the plane grating for readings up to -001 A. At the Mt Wilson obser- vatory, however, exceptionally accurate work had been done with the plane * Astro. J. 28, 167 (1908). t Ib. 32, 217 (1910); Z. 8. wiss. Phot. 9, 173 (1911). 8 ANALYSIS OF SPECTRA [OH. grating fitted with objectives of very great focal length. Messrs St John and Ware* of this observatory, in attempting to measure accurately certain lines of the band at about 6300 A., found that Kayser's proposed system was not consistent. Incidentally also they found that three of the tertiary lines differed considerably from those of Kayser, and the important result was come to that these formed part of a group of iron lines which are very susceptible to dis- placement by change of pressure. The deviations observed were found to be due to the fall of pressure, about one-fifth of an atmosphere, due to the altitude of Mt Wilson (1794 metres). They say that lines showing such pressure shift are not suitable for standards, but that this is only practically a disadvantage if the change produced by a few cms. of mercury is sufficient to alter the wave length by an amount comparable with the degree of accuracy attainable in the actual measurements. This is not the case with these lines, but if the place of observation is at a considerable height the pressure shift must be known and allowed for. A systematic investigation was then undertaken by them, plates being taken at Mt Wilson and at Pasadena, 224 metres below. The result was (1) fully to establish the accuracy of the international secondary standards so far published within at least -OOlf; (2) to provide a table of tertiary standards between 6494 and 5371 ; and (3) a corresponding table of lines not recommended for standards, chiefly on account of pressure shift. These tables also indicate, by the differences between the corresponding measures at the two observatories, the shift p'er atmosphere. Already before the work of St John and Ware, an investigation of the iron arc with respect to pressure changes had been begun by Gale and Adamsf . They found that the iron lines between 6678 and 3609 could be arranged in four well- defined classes which they named a, 6, c, d. In a later paper they confirm the existence of a fifth (e) indicated by St John and Ware and added a sixth. The distinguishing features of these classes are as follows : (a) mainly low temperature "flame" lines with small displacements of from -003 A. to -004 A. per atmosphere at about A = 5000 (6) all lines of moderate displacement and symmetrically widened under pressure (c) lines of larger displacement (d) lines of very large displacement to the red and greatly widened to the red under pressure (e) lines of similar nature to (d) but displaced to the violet. The distinction between the types (a), (e) is clearly shown by the curves in Fig. 2 which give the intensity distribution of a line of each type, when the light comes from the centre of the arc and from the negative pole. It is taken from a paper by St John and Babcock||. Independently and about the same time Goos^j carried out complete sets of measurements by the use of both plane and concave gratings supplemented by interferential methods. He found the international standards completely * Astro. J. 36, 14 (1912), 39, 5 (1914); Contribution from Mt Wilson observatory No. 61 f Only two required adjustment by -002 and two others by -001. j Astro. J. 35, 10 (1912). Ib. 37, 391 (1913). || Ib. 42, 231 (1915). U Ib. 35, 221 (1912), 37, 48 (1913), 38, 141 1913); Z S. wiss. Phot. 11, 1, 305, 12, 259. DATA 9 established. He suggested that the deviations found by Kayser were due to his treating the spectra formed by concave gratings as rigorously normal. As a fact, owing probably to the impossibility of obtaining exact adjustment, this normality is only approximate, and a special curve of corrections is required for a given grating. Burns* has made also a determination by interferential measures of a much larger number of iron lines than are yet included in the official standards and has obtained wave lengths up to 8800 A. He points out the advantage of having standards involving both faint and strong lines for use where long and short exposures are required. The necessity for standards at intervals of 10 A. is also insisted on by Fabry. 3365 >4 5364-8 group a group e Fig. 2. Upper curves, at centre of arc ; lower curves, at negative pole. It is known that in many spectra the wave lengths of certain lines show small shifts when the light is taken from different parts of the arc. It is clearly necessary that the lines when being measured should be pro- duced under conditions that no shifts shall take place. The International Union at their Bonn meeting therefore recommended that the length of the arc used should be 6 mm., the current should be 6 amps, for wave lengths > 4000 A. and 4 amps, for shorter. The current should be continuous from a 220 volt supply, the iron rods 7 mm. diameter with the upper pole positive, and only the middle of the arc should be used. The question of freedom from the pole effect of standard lines, and also whether the International arc gave this freedom, required a definite answer. It was taken up by Messrs St John and Babcock and answered after a long and most careful investigationf . In their first paper they give their results as to the * C.R. 156, 161 (1913); J. de Phys. (5), 3, 457. f Astro. J. 42, 231 (1915); 46 138 (1917). W ANALYSIS OP SPECTRA [OH. iron standards sensitive to this effect and its dependence on position in the arc and intensity of current. They find that the same lines which show the pressure shift, show also a pole effect, and also that the International arc does not free these lines from a shift. In the second they discuss the conditions for the elimina- tion of the effect. They find it is worse in the International arc when the positive pole is above than when below, and that the metal of the negative pole makes little difference. They recommend that the arc length shall be 12 mm. with 5 amps, or less with the positive pole below. An upper negative pole of carbon steadies the arc. The light should be taken from the centre of the arc. Clearly in all spectral measures where an accuracy of a few thousandths of an angstrom is desired this pole effect ought to be specially tested. As yet no table of tertiary standards has been officially adopted; but at present the following contributions towards the creation of such tables have been made: Kayser ...... between 6500 and 4100. Astro. J. 32 (1910). Goos ...... 5320 ,,4282. Astro. J. 35, 37, 38; Z. 8. wias. Phot. 11, 12. St John and Ware 6494 5371. Astro J. 36 (1912). 5363 4100. Astro. J. 39 (1914). Burns ...... 8824 5434. J. de Phys. (1913). Paschen ...... above 27000. Ann. d. Phys. 27, 537 (1908). There is therefore now some hope that within a few years a complete and satisfactory system of standards will be at disposal for accurate spectroscopic measurements. Reduction to Vocuo. 5. To the physicist whose interest is fixed on the problem of molecular structure, the essential point is the frequency of the light-emitting source and not the wave length set up in the surrounding medium, except in so far as this is a first step to obtaining the frequency. The frequency is given by v/X = F//zA, where v, V denote the velocities of propagation in the medium and in vacuo respectively, and /-i is the index of refraction. The product ^X denotes the wave length in vacuo and this has first to be found. It requires a knowledge of the refractive index of air at any given pressure and temperature and for any given wave length. In a gas p = 1 -f /c, where K is a small quantity which for a given wave length is proportional to the density of the gas. If then K denotes its value at a pressure p and absolute temperature , the value at p, 6 is Kp9 Q /(p 0), and or the change in A is given by dX_- p6 The determination of K as a function of the wave length has been the object of a large number of investigations*. These were superseded in 1903 by a very * See Meggers and Peters, Butt. Bur. Standards, 14, 697 (1919), who also refer to a complete list in a prize essay by C. Bruhns, Die Astronomische Strahlenbrecbung, Leipzig, 1861. i] DATA 11 complete set of measurements by Kayser* and Runge for wave lengths between 563 juifji and 236 ^. They found that a three constant formula of Cauchy's form was sufficient to represent all their observations. Their formula for dry air at C. and 76 cm. pressure can be expressed thus ic = 10- 3 {-28817 + -1316A!- 2 + -SieGA^ 4 } in which X l = A/1000 and A is measured in angstroms. Hence dX = A! {-28817 + -1316Ar 2 + -SieOA^ 4 } . 273/0, the pressure being 760 mm. Rowland's standards are at 20, the international at 15. Hence d\ = A! {-26850 + -^eA^ 2 + -2944Ar 4 } for Rowland, d\ = A! {-27316 + -1247Ar 2 + -2995V- 4 } for I.A., to be added to the line in air to give the line in vacuo. According to Rungef this formula ceases to hold for wave lengths shorter than 1850 at which air begins to show considerable absorption. As air does not show great absorption for ultra- red light, the formula probably gives correct values when used for extrapolation above the experimental limit of 5630 A. By means of this formula Kayser J has calculated a table of reductions for wave lengths between 8000 and 2000 from Rowland's scale to vacuo. His numbers are reproduced in Table I in * the Appendix, to which is added a corresponding set for reductions from I.A. for wave lengths between 10,000 and 1850. Quite recently a still more complete investigation with observations on dried air has been published by W. F. Meggers and C. G. Peters for wave lengths extending from 9000 to 2218 and aiming at an accuracy of a few units in the fifth significant figure. Their results are expressible by the Cauchy formula K = 10- 3 {-287566 + -13412AJ- 2 + -3777A!- 4 } . 273/0. From this they have calculated a table of corrections to vacuo at intervals of 50 A. The results are incorporated in Table I. As the variations in the corrections over any 100 A. are strictly proportional to the wave length variations, the odd 50 A. have not been reproduced. So long as wave numbers (10 8 /A) are not re- quired beyond the second decimal place the table corrections beyond the third place are not required. The calculated values of I/A from Kayser and Runge' s tables and from those of Meggers and Peters do not differ by so much as unity in the second place, except in the neighbourhood of 5000 where the first is less by unity and between 3000 and 2000 where it is greater by unity. As Kayser and Runge' s table has been the basis of reduction to vacuo from 1903 to the present time (1921) both are given in the Appendix. , Wave numbers. 6. If A be expressed in angstroms the wave length is A 10~ 8 cm. The number of waves per cm. is n = 10 8 /A. This quantity is called the wave number and is * Ann. d. Phys. 50, 293 (1893). f Ib. 55, 44 (1895). J Handbuch, n, 514. . Bull. Bur. Stand. Wash. 14, 697 (1918). 12 ANALYSIS OF SPECTRA [CH. clearly proportional to the frequency, in fact it gives the frequency in terms of a new unit of time = l/v = -J x lO" 10 sees. In discussing the relationships of the frequencies of a spectrum, the latter are generally expressed in terms of this unit, although we may look on the numbers also as expressing the number of waves per cm. For lines between 10,000 A. and 1000 A. the decimal point comes after the fifth significant figure. If then A is given to -001 A. the wave number can be given to -01. In tables of wave lengths as published by observers the degree of accuracy of a particular line may vary very considerably from, say, -5 A. or more to -001 A. In forming a table of wave numbers for use from these it is advisable to treat observers' numbers as if they were correct to the third decimal place, to reciprocate the wave lengths by the use of a table* to seven significant figures and to place opposite to them in a separate column the factor which will change any dX into the corresponding dn. This is quickly done by moving the decimal point in n back four places and from a tablet inserting the square of the first three significant figures, retaining only as far as the second decimal. This will give correctly the change in n due to a change of one angstrom in A down to A = 2200 or down to A = 1000 for a change dX < -1. Thus for instance a line given as 3000-1 I.A. is treated as 3000-100. The reduction to vacuo (Table I) is -871. From the book of tables the reciprocal of 3000-971 is 33322-55. The conversion factor is then the square of 3-33 = 11-09. If later a more accurate value of say 3000-125 is known, the change in n is - -025 x 11-09 = - -27. In converting a list of wave lengths into wave numbers, each kind of the above operations is carried out at one time throughout the list. In making such hand lists for 'use, it is advisable to have at least seven columns: the first for the intensity and character, the second for wave length, the third for wave number, the fourth for the conversion factor, fifth for possible error when given, sixth for corresponding dn, and the last a broader one for remarks in which may be entered its series or other relationship or notes as to its Zeeman pattern, electric or canal ray effect, pressure shift, fine structure, or other references to special properties. The character and degree of accuracy of data. 7. When any spectrum is closely examined, we are at once struck by the great diversity in the types of lines exhibited, not only in intensity, but also in their general character. What we really observe in a line is the combined result of several effects as shown in the optical image. These are due partly to the optical apparatus forming the image, partly to causes not affecting the emitting centres, and partly to effects in the radiating centres themselves. We will briefly consider these in order. If the light emitted is completely monochromatic, the image formed by even a perfect optical apparatus is broader than the geometrical image of the slit. * E.g. Tables of reciprocals, by Lieut. -Col. Oakes (C..and E. Layton). t Barlow's Tables of squares, etc. (E. and F. N. Spon). DATA 13 Even when the latter is vanishingly small the diffraction image consists of a strip with maximum brightness at the centre shading off on each side, with a smaller maximum beyond, generally too weak to be noticed. The effect is illustrated by Fig. 3, in which the ordinates represent intensity. It is a con- vention to define the "width" of the line as the distance between points on either side where the intensity is one half of the maximum. The greater the resolving power of the apparatus, the narrower the line becomes, and the more rapidly the intensity falls off. In general a point in the spectrum or on the photo- graphic plate is associated with a definite wave length, but here the whole breadth of the image is due to light of the same frequency. Nevertheless we can express the breadth in terms of a wave length b = dX corresponding to the scale of wave lengths on the plate or in other words as the wave length difference of two lines whose respective maxima occupy these half-maximum positions. It follows that in a continuous spectrum any point associated with a wave length A con- Fig. 3 tains also light with wave lengths lying between about A b or the spectrum is not pure. The quantity 6 may be taken as a measure of the impurity from this cause, the greater the resolving power the less 6. In any actual case the purity depends also on slit width. If the emitted light consists of two or more definite frequencies their diffrac- tion patterns are superposed with the result that we have a line with an intensity distribution the sum of the component patterns. The resulting images may appear as "lines" with broader maxima and shading off on each side either symmetrically or more gradually on one side than the other. If it indicates more than one maximum we conclude that the line is really multiple and with increased resolving power it is often possible, Jbo get the components completely separated. With lines shaded symmetrically the position of the maximum is determinable with considerable accuracy. In the case of monochromatic lines this maximum definitely corresponds to the frequency. In other cases it gives the wave length 14 ANALYSIS OF SPECTRA [OH. corresponding to a rough mean of the original light. When, however, the shading is different on the two sides the maximum intensity of the observed line does not correspond to the maximum intensity of the light emitted, but is displaced towards that side on which the shading is the more gradual. This effect has been discussed by Merton and Nicholson* for a special kind of asymmetry. The asymmetry is such that with a well marked maximum the intensity at a distance x from it is proportional to e~ kx with k different on the two sides. They have shown that the observed maximum is displaced from the true by an amount b (i l)f(i + 1), where b denotes the breadth of the diffraction image and depends on the resolving power used whilst i is the ratio of the half breadths on the two sides. Two other possible effects depending on the optical apparatus have been discussed by Rayleighf, one depending on a possible damping of emitted light and the other on the existence of a number of emitting centres in the line of sight. In practice, however, no effects are observed which can be put down to these causes. We may conclude that in any individual emission the time of dying down is very small compared with the whole duration of the emission. 8. Of changes caused neither by the optical apparatus nor occurring in the radiating centres themselves, the most important are those due to Doppler effects (1) by translatory motion depending on temperature, (2) by rotation of the molecules, (3) when the centres have had velocities impressed on them by special causes such for instance as in canal rays. The last will be considered more fully in Chapter V. The other two have been treated fully by Rayleighf and also by Schonrockf. On account of the temperature effect a single frequency appears to the recipient transformed into a pencil containing all frequencies in proportions determinable by Maxwell's law of velocity distribution. The consequence is that whilst the original light may be capable of giving interference fringes of a high order those produced in the light as modified become confused and disappear as fringes at a much lower order. On the supposition (supported by experiment) that a fringe can be detected when the intensities of the maxima and minima do not differ relatively by more than 5 per cent. Rayleigh showed that the order of interference when the fringes disappear is given by 1427 x 10V(w/0), where m is the mass of the emitting source and 9 the absolute temperature. This temperature effect changes the optical image of a line into one shaded on both sides and the line produced on a plate becomes a broadened copy of that due to a monochromatic diffracted image. It follows that increased temperature broadens a line and that, other things being equal, the heavier the source the finer is the line observed. Rayleigh's formula has been experimentally confirmed by Fabry and Buisson, who have determined the ratio of the order of dis- appearance in He, Ne, Kr in light from vacuum tubes at ordinary room tem- * Proc. Boy. Soc. 98 A, 255 (1920). t Phil- Mag. 27, 298 (1889); 29, 274 (1915). Coll. Papers, i. 185; iii. 258; vi. 291. J Ann. d. Phys. 20, 995 (1906). C.R. 154, 1224 (1912). i] DATA 15 peratures and at the temperature of liquid air. For these temperatures the formula gives a ratio of 1-73 in each gas. The observed ratios for the three gases were respectively 1-66, 1-60, 1-58. The close agreement of numbers would seem to show that the actual temperature of the gas in the tubes when electrically excited can differ little from that of the surrounding medium. In fact the ratio 1-66 would correspond to a heating of the gas by the discharge by 20 above the surrounding medium. Rayleigh* has pointed out that the effect produced by a rotating molecule should be greater and more complicated than the translational temperature effect. That it is not so in practice is explained by Schonrock's assumption that the vibrating systems are atoms and not molecules. This is in accordance with our later knowledge of these sources in line spectra, the evidence for which will be discussed in Chapter V. 9. The effects considered above change the observed frequency without affecting that actually emitted by a source. But the frequency emitted by such a source may also be directly affected by surrounding physical conditions, such as the presence of electric or magnetic fields or the contiguity of neighbouring sources. These are considered in more detail in Chapter V. Here it is only necessary to remark (1) that to obtain the real frequency of a freely vibrating source it is necessary to test if it is subject to change by altered conditions')", and if so to determine a correction; (2) that when the light is emitted in a region where these conditions are not uniform the emission from different individual sources will be differently affected, and the total emission received by the observer will consist of a mixture of frequencies in more or less fortuitous proportions. The result is a broadened and asymmetrical line whose general features vary widely between different lines and under different excitations. It is probable that a great proportion of observed diffuse and asymmetric lines may be due to causes of this nature. 10. Undoubtedly a large number of asymmetric lines are due to the presence of two or more unresolved close components. Such close components or fine structure in lines are very common and a considerable amount of investigation relating to it has been carried out by many observers. Very little, however, has been done on the difficult problem of determining the distribution of intensity in lines which are not resolvable into individual components. Yet the spectrum of an element cannot be considered as really known until this has been done and the effect of disturbing causes eliminated. It would, for instance, even be one important result if such a discussion were to show that a freely vibrating source always gave purely monochromatic frequencies; in other words that there were no such effects as occur in ordinary elastic vibrations in which the frequencies are modified to a small extent by amplitude or damping. Examples of such intensity analysis are given in the accompanying figures. Fig. 4 is taken * Phil. Mag. 34, 407 (1892). Coll. Papers, iv. 15; vi. 297. f Already referred to under iron standards. 16 ANALYSIS OF SPECTRA [CH. from a paper by King and Koch* giving photometric curves for a sharp and a diffuse line of about the same intensity. The areas of the two curves are practically equal. They were made on the two titanium lines 4009-8, 4013-7. Fig. 2 (p. 9) gives the curves illustrating the pole effect on lines in the a and e groups of iron standards taken from the paper by St John and Babcock. Not only is practically nothing known at present as to intensity distribution within a line, but very little has been done in the simpler problem of determining the absolute, or the proportional total intensity of different lines. It must be remembered that the ap- parent intensity of a line is due to the com- bined effect of the intensity of emission from each source and the number of sources emit- - diffuse sharp ting it at a given instant. Certain theoretical Fi 4 reasons*}", for which there is considerable ex- perimental support, lead to the belief that the energy emitted by any source is the same for the same frequency, and is proportional to the frequency. In this case the observed intensity of lines in the same region of a spectrum would be a measure of the number of the respective sources taking part in the emission, and any changes in intensity under different excitations would be due to a change in this number. If, for instance, an emitting source is a modified con- figuration of the normal atom, the intensity would give a measure of the number of these configurations produced. Failing definite measures of intensity, and of distributions of intensity within lines, it is usual for observers to give estimates. The intensities are estimated usually by numbers from 10 downwards to 0. In certain ultra-red bolometer measures by Paschen and his students, the galvanometer deflections are given. A few observers also, where extremely strong lines are involved, use numbers decreasing by 10 from 100 to 10. These numbers are valuable as giving a general picture of the variation of intensity within a spectrum, and a comparison of spectra of the same element taken under different conditions. But here to obtain a picture of the real intensity- distribution allowance must be made for sensitiveness of plate, and absorption in the optical media. Thus a line given as intensity 1 in the ultra-violet may, through absorption in the spectroscope, be equivalent to one of 10 in the visual region, or a low estimate in the red may, on account of photographic insensitiveness, correspond in reality to an intense radiation. In the impossibility of giving a complete description of the character of a line it is usual to arrange the characteristics in a few classes, represented by attaching different letters to the individual wave lengths. They are as follows: * Astro. J. 39, 218 (1914). t Energy = hn, where h is Planck's constant and n the frequency. i] DATA 17 R, denotes a reversed line. s, sharp, one in which the intensity falls off rapidly on each side. n, nebulous or diffuse, one in which the intensity falls off gradually. nr, when the intensity falls off more slowly on the "red" side. nv, when the intensity falls off more slowly on the "violet" side. nn, very nebulous. b, broad, when the maximum intensity is not concentrated in a definite position. d, double, i.e. indications of two maxima not sufficiently definite to give measures. It is used by some in place of nn. For the purpose of dealing with the constitution of spectra, and their inter- relationships, a knowledge of the degree of accuracy of wave length determina- tions is of the highest importance. It is desirable that all observers should, where possible, give estimates of their maximum possible errors, following the example of Kayser and his co-workers-. Many observers give their probable errors, deduced from the agreement between a series of readings, or from in- dependent plates. This gives a rough measure of their power of identification of the same feature of a line, but does not include the possibility of that feature not giving the true wave length. The reliability of a reading depends chiefly on the nature of the line in question and the apparatus used. The estimate can only be given by the actual observer. It may be taken in general that with good lines and spectroscopic apparatus of fair resolving power an accuracy of from -03 to -05 A. is attainable, but it is easy to overrate the accuracy attained. When no estimate is given it is safer, when testing for evidence of laws, to over-estimate the accuracy. H. A. S. CHAPTER II TYPES OF SERIES 1. The material at disposal at the present time relating to the wave lengths of the various spectra of different elements is very large. Before this can be made available for drawing conclusions as to their origin or as to the nature and constitution of the vibrating systems which give rise to them, it is necessary to discover whether the different lines of a given spectrum are related to one another in any way and if so the laws to which these relationships are subject. We shall begin the discussion of this by considering the case of spectra emitted by the flame and arc which are in many ways of a simpler and less crowded nature than the others. Amongst these for gases the spectra emitted in vacuum tubes will be included, although in some respects they are more analogous to spark spectra. The first attempts were naturally directed to discover whether the wave lengths or the frequencies followed laws similar to those known in mechanical systems or elastic bodies. Many investigators, for instance, sought to obtain evidence of harmonic relations between lines. If, however, the ratio of the wave lengths of two lines were in the ratio of two whole numbers, the ratio should appear as exact, and it is doubtful whether the accuracy of measurement attain- able at this time was sufficient to test this. No definite or certain conclusion could be drawn unless the number of cases found to exhibit it was very large. In 1881, however, Schuster* showed that the number of such cases found was not greater than should be expected on the supposition that they were chance occurrences. He dealt with the stronger lines in Na, Cu, Mg, Ba, Fe and in each element found the wave length ratio of each line to each of greater wave length. Confining his attention to ratios of integers less than 100, he formed an auxiliary table of the ratios of every integer to those of greater value. In the case of the ratio of any two lines it was thus possible to determine between what ratios of two numbers it lay. For instance the ratio of the two Na lines 5688, 5896 is 964760. The auxiliary table shows that this lies between 55/57 - -964912 and 82/85 = -964706. The line ratio therefore is distant from the nearer integer ratio by 54/206 = -262 of the distance between the two integer ratios. If the distribu- tion of lines were purely chance, these ratios should vary evenly between and 0-5 or their mean value should be 0-25. If, on the other hand, there is a dis- tribution giving harmonic ratios, this corresponding fraction should approximate on the average to a small value. The result of the application of this test to the material discussed is shown in the following table, in which the figures in brackets after the chemical sign denote the number of fractions considered : * Proc. Roy. Soc. 31, 337 (1881). GH. n] TYPES OF SERIES 19 Mg(18), -2626 Ba(303), -2592 Na(40), -2399 Fe (10404), -2513 Cu (101), -2430 Mean (10866), -2514 This would seem to be conclusive against any considerable proportion of lines following an integral ratio law, and by a more refined analysis he arrived at the same result. As, however, our knowledge of the real relationship of lines is now more complete, it is not necessary to describe his method in further detail. The great merit of Schuster's work was that it turned attention at the time away from an unprofitable field. 2. The first indication of the true direction in which to search for regularities was given by Liveing and Dewar*. In carrying out wave length measurements in the ultra-violet they brought to light the existence of series in which large numbers of repetitions of similar doublets or triplets were shown. They appeared to form two sets of alternately sharp and diffuse doublets, or triplets, which crowded more closely together as they lay more towards the ultra-violet. The lines also diminished in intensity with decreasing wave length. In the diagrams of the spectra published by them, these doublets and triplets strike the eye as forming a related series of lines and suggested to them an analogy with the overtones of a bar or bell. The arrangement of the groups showed that the lines could not obey the ordinary harmonic law, but that they apparently converged to definite limits. The authors were, however, unable to determine any numerical relations either between the arrangement of the lines in a multiplet group, or that in which the groups follow one another. 3. The first step towards this was made by Hartleyf by considering fre- quencies instead of wave lengths. He pointed out that the differences of the frequencies in the multiplet groups in any one element were constant, but that this constant difference increased from element to element as the atomic weight increased. This constituted the first numerical relationship in spectral lines brought to light. The second step was the quantitative relation between the wave lengths of the different lines of the series of a special element that of hydrogen. This was due to the Swiss Balmer J. The spectrum of hydrogen on a scale of frequencies is shown in diagram in Fig. 5. It is of a much simpler nature than that of any other element, consisting of a single series of lines, but at the same time a very considerable number of the lines belonging to the spectrum have been observed. It therefore serves to exhibit in a striking way the manner in which the lines of a series converge to a finite limit. At the time Balmer published his formula only nine lines of the hydrogen spectrum had been observed. Of these four had been measured by laboratory methods by Angstrom and others and five others had been observed in the spectra of white * The Spectra of Sodium and Potassium, Proc. Roy. Soc. 29, 398 (1879); The Spectra of Magnesium and Lithium, Proc. Roy. Soc. 30, 93 (1880); Investigations in the spectrum of Mag- nesium, Proc. Roy. Soc. 32, 189 (1881); The ultra-violet spectra of the elements, Pt. I, Trans. Roy. Soc,. 174, 187 (1883), or Coll. Papers, pp. 66, 78, 118, 221. t Journ. Chem. Soc. 43, 390 (1883). t Verh. (1. Xatur. . hi /,W/, 7 (I88f>); also Ann. where ^V = 109679*2 for international units and 109675 for the Rowland scale. The limiting frequency to which the series converges as m increases indefinitely is ^N = 27418-8 or A = 3645-96 I.A. This is shown in the figure by the dotted line on the left. The figures below the spectrum give the corresponding value of m. This formula reproduced the observed wave lengths with extraordinary precision. The remarkable agreement between the observed and calculated wave lengths is shown in the table given in Chapter III, sect. 3, in the section devoted specially to this element. 4. These results greatly stimulated further investigation. On the one hand J. R. Rydberg at Lund undertook a thorough discussion of the material then at disposal chiefly drawn from observations due to Thalen, Liveing and Dewar, and Cornu. On the other hand Kayser and Runge at Bonn, recognising that before any definite conclusion could be arrived at more systematic and accurate measurements were called for, began a long series of spectral measurements of the elements. The first publications of both appeared in the same year 1890 although Runge had given a short statement of some of his and Kayser's results at a meeting of the British Association in 1888. Rydberg's results* were given in full in a memoir presented to the Swedish Royal Academy of Science in November, 1889. Those of Kayser and Rungef began with the presentation of their measurements of the line spectra of the alkalies to the Berlin Academy in 1890 and were continued in a succession of papers of fundamental importance for establishing the general theory of these series. The work of these investigators fully established the existence of series in which the successive frequencies converged towards a limiting value on the violet side. Three types were recognised to which a fourth was afterwards added. In the odd_groups of the periodic table of elements, so far as such series were observed, the predominant series consisted of doublets, whilst in the even groups they consisted of triplets. At the same time doublet and singlet series are also * J. R. Rydberg, Z. S.f. Phys. Chem. 5, 227; Phil. Mag. (5) 29, 331; C.E. 110, 394, all in 1890; Recherches sur la constitution des spectres d'emission des elements chimiques, Kgl. Svensk. Vet. Akad, Hand. 23, No. 11. t C. Runge, Report Brit. Ass. 1888, p. 576. Kayser and Runge, Ann. d. Phys. 41, 302 (1890) (alkalies); 43, 384 (1891) (2nd periodic group); 46, 225 (1892) (Cu, Ag, Au); 48, 126 (1893) (Al, In, Tl); 52, 93 (1894) (Sn, Pb, As, Sb). Runge and Paschen, Astro. J. 3, 4 (1896) (He); Ann. d. Phys. 61, 641 (1897); Astro. J. 8, 70 (1898)(0, S, Se). 22 ANALYSIS OF SPECTRA [OH. found in spectra where triplets are the most prominent. But whatever their multiplicity they all tend to conform to one of the four types. Confining attention in the first instance to the three originally discovered, Rydberg gave the names Principal, Sharp, and Diffuse, whilst Kayser and Runge attached the respective names Principal, 2nd associated series, 1st associated series (Hauptserie, II and I Nebenserie). In this treatise we shall employ Rydberg's names and notations though neither his nor Kayser and Runge' s are altogether satisfactory. On the one hand the sharp and diffuse series are not always composed of sharp and diffuse lines, although this is the distinguishing feature in the alkalies. On the other hand the three types are associated with one another. The name principal was given because in the alkalies, where they were first most fully in evidence, the strongest visible line belonged to this series : but it is possible, even probable that the greatest energy appears in the fourth series which, in the alkalies, lies wholly in the ultra-red. The sharp and diffuse series run down to common limits, and when doublets or triplets occur, the differences of the corresponding wave numbers in any one element are the same. In the principal series, however, whilst these differences for the first set are the same as in the sharp or diffuse, for succeeding lines they become closer and closer, and they all converge to zero at the same limiting wave length. This convergence of successive multiplets distinguishes the principal series from the others. At their first discovery no criterion of distinction between the sharp and diffuse series was recognised beyond the difference in the aspect of the lines composing them. In fact both Rydberg and Kayser* and Runge interchanged the sharp and diffuse in potassium an error corrected later by Ritzf. Such criteria will be obtained later. 5. The types of the series are illustrated in Figs. 6 and 7 by diagrams of the portions of the spectrum of potassium and magnesium. That of potassium includes the portion between nn 1346 and 35000 or AA = 74260 and 2850. The scale is too small to show the lines as doublets. These are illustrated below the diagram of the spectrum on a larger scale. That on the right represents on this scale the doublet magnitude, 57-7, for the first principal set and any S or D set. The doublets on the left show how the principal doublets close up as the order increases. In the diagram the central band gives the lines as seen in the complete spectrum, whilst the other two show the complete P, 8, D series as weUUs the fourth" or F series. The P and F are shown in the upper band, the six lines on the right belong to the F series, converging to the dotted line. The strong line just on the right of this is the first of the P which are shown converging to the dotted limit on the extreme left, twenty-four of these lines having been observed. The S and D series are shown in the lower band, but these two series are very close to one another. The sharp are indicated by being drawn slightly longer. This peculiar arrangement led some of the earlier investigators to speak of them as quadruplets. * The error is repeated in Kayser's Handbuch, n. 523 (1902); v. 633 (1910). t Ann. d. Phys. (4), 12, 444 (1903); (Euvres, p. 85. ii] TYPES OF SERIES 23 In the second diagram the spectrum of magnesium between nn = 16000 and 40000 or AA = 6250 and 2500 is shown, the S lines above, the D below. The constant triplets are just seen. The two lines slightly projecting above on the right belong probably to the principal series and the series slightly projecting beneath belongs to a singlet series which will be considered later. 6. In each periodic group of elements both the sharp and diffuse series in the elements of low atomic weight have doublets or triplets of the same magni- tude. When, however, Kayser and Runge published their measures for the alkaline earths, it appeared that the values for the diffuse from Ca upwards were different from and smaller than those of the sharp. Rydberg* pointed out that this was only apparently the case and that the diffuse sets were in this case of a composite character. Their nature is indicated in Fig. 8 which gives diagram- ma tically the first two composite diffuse triplets of calcium. The two groups are superposed, the first above and the second below, so as to bring out their relation to one another. The intensities of the lines are also roughly indicated by their lengths. It will be noticed that the first constituent of a triplet that on the right of the diagram consists of one strong line and two weaker ones; the second of one strong and one weak, and the third of a single strong line. The accompanying fainter lines are called satellites. The important point established by Rydberg is that the triplet separations must be measured from the satellites in the manner indicated by the dotted lines. The appearance suggests that the third strong line and the two extreme satellites form the normal triplets. Then that the two lines occupying the latter positions are split and a pair pushed towards shorter wave length, and that finally the first line is again split and one pushed still further in the same direction. It will be noticed also that this apparent displacement diminishes as the order of the set increases. As it is useful to have a special name for the magnitudes of the doublets and triplets, we shall, in future, use the word separation for the difference in the wave numbers of two lines, reserving the word difference of two lines to denote the difference in their wave lengths. We shall also, after Rydberg, use the notation v^ , v 2 for triplet separations and v for doublet. In general the ratio v-^v 2 is some- what larger than 2. The full evidence for the law of the constancy of these separations in the different orders of the sharp and diffuse series, and their equality for the two, will come later when each element is separately discussed in more detail. It may be said that the rule holds almost universally within observation limits however accurate these limits may be. There are single cases where there is an apparent failure and these are of importance in the general theory of spectral structure. The above statement may be illustrated, and at the same time the structure of the composite triplets clearly brought out, by the following numbers which give the wave numbers and the separations for the diffuse series of calcium the first two of which the diagram in Fig. 8 has already dealt with. This spectrum is taken because the wave lengths have recently been determined between * Ann. d. Phijs. 50, 629 (1893). 24 ANALYSIS OF SPECTRA [CH. AA 7326, 2103 by Crew* and McCauley, and also by Holtzt, in I.A. with an accuracy comparable with -001 A. The first diffuse triplet is in the ultra-red and is due to Paschen with possible observation errors of -25 A. or dn = -25. An error of -001 A. only produces an error dn = -01 beyond n = 27500. The numbers in brackets before a wave number indicate the intensity of the line whilst the separations are given in thick type. In the first set the numbers for intensity are only comparable with one another, and not with the other sets. (80) 5019-37 14-56 (11)5033-93 20-99 (60) 5054-92 (3) 22432-29 3-71 (5) 22436-00 5-59 (9) 22441-59 (0) 27427-13 1-72 (3) 27428-85 2-71 (7) 27431-56 (0) 29733-20 1-32 (2) 29734-52 1-88 (6) 29736-40 (1) 30988-00 2-34 (5) 30990-34 (1) 31723-97 5-36 (4)31729-33 105-59 105-32 105-89 105-86 105-87 105-84 105-77 105-90 [105-87] 105-84 [105-87J 106-04 (30)5124-96 52-15 (40)5177-11 14-29 (50) 5139-25 m=2 (8) 22538-18 52-17 (9) 22590-35 3-68 (9) 22541-86 (2)27533-00 52-17 (6)27585-17 1-69 (6) 27534-69 w=4 (2) 29838-97 52-23 (5) 29891-20 1-45 (5) 29840-42 (1)31092-01 52-35 (3)31144-36 1-83 (3) 31093-84 (0) 31826-14 3-87 (2) 31830-01 52-38 (2) 31878-52 The last sets show the influence of observation errors, whilst the extreme satellites of the first lines are too weak to be seen. The corresponding wave numbers of the S series are m = 2 (9)16223-55 105-89 m = 3 (4)25158-27 105-93 m=4 (5)28664-73 105-89 m = 5 (3)30422-84 105-89 m = Q (2)31432-32 105-75 w = 7 (1)32066-11 105-96 * Astro. J. 39, 33 (1914). (8) 16329-44 (5) 25264-20 (3) 28770-62 (2) 30528-73 (1) 31538-07 (1) 32172-07 52-18 52-18 52-19 52-02 52-20 52-14 (8) 16381-62 (3) 25316-38 (2) 28822-81 (1) 30580-75 (1) 31590-27 (0) 32224-21 t Z. S. wiss. Phot. 12, 101 (1913). n] TYPES OF SERIES 25 The following wave numbers from the same observers of a doublet series in calcium illustrate the similar rules for diffuse doublets. (6) 31424-80 19-19 (10)31443-99 (1)47306-89 9-56 (2) 47316-45 222-88 (10)31647-68 223-78 (2) 47530-67 7. The doublet or triplet separations in general increase with the atomic weight. In any periodic group of elements it was found that their magnitudes were roughly proportional to the squares of the atomic weights. This is illustrated by the following numbers for the doublets of the alkalies (I); the doublets of the Al group (III) and the triplets of the Zn group (II). The numbers respect- ively give the values of lQ*v/W 2 . Further in the triplet example the values of v-Jv 2 are given. I III N. J =324* K ^ =379-2. TK ^'"O4 OOK.7 7~QK^T\~2 W" ' 553-80 Cs CF?^ 314 ' - Al 112-15 (271) 2 = 1527. Ga (7 826-10 = 1690. ii. Zn 388-90 = 909-3; (-654)2 K=' Eu 2630-5 (1-519) 4630-65 -, = 1141; ^ (2^oo3r 1154; 190-09 (654) 2 541-89 (M23) 2 1004 (1-519) 2 1767-0 In Tl 2 = 446-3; = 429-7; =435-2; 2212-38 (1-148) 2 : 7792-39 (2-040) 2 = 1872. 2-04. 2-16. 2-62. 2-62. 8. Rydberg introduced a notation for the lines in these series which has been very generally adopted, although that proposed by Kayser and Runge is frequently used. The Principal, Sharp, and Diffuse series are represented by the letters P, S, D respectively. When the series are multiplet they are expressed by subscript numerals 1, 2, 3. In the S and D the strongest lines of a doublet or triplet are on the longwave or red side, and these take the subscript 1. The case is reversed in the Principal series, the strongest line being on the violet side and this takes the subscript 1. The reason for this will be considered below. In the case of the diffuse composite multiplets with satellites, the lines take a second subscript in a manner made evident by the following scheme for a triplet. -LJ-tt -L/OQ A/>I 26 ANALYSIS OF SPECTRA [OH. There are cases in which more than two satellites occur. The notation can then be extended in an obvious way. The first term* of a series is of order 1, the mth. from the first of order m. If the element requires signification the chemical sign is prefixed. When different multiplet series are present we shall denote this by dashes placed over the series sign or qver the sign for the elements, one dash for a singlet, etc. When, however, we are dealing with a particular series, or where no ambiguity occurs, these dashes will not be put in evidencef. The following examples will serve to illustrate and make plain this notation. The corresponding notation in Kayser's system is also given on the right. X. 11 2881-34 or 34696-09 is Cd Z> 23 '" (2) CdlNII2 3362-28 , 29733 , Ca D 18 '" (4) Ca INI 4 2112-763 4306-98 5889-96 4341-664 47316 23211 16973 23032 Ca Z> u " (3) Ca Ltfl 3 Cd S' (3) Cd UN 3 NaP^l) Natfll H D (3) H NI 3 In Kayser's scheme of notation it is to be remembered that H, N stand respectively for Principal series (Hauptserie) and associated series (Nebenserie) H I = Pi, H II = P 2 , 1 N = D, UN - S, II N I = S 1 . No distinction is made between the satellites composing one element of a doublet or triplet. The multi- plicity of a series might here be represented by dashes over N and H in the same way as for the P, S, D notation. 9. The wave number of a line in a series with a given limit is known when its separation from this limit is given. These separations in a series of lines form a sequence of values each of which depends in some way on the order (m) of the line. Any sequence will be a function of m in so far as it is definite when m is given, and in the normal types it appears to be a single-valued function, although as will be seen later many-valued functions occur in special circumstances. Whether this functional relationship can be represented as a continuous function of the variable m, whose value is required for integral values (the order) of m must not be assumed as necessarily the case, although it is natural to make it as a first trial assumption. Evidence will be obtained later which tends to throw some doubt on the truth of this assumption at least for certain series. Mean- while, however, we shall assume with Rydberg, Kayser, and other investigators, that this functional relation exists. We shall represent these sequences by the notation p (m), s (m), d (m) for the P, S, D series, and it will be convenient to refer to a particular value as the mth sequent. In the doublet P series there will be two sequences p (m), p z (m) tending to equality with increasing m, in the S series one sequence s (m), in the D series one sequence d (m), but two sequences d (m), d 2 (m) when satellites occur. The case for triplets can be treated in an analogous way. If for the moment (f> (m) denotes any sequence, and A the limit, the wave number is n = A (m) in which (m) must diminish to zero as m increases to infinity. * This word has been used by Paschen to denote the quantity referred to below as the sequent. To avoid confusion it will be advisable to replace the expression mth term of a series by mth order. f Paschen indicates the multiplicity of a series by using different type, viz. small Roman p, s, d for triplets, German $, f, t for doublets and Roman Caps P, S, D for singlets. n] TYPES OF SERIES 27 10. The author* has found indications of allied series in which the lines run up in a corresponding way to the limit. In other words, their frequencies can be represented by formulae of the type n = A + (/> (m), where (/> (m) is one of the four types of sequences. The two systems can be referred to as difference and summation series. It is clear that the low orders in a summation series, i.e. the strongest lines, will lie in the far ultra-violet. This may be the chief reason why they have not been noticed by the early observers. They will be indicated by using Clarendon typef with corresponding signs to denote multiplicity and sets. Thus : S(m) = p(l)-s (m) ; 5 (m) = p (1) + s (m). 11. In the case of hydrogen the form of cf> (tu) is known with great accuracy as given by Balmer's formula, viz. (m) = N/m 2 . This is, however, very far from being the case for other elements. Rydberg, and Kayser and Runge, in their original work employed forms of cf> (m) which were modifications of Balmer's simple law. Kayser and Runge used the formula for n B C B C n A ^ H . or A 2 H , m 2 m 4 m 2 m 3 a three constant formula whose constants required for their determination a knowledge of three lines, which were consequently reproduced accurately. A rough agreement of succeeding lines was obtained, although in many cases considerably outside the observational degree of accuracy. Rydberg used the formula -^ /vi A /(/ ^ ; rs < (m + /x) 2 where N had the same value for all series and all elements the same as for H = 109675 on Rowland's scale. This required only two lines to determine the constants. It also gave a rough agreement with observation. The great value of Rydberg' s form was that it enabled him to enunciate certain general rules and relationships between the different types of series, which have been of enormous assistance in further investigation. This form has been universally adopted as giving at least a first approximation to the form of the sequence function. These rules must now be considered. It is seen that Rydberg assumes for the sequence function< (m) = N/(m + /*) 2 . It is found in general that /x is either a fraction, or 1 -f fraction. Its real value, as calculated directly from the wave number of a line and the limit, is, however, not constant as assumed by Rydberg, but varies from line to line. We shall call it the mantissa of the line in question. As the wave numbers are, as a rule, given to seven significant figures, (m) is the difference of two such numbers * [vj. Phil. Mag. 38, 1 and 301 (1919); 39, 458 (1920). Other examples are also given in the Appendix. f It is convenient in writing to express these signs by reversed capitals, i.e. as seen in a mirror. 28 ANALYSIS OF SPECTRA [CH. and may therefore contain fewer in general six unless the order m is high. Consequently m + p contains seven digits and the mantissa six after the decimal point. These mantissae are of importance as forming the raw material on which a great part of the discussion in succeeding pages is based and from which the general structure of spectra and their dependence on the element are deduced. In dealing with them in general the decimal point will be dropped, or which comes to the same thing, they will be treated as multiplied by 10 6 . Rydberg expresses the limit in his sequence form, and writes A = N/(l 4- ft') 2 so that the wave number is _JL. N "ii + fiV (" + /*)*' He deduced his rules by the use of this formula. But as these rules are really independent of the form of <, it will be well to give them here in a more general- ised manner. They may be stated as follows: (1) N is the same for all series and all elements. (2) The Principal series in doublets are given by (!)-&() -*<) s (1) - Pl (m) = P 1 (m). (3) The Sharp series are given by p 2 (1) - s (m) = S 2 (m). (4) The Diffuse series are given by Pl (1) - d (m) = D l (m) p z (1) -d(m) = D 2 (m). (5) In his formulae the /z for s and p differ roughly by -5. We thus owe to Rydberg the conception of the dependence of the frequency of a line on the difference of pairs of sequences. Since S^ has a smaller wave number than S 2 , p 2 (1) > p x (1), consequently P x has a larger frequency than P 2 and lies on the violet side of P 2 . Rules 2, 3, 4 state that the limit of the principal series is the first s sequent and the limits of the sharp and diffuse are the first sequents of the two p sequences with similar rules for triplets. The wave number for the first line of the P l series is s (1) p l (1). In other words it is equal to the difference of the limits of the principal and sharp series, and also, if no regard be paid to sign, the first lines of the sharp and principal coincide. It is not possible to prove the truth of these statements from direct observation because the limit of any series is never visible, or perhaps we should say, its intensity is too weak to act on a photographic plate. In a given case the limit is found by fitting a formula to a few of the lines of lowest order. The value found will therefore vary with the form of the sequence function adopted. But it is remarkable how closely the limits agree when calculated from any functional ii] TYPES OP SERIES 29 form which reproduces the early lines with fair accuracy. In one case only, besides that of H 9 has it been found possible to settle a limit directly from obser- vation, viz. the P (oo ) or s (1) of sodium. This is possible on account of Wood's* measurements of the P series up to the 57th line, all within an accuracy of close on -001 A. With this high value of m the lines converge asymptotically to the limit so that it is possible to find the limit to the same degree of accuracy. This limiting value in international units for the two series is 41449-00. The wave number of P x (1) is 16973-34. Hence p (I) = 24475-66. We cannot find the limit of the S series directly in the same way. The value found as a formula constant is 24473-00 with an uncertainty 3-8 due to observation errors in the three lines used for its determination. In this case then the rule is verified with remarkable closeness. We postpone for the present evidence for and against the rigorous validity of these rules until the experimental data at disposal have been considered in the next chapter. They are, however, undoubtedly approxi- mately correct. 12. We are now in a position to deal with the fourth type of series before referred to. Saundersf had observed in the Cs spectrum a number of lines in the ultra- red, which he recognised as giving all the signs of belonging to a doublet series whose separation was of the order 96. Later Bergmannf working in Paschen's laboratory on the ultra-red portion of the spectra of the alkalies, observed not only these lines of Saunders, but a number of new lines in the other alkalies all showing the now well-known series appearance. Runge drew atten- tion to the fact that in Cs the separation of the first pair was equal to that of the satellite of the first D line, and expressed the opinion that it would be found to have a similar relation to the D series that the P has to the S, and that the doublet separations would be found to diminish with rising order as in the P. It was, however, left to Bitz|| to point out the true relation, viz. that the limit of the new series is the sequent d (1), or when satellites are present the limits are d (1), d 2 (1), .... From certain considerations Hicks was led to think that these new sequences had a more fundamental basis than the other series and used the symbol F to denote the series and f(m) the sequence. Funda- mental however, has no more to be said foi it than for Principal, Sharp and Diffuse, and in employing it, it must not be considered as more than a name, e.g. as standing for the fourth series. The series for potassium is shown in Fig. 6 . For the alkalies they lie wholly in the ultra-red. In elements of group II and the rare gases, however, they come into the visible region. They will be considered in detail later. The immediate point is, that a new series is found of the form d (1) /(m), so that at least four types of sequences exist. 13. These rules do not depend on the exactness of Rydberg's formula as representing the sequence function. This formula gives a rough approximation but leaves much to be desired in the accuracy with which any series is reproduced * See later, Chapter III, sect. 11. t Astro. J. 20, 188 (1004). 1 Z. 8. iviss. Phot. 6, 113 (1908); see Sr. Abstract*, 11, No. 015. Astro. J. 27, 158; Phys. Z. S. 9, 1 (1908). || Phys. Z. S. 9, 244. 30 ANALYSIS OF SPECTRA [OH. within even easily obtained observational exactness. Led by certain theoretical considerations, Ritz* proposed a modification of Rydberg's formula in one or other of the forms -r (2) * = ( *>" He tested these forms for the P and S series of He, the alkalies, Cu, Mg, Ca, Sr, Zn, Cd, Hg, Tl and except where, as in Ca and the elements of group II, the P series had not been observed, and for the D series of Tl. For the S series he takes m = order + -5, so that in his formula m has the series of values 1-5, 2-5, 3-5, etc. He found in general good agreement with a very great improvement on either of the old formulae. They involve three arbitrary constants requiring three lines of a series to determine them. The supposition that m enters as m + -5 in the general sequence is not sustained by observation and indeed is meaningless as applied to the second form. His notation for the various sequence terms has been used by a considerable number of investigators. Paschen has also employed a third. The three methods are illustrated in the following scheme. Ritz Paschen p l m m,p 1 ,ir 1 s (m) (m + -5, is expressible in the form N/{m + ' (w?)} 2 in which ' (m) diminishes to a constant value as m increases indefinitely. It should therefore be capable of expansion in powers of 1/w, or It is natural to take therefore as a first approximation /z + a/m, and see how nearly the formula reproduces observations. Both this and the formula /x + j8/w? 2 give on the whole good agreement, but the a/m is slightly better ||. It is moreover easier to calculate the constants in it and an important point there appears, as will be seen later, to be a definite relation between a and //, in at least the p sequence. This formula will be used therefore in general in this * Ann. d. PJiys. 12 264, (1903); (Euvres, p. 1. f Or mp, ... ifor doublets, and mP, ... for singlets. $ Ron. Akad. v. Wetens Amsterdam Proc. Dec. 21, 1906. Trans. Roy. Soc. A, 210, 57 (1909). || See e.g. [i. pp. 67, 68]. ii] TYPES OF SERIES 31 treatise. Ritz' second form gives the sequent value as the root of a cubic equation. Not only is it cumbrous, but the values given by it show little, if any, better agreement with observation than those by formulae in a/m or j3/m 2 . In his original memoir, Rydberg expressed the conviction that the wave number was expressible as a function of m + /x, with his formula as a first approxi- mation. If so the above second approximation should be m + /z + a/(m + //,) and since a is always small, a very slight adjustment would enable this to be written as a continued fraction, whence it is easy to see that cf> can be written in the form % or n = A - B {^(m 2 + ma + 6) - (m + a)} 2 . Similar considerations show that Ritz' second form is a close approximation to = N/{m + fi + j8/(m + /z) 2 } 2 . 14. The preceding considerations show that success in the analysis of spectra depends on the facility with which series can be detected and the sequence constants determined. This is greatly assisted by a table of the value of N/(m + fji) 2 due to Rydberg and published in his original memoir*. The table gives the values of N/(w, + /t) 2 from m = I to 9 and /z from -00 to -99 at intervals of -01. It also gives the differences between successive values of (f> (m) with the same //,. As this table is indispensable in the search for series it is reproduced in Table II f . If Rydberg's formula were exact this table would be directly applicable. But it is not, and it gives results with considerable errors when the order is small. When m is considerable (> 4, say) the calculated and observed agree fairly well. In searching for a series therefore with his table considerable latitude must be allowed when m= 1, 2, 3. The table is calculated for his earliest value of JV = 109721, but for the purposes for which it is used it is equally applicable to the international scale. If correct I.A. values are desired they can be obtained by deducting a correction found by moving the decimal point back four places and multiplying by 3-9. The method of using it may be illustrated by the following example from Na P l , using the measures of Wood and Fortrat in international units. 15. Let us suppose we have before us the observations of the whole sodium spectrum reduced to wave numbers in the manner indicated in Chapter I, but that the series lines have not yet been allocated. The P series is to show doublets converging with rising order and the P lines are always easily reversed. We notice two strong doublets with their higher frequencies at 16973-34 and 30272-87, reversed, of intensities 10 and 8, and with separations 17-18 and 547. They look like P lines. The difference of their wave numbers is 13299-53. Examining the columns of differences in Rydberg's table this is seen to lie between 13300 due * A similar table with the international 2V has been calculated by Del Campo and Catalan, Annies Soc. Expafi. de Fix/ctt // Qnhn.irti, \. \viii, lift (1920). I Another method has been proposed by Nicholson and Savidge, Phil. M4. -6512301 86-44 -9914832 279-96 5. -3256150 43-22 -4957416 139-98 6. 2-116483 3-131422 (ii 1116483 43-22 1146361 ^. 2a 2 ' 2262844 -4871 279-9(5 1141490 3tf 3 ' 3404334 966-78 4871 35042-66 6415-34 3-8072197 1-2329045 6164522 4-134778 236-74 45( 686-82 ^7-18. 31972) - '450-08' W ju = 1-146361 + 10-82x236-74 2561 "1-148922 a -1-116483 + 10-82x43-22 -,u 467 M16960 1-148922 - -031972 TO =41447-18 -N / \m+ 1-148922-' In the first column of six lines, (1) is the wave number, (2) is A n, (3) ]og(A-n), (4) \ogNI(A-n), (5) J log N/(A - n), (6) m + a m '. In 34 ANALYSIS OF SPECTRA [OH. dealing with a number of such calculations log N should be written on a separate paper and held over (3) while making the subtraction. But this is unnecessary to anyone accustomed to making these calculations as log N can easily be remembered in the reverse order, especially on the Rowland scale, when logN = 5-0401077, remembered as 77-01-0-40. In the second column of three lines, the first is the result of subtracting (3) from (5) in the preceding column. It is therefore log N^/(A rifi. The second line is N^/(A nfi, and the third is half this or b m f . Now in the principal sequence, as will be seen later, the mantissa is 1 + frac- tion. Hence the fji is of this form and the values of m are 1, 2, 3 and % = a/, a 2 = 2a 2 ', etc. The differencing is carried out beneath, and the constants follow at once by applying the general rule deduced above. If it is desired to treat the order as of the form m -f *5 the same method precisely applies. The example has been chosen for two reasons. First because it is one in which the simple Rydberg form distinctly fails, as is evidenced by the consider- able value of a. Secondly because this is, as already referred to, a series in which the actual limit can be determined in an asymptotic manner, since the lines are known up to m = 56 with an accuracy close to -001 A. It is thus possible to see how closely the limit calculated by the formula from the first three lines agrees with the true value. The lines for m = 54, 55, 56 will be omitted for a special reason (see Chapter III, sect. 11) as irregular, and the lines for m = 49 ... 54 employed. The order is now so large that a/m is negligible and a Rydberg's formula, N/(m + 1-148) 2 , will be sufficiently close. If the true limit is 41447-18 + f . the differences between the calculated and observed values for these m are | - 1-81, - 1-82, - 1-79, - 1-79, f - 1-83, f - 1-82, or a mean value of 1-81, which should vanish. Hence = 1-81 and the true limit is 41'448-99. It is remarkable how closely the limit is obtained by the use of the three first lines only. If the second, third, and fourth lines had been used for the calcula- tion, the limit found would have been 41448*45. 17. All proposed formulae with three constants fail to produce the first line in every case when the limit is correct. But the value of the constants will be inaccurate also on account of observation errors in the lines used for deter- mining them. For many purposes it is important to know how the constants will alter when the errors or limits of errors are known. For this purpose it is always desirable that observers should give estimates of their maximum possible errors, as Kayser and Runge have always done. The method of obtaining the changes in the constants due to given observation errors can best be exem- plified by a numerical example. Suppose in the case of Na P l just treated the maximum possible errors in A are -03 A. in each case, say -03p, where p lies between 1. The changes in n for the three first lines are then -f- -09^ , + '27p 2 , + '37^3 . Dropping the decimal point in the mantissa, the corresponding changes in the mantissae are 09^ x 43-22 = 3-9p l5 -27p 2 x 140 = 37-8p 2 , -37p 3 x 322 = 89-lp 3 , and the changes to be differenced will be 3-9ft , 75-6p 2 , 267-3p 3 . ii] TYPES OF SERIES 35 Hence 3 * 9 ^i ~ 151-2^2 + 267- 450 since is only determined to the second decimal place. The maximum varia- tion of the limit is therefore found by putting p 2 = p 3 = 1, i.e. dg = db '94 .or, say, 1. So also dfjL = 75-6p 2 - 3-9^ - 2369 = - 3-9^ + 154p 2 - 141/? 3 , The maximum uncertainties therefore due to observation errors, apart from formula errors, are 9f = 1 ; a/x = qp 299; da = 263, i.e., replacing the decimal point 9 = 1 ; dfji = =p -000299, . da = -000263. 18. It may be taken as certain that the sequences are of the form N/X 2 , where N is not necessarily a universal constant and where X depends on the order. In considering the behaviour of any series it is therefore the properties of X which are to be studied. These can be calculated when the limit is known. It is therefore a matter of prime importance to be able to determine this latter quantity with great exactness. We have seen how this can be done by their asymptotic convergence, when a large number of lines in the series exist. It is also possible when the allied summation system A + (m) is known. For if n and n denote lines of the same order in the two systems A = J (n + n), whilst the sequent is given by (m) |- (n n). If the sequence mantissae in X lt X 2 , X 3 , ... continually increase or con- tinually decrease, either of the formulae in a/m or j8/w 2 may, and in general approximately does, represent their magnitude. In certain cases, however, they first increase and afterwards diminish or vice versa, and it is clear that neither formula will suffice. A quadratic at least is required, i.e. a function of the form fji + a/m + j8/m 2 . This is the case, for instance, in the D series of calcium. The denominators are 1 1-992310 or n= -992310 2 3-082012 . 1-082012 3 4-089973 1-089973 4 5-078952 1-078952 5 6-048590 1-048590 6 6-968081 968081 Either the series is not of normal type*, or it cannot be represented by a formula of the type in a/m or j8/wi 2 alone. The march of these denominators may be completely altered by an error in the value of the limit from which they are calculated. With a given f , the change in X m is b m 'g and b m ' increases very rapidly with the order m. Consequently the high orders are affected by very large amounts for small values of whilst * We shall see later (Chapter ITT, sect. 27) that it is probably not normal, but that certain definite changes from a normal type have taken place. 32 36 ANALYSIS OF SPECTRA [OH. the changes in the first order may be almost negligible. Thus a positive f may change an ascending sequence into a descending one and vice versa. It is this great change in the high orders produced by a small which makes the condition of convergency to a limiting value so effective as a means of determining exact limits especially when the observation errors are not large. Many other functional forms of sequences . have been proposed*. Those,- however, in a/m and j8/m 2 are the simplest to use and are sufficient for the purpose of identifying series lines, which is one of their chief objects. If the constants involved in any form of sequence function can be shown to be definitely related to one another, or to be dependent on some physical property of the element, that actual functional form becomes of more importance. As will be seen, this appears to be the case in the form (f> (m) = m + /^ + a/m. Whatever form for such a function may be adopted, it must at least conform to one essential condition. All the evidence points to the fact that the different sequence types are independent. Any form therefore which makes one type depend on the value of another must be regarded as inadmissible. This objection would seem to apply to a form suggested by Lohuizenf in which the sequence is expressed in the form . , T/ , ... = Nj{m + JJL + a/A} 2 . Now A depends on the difference of two sequence types, say 10 8 /A = fa 2 . Hence 2 (m) = N/{m + ^ + j8 (^ 2 m )} 2 > or 2 is a function of m and (f> l . It should be noted that this objection does not apply to Ritz', at first sight similar, form in which (/> is given by (f> = N/{m + /z + a} 2 . 19. The series so far discussed are such that the wave numbers are given by the differences between the first .sequent of one type and the ordinal sequents of another, and indeed by the forms s (1) p (m), p (1) d (m), p (I) s (m), d(l) f(m). To Ritz J we owe a very important generalisation his theory of combination which states that lines may also exist which are differences of sequents of any order and any type. One part of his theory that the/ sequence is compounded of the two p doublet sequences in the way indicated by has not stood the test of experience, but his general theory is now well established. The observational material fully confirming the theory will be considered when the details for individual elements are discussed in the next chapter. It will be sufficient here to give a few of his own examples to illustrate the relation, although later and more accurate measures will be used. In the actual determination of the value of a sequence it is necessary to deduct the observed wave number from the limit, or to calculate it after the functional constants have been determined from three lines. Thus the value will depend not only on the observed error of the line from which (m) is determined, * See, for a more complete reference, Konen, Das Leuchten der Gase (1913). A later proposal by Johanson, Arkiv f. Matem. Astro, o Fysik. K. Svensk. Vetenskap. 12 (1917); see also Paulson, Kong.fysiog. Sails. Hand. N. F. 25. f Z. S. wiss. Phot. 11, 397 (1912). % Phys. Z. S. 9, 521; Astro. J. 28, 237 (1908); (Euvres, pp. 141, 163. ii] TYPES OF SERIES 37 but also on the error in the adopted limit which depends in an unknown way on the functional form adopted for the sequence and on the observational errors of three lines. In testing Kitz' theory, however, we can in general avoid all these errors even when we do not know the actual values of the sequences in- volved. Thus suppose the value s (m^ d (m 2 ) has to be found. It may be p (1) - d K) - {p (I) - s K)} = D K) - S (wj; or the difference of the wave numbers of two observed series lines, one .of order m 2 of a D series and the other of order m^ of a S series. From amongst the ex- amples given by Ritz, the following may be selected. In Li and Na lines with a wave number p (1) p^ (m), p 2 (I) p z ( m ) are found, although they are in general very diffuse. E.g. in Li, in which the doublet separation is practically zero, or p l =* p 2 , p (1) - p (m) = P (m) - P (1). P (1) is A = 6708-06 oin = 14904-69. m 2 P(m) 30924-61 P(TO)-P(1) 16019-92 X(calc.) 6240-5 X (obs.) 6240-8 3 36467-33 21562-64 4636-4 4636-3 4 39011-45 24106-76 4147-0 4148-2* 5 40390-00 25485-31 3922-8 3921-8 * very diffuse. Again, the set p t (2) s (m)', p 2 (2) s (m): p (2) - 6- (m) --p(2)-s (1) + * (1) -p(l) + p(l)- 8 (m) - P (2) + P (1) + S (m) = X (m), say. In Na, P l (1) = 16973-34, P (2) = 30272-87. P 1 (1) - P x (2) = - 13299-53. P 2 (1) - 16956-16, P 2 (2) = 30267-38. P 2 (1) - P 2 (2) = - 13311-22. #! (TO) ^i () tf. (m) *, (m) X (calc.) X(obs.) \ 8766-69 :2 \ 8783-48 - 4532-84 -4527-74 22056-2 22080-7 22056-9 22084-2 -f 16226-87 m - 3 \16244-09 2927-34 2932-87 34152 34088 34203 34165 These are all in the ultra-red and observed by Paschen. The differences between observed and calculated are within observation errors in this region. The type s (1) - d (m) = + P (1) + D (m), or - S (I) + D (m), may be illustrated from the spectrum of He. Here P (1) is A = 10830-51 or n - 9230-76. D (2) is A 5875-870 or n = 17014-13. The combination is therefore 26244-89 or A = 3809-20, which is the value of an observed line. The fact that these new lines appear with frequencies which are the differ- ences of the frequencies of other lines led Mogendorff* to propose the hypothesis of the existence in light of a phenomenon analogous to that of difference and * Kon. Akad. v. Wetens. Amsterdam (1911). 38 ANALYSIS OF SPECTEA [OH. summation tones in sound, pointing out that they occur only when the sequences in question belong to the strongest lines. The actual frequency differences, however, adduced by him reduce to the difference of two ordinary sequents. For instance the series of lines P (m) P (1) is called by him the first differential series (X (m), say) with lines for m = 2, 3, . . . . With these other differential series X (m) D (n), X (m) S (n) are found. These, however, are respectively X (m) ~D(n) = p(l)-p (m) - (p (1) - d (n)) = d (n) - p (m); X (m) -S(n) = p(l)-p (m) - (p (1) - s (n)) = s (n) - p (m). They reduce therefore to the ordinary Eitz combinations. As examples of summation lines he gives F (m) + D (1); but again this is d (1) -/(m) + p(l)-d(l) = p (1) -/(). A case in point would have been F (m) + D (2) = d (1) - d (2) + p (1) -/(m') but no such line is observed. The examples given by Mogendorff therefore are not relevant. We shall, however, find evidence later in considering spark spectra for phenomena which have some analogy with his theory. 20. The series systems are fully developed in the first three groups and the group VI of the elements. If, as is probable, they exist in the other elements, they have not yet been assigned, although in late years some further progress has been made. Other regularities, however, have been brought to light, to which Eydberg has given the name of spectra of type II. They are distinguished by the presence of systems of lines with sets of constant separations, pointing to a functional relation of the kind A + < (m) + x (n), where m and n are two independent sets of ordinal numbers, but < and x are apparently not of the ordinary series sequence form. They will be considered more fully in Chapter XI. It will be sufficient here to indicate their nature. They were first found by Kayser and Eunge * in the spectra of Sn, Pb, As, Sb, Bi. Later also Eydbergf 'brought to light similar relations in Cu and still more complicated ones in the red spectrum of argon. Again the relation is found between wave numbers or frequencies. The following table from Kayser and Eunge' s work shows the relation as ex- hibited in the spectrum of tin. The first column gives the wave lengths of certain lines in the spectrum. If 5187-03 be added to their wave numbers and the corresponding wave lengths calculated, a new set of observed lines is found. They are given in the second column, with the correction required to reduce the calculated to the observed. The third column gives a similar result when 6923-26 is added to the wave number of the corresponding first column, or 1736-23 to that of the second column. The C differences are all within observation errors. * Abh. Berl. Akad. (1894); Ann. d. Phys. 52, 93 (1894). t Astro. J. 6, 239, 338 (1897). n] TYPES OF SERIES 39 3801-16 3175-13 --01 3009-24 + -00 3330-71 2840-05 + -01 2706-59 + -02 2850-72 2483-49 + -01 2380-83 - -01 2813-66 2455-32 - -02 2354-93 + -01 2785- 14 2433-57 - -04 2334-93 - -04 2779-92 2429-59 - -01 2594-49 2286-75 + -04 2199-42 + -04 2571-67 2269-00 + -03 2524-05 2231-85 --05 2148-59 + -11 2495-80 2209-73 + -05 2408-27 2140-84 + -26 2064-12 --32 2358-05 2101-06 --16 2317-32 2068-67 + -03 The nature of the relationship is perhaps best illustrated diagrammatically. The spectrum may be considered as built up, by a certain grouping of lines, arranged on a wave number scale, which is then pushed towards the violet, by definite amounts. Fig. 9 is reproduced from Kayser and Runge's paper. It Li Fig. 9 illustrates the spectrum of antimony, in which five such displacements were observed. It should be noticed, however, that the first line is not repeated after the first shift. The following is taken from Rydberg's paper and gives the wave numbers of argon lines which show this effect. The separations are in thick type. The columns of separations give the difference between the lines of the next column and the first, and the rows of separations those between the next row and the top row. 21265-27 846-94 22112-21 1649-64 22914-91 2256-79 23522-06 339-43 339-56 339-50 21604-70 ... 1649-77 23254-47 2256-86 23861-56 491-81 491-31 491-66 491-53 " 21757-08 846-44 22603-52 1649-49 23406-57 2256-51 24013-59 524-07 523-92 52379 21789-34 ... 1649-49 23438-83 2256-51 24045-85 903-50 903-49 22168-77 ... 1649-63 23818-40 1747-98 1747-52 1748-05 23013-25 846-48 23859-73 1649-71 24662-96 1800-17 1799-78 1800-69 1800-12 23065-44 846-55 23911-99 1650-16 24715-60 2256-74 25322-18 1809-63 180906 1809-63 1809-50 23074-90 846-37 23921-27 1649-64 24724-54 2256-66 25331-56 2211-71 2211-92 23476-98 1649-85 25126-83 CHAPTER III THE SERIES SYSTEMS THE mass of material, in the way of measured lines, at disposal for the study of the constitution of spectra, and of relationships between the lines of the same spectrum is immense. The larger proportion of this still remains practically untouched so far as any analysis has been attempted. It is only in the first four (0 ... Ill) and in the sixth of the periodic groups of elements that series have, as yet, been recognised and a beginning of any analysis made possible. In a few elements repetitions of sets of lines Rydberg's type II have been found. In others nothing is known beyond the discovery of sets of constant frequency differences, chiefly by Paulson*. The present chapter will be devoted to giving a general survey of these preliminary results. Complete data for wave lengths and wave numbers are given in Table III. 1. It is found that in elements belonging to an odd numbered group, doublet systems seem to be the rule whilst in those of even numbers, triplets appear as predominant, accompanied also by doublet and singlet systems. In each sub-group of the same family the spectra are built on very similar lines while the two sub-groups those of high and of low melting point show rough analogies with one another. With the exception of He, Li, (groups 0, I, VI) the first element of each group possesses few lines, amongst which no series relations have been found. In each group the complexity of the spectrum increases with the atomic weight and in these cases the arrangement of a series often appears upset as if a break up of a normal configuration has taken place. Frequently also signs are present of more than one system of series of a given type. Hydrogen. 2. In hydrogen, six spectra at least have been recognised. (a) That already referred to as containing the Balmer series, and named the first line spectrum. The lines of this spectrum are enhanced in the condensed discharge. It consists of comparatively few lines. (6) The second or many-lined spectrum given with low excitation and weakened or vanishing with the condensed discharge. (c) A line spectrum in the extreme ultra-violet stretching from about 1670 to at least 900. All the Hues with the exception of a few are weakened by the condensed discharge. It is sometimes called the Schumann spectrum. (d) A spectrum also in the extreme ultra-violet consisting of a few lines, enhanced by the condensed discharge. * Mostly collected in Beitrdge zur Kenntnis der Linienspektren, KongL fysiogr. Sallskapets Handl. N. F. Bd. 25, Nr. 12. *CH. HI] THE SERIES SYSTEMS 41 (e) A continuous spectrum stretching from about 3668 towards the ultra- violet. (/) A continuous spectrum in the extreme ultra-violet. Band spectra have also been suspected, but the evidence is not conclusive a portion of the second hue spectrum may contain band systems. It is possible if not probable that (6), (c) form portions of a single spectrum. They are separated by a gap from 2483 to 1675 in which no lines appear, but they behave in a similar manner under changing circumstances and their wide extent with a sparse region between has some analogy with the spectra of the rare gases. In the case of (a) and (d) there is definite evidence that they belong to a single system. It is therefore probable that there are two distinct spectra stretching into the extreme violet, but this will not exclude the possibility that the lines observed in the many-lined systems (6), (c) may not be a mixture of spectra of different origins i.e. due to different configurations or different excitations in the hydrogen atoms or molecules. The first and second spectra of hydrogen have some analogy respectively with the spark and the arc spectra of metals. In hydrogen and the rare gases, however, the spectra enhanced by the condenser, or those produced by canal rays, give much simpler series relations and will be considered here, although this chapter deals chiefly with the arc or low potential spectra of the other ele- ments. In the second line spectrum of hydrogen no series have yet been dis- covered, although their existence may be expected. 3. The first H spectrum is distinguished by four strong lines in the visible region, in the red, green, blue, and violet, and two in the ultra-violet. These are produced by ordinary laboratory methods. In addition a large number have been observed in the spectra of white stars*, and a much larger number in the spectrum of protuberances at solar eclipses. Evershedf and DysonJ have measured up to an order m = 31 and Mitchell more recently up to m = 37. Wood 1 1 has been able to obtain the orders up to m = 20 in the laboratory. The failure of preceding investigators was due to the intensity of the continuous spectrum and to the secondary spectrum being comparable with, or greater than, that of the Balmer lines. By using long tubes with suitably adjusted conditions he succeeded in suppressing the two former whilst at the same time increasing the actual strength of the latter. These lines have been designated by the symbols H a , Hp, H y , ... up to the limit of the Greek alphabet and thereafter by numbers. It is better to adopt numerical values throughout denoting them as HD (m) starting with Ha as HD (3). The designation of the series as of the diffuse type should not, however, be considered as established. Curtis [[ has given special attention to securing * Muggins, Proc. Roy. Soc. 25, 445 (1876); Trans. Roy. Soc. 171 (2), 669 (1880); Vogel, Bcrl. Ber. (1880) 192. f Trans. Roy. Soc. 197 A, 381 (1901); 201 A, 457 (1903). J Proc. Roy. Soc. 68, 33 (1901); Trans. Roy. Soc. 206 A, 403 (190G). Astro. J. 38, 407 (1913). || Proc. Roy. Soc. 97 A, 455 (1920). If Proc. Roy. Soc. 90 A, 605 (1914); see also ib. 96 A, 147 (1919). 42 ANALYSIS OF SPECTRA [cn. f accuracy in the measurement of the six lines appearing in the vacuum tube, using the latest standards. He has thus been able to show that Balmer's formula, although reproducing the lines with very great accuracy, is not, however, exact. For if so, the value of N calculated from the expression 10 8 /A =N(- 1/m 2 ) must be the same within the limits of observational error. The values of N found decrease with the order of the line from 109679-09* to 109678-72, the probable error in no case exceeding -04. He calculates a Rydberg formula on the supposi- tion that the limit is 2V/4, by the method of least squares and finds -j - (4 (m + / where //, = -0000069 and N = 109678-67 in i.A.- 1 . It is interesting to note that this gives for the Rowland scale N = 109675-0 or the final number calculated by Rydberg. The following table taken from Curtis' paper shows how closely the observed and calculated values agree. m O-C m 0-C m O-C m 0-C C. D. D. D 9 --01 19 -03 29 -03 3 -0001 10 -01 20 --03 30 --05 4 --0006 11 -01 21 - -01 31 01 5 -0009 12 -03 22 -04 M. 6 -0004 13 -01 23 -00 32 -05 7 -0002 14 --03 24 -01 33 8 --0006 15 -01 25 --03 34 -02 16 -01 26 -07 35 -12 17 . -00 27 --03 36 --01 18 -00 28 --04 37 --01 In the first column the calculated lines are compared with Curtis' very accurate laboratory measures. In the other columns under D. the measures of Dyson and under M. those of Mitchell are taken for comparison. The observation errors of the two latter are naturally considerably larger and the variations shown in the table are certainly within them. The values extrapolated from the series for m 2 and m = 1 would be of the order 5 cm. and 1215-65 LA." 1 in vacuo. Lyman has found that the latter appears in the extreme ultra-violet at 1216 of great intensity (8) broadened and intensified by the disruptive discharge. The first two lines H a ,Hp, each consist of two close companions. Michelsonf, in 1892, found dX = -14 and -08 for the two. For the first, Fabry and Buissonf give '132, Meissner and Paschen, -124. Gehrcke and Lau||, -126, -058, for the first and second. Michelson's measures give a separation of wave numbers of 32 for the first three lines and thereby indicate a doublet series of the associated type. The intensity ratio of the two possibly depends on the excitation. Michel- son gives the red companion as the stronger in the ratio 10:7. Fabry and Buisson also make this the stronger. * Corrected from Curtis' values for an error in reduction to vacuo. t Phil Mag. 34, 280 (1892). % C.R. 154, 1500 (1912). Ann. d. Phys. 50, 901 (1916). || Phys. Z. S. 21, 634 (1920). m] THE SERIES SYSTEMS 43 Merton*, by using He as an impurity and observing at the temperature of liquid air, has obtained the first line with great sharpness and has been able to measure the difference of the two components with great exactness as dX = -145 with intensities 10 : 4-6. For the second line dX = -093. These give separations -336, -392, the same within errors, and the same as Michelson's. This series has generally been regarded as of the diffuse type, partly because the lines are themselves diffuse. The Zeeman effect here gives no evidence. The Stark effect shows that the lines behave in a similar way to those of the D in He, Li. This would seem to exclude their being of S or P type. The duplicity of the lines might be regarded as due to the satellite effect, but this is negatived by the constant separation in the orders indicated by Michelson's and Merton' s measures and by the fact that the red component is the stronger. Moreover, if -33 is a satellite separation for the order m = 3 we should expect a satellite on the violet side of 1216 (m = 1) with a separation of about 11 (dX = -16) and sufficiently intense to have been observed. It would seem natural therefore to regard them as typical doublets, but there are important theoretical considera- tionsf which explain them on other grounds. It may indeed be a question whether these enhanced lines depending on formulae of the exact Balmer type have any connection with S and P sequences, but are not rather of the form of F, i.e. n = d(l)-f(m). Using, however, the usual assumption that they are D lines, the sequences are in which /x, is very small, about -000007, according to Curtis. Paschen has also observed two lines in the ultra-red at AA 18751-3 and 12817-6 R. A. If we consider p (m) as N/m 2 these are the combinations p (3) p (4) and p (3) p (5). If the series is of the diffuse type, a sharp series should be expected with the same limit and of the form 1 1 ) No such series has been observed (see, however, below under He). This again would point to the series being really of the F type. From analogy with the other elements in which the frequency depends on formulae of the type N/(l + /*) 2 N/(m + /z') 2 and /x is a fraction or 1 + fraction with the fraction small or near -5 when the element is of low atomic weight, H might be expected to follow a similar rule with the fraction practically negligible. In other words the series would be C>> 2V I 1 (5) (I 2 (W+-5) 2 }- 'l2 2 ~(m+-5)< < 3 > Hw-i * Proc. Roy. Soc. 97 A, 307 (1920). t The extremely interesting theoretical considerations by Bohr, Soininerfeld, and Epstein do not come within the scope of this volume. 44 ANALYSIS OF SPECTRA [OH. Of these the fourth gives the first line spectrum, and the fifth has not been found. The first and second would he in the extreme ultra-violet. The first gives lines at 1215-7, 1025-7, 972-5, 911-8. The line 1216 is also the first given by the recognised H spectrum formula as explained above. The others are beyond Lyman's measurements, his shortest being a weak line at 1030-8. Saunders*, however, has found 1026. It ought to be a strong line and its actual existence is therefore of special importance for 1216 is not sufficient of itself to establish the existence of a series p (1) p (m). Formula (2) gives lines at 1641-20, 1085. Lyman gives several lines of medium intensity about 1641 forming parts of definite groups but not enhanced by the spark, although one at 1650 indicated such a behaviour. There is no line at 1085. The first line of the third formula agrees with that of the* second and the succeeding are 4687, 2735, which have not been observed. So far, therefore, as any evidence is attainable, the "first line spectrum" of H consists of a single doublet series. The second spectrum of hydrogen is very rich in lines. It enters in the vacuum tube at small pressure and weak discharge. With strong discharge it fades out although according to Hasselberg it can enter with heavy discharges at pressures as high as 22 mm. It shows itself most strongly in the neighbourhood of the cathode. For long it was questioned whether it belonged to hydrogen, but the matter may be considered settled in the affirmative by Dufourf . Ac- cording to him the magnetic field does not affect the greater number of the lines, but in certain cases the Zeeman patterns allow them to be arranged in related groups. Merton { has found that if the discharge is taken when a large quantity of helium is mixed with the hydrogen the relative intensities of the lines are completely altered, some being extremely weak, whilst others are greatly en- hanced and a number of new lines appear. No series have as yet been allocated, but they probably exist and Dufour's observations on the effect of the magnetic field and those of Merton referred to should help to their discovery. Fabry and Buisson have shown, by measuring the order of interference as depending on temperature effects (Chapter I, sect. 8), that the source of many of the lines in this spectrum is to be found in the atom of hydrogen. Helium. 4. The spectra of the rare gases, helium excepted, are extremely rich in lines. A, Kr, X give two distinct spectra, one with a condensed discharge, the other without. Neon is noticeable for the sharpness and homogeneity of its lines. With the exception of helium and neon they all show triplet systems, but their full discussion requires a knowledge of laws to be developed later. It will therefore be deferred and helium alone be considered here in detail. This is also the less undesirable since the spectrum of helium seems to show little or no analogy with those of the other rare gases. Four apparently independent spectral systems of helium have been observed. * Astro. J. 40, 377 (1914). f Ann. Chim. et Phys. 9, 361 (1906). % Proc. Roy. Soc. 95, 30 (1919). C.R. 154, 1500 (1912). m] THE SERIES SYSTEMS 45 (1) The spectra known from the date of the first discovery of the element. (2) A spectrum corresponding to the enhanced type and requiring a higher potential difference for its development. (3) A far ultra-violet spectrum observed by Lyman. (4) A spectrum analogous to the band type. We consider these in the above order. The first spectrum has been measured with great accuracy by Runge and Paschen* between 7281 and 2644 and in the ultra-red by Paschenf. A number of lines have also been measured by interferometer methods; they are collected in Table IIIJ. Runge and Paschen found that all the lines could be arranged in two sets of apparently principal, sharp, and diffuse series. Of these one consisted of single line series, the other of doublets in which the S and D separa- tions remained constant and equal to 1-007 for all orders, whilst in the P that of the first order only which was in the ultra-red was seen to be double, with separation = 1-02 the same within observation errors as that of the others. The absence of observed duplicity in the other orders points to the decrease of separation with order which is the distinguishing feature of a P series. In the doublets the weaker constituent is on the red side in opposition to the ordinary type. It is also remarkable that while the stronger components diminish in intensity in the usual way with increasing order, the weak ones remain of about the same intensity for seven orders in S and eight in D, until both become so weak that they appear as one. It might almost be suspected that in the orders where only one line is seen it is the weak companion which survives but the agreement between the calculated and observed values shows that this is not the case. At first it was thought that two complete series systems pointed to the existence of a mixture of two different elements and the name Helium was given to that producing the doublets and Parhelium to the other. Although this supposition is now known to be wrong the names are still sometimes used as a convenience to distinguish between the two sets. Runge and Paschen' s measures are given as subject to probable errors in the neighbourhood of -005 A., but this is possibly exaggerated as it involves the correctness of the old Rowland standards as well as observation errors. The accuracy, however, is so good and the number of lines observed in each series so large, that they afford good material for the testing of Rydberg's rules. Neither formulae in ]8/m 2 nor in a/m give sufficiently close agreement with observation if Rydberg's value of N be adopted. For this reason Hicks [i. p. 102] * Astro. J. 3, 4 (1896). t Ann - &. Phys. 27, 552 (1908). J It may be well here to draw attention to an effect which frequently occurs and which may be of assistance in dealing with the analysis of spectra. The measures given in the table of inter- ferometer measures by several observers are supposed to be correct within one or two thousandths of a unit. If, however, the numbers be compared it will be seen that the differences between Eversheim's values and those of Merrill and Lord Rayleigh are very considerable in four cases. It will be seen also that these cases occur on all the S" and D" lines common to them. The differences are too large to be ascribed to observation errors; they are probably due to a shift on these types of lines produced by the nature of the excitation used in producing them. When such a large difference is noted in a restricted set of lines, it may be inferred as highly probable that they belong to related systems, as is the case here. 46 ANALYSIS OF SPECTRA [CH. applied the method of least squares to all the lines except S' (2) and S" (2), each weighted with its supposed probable error, and determined the best value of N to use for each series. The agreement between observed and calculated values was now good, but each series required its special value of N. Since then, however, a considerable number of lines have been measured by interferometer methods by Merrill which include from three to five in each series and thus give the means of determining constants with great accuracy. The P and the S series have each three of these measures but both P have one far ultra-red line measured by Paschen with considerable accuracy and his possible errors will have an inappreciable effect on the values of the constants obtained. We may therefore consider that the two P and D series have four lines each measured with great accuracy and the two S series have three each. The four constants Emit, N, fj,, a can thus be calculated directly and the N, p, a for the S by assuming S (oo ) = D (oo ). The results in i.A." 1 are, giving only the stronger lines for the doublet sets, P', n = 32033-783 - 109783-4/{w + 1-013933 -.-004038/m} 2 S f , n = 27175-711 - 109764-3/{w + -862935 - -011510/m} 2 D', n = 27175-711 - 109714-5/{m + -997623 + -001031/w} 2 P", n = 38454-198 - 109651-61/{w + -929148 + -007916/w} 2 S", n = 29223-788 - 109795-l/{m + -707590 - -017465/m} 2 D", n = 29223-788 - 109707-5/{m + -996566 + -002124/w} 2 . For the weaker component in He" the limits for S, D are 1-007 less and the mantissa of the p sequence is 33 larger. D" (6) is the only interferential measure at disposal wherewith to test the calculated. They agree within -001, an error comparable with calculation uncertainties when 7-figure logarithms are used. It is difficult to institute a comparison with Runge and Paschen' s measures for higher orders, as their relation to the international units is not known with sufficient accuracy. With the least square method, however, applied directly to their lines the agreement was found to be very close for all orders*. It will be noticed that the sequences for both the D series are very nearly the same. If they are accurately the same the two series must form two parallel sets in which the separations of corresponding orders must be the same. But this is not the case. The differences as found from the interferometer measures for the first four orders are 2044-699, 2046-094, 2046-98o, 2047-414. These are accurate to a few units in the last digit, and indicate values gradually increasing to about 2047-7 in a systematic way. The two limits calculated in the formulae above do as a fact differ by 2048-07. With a common value of N = 109710 for the two D series, and allowing 2047-9 for the difference of their limits, the two ^-sequences are such that the d" have mantissae less than those of the d' by 401 for the first order and equal amounts = 550 for the other three orders. This is a common effect in D series showing satellites. In fact if the wave numbers of D' were increased by 2047-9, they would, with D", form a typical diffuse set * For numerical values of - C, see [i. p. 102]. The formulae are given in Table IV. m] THE SERIES SYSTEMS 47 with satellites in which the new lines would appear as a D n set, the weak D" as D 12 > an d the strong as D 22 . The satellite separation would, however, be quite anomalous being three times that of the doublet. There are analogies of this in the other rare gases. The wave numbers for the first set would be D 12 (1) 17013-14, D 2 (10) 17014-13, [Z> n (6) 17017-55.] This explanation the suppression of the D n line would explain the fact that in D" the weaker line is on the red side of the doublet. It would not, however, explain the similar effect in S". The combination p f d" would give satellites on the violet side of D'. They have probably been observed in the magnetic and electric field see Chapter V. 5. In the preceding statement the allocation of the lines to two distinct systems of P, S, D series made by Runge and Faschen, the first observers, has been employed. If, however, the formulae are compared an essential difference in form between those of the P' and P" will be noted, while the two d sequents as has been seen are practically the same. It will be found later that a negative a is a distinguishing feature of p, s sequences whilst a positive a is universal for / and typical for normal d. These reasons led Hicks* to suggest that the P" series depends on the/ or d sequence and that the complete system would be represented by the scheme He' He" ' s' (1) -p' (m) s" (1) -/ 2 (m), s" (I) -/! (m) p' (l)-s' (m) A (1) -s" (m), f z (I) -s" (m) p' (1) -^ (m) /! (l)-d t (m), f 2 (l)-d 2 (m) EA<1) -*,<)}, where at present, however, there is nothing to show whether the d and /"should not be interchanged. The objection to regarding the P" as a real p series is supported by the following additional facts. (1) If the values of N obtained by the formulae be compared it is seen that those for p', s', s" are about the same and correspond to that which other evidence shows is typical of p sequences. The D', D" also take equal values, smaller than that of the P'. On the other hand that for P" is distinctly different from the others and close to Rydberg's value. (2) A comparison of the JJL'S in p f , .s', s" shows values decreasing by very nearly the same amount 151. There is apparently no such connection with the fM of p". 4 (3) In the electric field the P" lines are all displaced to the red, whilst those of the P' are shifted to the violet. On the other hand, the $', /S" both shift to the red. The important fact here is that P', P" behave in different ways. The D', D" split up into several components in consonance with the typical Stark effect in the D. Here the D f also show the presence of a satellite and the satellite and main line appear to influence each other's Stark patterns. Taka- * [i. p. 105] 48 ANALYSIS OF SPECTRA [OH. mine has observed a third satellite in He D" (4), on the violet side as would be indicated by the suggested Z) n set above. But he also finds two satellites on the violet side in D' (3), which can have no relation to this set. In the magnetic field close components are thought to influence each other's patterns, and if so no evidence is obtainable under this head. The pattern for the P f is a triplet, a typical form for singlet series. None have been studied for P" lines. (4) The combination lines p" (1) p" (m) are shifted to the red and en- hanced by the electric field. The argument from this is given later under lithium (sect. 16). (5) The Zeeman effect (see Chapter V, sect. 9). Until the true nature of the sequent is definitely settled, it would only cause unnecessary confusion to depart from Runge and Paschen's original allocation. Consequently the notation proper for this will be used throughout. 6. In connection with this spectrum a very considerable number of com- bination lines have been observed, one of which (A = 3809) was given by Ritz as an example in his original paper on combination lines. The majority require the presence of a strong electric field to bring them out, and they are shifted to the red by it. The discovery of these is due to Stark and his pupils. They correspond to the combinations s (1) d (m), s (1) s (m), p (1) p (m) in both the He' and He" systems. It may be interesting to note that those lines require the strongest electric fields which correspond to the last two types involving the same sequence in both terms. In these the line f or m = 1 has infinite wave length or zero frequency. We might suspect that these correspond to instability and that the configurations necessary for their existence cannot subsist unless they are rendered stable by the previous imposition of an electric field of at least 10,000 to 20,000 volts per cm. The wave lengths of these com- binations are given in the helium table, together with references. In addition to these, other combination lines had previously been observed by Paschen in the ultra-red. They were allocated by him to p (2) d (3), d(2). /(4), d (2) /(5) in 'each set. The first is quite clearly correct but a difficulty occurs with the others. Thus p (2) -d (3) =p (1) -d (3) +s (1) -p (1) - ( 8 (1) -p (2)) =D (3) +P (1) -P (2). For He' w = 20310-98+ 4857-30 -1 - 19931-81 = 5236-47-l. Observed 5236-78 -4 He" w = 22356-97+9230-76-12 -25707-82 = 5879-91 -12. 5879-64-33 the same in both instances within error limits. The other lines are in i.A.- 1 , nn=(2) 5348-03 -6; (3) -5350-89 3; (8) 7815-14 1-2; (1) 7820-15 6. He applies Ritz' erroneous theory to the constitution of the / sequence and deduces /' (m) = N/m 2 ; f" (m) = N/(m - -00003) 2 . It would seem better to take/(m) = N/m 2 for both systems, i.e.. take/(m) to be a sequence in the enhanced set to be considered immediately. In determining the values of d (2) /(w), we require the value of the D limit and so introduce an extra uncertainty, but any error here will be very small. The uncertainty in the value of N is more serious. Then in i.A." 1 m] THE SERIES SYSTEMS 49 d' (2) = 27175-711 - 14970-075 = 12205-636 d" (2) = 29223-788 - 17014-775 = 12209-013. Whence the calculated values, with N = 109679 and N = 109720, in ft ^ N /M = *. are 109679 109720 He' 5350-77; 7817-49 5348-14; 7816-84 He" 5354-15; 7821-87 5351-51; 7820-21 It is thus clear (1) that the allocation can only be sustained by using a value of N much closer to that determined by the formulae of sect. 4 than the old Rydberg value deduced for H, (2) that with a value near this the agreement between observed and calculated is good except in the case of the line 7815-14. Now this has a much larger intensity than any of the others, whereas the corre- sponding combination should be of less intensity than 5348. It is therefore probably not d' (2) /(5). But it is very close to d* (2) - d" (4) = D" (4) - D" (2) = 24830-39 - 17014-77 = 7815-62 where no uncertainties as to limit or N enter. It is, however, curious that what should be expected to be a more intense combination d" (2) d" (3) = 5342-94 does not seem to have been seen. They are entered in the Table as d f with a query for the last. 7. Enhanced series. In 1896 Pickering* observed in the spectrum of the star Puppis a set of lines showing relations analogous to those of the known hydrogen series. It was ascribed by him to hydrogen and later Rydberg f suggested that it was a sharp series corresponding to Balmer's as a principal. The lines were closely represented by the formula n = N {1/2 2 - l/(m + -5) 2 }. None, however, were produced by ordinary laboratory methods. Some years later Fowler J succeeded in obtaining a considerable number of new lines, one of which could represent the first of the Pickering and the others formed a new series. They were obtained with the condensed discharge at the commencement of the glow in vacuum tubes containing both H and He. They were at first arranged by him as two independent series involving Rydberg's N. Led by his theory as to the origin of spectra, Bohr had predicted the existence of spectra in He analogous to those in H but involving 4N in place of N. Later this was modified by taking account of the mass of the nucleus with the result that N should be taken as N/(l + m/M), where N is an absolute constant and m, M the masses, respectively, of the electron and nucleus. In H, m/M = 1/1850, whence the constant N* = (1 + 1/1850) x 109679 in i.A.- 1 = 109738. From this, N for He should be close to 109723. With this the new series was found to be very closely represented by 42V (1/4 2 1/m 2 ). It in fact suggested a method * Astro. J. 4, 233 (1896); 5, 92 (1897). t Astro. J. 7, 233 (1899). I Monthly Notices Roy. Astro. Soc. 73, 62 (1912). H. A. s. 4 50 ANALYSIS OF SPECTKA [CH. for the determination of the important quantity m/M, by finding the value of N from the formulae and the observed first lines in the analogous series in H and He*. As the actual series had been observed by Fowler in a mixture of H and He, it was obviously important to determine to which element they were due. It was definitely shown by Evansf by the use of pure He tubes that the line belonged to He. At the same time also he discovered other lines, three of which corresponded to Pickering lines. Observations by Starkf and Rau also indicated that the first line 4686 at least was due to He. Fowler's measures for the first series (4686) and Evans' for the second that containing the Pickering are given in the table. A comparison of the latter with the Pickering shows that the Pickering is composed only of the odd m lines. This absence of the even m lines would suggest that the Pickering lines were not due to He. But such even order lines would occur close to the H lines which appear in the same spectra, and might be overshadowed by these diffuse lines. Quite recently this has been tested by Messrs Plaskett|| in the case of two stars of this type. The even order Pickering lines were definitely located and measured as separate from the H lines. Fowler also, in the same paper, succeeded in observing another enhanced series depending on the strong line 4686 and represented by the formula 42V T /{l/3 2 - 1/m 2 } 2 , the line 4686 corresponding to m = 4. Lyman^f has also observed the line corresponding to m = 2 at 1640-2. This may also be considered as the first line of a series 42V/{l/2 2 1/m 2 }. Hicks** has suggested a completion of this series up to m = 8 out of lines observed by Lyman. But the latter ff has criticised the allocation on the grounds that these lines are not really He lines. They are given in the table with a warning as to their reality. The C are alternately + and suggesting a difference between odd and even terms similar to that in the series 4#/{l/4 2 - 1/m 2 } 2 . 8. The structure of these enhanced lines has recently become of importance through the extension of Bohr's theory of their origin by Sommerfeld JJ. This requires that each of the lines involved should consist of a group of close com- ponents whose separations can be calculated from the theory. To test this theory Paschen undertook a close investigation with high resolving power. He * Later this formula was modified to allow for the increased effective inertia of the moving field of the electron to 4 where a = 2ire 2 /hc, h = Planck's constant, and c= velocity of light. The theory has been further extended by Sommerfeld, Epstein and others to account for multiple lines, Stark effect, etc. This extraordinarily interesting and suggestive theory does not come within the scope of our present purpose, but its suggestions have, as is seen here, helped in the analysis of the spectra of H and He. t Nature, 92, 5 (1913); Phil. Mag. 29, 284 (1915). j Verh. d. DeuUch. Phys. Ges. 16, 468 (1914). Sitz. d. Phys. Med. Ges. Wurzburg (1914), reference taken from Stark. II Nature, 108, 209 (1921). ^ Nature, 104, 314 (1919). ** /&., p. 398. tf #> P- 565. {% Ann. d. Phys. 51, 1 (1916). Ib. 50, 901 (1916). in] THE SERIES SYSTEMS 51 fortunately discovered that the lines were produced with great intensity if the cathode were in the form of a tube or box with open ends. In this case the glow appeared in the inside of the box. The gas pressure was from -5 to 1 mm. and in general the excitation was that due to a continuous current at 1000 volts, though for the observation of the line 4686, the spark was also used with spark- gap and condenser. The result was the discovery of a large number of components in general agreement with the theory. By supposing that the breadth of the images of these components covered some of the weaker lines, he came to the conclusion that his observations could completely establish the numerical results of Sommerf eld's theory. In the tables at the end Paschen's measures are re- produced in a special list without the further interpretation required for the theory. These investigations of Paschen and Sommerfeld with those of Epstein on the Stark effect are amongst the most striking in modern physics and are convincing that the quantum theory which is their basis must be applicable to light emission, directly to these enhanced series in H and He and modified in some way for other series, in spite of certain phenomena, such as summation series and others to be considered later, which appear directly to contradict it. 9. Band spectrum. A new spectrum in He was observed and described in- dependently about the same time by Fowler and Curtis* and by Goldstein")". "The spectrum includes some conspicuous bands with single heads, others with double heads and a number of complex regions in which no heads are recognisable at sight." But it is peculiar in that the double-headed bands follow closely the series law, corresponding lines in each band being represented with rough accuracy by the ordinary series formulae. They are best developed in the wider portion of the vacuum tube filled with He at a pressure rather higher than is usual, with a small capacity and a small spark-gap in the circuit. There are two series of converging doublets with limits about 34295 and 32000 with sequence denominators m -f- -9284 and m + -9644. The full data have not yet been published or discussed. It may be noted, however, that the second limit is close to that of He' P and the first sequence to that of He" P, i.e. a sequence for which we have suggested the d type. It may be suspected that the supposed bands are only apparent and that the observed lines are analogous to the very large number of D satellites which we shall later find to be conspicuous in the blue spectra of the rare gases from A onwards, and that they may be repre- sentatives of the triplet series. I (a). The Alkalies. 10. In addition to the arc and spark typical spectra, all the alkali metals except Li exhibit a continuous spectrum stretching from the red towards the violet. The respective maxima for these continuous regions are about 440 /x/x, for Na, 480 /z/x for K, 500 /z/x for Rb and 520 /x/x for Cs. Li shows a weak con- tinuous spectrum in the blue. There are indications of band spectra but little definite is known with regard to them. All the elements in the arc or flame give * Proc. Roy. Soc. 89, 146 (1913); 91, 208 (1915). f Verh. d. Deutsch. Phys. Oes. 15, 402 (1913). 52 ANALYSIS OF SPECTRA [CH. spectra constituted on a similar plan, of the doublet type, and so depending on two p two d one s and one/ sequences. With a few exceptions all the observed arc lines can be allotted to one of the four typical series or to combination lines. In other words they can all be expressed as the difference of two sequents. Lithium is the only case where the statement as to exact similarity of constitution may possibly be doubtful. It was also for some time considered as exceptional in that its series were singlets, but later they were shown by Zeeman* and by Kentf to be close doublets with a separation of -339 in S (2,3) and P (1), with 309 for D (2) and -328 for D (3). The full significance of these numbers will be seen later (sect. 13). 11. P series. The P lines are all remarkable in that light with their fre- quencies is totally absorbed by the metallic vapour, whilst those of the other lines are transmitted. Consequently it is possible to obtain the P series isolated as absorption spectra, and since the intensity of the incident light is at disposal, an extremely large number of individual lines may be seen and large dispersions may be used. The method was first employed by Wood! in the case of sodium. Later by using a spectroscope of large dispersion he and Fortrat were enabled to measure the whole set of Na P lines up to the 57th order with an accuracy comparable with -001 A. Bevan|| has shown that the same phenomenon occurs with the other metals of this sub-group, and has measured from 25 to 30 lines in each, though not to the same degree of accuracy. It has already been seen how this enables a value of the P limit in Na to be obtained, practically by direct observation, without having to rely on a doubtful and empirical formula applied to the first lines in the series. The same method is applicable to the other alkalies. Although the result has not the same exactness as in the case of sodium the values deduced are probably subject to a considerably less error than those of the individual lines on which they are based. The formula constants for P, given in Table IV, are based on limits thus determined. The measures on which Rb P (oo ) depend are much more reliable than the others, and its error is prob- ably not greater than 0*1. It is found that for the P series Rydberg's /z, must be greater than unity or 1 + fraction. In other words, the sequence denominator is either m + 1 + p + a/m with m = 1 for the first order, or m + ^ + a/(m 1) with m = 2 f or the first. Further the values of a are negative for the p and s sequences and positive for the d and/, Li excepted, in which p has a positive a. This means that the mantissae increase with the order in the S and P series and decrease in the D and F. In the formulae the constants have been calculated from the values of the first two lines with the limits determined as explained above. The only exception is that of lithium in which the high order measures of Bevan seem to be less reliable than in the other elements. They would make the limit 2-9 larger. In lithium the C values for m = 4, 5, 6 are just beyond Kayser's estimated * Versl K. Ak. van Wet. 21, 1164; Phys. Z. S. 14, 405 (1913). f Astro. J. 40, 337 (1914). j Phil. Mag. 16, 943 (1908); Astro. J. 29, 97 (1909). Astro. J. 43, 73 (191B). || Phil. Mag. 19, 195 (1910); Proc. Roy. Soc. 85, 54, 58 (1911). Ill] THE SERIES SYSTEMS possible errors. Otherwise the general agreement throughout the whole group is very good. The C values are given in the lists of lines in the tables. It is only in the case of sodium with very accurate measures up to -001 A. that devia- tions clearly show themselves in a systematic manner. Wood and Fortrat pointed out that these showed a periodic quality and Hicks* has discussed their results more closely. They are indicated by the curve in Fig. 10. They show a curious alternating difference superposed on a primary difference fluctuating in a period of a few orders. The result is of great importance as bearing on the nature of the ^-sequence. It shows that the formula adopted gives results in extremely close accordance with observation, but that when the measures are known to within a few thousandths of an angstrom, the sequence cannot be represented by a formula in which the mantissa is of the form //, + a/m + )8/m 2 , and arouses a suspicion that it may not be representable by a continuous mathe- matical function of m. This will be returned to later (Chapter IX, sect. 6). The other alkalies indicate a similar fluctuation. Measurements of the P series of -020 -010 >-000 I 1 A / ^ V \H / 2 S < 5 >\ Values of m Fig. 10 the same accuracy as those in sodium are greatly to be desired as giving the promise of important information on the properties of the ^-sequence. The displacement at the end of the curve in Fig. 10 is too large to be due to observation error, as a fact the measures show that the lines for m = 56, 57 are the combina- tions s (1) d (56), s (1) d (57), with d sequents in place of pf. It should be noticed that the values of a in P l , P 2 are the same within obser- vation errors. 12. S series. For the S series the limit has been calculated as since the P (oo ) were deduced directly from the observations. In order to re- produce observed lines within error limits it is necessary to take a/(m ^) in the sequence function, instead of a/m. In this case the agreement is very good * Astro. J. 44,229(1916). t It is much to be desired that these observations should be extended to the other alkalies to test if this change of sequence is common. It suggests that the first process is the formation of ^-configurations and that these are at once transformed to ^-configurations, but that the last higher orders in Na have not been so transformed. This would then explain the Li anomaly (sect. 16). The Li sources would have remained in the same state as the last of the Na. 54 ANALYSIS OF SPECTRA [OH. for all the elements but caesium, in which the data for P (oo ) are doubtful. The actual formula for Cs S depends on a value of S (oo ) = P (oo ) P (1) 3-2, and of Li S on P (oo ) - P (1) + 1-9. If the a term be written a/(2m - 1) it will be noticed that in all the elements the a in the p and s sequents agree quite closely. This is curious as we should expect to correlate 2a/(2m 1) with 2a/2m if Ritz' assumption that the order in the s-sequence is m + -5* is valid. 13. D series. The D series are well developed in the number of lines observed but they are very diffuse and difficult to measure with accuracy. This is specially so in K where there appears to be some cause for non-occurrence or abnormality in the red region. D 1 (3) has only been observed by Ritz and Saunders and D 2 (3)| not at all. Moreover the agreement between observed lines and those calculated from formulae in a/m + j8/m 2 is most unsatisfactory. The C values are given in Table III. The agreement may be accepted for lithium, is not good for sodium, and quite outside experimental errors for the others. Agreement is better if fju is taken as 1 + fraction, which is also suggested by the fact that the lowest order in d (m) is m = 2. Also much better general agree- ment is found, especially in Rb, Cs, if the formulae are calculated from m = 3, 4, but now the C for m = 2 becomes large. The ^-sequence cannot be expressed by the functional form adopted, either in a/m or jS/m 2 . Further consideration of its properties will be deferred at present and taken up in Chapter IX. One very important result, however, can be settled now, viz. that the limit of the series in each element, as indicated by the high orders, is very close to p (1). The existence of satellites is clearly shown in caesium, both in the D series (or = 97*96) and the corresponding doublet F series, with separation 97-50. They should be expected in rubidium but the evidence is not conclusive. The separation for m = 2 as measured by Paschen shows a doublet with the full normal separation i.e. no satellite. For m = 3 on the contrary Saunders saw a triplet, since confirmed by exact measurements by Meissner and by Meggers, with a satellite separation of 2-95. Form = 4 there is only a doublet with measured separation 235-32 in place of the normal 237-58 pointing to a satellite too weak to be seen with separation 2-26. With 2-95 for m = 3 we should expect a less separation f or m = 4 than 2-26 and one about 6-9 for m = 2J. The 6-9 should be reproduced in a doublet F series, but as yet there is no evidence for such. If as is suggested in the lists n = 2129 is taken as F 1 (2) a line observed at n = 2156-1 with a separation of 27-1 might be a possible F 2 (2). Later, when the origin of these separations is investigated, it will be seen that this value of 27-1 is the very close analogue of 97-5 for caesium. There are other cases where a similar phenomenon is exhibited of normal non-satellite separation for m 2, * It is curious how many writers persist in this erroneous assumption even when they employ a sequence function = N (m + n + /c$)~ 2 , in which it is meaningless. f Z> 2 (3) should, however, be so close to ^ (3) that the two may appear one. J On the supposition that the satellites are due to differences in the sequence denominators which are of the same order of magnitude in all the orders. This is the general rule see later, Chapter VI. E.g.,Ba in] THE SERIES SYSTEMS 55 whilst higher orders show the satellite effect. But in such cases the D (2) are high up in the ultra-red and the real normal D (2) set are possibly higher up and unobserved. The observed is only related in some way to a normal D (2). This suspicion is supported by the fact referred to above that while the formula calculated from m = 3, 4 agrees fairly with observation for higher orders, it is enormously in error for the observed m = 2. The energy will have passed to the abnormal and observed line. Considerations based on the constitution of the ^-sequence dealt with later also favour this hypothesis. There is no direct evidence of satellites for sodium or potassium. The lines would in any case be such close pairs that no separation would probably be observed with these diffuse lines. In potassium, however, the satellite effect is indicated by two combination lines p 1 (2) d l (2), p (2) d (3), which are double with separations 1-39 and 1-17 respectively, due to the two d , d 2 se- quences. Similarly also quite recently Datta* has found a combination pair s (I) d (2) indicating a satellite separation of 2-73, which is in exact agreement with 1-17 for d (3). As small observation errors are a large percentage of these values no exact deduction can be drawn. But the 1-39 would seem quite in step with that of rubidium (6-9) above or of lithium. On the contrary Kent's measures before referred to as to the duplicity of the P, S, D series in lithium show small but real diminutions of the separation for the D (2, 3) doublets which indicate the existence of a faint but unobserved satellite. The doublet separation is here -339, those for D (2) and D (3) are -309, -328 pointing to satellite separa- tions of -030, -Oil respectively. These correspond to the same change in the mantissae of D (2), D (3) and thus conform to a general rule in connection with satellites. 14. F series. The discovery of the type of F series by Saunders has already been referred to. As its limit is the first d sequent and as this depends on m = 2 with a denominator of the order 2-9, it must be in the red region. Consequently the lines of lowest order and naturally those to be expected the strongest lie far up in the ultra-red with extremely long wave lengths. All the alkalies show representatives f or m = 3 and 4 characterised by having their mantissae, or /z -f a, very close to unity. In many respects they approach closely to the pure Balmer type and suggest that small changes in N or in the limit might produce exactly that type. Lithium and sodium give only lines for m = 3, 4. The formulae in the table are calculated from these. They indicate lines f or m = 2 respectively of n = 53 and 88, that is, with wave lengths so large that, if existent, they could not possibly have come within range of Paschen's longest measurements. For potassium I have suggested Paschen's n = 1346. It comes within range of the value required by the formula based on m = 3, 4. But this point is further discussed below under combination lines. The other observed lines m = 5, 6, 7 are reproduced within errors. In rubidium I have taken n = 2129-0 for F (2). The formula is calculated from m = 2, 3, 4 and requires a limit about 3-9 less than the d (2) as calculated * Proc. Roy. Soc. 99,*74 (1921). 56 ANALYSIS OF SPECTRA [OH. from the adopted P ( ), which may quite well be due to observation errors. The observed for m = 5, 6 are well reproduced. The matter as to the existence of D satellites has been considered above and it is possible that n= 2156-1 may be F 2 (2). This is also discussed under combination lines. In caesium representatives appear f or m = 3 ... 9. The limit supports the change found in S for the P (oo ) based on high orders of P (m), the agreement between observed and calculated being all within errors. The line calculated for m = 2 is at n = 4505. No line has been observed here, but Moll* gives lines at 235 fjifji, 203 /LI/A, 170 \L\L. The first corresponds to n = 4255. Allowance being made for Moll's wide measure limits and the formulae errors this may possibly correspond to the missing F l (2). Besides these normal F lines, Meissnerf has observed two other pairs with the same separation, viz. X n \ n (2nv) 8053-35 12413-79 (4m;) 7270-70 13750-04 97-35 97-14 (2nv) 7990-68 12511-14 (4m?) 7219-70 13847-18 They would seem related to F (4), F (5). The consideration of the nature of this relation must be deferred for the present J. Meanwhile it may be noticed that they are all diffuse towards the violet whilst the F are diffuse towards the red. For the present they will be denoted as F' (4), F' (5) with sequences/' (m). The existence of ^-satellites is clearly indicated. The separations of the F lines for m = 3, 4, 5 are 97-26, 97-50, 98-03 in which the last two can only be in error by a few units in the second decimal. The uncertainty as to the normality of the observed D (2) lines produces a corresponding uncertainty in the exactness of 97-96 as the normal D first satellite i.e. of the F doublet separation. The F separation of 98-03 although just within extreme error limits of 97-96, indicates that the true F doublet is just wider, say 97-96 + x with x small. The jP-satellites would then show separations of -70 + x, -46 + x, -07 + x. Considerations to be developed in Chapter VI would enable estimates to be made of x, if observa- tion errors could be treated as small. 1 5 . Combinations. A large number of lines in the ultra-red have been observed by Paschen and by Randall who have allocated the majority to combinations. It is remarkable that two sets of lines appear to be repeated in all five elements. These are: (1) a line about n = 1345. The measures give Li, (10) 1344-4; Na, (8) 1343-2; K, (10) 1346-3; Rb, (15) 1345-9; Cs, (10) 1346-4. Paschen attri- butes them to a common formula 2V/5 2 TV/6 2 . With this the calculated would be from 400 to 600 angstroms in excess of the observed. But even if there exist a common sequence of this form for all lines, we should expect to find the other lines for lower orders than 5, 6. The suggestion might be hazarded that they are due to a common contamination of all the metals producing the spectra by one of them. As a fact the line for K falls where K F (2) should be expected, so that if the suggestion were sustained, potassium would be the * Arch. Neerl (2), 13, 100 (1908). t Ann. d. Phy*. 50, 723 (1916). | See note in Tables. .-, f , ; in] THE SERIES SYSTEMS 57 common impurity. On the other hand some doubt might be felt against the adoption of either of these explanations in that in Rb and Cs there are second lines present separated by an amount which recalls the F doublets, although they are not the F (2) lines themselves. The sets in question are in wave numbers 1345-9 1346-4 Rb 29-4 Cs 96-0 1375-3 1442-4 Further for Rb the two satisfy numerically the combination lines s (2) / 2 (2), and s(2)-/ 1 (2). Thus = F(m) + D(2)-S (2). Hence s (2) -/ 2 (2) = 2129-0 + 6776-0 - 7552-54 = 1352-5 s (2) -/! (2) = 1352-5 + 27-1 = 1379-6. The agreement is perhaps possible within error limits. There does not, however, appear to be the corresponding combination in Cs. (2) The second set of analogues consist of apparent close doublets although Paschen seems to be uncertain as to whether they may not be the effect of reversal. Their wave numbers are Li Na K Rb Cs (20)2469 (30)2467-1 (20)2490-36 (30)2505-69 (30)2537-5 (20) 2471-6 (20)2471 (20)2475-1 (20)2493-88 (15)2510-16 Here the change from element to element shows that they cannot be due to a common impurity. As a whole they would seem to fit the combination /(3) / (4) best, although d (3) d (4) are near the first two and correct for K. The two sets as calculated from the data given in the tables for F and D are Li Na K Rb Cs /(3)-/(4) 2474-1 2470 2473 2480-8 2498-8 or 2538* 2471-1 2485-3 2490-4 2985-6 } 3459.0^ Since the D lines in Rb and Cs are doubtful, the question of definite allocation had better be left open, although perhaps the most probable is that of /(3) /(4). In judging coincidence here it is probable that allowance must be made for the electric field in the arc as in the combinations to be mentioned immediately. If this is the case, the shift is to the red for Li and Na, to the violet for the others, a change which might be accounted for by a shift being supposed to take place in both the/ (3) and/ (4). It is perhaps straining probability to suggest that the observed duplicity is also due to the field. The tables show that the p (n) p (m) combinations occur only in Li and Na and do not appear in the others. The calculated values for these lines do not agree so closely with the observed as is general. It has already been noted that the corresponding lines in He require strong electric fields to bring them out, and that the field then shifts them towards the red. Stark* finds a similar * Ann. d. Phys. 48, 210 (1915). 58 ANALYSIS OF SPECTRA [OH. effect in the p (1) p (m) of Li. The amount is considerable, being as much as 7-8 A. for 4146 and 16 A. for 3923 in a field of 80,000 volts per cm. In consequence it is not possible to obtain the correct wave lengths (i.e. in zero field) from the lines observed in arc spectra, but it is necessary to extrapolate from measures in different fields. Stark's results for the two Li lines give 4146-7, 3923-2 as against the formerly accepted measures of 4149-1, 3924 by Konen andHagen- bach, or, nn = 24108-9, 25482-3 as against 24095-0, 25477. The values calculated from observed P (1, 4, 5) are 24108-07 db -46, 25486-62 1-6. The results show that the Konen and Hagenbach lines were very largely affected by the electric field in the arc they used. The pole- effect referred to in Chapter I is here very great. In the corresponding combinations in Na the observed lines appear as shifted in the opposite direction towards the violet from their calculated values. The following numbers show this clearly, the p (2) p (m) being calculated as P(m)-P (2). Calc. Obs. Calc. Obs. i = 3 18069-32 ...69-43 w = 6 22325-92 ...52-6 18084-02 22342-31 m = 4 20324-39 ...26-37 m = l 22821-62 ...66-0 20340-07 ...44-47 22837-50 w=5 21568-24 ...77-90 21583-94 ...95-16 The two sets are sufficiently parallel to show that they relate to the same series, but that by the pole- effect in the arc they are shifted towards the violet by amounts which increase with the order, and apparently are larger in Na than in Li. In potassium none have been allocated, but the following may be suggested. The first three calculated sets should have wave numbers given by 11676-7 15963-7 18030-8 11715-8 16013-0 18083-9 Bergmann has a line with n= 11761 with considerable possible error. It has already been allocated to F (7) with dX = 9. If it is the combination it is shifted to the violet. There is a spark line at A = 6246-5 or n = 16005 2 which might be the mean p l (2) p (4), p 2 (2) p 2 (4) displaced to the violet. Further there is a spark line at A = 5516 or n = 18125 4 which might represent Pi (2) ~ Pi (5) also displaced to the violet. These allocations cannot be regarded as established, though possible. The fact that they appear in the spark with its stronger electric field does, however, support them. It should be noticed that in contradistinction to helium none of the alkalies show the combination s (1) s (m). 16. A comparison of the formula constants in the table shows that with the exception of lithium, the a is negative for the P and S series and positive for the D and F; i.e. the mantissa increases with the order in P, S and decreases in D, F. In lithium the sequence in what has usually been called the P series would seem to be of the d or /type, and in the F series of the p type. In other words the so-called principal series depends on the /-sequence and the F on the in] THE SERIES SYSTEMS 59 p. It is noticeable also that while as we pass from caesium to sodium the P (1) lines are pushed further to the violet, in lithium it is considerably on the red side of that of sodium. The four Li series would then really be P(m) = s(l)-f(m\ 8(m)=f(l)-8(m), The observed doublet in Li would then be due to a F satellite. Its separation is indeed anomalous* as an ordinary doublet. A similar arrangement as has been seen is apparently called for in the He" sets. If this be the case the combination p (I) p (m) is really d (1) d (m) or /(!) f(m). Now the p sequences are only slightly affected by the electric field, whilst the d and / are extremely sensitive to it and receive great changes. This would explain the apparent anomaly that while p itself is so neutral, the assumed p (1) p (m) is so sensitive in He" and Li. But the striking fact is that in both He" and Li these combinations are shifted to the red, whilst in Na and the suggested K where the sequences are undoubtedly p they are shifted in the opposite direction. 17. Summation series (see Tables III). The F series excepted, the summation lines would lie in the ultra-violet. None appear in arc lines, but they seem to require the spark for their development or if we may judge from the single instance of sodium the arc in vacuo. In the foregoing the limit of F has been calculated from the first D line and some doubt has been cast on the normality of these in Rb and Cs. This may possibly explain the failure to identify their F lines. Li. The P, S, D are beyond the observed region, and no F lines have been identified within it. Na. All the P would be beyond the observed region. There are several S, and D, but the most suggestive fact is that for this element Zickendrahtf has observed in the vacuum arc a crowded set of lines, many strong, between 4744 and 3848. As the limit of the S and D series is at A = 4086, the region between this and 3848 involves the higher summation lines and it is noticeable that it gives representatives of summation lines up to the last order observed in the S, D. If we may judge from what occurs in the rare gases we should expect to find not only the normal summation lines, but a large number of others related to them in definite ways (see Chapter VI). The result is a crowded region. It is unfortunate that the crowding explained by this fact renders any identifica- tion more uncertain as mere coincidences are more likely. In the list therefore lines are included which may be questionable. A line has been found for F (3). It has been seen that the formula gives F (2) as n = 88. This should give jF (2) as A == 4088, and a line is seen at (3) 4088-8 in Zickendraht's list. If this line stood isolated, it might be regarded with some confidence as the real F (2), but there are so many in the neighbourhood and F (2) is not known directly that it is probably a mere coincidence. K. Potassium shows representatives of P and several S, D. * See Chapter VI, sect. 2. t Ann. d. Phys. 31, 233 (1910). 60 ANALYSIS OF SPECTRA [OH. Rb. The first orders of P are outside the observations. No 5" and only a doubtful D have been identified. Cs. Caesium shows P l (3, 4), no S and doubtful D (4) and F l (3). It is possible that, with a wider experimental investigation of the spark and the arc in vacuo, more complete sets might be brought to light. 1(6). Copper. Silver. Gold. 18. The metals of this group all show a band spectrum shaded to the red. The spark spectra are very rich in lines, containing over 700 each. In silver and gold the arc contains comparatively few lines about 70 whilst copper shows a noticeable difference in this respect, containing about ten times as many. As in the alkalies the arc spectra show the preponderance of the doublet system of series. The series themselves are not so fully developed in the number of orders observed as in the former group, so much so indeed that there has been considerable difficulty in allotting sufficient lines to deduce with any exactness the formulae constants. This is specially the case with gold. So far as the strongest lines are considered the similarity of build of the three spectra is striking. Strong pairs for S (2) in the red, for D (2) and P (1) in the violet, together with a well- marked set of inverse D types, all in step in corresponding parts of the spectrum, are characteristic. The evidence from the Zeeman effect also supports the allocations. With the exception of the order m = 1 the P lines lie far in the ultra-violet in a region observed as spark lines by Handke. For this reason it is necessary to take the consideration of this series after that of S and D. Kayser and Runge gave three sets for S, D each in copper and four in silver. But the S and D limits calculated from them disagree by an amount in each element which is greater than the uncertainty due to possible observation errors in the lines used. That they must actually be the same is proved by the fact that the separations as shown by both the S and D sets are the same within -01. A consideration of summation lines, however, settles these limits quite definitely within a few decimals. These lines are given in the tables with the corresponding mean limits. The directly observed S l (2), S 2 (3), D n (3), D 22 (3), D l (5) in copper settle the limit as lying between the above two calculated values, whilst in silver those for 5 X (3), S 2 (3), D u (2), D 22 (2), D 22 (3), jD x (4) settle it also as between the two calculated. From these limits with the two strong and well- defined sets for m = 2,3 the formulae for S, D are determined. The corresponding problem in gold was apparently at first sight hopeless of solution. In Kayser and Runge' s original measures only the characteristic inverse D set, and the problematic strong P lines in the violet, could be definitely allotted to their proper types. But they gave the important quantity v = 3815-5 -1 as a definite datum. Lehmann later added an ultra-red line which, with one of Kayser and Runge' s, gave the same v. The pair were in step with the S (2) in silver and copper, and moreover Hartmann's* measures of the Zeeman effect proved that Kayser and Runge' s line was definitely of the S z type. The problem was, however, solvedf by the application of principles to be developed later. *.Diss., Halle (1907). t !>'. p. 405]; Phil Mag. 38. 1 (1919) m] THE SERIES SYSTEMS 61 The limit S ( ) is very close to 29469-85 with a probable uncertainty of only a few decimals. The only doubtful assumption is possibly the allocation of D lines for m = 2, 3 ; but as the assumption has been justified by the results it is here adopted. At present we must take the limit as determined from the summation lines. The lines indicated by the formula calculated from these data for the next six lines are found with small C values. With these, the limit determination depends on the summation lines D 22 (2), and the whole set for D (3). The S series, however, appear to be completely dissipated after the undoubted S (2). With the S t (2) is found a corresponding S : (2), giving the same limit within error limits. In the region where S (3) should be expected there is only one doublet which might be the real S (3), but the Zeeman pattern for the suggested Sj_ (3) is that of a Z) 22 line. No corresponding S (3) are found. By taking it as S (3), the formula found is that given in the tables. Although the IJL is in step with Cu and Ag the a is much less, and the whole is doubtful. It is curious that the /S^ (3) was not observed by Kayser and Runge. It is quite clear that some great disruption has taken place. The only calculated lines really observed are the two for S (5). 19. The lowest order observed for D is m = 2, in each metal, but the formula shows that any lines depending on m = 1 would lie far up in the ultra-red beyond Randall's measures in this region. Several considerations lead to the opinion that the lowest order is m = 1. An important one amongst others depends on the F series, whose limits are the lowest d-sequents and whose separation is that of the satellites of this order. These last for m = 2 are 6-9, 21, 81 respectively for Cu, Ag, Au, and no doublet series are found with these separations. If D (1) lines exist, the satellite separations would be due to mantissae differences of about the same amount as in D (2). It is then possible to calculate with some approximation what separations should be expected. Large numbers of such pairs are found and it is possible to allot F series on this basis whose limits must be d^ (1), d 2 (1). In the first instance these were indicated by certain known properties of the ^-sequence with which we deal later. There are several further tests which can be applied to obtain evidence for their existence. At present two are at our disposal, in addition to that of the existence of F lines, viz. com- binations with other sequences, and summation lines. The latter lie in the ultra- violet. In copper and silver only the D n the strongest line of a set are seen, but Ag D 22 would lie beyond the observed region, whilst in gold only the weak JD 12 is missing. Combinations with the inverse D sets are also found. The evidence for the existence of these first order D lines, although not direct, is nevertheless decisive. The curious and characteristic inverse D sets have the following denominators for the d z sequent Cu Ag Au 1-495251 1-487161 1-492907 A comparison with the D or F mantissae (Tables V) shows that they cannot be direct D or F series, but seem to be related to them in a similar way to that occurring between S and P, viz. the mantissae differ by about -5 from those of 62 ANALYSIS OF SPECTRA [CH. the D and F. As in the case of the P, S the Zeeman patterns are also of the same nature for these sets and D. 20. The P series. The characteristic strong ultra-violet doublets before referred to are ascribed to the P (1) sets. In copper the Zeeman patterns are distinctly of this type, in silver no observations have been made, whilst in gold that for P 2 has been investigated, but the measures are probably not very exact. They show merely a general similarity with the P 2 pattern. Further, the gold doublet, as Kayser and Runge have pointed out, would seem to lie too far to the violet to be in exact step with the others. The P (oo ) calculated as P + S (oo ) should, as being the sequent s (1), have a mantissa in step with that of s (2), but in gold this would seem impossible. That of Au P (oo ) or s (I) is -246, whilst that of s (2) is -545. It would seem highly improbable that these should belong to the same sequence. With the exception of these strong doublets there appear to be no definite sets representing higher orders. There are on the contrary a large number of lines in the region in which P (2) should occur, several showing the character- istic P reversal. It would seem that in place of definite strong lines for this and higher orders congeries of lines occur out of which it is possible to select different series satisfying an equation of the usual form. With some of these are found combinations of the form p (1) p (m), but no complete analysis of these lines has yet been attempted. In gold it is possible to select lines for the P series subject, however, to the abnormality in the limit above referred to. In the copper spectrum a series apparently of the P type has been observed which is interesting as having been first discovered through its summation lines which are well and fully developed (see Tables III under Cu Q). 21. The F series. The failure to find F series based on the d (2) limits has already been referred to, although Randall has been enabled to find the sequents /(3),/(4) in some cases from a consideration of combination lines. They exist, however, as doublets with suitable separations and with limits depending on d (1), d 2 (1). It seems to be the normal characteristic of the /-sequence to show great instability in the lower orders, whilst orders above these have definite and even strong representatives. The complete disappearance or the weakening in intensity of an order is frequently found, accompanied in many cases by the presence of a large number of other weak lines of the same spectral character. We shall find the same phenomenon exemplified also in the groups of the rare gases and of the alkaline earths. An inspection of the directly observed lines in the tables will show this*. It should be noted how much more defective the sets of even order are than those of odd. One result of this instability and of the apparent replacement of a strong single line by several components is that the spectrum especially the arc in certain regions is very crowded. The rela- tions between these related and normal lines depend on conditions developed later in Chapters VI and VII. * The lines enclosed in ( ) refer to selected lines and are not here in question. in] THE SERIES SYSTEMS 6S 22. The spectra of all these elements are distinguished by the possession of numerous combination and summation lines. In Cu may be specially noted the presence not only of five orders of the series p (1) f(m) but also a corre- sponding series p (1) +f(m). Also as illustrating the remark above as to the frayed out character of S and P series we find several combinations of the nature p (1) p (m) due to different representations of P (m). These spectra are also of the highest importance in connection with certain fundamental relations con- sidered in Chapters VI and VII. A complete discussion of their connections may be expected to throw much light on the intimate structure of spectra. Group II. 23. The distinguishing features of the second group of elements are the existence of (1) systems of triplets, (2) systems of singlets, (3) systems of doublets analogous to those in group I. The triplet and singlet systems appear most strongly in the arc and are weakened in the spark whilst on the contrary the doublets are enhanced by the spark. There is other evidence to show that the triplets and singlets really belong to a common system with a quite different origin from that of the doublets. The lower orders of the singlet series are as a rule amongst the strongest in their respective spectra and almost without exception consist of absolutely monochromatic lines. For instance, the famous red Cd line is Cd D' (2). On the contrary, the triplet lines of lowest order are in general composite with close multiple companions. Triplets IL 24. The two triplet separations in a series are in the ratio of about 2:1, whilst those of the satellites are very close to the ratio of 5 : 3. How closely this is the case is shown by the following numbers calculated from the data given in Chapter VI. To complete the scheme the corresponding values for the rare gases, and group VI, which also form triplet series, are included. II (a) 11(6) Mg 2-03 ? Zn 2-04 l-3f Ca 2-03 1-63 Cd 2-12 1-64 Sr 2-11 1-67 Eu 2-62 1-66 Ba 2-37 2-09, 1-65* Hg 2-62 1/1-70 Ra 2-46 ? * Two sets. f Actual separations small. VI A 2-37 . O 1-81 Kr 2-31 1-69 S 1-55 X 2-18 1-65; 1- 66* Se 2-32 Ra. Em 2-02 1-68; 1- 75* * Two independent D sets. The peculiar difference in the march of the ratios vjv 2 between groups II and should be noticed. Whilst in group II it increases with atomic weight from 2 to 2-6 in the rare gases it decreases from about 2'4 to 2. In the satellites the normal ratio seems always quite close to 5 : 3 with the one exception that Hg shows an abnormality of 3 : 5, which also is reproduced in its F separations. 64 ANALYSIS OF SPECTRA [OH. 25. The terminology of S, D, P, F has been applied to these series, viz. P to that series in which the separations decrease with increasing order, S to that in which they remain the same, D to that which shows the same constant triplet separations as in S, together with satellites, and F to that whose constant separations are equal to that of the D satellites, i.e. whose limits are the ^-sequents of first order. Until, however, we have some definite criteria to distinguish between the nature of different sequences we must remember that it is an assump- tion to take what are called e.g. the s-sequents in the doublet and triplet systems as having some particular s-essence in common. That the D doublets are analogous in groups I, II, as also the S, P sets, is definitely proved by their showing the same Zeeman pattern in a magnetic field, though whether the S, P in one correspond to the S, P in the other is left open by this effect. The sequences as deduced for the S'", P'" of this group show* analogies to those of the P", S" in the alkalies, that is, they suggest that the S'", P"' depend on sequences of the same nature respectively as the p, s of the alkalies. There is, in fact, other evidence in support of this, as we shall see in Chapter IV, sect. 3 and Chapter VIII, sect. 5. For the triplet the S, P also possess a common Zeeman pattern and we may suspect that there is some s-ness or p-ness which denotes some common property in the sources of S, P both in doublets and in triplets. A similar sus- picion is aroused also as between the d and/ sequences. In general none of the ordinary simple formulae in a/m or j8/m 2 , seem capable of reproducing all the orders of the series within observational errors. This is especially the case with the D series. The P lines, and in II (a) the F, lie in the red or ultra-red regions, while the S 9 D run down into the violet. Consequently any summation 5" and ) lines must lie in the extreme violet, and only their higher orders be capable of observation. Only a few doubtful P and F lines are observed, except in the rich spectra of Eu and Hg, where very complete sets are in evidence, affording good illustrations of these summation series. 26. Mg. In many respects Mg seems to approximate more to the type of the Zn sub-group than to that of the alkaline earths. The latter all show a first D'" line of order m = 1 whilst the Zn group have the first set for m = 2. The lowest observed order for Mg, however, has m = 2 like Zn. A similar condition is also indicated by the doublet and singlet systems. In the D series orders up to m = 12, and in S up to m = 9 have been observed, and are sufficient to deter- mine, the limit with some precision. The formulae for the S lines require an additional term in ]8/w 2 , and even then fail to reproduce all the lines within observation errors. As a contrast, in Ca and Sr, the usual formulae calculated from the second and third lines are quite satisfactory except, as seems to be the rule, for the first line. In the D the formulae are so hopeless that for the study of the sequences it is necessary to calculate direct the mantissae for each order. This shows that the limit chosen gives mantissae converging asymptotically to a final value. If this condition be made exact the limit is very close to 39757-18 R.U. and gives for P (oo ) = s (2) = S (oo ) - S (2) a value 20471-58. This is supported * [ii. p. 35.] in] THE SERIES SYSTEMS 65 by a single P (2) set which with P 1 (2) gives the mean lines 20470-49 -7. Only three orders of P have been allocated. For the F lines Paschen has proposed the two given in the tables for m = 3, 4. The other earths all possess F lines with a large number of orders, whilst the Zn group have few. Thus again Mg shows analogy with the latter. The F series here is based on a limit = d (2), and it might be thought that its shortness was due to the existence of a true F series based on d (1), Paschen's lines being then regarded as combinations d (2) f(m). If so, this F series ought to have been observed, while none such have been recognised. 27. Ca, Sr, Ba, Ra. The remaining elements of the first sub-group show a very close analogy with one another, although in Ba there is evidence of some disruption and in Ra the spectrum in addition is not sufficiently determined to permit of definite conclusions. All the d sequents are found quite unamenable to formulae relationships whilst the S and F are satisfactorily represented by the normal formula, with the usual S exception for m = 1. In Ca and Sr the triplet separations are quite accurately the same in the S and D. It follows definitely that the S and D limits are the same. The formulae for S, calculated from the lines for m = 3, 4, 5, not only reproduce succeeding lines, but the limits agree with those calculated independently from the F series. Thus in Ca, S (oo ) = 33988-23 giving F(ao ) = 33988-23-5055-08 (=D l ( l)) = 28933-15, whilst F(ao ) calculated directly from the F series is 28934-33. The corresponding values in Sr are 27609-77 from the D (1) and 27609-34 from the F series. Similar connections hold in Ba. The uncertainty in the limits is therefore very small. In Sr with the corresponding D(ao) the d mantissae increase with the order towards a final asymptotic value. In Ca, however, the mantissae first increase up to m = 3, then decrease rapidly up to m = 8 and then asymptotically up to the last observed at m = 14. In Ba the allotment of lines and the determination of formulae constants are matters of some difficulty. Four triplet sets, to which Saunders has recently added a fifth, have been generally accepted as representing the S series. But the first is quite out of step and the formula calculated from the next two and the D limit gives a value about 1000 I.A.- 1 too small. There is a doublet here with a much stronger first line, 966 behind the doubtful one. This separation shows that the two sets are definitely associated linked in a way which will be developed later (see tables). This set is entered as the normal S (2) but S 2 is weak and S 3 absent*. With this set the first three lines give the same limit as D (oo ), and reproduce the fifth within error limits, but the fourth line is shifted * The order of intensities is instructive. The normal set have 10, 1, abs., the linked set have 3, 5, 5 instead of a descending order. Only a few of the configurations giving normal S { are dis- rupted into those giving the second set, consequently the intensity of S t remains large, and that of the linked S l only a moderate amount. On the contrary almost all the S 2 configurations are disrupted into the linked, so that S 2 has a very small intensity and the linked S 2 a greater one than its S : . In S 3 practically all have changed to the linked S 3 with the result that S 3 is absent and the linked S 3 has an intensity equal to that of the linked S 2 instead of less, as is the rule. H. A. s. 5 66 ANALYSIS OF SPECTRA [CH. by an amount greater than can be accounted for by formula failure. Saunders' original measure for S 2 (4) gave a value of v 1 definitely less than the normal. It is naturally explained by later knowledge. On the other hand the strong set of S (2) would appear at first sight as the normal and the weak as related. If so, the limit should be near 28629-29 or 115 larger than the D (oo ). There are other reasons depending on later knowledge* in support of this. It will require further investigation to decide between the two suppositions. The Ba D lines are very confused. There can be no doubt about Randall's lines for D (1) being a kind of D (1) set. It is, however, an inverse or negative set of lines whilst in the other elements they form a direct set. This alone would not be a difficulty for, being all far up in the ultra-red, the sequents would be of the same order of magnitude in all. But the great difficulty is the abnormal ratio in the satellite separations which is here 2 : 1 in place of the almost uni- versal ratio 5:3. Their reality as a kind of D set, however, is established by the fact that the satellite separations are reproduced in a corresponding F triplet series: traces of a second F series point to a second D (1) set with satellites in the normal ratio. For the second order the lines allocated to D n and D 22 show the Zeeman pattern proper for these lines, so that these may be considered as established. For the D 3 (2), the set marked in the tables with an asterisk has been proposed, but 18060 is too strong in proportion ; it shows a Zeeman pattern of a singlet type instead of a D^ , and the satellite separations are quite out of step with those of the first. Moreover, they form part of a mesh, an arrangement considered in Chapter VII. But there is no other set of lines observed which can take their place. There is a single very weak line n = 18457-51 which, as the weak remnant of the strongest of the set or D m would give a satellite separation of 26-8 in better step with the first one of 67-5 and satisfies the other evidence. A similar difficulty arises in the order m = 3. Here the proposed lines for D^ , D^ give the second satellite separations larger than that of the first. A line n = 23114-09 as D^ gives the second separation as 11-48 or a little less than one- half the first, i.e. the same ratio as for m= 1. But there is no Z) 33 . This more detailed discussion of a special case serves as an illustration of an effect which is frequently met with, especially in elements at the high atomic weight end of their groups. The effect shows itself as a kind of disruption of what should be normally expected, with a consequent weakening of intensity (even to vanishing) and the production of other weak lines in the neighbourhood. The same effect is shown also in the Ba F series which is very fully developed, having been traced by Saunders down to m = 14. A more detailed discussion must at present be deferred. A glance at the march of F^ (oo ) for Ca, Sr, Ba 28934, 27609, 32433 will show that the value here obtained for Ba is quite out of step with the others, even if the d (I) be taken as the true value of F l (GO ). Yet it clearly belongs to the F series associated with the observed negative D (1). Now it is interesting to notice that Hicksf, before this D (I) set had been observed, had allocated an F series with ^(00) = 25922 and separations 260-3, 156-9. These are close * See Chapter VI, note to table; also sect. 6, Ex. (a). f [m. p. 388.] m] THE SERIES SYSTEMS 67 to the normal ratio of 5 : 3 and the F l (oo ) is quite in step with those of Ca, Sr. It indicates D lines in positive order, similar to those of Ca, Sr, and lying in the ultra-red beyond Randall's farthest except D 22 close to his A = 29790, and D^. It would appear that there are two D (1) sets at least, each with its dependent F series. The new set is not so well developed as the other, but it would appear to correspond to the normal series. The F series in all elements of this group are well developed and come down into the visible region. A comparison of the F series of these alkaline earths shows a remarkable characteristic in an apparent instability of the lower orders, which in other series are the most definite and the strongest. Indeed, for the first order, m = 2, the set is always weak and shows indications of scattered fragments in the neighbourhood. For instance in Sr we find the first triplet represented by the system 14802-06 101-80 14903-86 15048-05 59-75 15107-80 in which the second satellite set appears shifted forward. In Ca also, a similar effect is noticeable, with the second shifted back. Thus 6171-18 14-4-5 6185-63 6171-18 21-12 6192-30 with a similar effect for m = 2, with equal shift 16205-52 13-89 16219-41 16204-08 21-74 16225-82 13-82 16239-64 In Ba with F satellites 18849 . 96 179 . 56 19028 . 52 18935-50 380-49 19315-99 35-28 18980-78 whilst the second Ba F set show the same effect in an extended degree. This effect is so common, not only here but in other groups, that we are led to regard it as a normal property of the F sequence, and to expect changes in, and non-appearance of, the lower orders, with greater regularity in the higher. In all this group the P, in the red, are so ill developed and uncertain as to suggest the suspicion that there is a s (1) sequent, and that the true P series is s (1) p (m), in the ultra-violet. 28. The close resemblance between the spectra of the alkaline earths Mg excepted is exemplified by the foregoing statements. This resemblance is further illustrated by the existence of certain remarkable sets of lines related in each set in a way similar to those of a diffuse triplet and involving the F and S separations with others. They exhibit also common Zeeman patterns different from those of the other series; one involving a triplet with one and a half the spread of what is usually called the normal Zeeman triplet. Although their actual relation to the other series has not yet been settled, they clearly play a very prominent part in the constitution of the spectra. They are of several types. The principal ones may be represented by the following diagrams, in which a dot means that the corresponding line exists, X stands for the unknown sequence 52 68 ANALYSIS OF SPECTRA [OH. in the set, the wave number of a line being d X or p X. For comparison the corresponding diagram for a D set is also given. A B L Pi Pi PS D Pi Pz The more complete data are given in the tables, to which the reader should refer. It will be noticed in A that (1) Comparing the X 2 X 1 separations in each element 40-03 : 177-8 : 449 = 1 : 4-44 : 11-22 (Ca) 2 : (Sr) 2 : (Ba) 2 - 1:4-4: 11-72 in which (Ca) . . . stand for their respective atomic weights. The X separations, therefore, like the triplets and the satellites, are very closely proportional to the squares of the atomic weights. . * (2) Comparing the ratio of the X separations in each Ca, 40 : 26-7 = 1-50, Ba, 241-6 : 158-9 = 1-52 Sr, 177-8 : 117-5 = 1-51, Ba, 450 : 300 = 1-50. These show a ratio close to 3 : 2. A further discussion of these forms is taken in Chapter XI. 2 9. Zn, Cd, Eu, Hg. Spectrally europium, as its atomic weight also indicates, belongs to the Zn sub-group of elements. Its series relationships are a close copy of the schemes of the other metals of this group. As this is a matter of some theoretical importance it justifies a more detailed description than would other- wise be called for. In contradistinction to the alkaline earths the P'" series are well developed, but with the exception of Zn they do not show themselves well amenable to the usual formulae, when the latter are made to include the first line. The difference between the mantissae of the first and second orders is so excessive compared with those between the others that any formula in a/m or /3/m 2 cannot represent it, and at the same time the more moderate differences when m > 2. It can be met, however, by taking a form in a/(m x) or in cases by aj(m -5) in place of a/m. Of combinations they all show a considerable number, especially the p ( 1 ) p (m), Zn excepted. Of summation lines P ( 1 , 2) would lie in the extreme ultra-violet, Zn offers several examples of P lines, Cd only one very doubtful, but Hg and Eu possess very complete sets up to the same orders as the P. The m] THE SERIES SYSTEMS 69 complete allocation of the Hg P offers, however, certain peculiar difficulties. There appear no lines which can quite definitely be assigned to P (2). Moreover after m = 4 the mid P 2 lines appear to be wholly absent with the possible exceptions of m = 7, 8. The Hg P series, however, exists practically with all corresponding P lines up to the last order of m = 18. Europium possesses representatives of the P series up to m = 11 and a still more complete P set. In fact the Eu P is one of the most complete summation series known, and the lines fall in with the formulae values very closely. The spectrum of Eu has not been observed in the red or ultra-violet. The existence of combination lines p (1) - p (m) enables, however, the P (2), P (3) sets, which he in the red region, to be determined, and they are entered in the table as if observed. With them also go the observed P (2), P.(3). It will be seen on reference to the table of formulae how the various limits and formula constants in Eu march with the corresponding values for the other elements. 30. The S'", D'" series in each element are well developed up to m = 6 to 7. The S are represented quite closely by the formula in a/(m 1), i.e. a/m when jit is taken 1 -f /, and in all cases their mantissae increase with the order or a is negative. The D again fail to follow the formulae, but their mantissae increase asymptotically with the order, and so support the values of the limit otherwise determined. Hg D gives the appearance of having three satellites in place of two, but this is now known to be due to the fact that the apparent third satellite is really the combination with a singlet sequence p' (1) d' (m). There is, how- ever, an anomaly in the satellite separations which are in the ratio 3 : 5 instead of the usual 5:3. In Eu the S series again are in step with the others, but the D systems seem to be excessively broken up. D (2), although complete, is much weaker than is the rule, and the other orders seem much dislocated. Its satellites, however, differ from those of Hg in giving the normal ratio. Whilst, as we have seen, the P series are better developed than in the earths, the F are far less so. They all show the combinations p (1) f(m), m = 3, 4, as well as F (3) and F (4), but Zn only a strong set for F (3). The summation lines should be seen if existent, but they are exhibited only in Hg and Eu. The question as to the lowest order in F is important, but not easy to settle definitely. Any F (2) lines would be far in the ultra-red. In Cd, there are two spark lines nn = 28274-07, 29441-86 which, as p l (1) - / (2), p 2 (1) -/(2), give /(2)= 12436-53, 12439-74 indicating a possible satellite effect. This makes F (2) 586 far out of sight in the ultra-red and F (2) = 25459 not observed. F (1) would give a negative set in the red not observed. An arc line by Hupper n = 41288-70 taken as F l (1 ) would give /(I) = 28266-12 and F l (1) = - 15243-54 (A = 6560). Zn gives nothing except the F (3) set. On the other hand Hg shows both F and F for m = 3, 4, and two possible sets for F (2), whilst Eu gives complete F from m = 1 to m = 5 with the corresponding negative values for F (I), the higher orders of F being in the unobserved red. We have, therefore, indications of the 70 ANALYSIS OF SPECTRA [CH. /(I) sequence, but the evidence cannot be regarded as conclusive, although absence or weakness of direct representatives is not to be unexpected in view of the known instability of the lower orders of the/ sequence. Singlets II. 31. In 1910 Saunders* discovered three sets of corresponding series lying in the violet in Ca, Sr. Of these two are parallel series called by him SL 1 , SL 2 (SL = single lined), and the third SL 3, converging to the same limit as the longer wave set SL 2. He says they do not appear in the spark spectrum with the doublet system, but when the spark is replaced by the arc, the higher orders of the former disappear and the singlets come into evidence. They appear chiefly near the positive pole of the arc in contradistinction to the doublets found most strongly in the neighbourhood of the negative pole. None of the usual formulae fit them. He determined limits by using the high order lines, with the conse- quence that their values are very uncertain. The changes in the mantissae with increasing order are far in excess of those in any other of the known series. This accounts for the difficulty of finding suitable formulae with only two constants, /u,, a. The effect is shown in the following table giving the nfantissae to four places of decimals of the SL 1 sets in Ca, Sr, with limits 49300, 45935 respectively: Ca Sr m Ca Sr 1 1-0679 1-1273 6 -2366 -4827 2 -9539 1-0440 7 -1993 -4042 3 -7935 -9503 8 -1810 -3526 4 -5205 -7986 9 -1814 -3571 5 -3199 -6199 10 -1396 -349 It will be seen at once that the differences of mantissae of succeeding orders are quite out of analogy with other known series and some doubt might well be felt as to whether they form actual series or not. But the absolute agreement in the separations between corresponding lines in SL 1, and SL 2 21849-23 for Ca, 20149-61 for Sr their analogous positions in the spectra of both metals, and the convergence of SL 3 to the same limit as SL 2, are clear evidence as to the reality of their series relationships. The mantissae difference of the limits is in both elements about -5, which suggests their connection with the p, s sequences. In fact Saunders regarded the SL 1 as a principal series, and SL 2, SL 3 respectively as S, D. This last suggestion has, however, been criticised by Lorenserf. He regards them as two combination series X p (m), X (m), and allocates other lines to normal S, D in Ca. The data given in the Tables are from a later paper by Saunders J which gives a different and more satis- factory relationship as well as more complete data. We may suspect that all the series belong to combinations either of p, s type or d,f type. Several facts point to the latter : ( 1 ) the great and irregular mantissae changes in the SL sequences illustrated above point rather to d, f sources than p, s; (2) the mantissae decrease with increasing order whilst the opposite is the rule in the known p, s sequences; (3) there is a considerable number of examples * Astro. J. 32, 153 (1910) f Diss -> Tiib - (1912). \ Astro. J. 52, 265 (1920). in] THE SERIES SYSTEMS 71 in which an element shows the possession of several different d and / systems ; (4) also later knowledge as to the properties of these sequences provides some evidence to the same effect. At present the question must be regarded as un- settled. Lorenser has proposed lines for the combination p 2 r " (1) s r (1) both in Ca and Sr. In general in combinations, with sequences in the same system, the identification may be made to depend on the separation of two observed lines, and no uncertainty as to the correct values of limits occurs. In a case like this, however, with two different systems, the values of the limits must come in and the identity here depends on the limits S 2 '" (oo ) and P f (oo ). With the great uncertainty in P' (oo ) present in this case, the evidence for such an entirely new kind of combination would be quite worthless. We shall see, however, that the Zn group gives clear evidence that it exists in all its elements. Conse- quently its existence should also be expected here, and the presence of lines suitable for the combination may be used for the purpose of determining more exactly the P f (oo ) from the more accurate S 2 '" ( ) 32. Mg, Zn, Cd, Eu, Hg. The singlet series are far more fully developed in the Zn sub-group than in the earths, not only in number but in types. Again Mg approximates to this group rather than to II (a). The first singlet series was discovered originally in Mg by Rydberg and published as a new kind of series. The more complete determination of this system for this sub-group is due to Paschen and his pupils. Using his allocations, the framework of the system consists of (1) series which may be designated S', D', P' (2. m), P' (I. m) in which the two P form parallel series with respective limits s' (2), $'(1); (2) a considerable number of combination series, some of which involve sequences belonging to the triplet system. The chief of these are p' (1) p' (m), p 2 '" (1) - s' (m), s"' (2) - p' (m), and sets p' (1) - d 2 , is correct. They were observed from light close to the negative pole in vacuo and end on. We may therefore suspect that his measures are subject to a greater uncertainty than that due to observation errors proper, owing to the pole effect. There is some indication that this is the case in a small discrepancy between the measures of D (2) given by him and by Nacken, whose probable observation errors would be about the same. The formula for F l , calculated from the first three orders, is n = 49775-64 - 4#/{m + -994644 + -005944/m} 2 . It may be noted how close the/ (m) is to a Balmer's formula. It reproduces the succeeding lines with great exactness (see table). The F doublets show a slightly decreasing separation with increasing order, which is quite definite, and for the first is larger than that of the supposed Z)-satellite. This evidences the existence of F satellites of the same nature as the Z), that is/j >/ 2 . The separations for the first three sets are -99, -96, -92. Although observation errors are very small (dX < -005) it is possible that these separations may be all equal with a value -99 or -98, but the systematic decrease towards the D-satellite value would seem to point definitely to the satellite effect in the /-sequence as well as in the d. The first observed line is F (3). It is important to determine whether this is the first line of the series or not. For m = 2 the formula gives n = 950 in the far ultra-red beyond any test. If it exists we might expect to find combination terms / (2) /(m) similar to others actually found for /(3) / (m). Form = 3, 4, they should be in the neighbourhood of n= 21358, 31248, but they have not been observed by Fowler, Nacken, or Lorenser. In the D series the first D lines definitely allocated belong to the order m =- 2, not only in Mg but in the other metals of this group. It is, however, to be noticed that negative sets are found in the Zn sub-group which will fit in positions f or m = 1 . Any corresponding F series would lie in the extremest ultra-violet so that this evidence in support of these allocations is not attainable. The fact 74 ANALYSIS OF SPECTRA [OH. that orders of the d (2) f(m) are observed up to m = 10 might seem to militate against the existence of a d (1) f(m) were it not that seven orders are also found in d (3) /(m), and that in the other series it also possesses a similar double set. For instance in addition to the p (I) s (m), p (1) d (m), d(2)f(m), or the normal S, D, F, it possesses also, series p (2) s (m), p (2) d (m), /(3) f(m), the last f or m = 5 ... 11. The two sets may con- veniently be written 8(1. m), D (1. m), F (2. m) and S (2. m), D (2. m), F (3. m)* respectively. There are also representatives for P (1. m), P (2. m). In S (I. m), lines for m= 1. 2. 3 are found, whilst those observed for S (2. m) depend on m = 4 ... 7. So in D (1. m), lines for m = 2. 3 have been observed and in D (2. m) for m = 3 ... 7. The common d (3) sequents found from the two lines for m = 3 agree within error variations. The values of p (1), p (2), found as the limits of the two sets are 85505-05 and 40618-19. These two give for the p sequence , -042680) 2 -307827- p (m) = 4ffm+ 1 35. In Ca, Sr, S (I ...5), D (I ...5) are known; also F lines of orders m = 3 ... 6 in Ca, 2 ... 4 in Sr. The equations given for S and F satisfy the measures (except as usual, S (1)) within the large possible observation errors, but the limits are subject to much uncertainty. They make the d-mantissae converge asymptotically. Ca, like Mg, shows S (2. 4), D (2. 4) but no series, whilst no analogous sets have been noted in Sr. The material for the discussion of the Ba doublets is inadequate for any accurate determination of the limits. S (2, 3) are good measures, and both show the proper Zeeman patterns, but the first order, as a negative set belonging to the P series, is, as we know, not avail- able for determining the formula. They give, however, the doublet separation definitely as 1690-93 -02. The third line, measured to three places of decimals by Schmitz, gives v = 1690-58, a deviation from the normal S too great to be accounted for by observation errors. This points to some change from the normal line having taken place and renders it misleading as a means of finding formulae constants. The next is not a good measure and gives signs of an increased v. The calculated limit with ^ = 1 +/ from m = 3, 4. 5 is close to 58635 which also makes the D denominator asymptotic with increasing m. Ba D (2, 3) also show typical Zeeman patterns and the series also gives a limit close to 58635. But the value of d (2) deduced from it does not fit the limit of the F series which is given in the tables although the separation agrees with that of the D satellites. The spectrum contains a very large number of sets of lines with the same separation and shows evidence of considerable disruption. It should also be noted that the doublets, like the triplets, possess two sets of D (2) with different satellite systems and that two separate F series exist with separations depending on the satellites of each D. These doublet systems invite a much closer investigation than they have yet received. * To be distinguished from the notation (1, ... m) which means the whole set of S lines from m = 1 to m =m, or S (I, 2) the set for m = l and 2. m] THE SERIES SYSTEMS 75 It is notable that in Ra the doublet system is quite definite and free from the ambiguities of the triplet system. Runge and Precht have shown that the two first S sets and D u (2) behave normally in the magnetic field. In the Zn sub-group all the D series show a negative set corresponding to m = 1 . Only the first two S and D lines are definite, but they suffice to give the value of the separation. The higher orders lie in the extreme ultra-violet, and failing the presence of the doublet separations amongst observed lines, any allocations of S or D n lines are doubtful. Consequently no reliable limits have been settled. I have added in the table sets for Eu, but in this element great- disruption is prevalent and made conspicuous by the presence of very large numbers of normal doublet and F separations with corresponding diminution of intensity. Group III. 36. The two sub-groups of this family on a superficial glance stand in strong contrast, as the high M.P. elements possess spectra crowded with lines, whilst those of the low M.P. are comparatively poor. But it is probable that in so far as the nature of the series substratum is concerned, they will be found to show an analogy of the same kind as that which exists between II (a) and II (b). As in group I, the series observed are of the doublet kind. Nothing is as yet known as to the series relationships of the high M.P. sub-group beyond an attempt to fix the S and P series of Sc, and the fact that the others Y, La possess doublet systems with separations in rough proportionality to the squares of their atomic weights. The spectra of Al, In, Tl have the great majority of their observed lines allocated to definite sequences. The metal gallium is so rare that its spectrum has naturally not been observed to the same extent as the others. Nevertheless it is definitely much poorer in lines than either Al on the one side or In, Tl on the other. This by itself leads to the suspicion that spectrographically Ga really stands at the head of this sub-group, whilst Al tends to show more resemblance to the Sc set, similar to that which in group II Mg shows to Zn rather than to Ca. This is supported also by a comparison of the Al D series with those of In, Tl. It is also noticeable that while Al, Sc, Y, La, all have well developed and strong bands in the red shaded to the red, In, Tl have at most only slight indications of any such and In on the contrary has bands in the violet shaded to the violet. Putting Ga aside for the present as its series data are doubtful and defective, the S series in all these metals (Al, In, Tl) are reproduced with great exactness by formulae in a/m, all closely similar to one another. There are orders 1-5 in Al, 1-9 in In, 1-13 in Tl. For D there are orders 2-10 in Al, 2-11 in In, 2-15 in Tl with the curious abnormality in In that for the last five orders only the D 2 lines survive. In Al, In, the d lt d 2 sequences show an abnormality in that their mantissas differences for the first order, which produce the satellite separations, are very small compared with succeeding orders. In Al the ordinary formulae are hopeless and in this respect recall the singlets of II. The Al D separations are accurately equal to those of Al S, consequently the D (oo ) must be 70 ANALYSIS OF SPECTRA [OH. accurately equal to S (oo ), which is very closely known. Calculated with this definitely known limit the mantissae run down from -631 f or m = 1 to 059 for m = 10 and exhibit the normal asymptotic quality with increasing order. In In again the formulae fail, though the changes are not comparable with those of Al. On the other hand Tl D is remarkable in that its mantissa decreases at first by about equal small amounts to a final constant value. It shows, however, some irregularity in the first order where the mantissa as calculated from D ( ) = S (oo ) is less than that for m = 2, instead of being greater. That some- thing has happened here is shown also by an abnormal increase of v 7793-08 from 779240 and by the fact that its satellite separation a is less than that of the F doublets 81-98 as against 8248. We shall later see evidence in favour of the first order of Al D being that of m = 2, and against m = 2 being the first in In D, Tl Z>. This again supports the suspicion raised above and the analogy with II, but the evidence is here not decisive. % The P lines lie in the red region and are not amenable to a simple formula, although in the case of In the C are not large. They all exhibit a few in- stances of the combinations p (I) p (m). Those of Al are specially interesting. There exist p l (1) p t (4), p (1) p (5), p 2 (1) p 2 (5). The corresponding sets for m = 2, 3, 4 appear to be disrupted into a number of others, each set showing similar peculiarities. There is a group of six lines 3066 3050 belonging to m = 2 and another six 2321 2312 belonging to m = 4. The two sets show separations of the same amount, indicating that the disruptions take place in the p (1) and not the p (m). No signs have been seen of p (I) p (3). In Tl combinations are so numerous as to form series similar to those observed in II. Thus besides the fourteen orders of D (1. m) there are four of D (2. m), four of s (1) d t (m), two of S (2. m), two of S (3. m) and two of F (3. m) in addition to two of F (2. m). Summation lines for P and F would be in observed regions, but none have been allocated. 37. In the other sub-group only the spectrum of Sc and that cursorily for a special point has been examined*. Its substratum consists of parallel and otherwise related series of doublets with separation 320. As in Eu the normal D series is very much split up and weakened, in the S there is evidence for several parallel representatives and the only, so far, well supported series is the P. In this the orders m = 3 10 for P l and 3, 4 for P 2 have been allocated. The formula calculated from m = 4, 5, 6 reproduces the succeeding lines with fair accuracy, the separations for m = 3, 4 are in step with that belonging to v = 320 f or m = 1, and there is also some supporting evidence in combinations p (I) p (m). Further, the formulae constants are in close analogy with the corresponding ones for Al. A series of three sets of lines with all the appearance of being S series is found which gives a formula for s (m), also in close analogy with that for Al, but the limit is quite impossible as representing p ( 1 ) calculated from the P series. There is, however, a parallel set consisting of the doublet for m = 2 and a representative of S 2 (3), which requires a limit 2870 greater and is close * [m. p. 409.] in] THE SERIES SYSTEMS 77 to the value of p (1) as extrapolated from the p (m) formula. It clearly seems to be the remains of the normal S. Group VI. 38. The spectra of this group correspond in general build with that of its first element oxygen. When the spectrum of is developed in the vacuum tube there appears with very weak excitation a continuous spectrum which is strongest in^the green. With a stronger excitation a line spectrum enters con- sisting of series of (1) narrow triplets and (2) of doublets. With still stronger excitation these lines vanish and there enters another line spectrum with greatly increased number of lines in which as yet no series have been allocated. In addition at the negative electrode there appears a band spectrum. Schuster, the first to separate out the two line spectra, has proposed the name of compound line spectrum for the first and elementary line spectrum for the second. Kayser has proposed the name series spectrum for the first which presupposes that there are actually no series in the second. It will be best to refer to them as the first and second line spectra. For our present purpose the first is the only one to be considered. In there have been allotted by Runge and Paschen (1) a system of S, D, P triplets, (2) a system of S, D, P doublets with (3) a set of two orders of triplets apparently of a D (3, 4) nature. The $, D in both triplets and doublets are fairly well reproduced by the ordinary formulae. The triplet separations are in the ratio 1-8:1 instead of being greater than 2:1. The corresponding ratios in S, Se are 1-6:1 and 2-5:1. The D separations are very slightly in excess of those of S. This, if real, would suggest the existence of satellites with the same kind of abnormality as has been found in Mg D". There is, however, no such indication in sulphur, and in selenium the apparent satellite effect is probably spurious. Although the doublet system is fully developed in 0, no trace of such appears in S or Se. In the lower orders m = 2, 3 have been completed by Paschen by measures in the ultra-red but unfortunately no such observations are at hand for S, Se, whose lowest observed orders in S, D correspond to m = 4. In Se the D series shows an arrangement which at first sight suggests a satellite system. But it does not seem of the ordinary satellite type either in separations, order of the doublet and triplet sets, or order of intensities. The normal satellite effect is due to changes in the d sequent and it diminishes with the order. Here equal "satellite separations" appear in successive orders (m = 5, 6) which point to changes in the limit as the source of the shifted lines. The statement may be illustrated by the following diagrams in which, for comparison, the first refers to a normal D triplet. The numbers in brackets give the intensities of the ob- served lines and the thick type the triplet and pseudo-satellite separations. Cd D" (2). (4) 1170-30 (8) 542-17 (10) 11-10 11-87 ^: ir, =2-17 (8) 1171-07 (10) 18-23 ^^2 = 5:3 (10) 78 ANALYSIS OF SPECTRA [OH. ra (3) 43-47 (4) 6-9 (5) 103-57 (3) m=5 f(5) 104-05 (1) 1-07 -52 (1) 103-50 (4) 45-18 (3) 6-84 (2) I (7) = 7-(3-6 (6) 103-85 (3) 7-44 100 -87 (1) 103-72 (I) 45-22 (4) 1-60 (2) 106-41 (1) 40-82 (3) 4-05 -67 1(2) 103*42 (7) 43-20 (4) No F series have been found as yet, nor are any summation lines known. Group VII. 39. In their paper giving the results of their measurements of spectra in groups IV and V Kayser and Runge * refer to the fact that they, had recognised two orders of S triplets and three of D in the spectrum of Mn. These lines are incorporated in Table III together with an extension in both series up to an order m = 7. The formulae reproduce each set with great exactness. The apparent D satellites are, however, possibly not true satellites. The spectrum is a very crowded one and should well repay a closer analysis. Its chief interest at present lies in the fact that the two series show the undoubted presence of triplet series in a group of odd order. This contravenes the rule found in all other cases that even order groups take triplets, and odd order doublets for their predominant types. * Wied. Ann. 52, 93 (1894). CHAPTER IV RYDBERG'S RULES 1. With the material collected in the last chapter it is now possible to test the degree of accuracy with which the laws formulated in Chapter II are obeyed, or to obtain some idea of the degree of confidence with which they may be applied. For convenience they may be arranged as follows: (A). The value of v (or of v , i> 2 ) is the same for all the members of either the sharp or diffuse series the separation in the diffuse series being estimated from the satellites as indicated in Chapter II, sect. 6. (B). The value of the separation is the same for both sharp and diffuse series. (C). The value of the separation for the first line of the principal series is the same as that for the sharp. (D). Corresponding S and D series tend to the same limit. (E). The doublet or triplet series of the P type tend to the same limit. With Rydberg's rules: (F). S n (oo ) = first order of p n (m). (G). P (oo ) = first order of s (m). (H). The value of N is the same for all series and for all elements. To these may be added : (G'). F n (oo ) = first order of d n (m). (A), (B). One illustration of the exactness with which these laws are followed has been already given in Chapter II from the very accurately measured wave lengths of the calcium spectrum. In further illustration may be taken the large separations of thallium and mercury. Thus Thallium 8(1) 7792-37 D (2) 7793-08 (2) 2-63 Z>(3) 2-64 5(3) 2-46 Z>(4) 1-69 Mean 7792-49 7792-47 Mercury 8(1) 4630-621 1767-338 Z>,(2) 4630-56 1767-62 8 (2) 0-56 7-08 The differences between the corresponding values are well within the obser- vation errors. If the D and S separations were really distinct we should expect their differences to have some relation to their absolute values. Nevertheless with the exceedingly large values in these two elements the equality is evident. There can therefore be little doubt about the validity of these laws in the normal case. When the law in any instance is departed from there must be some secondary cause for the abnormality which it must be the object of investigation to discover. As examples of such abnormality may be given (1) Tl S (4) with v = 7790-92 and 80 ANALYSIS OF SPECTRA [OH. Tl S 1 (4) of abnormal character and intensity, (2) Cu D l (4) (see Phil. Mag. 39, 458), (3) an abnormality common in the rare gases, e.g. in Kr the S (1) separations give v = 7864, v 2 = 309-2, whilst the very numerous satellite sets give values about 788, 307. In this case the higher orders show an approach to normal values. (4) An apparent anomaly frequently occurs in a D set due to the normal satellites being too faint to be observed. (5) Mg" with very exact measures shows different v for S, D. Mg S (I, 2) give v = 91-51 -03 and Mg D (2) gives v = 92-45 -05. (C). If Rydberg's laws (F), (G) are absolute, the first lines of the S and P series are common to the two, and this condition (C) becomes the same as (A). In group I the first S line is generally taken to belong to order m = 2 and the P to order ml. In the alkalies the measures are all very inexact with the exception of Na P (1) in which the separation has been found by interferential measures to be v= 17-175 which scarcely agrees within observation errors with the value as determined from the S by all observers previous to 1921. Quite recently, however, Datta* has been able to obtain the spectrum in the sodium vapour lamp with extremely narrow bright lines and has been enabled to show that the S and D separations agree with that of the P (I) within -005. In the copper sub-group the values are also the same in S and P. In groups II, III the P series have their first lines for order m = 2 and S f or m = 1. This (C) condition is then only true if S (1) be regarded as also P (I). (D). The difficulty of proving the exact truth of this statement depends on the fact that these limits cannot be directly observed. They are in general deter- mined by means of the series formula, and in consequence the values obtained will vary according to the form of the sequence function adopted. In fact if we had to rely only on this kind of evidence we should be led to the conclusion that the two limits are only approximately equal. For instance in copper and silver, using the formula in a/m, and taking account of possible observation errors, the limits thus found are Cu Ag 8(ao) 31536-292 30614-60 3-6 D (< ) 31515-48 10 30644-60 12-2 In neither case can the values found for S, D be equal. Nevertheless as will be shown immediately they must be the same. The error possibly arises from the imperfection of the formula for low orders. This is further illustrated by the example in Chapter II, sect. 16, where the limit Na P (oo ) is found by the formula calculated from the first three lines to be 41447-18, whereas the actual limit found in this case asymptotically from the number of high order lines observed is 41449-00. Unfortunately this asymptotic method of determining the limit is very rarely applicable as it requires a knowledge of a large number of lines of high order. In sodium lines up to m = 10 are known in S and up to m = 12 in D. The orders are too low and the observations too inexact to get a thoroughly reliable test, but they show (see below under (E), (F)) equality of (oo)andD(oo). * Proc. Roy. Soc. 99, 69 (1921). iv] RYDBERG'S RULES 81 There is, however, another method of direct attack on the problem through the co-existence of summation series. Even this is not generally applicable since their low order or stronger lines lie in general in the far ultra-violet beyond as yet observed regions. Nevertheless the number of instances where it is applicable is considerable. For instance, in copper and silver already referred to, the method definitely gives for Cu, S (oo ) = 31523-5 within a few decimals and D (oo ) as very close to the same value; and for Ag the two limits both very close to 30642*6. So also the summation series for sodium give the S (oo ), D (oo ) as very close. 2. Perhaps the most satisfactory proof of the exact truth of this law is an indirect one. The separations in doublet and triplet series are due to changes in the limits. These changes have their origin in different limit mantissae. If then the separations are the same in both S and D, but the S (oo ), D (oo ) are different, the two mantissae differences must themselves differ. Although it may be possible that in a single instance the mantissae may happen exactly to adjust themselves to the two limits to give equal separations, it is highly improbable that this should always happen. The method is illustrated in detail by the two following examples, one from Tl" with a large separation and the other from Ca'" with a small but accurately measured one. (1) As referred to above, the separations in Tl for S and D are the same, and close to 779248. This value is certainly within -07 and probably within -02 of the true value. Also #! (oo ) = 41470-23 = #/{l-626244} 2 , S 2 (oo ) = 49262-71 - N/{l-626244 - -134154} 2 . Let us suppose that A. ( ) = Si ( ) + f = #/{l-626244 - 19-607|} 2 and that D 2 (oo ) is found by subtracting the same 134154 from its mantissa. Then Z) 2 (oo ) = #/{l-492090 - 19-607} 2 = 49262-71 + l-295f . The separation for D is therefore increased by dp -295f . As the dv is certainly numerically less than -07, and probably -02, must certainly be < -2 and prob- ably < -07orZ)(oo) = >S(oo) within these values. (2) Consider /"> &/" in Ca - Here "i + "2 = 158-071, exact to about -003. S 1 () = 33988-250 = N/{1 -7963731 } 2 . The mantissa difference required for v + v 2 is 41627. Thus D! (oo ) = Si (oo ) + ( = Ay{l-796 ... - 264-26} 2 , D 2 (oo ) = Ay{l-7922104 - 264-26} 2 - 34146-321 + 1-007 Thus dv = -007, and since dv < -003, f is not greater than -5. Even with this small separation, the accuracy of its measure is sufficient to show that the two limits must be equal within -5. A similar reasoning is applicable to copper and silver above, for here the separations are large and accurately measured and are the same for both series. This indirect method has the great advantage of being 82 ANALYSIS OP SPECTRA [OH. of general application. We may therefore take the rule that S (oo ) = D (oo ) as normally exact. There are, however, several examples of abnormality, but where this occurs the D and S separations must also differ. 3. (E), (F), (G). These are sometimes combined in the simple but more restricted statement that the difference of the limits of the S and P series gives the first P line. Its proof demands a knowledge of the limits and so is subject to the same difficulties as in the preceding case of (D). In sodium the P l (GO ) is 41449-00 I.A.- 1 correct to a few -01. P x (1) is 16973-34 exact. Hence p (1) = 41449-00 - 16973-34 = 24475-66 or 24474-85 R.A." 1 correct to a few hundredths of waves per cm. The value of S 1 (oo ) calculated asymptotically from the orders m = 6 ... 8 of S from Datta's measures agrees exactly with this, whilst the value of D l (oo ) from the slightly less accurate D data gives a limit about -1 or -2 less. Thus p (1) and S (oo ) are equal within observation errors. The question has been considered in detail by the author* on a formula basis and with reference to the alkali metals. The result is that S (oo ) = p (1) within easy limits of observation errors, but that P (oo ) is not the same as s (1). The true deduction from this is that the formulae fail in completeness, and that s (m) determined from the S lines m = 2, 3, 4 does not give the true value of s (1). A similar result is found to hold in group II with the difference that while P (oo ) = s (1), S (oo ) is not p (1). This is explained on the supposition already arrived at that the P, S series in group II are based respectively on s, p sequences instead of p, s. The attempt was made to test the two rules by taking mantissae of the form a/m + /3/m 2 in sodium and potas- sium. It was found possible to make them hold within error limits in both elements. Whilst in p (m) the j8 was very small compared with a, in s (m) the and j8 were practically equal. From all the evidence available we may conclude that each law is separately valid, but we must be careful in applying it to our sequence formulae. If, however as we shall do later we attempt to discuss the properties of the sequences by dealing with their calculated denominators, the law can be directly employed. Thus while s (I) must not be calculated from the sequence formula, it may be calculated from s (1) = P (oo ) = P (1) + p (1). 4. (H). We now come to the important question as to the uniformity of N. Is N the same (1) for all series, (2) for all elements? The fact that the enhanced series in group II require a value of 42V might seem to answer this question in the negative, but as this is a definite simple multiple of N, it depends like the other series on the true value to be attached to N, and merely suggests the possibility of the existence of other series in which other multiples may enter although none such have yet been noticed. At first sight it might be thought that the question could be definitely settled by direct calculation of formulae constants from the different series. Indeed this procedure shows by the general agreement of calculation with observation that the law is true to a first approxi- * [i. p. 75.] iv] RYDBERG'S RULES 83 mation, and that any change in N, if it exists, can only be a very small percentage of Rydberg's value. This result alone is of the greatest importance. But, as will be shown immediately, not only does the determination of an exact value of N depend on a knowledge of the true sequence function, but any change dN in the deduced value of N is affected so largely by observation errors that in many cases the uncertainty is greater than the deduced dN itself. In two cases only the first spectrum of H and the enhanced of He is the form of the sequence function known with sufficient exactness to give reliable determinations of N. In both also the observation errors are small. The values in i.u. obtained are 109679-2 for H and 109725 for He. In these any observational uncertainties are extremely small and the result shows that the law as it stands is not exact. According to a theory of the origin of these special series by Bohr the true value M of the numerator in the sequence function should be -p. - N*, where M is the atomic mass of the element in question, m that of an electron, and N& is an absolute constant, which can be deduced therefore from the observed value for hydrogen. Thus * 1097384. This would give for He the value io97384 = 109723-6. The agreement with the observed is suggestive, and in so far supports the results of Bohr's theory. It would make N = 109736 for sodium, and practically the same for all heavier elements. But we are only dealing with evidence from observed facts and must not place reliance on any theory, especially by extending it from two very specialised series to series which it fails to account for. The result then of appealing to the only known cases where the functional form is sufficiently definite is to show that N is not an exact constant, although in those cases (1 + m/M) N is the same for both. Can we get any further evidence by using the incomplete formula in a/ml To apply this the method of Chapter II, sect. 15 may be modified as follows. Suppose the true value of N is N (1 + f ) 2 , where now N has Rydberg's value. Determine the denominators D m with the old N as before, say Then the denominator with the new N will be a = m + LL H say m or mp, + a = w 2 f + (a m -b *.()(! + f) ? 62 84 ANALYSIS OF SPECTRA [CH. whence p, = (2m + 1) + (Aa - A6.f) (1 + ), = (Aa- Thus y_ _ 2+ " If the first reference Hne corresponds to m = 1, and the old sequence mantissa = jLt + a/m, the new mantissa is The method requires four lines of reference, in which the observation un- certainties in dn in the higher orders must be considerable. As A 2 a . A 2 fe is in general small, its uncertainty due to these possible errors is a considerable fraction of its actual value, quite apart from that due to the functional form. In general, therefore, no result of any value is to be expected from this line of attack. The conditions of its applicability would seem to be : (1) An independent determination of the limit, either by the existence of summation lines, or by the asymptotic method when a very large number of orders have been observed. In this case f = 0, three lines are required in place of four and since A 2 a is in general small. (2) The observation errors should be very small. (3) Series should be used in which the ascertained value of a is small. In this case the functional defect is at a minimum. These conditions are met with in the ordinary vacuum tube spectra of helium and in Na P. Take first the case of sodium which gives an asymptotic limit of 41449-00. The measures are all good with the exception of that of P (3). Suppose that the true wave length of J\.;(3) is d\ = -1 x p greater than the observed. Its wave number is then 30272-89 -9p. The result, using the three first lines, is _ . 000406 _ .Q00254p. This illustrates the remark above as to the great percentage uncertainty due to observation errors. With p = 1, N = 109768 56. In any case the important fact emerges that N is at least considerably greater than Rydberg's value. Possibly some estimate of the value of p may be obtained by taking four lines and finding f in terms of p. The result is 487 - 756y 367-7 as | = 0, this gives p = -64, i.e. dX = -06 on Wood's value or -04 on Kayser's. The latter gives his possible error as -03, but the uncertain reduction from R.A. to I. A. may account for more than -01. With this value of p, the most probable values of , N for the p sequence are = -000256, N = 109735-5. iv] RYDBERG'S RULES 85 It may be noted how close this is to the value deduced for sodium by Bohr's modification given above. The measures of Na S and D are too inexact to deduce any reliable values of f for the s (m) and d (m). Also the functional form will have a large effect on the result. If the limits be calculated from P (oo ) and P (2) and Kayser's estimates of his maximum errors are used, it will be found, allowing for a small error f , that for s (m) - -000952 550 + 336 with a/m, = -000273 471 -1- 312f with a/(m - J), for d (m) = -001323 1035 + 384f . It is just possible that all may be the same as in p (m). The two results for S illustrate the uncertainty due to functional form. 5. Both He' and He" satisfy the conditions of applicability except that a larger number of observed orders might be desirable in order to get the asym- ptotic value of the limit. The author has applied* the method of least squares to all Paschen's observations except the S (2). The calculated and observed lines agree very closely. The values of N obtained are entered in the first lines of the subjoined table. The second number under each head is that obtained in Chapter III, sect. 4, using interferometer measures, and making S (oo ) = D (oo ). In this case the values of the limits do not satisfy exactly the law The limit obtained from D' is 27175-711, those from the old R.A. measures of Paschen expressed in i.u. give 27175-823 for S 1 and ...5-533 for D' whose mean, . . . 5-678, differs only -033 from that obtained from interferometer measures. The latter is therefore quite certainly correct within a few hundredths of a unit. P(oo) calculated from P(2) + (oo) is then 32033-172. With this value of P' (oo ) the value of N comes to 109756, given in the third line of the table: PSD (109814-6 109726-0 109672-2 He' J109783-4 (l09756-0 109764-3 109764-3 109714-5 109714-5 (109666-2 He" <109651-6 (109673 109719-6 109795-1 109795-1 109689-2 109707-5 109707-5 For He" the S and D limits in the least square determination differ by -1 only and their mean, equivalent to 29223-58 i.u., is probably more exact than in the former case. This gives P" (oo ) = 38454-64, from which results N = 109673. In comparing the values it should be remembered that in using least squares, the first order in both S series was omitted as its value depends so considerably on the functional form. The general evidence goes to show that the values of N may be the same, say 109760, for P', S', S", the same, say 109710, for D', D" * [i. p. 102.] t P ( 2 ) is the fi rst line 86 ANALYSIS OF SPECTRA [CH. iv and the Rydberg value for P", but the least square values suggest that the Z)', D", P" have the same N near Rydberg's value. In this connection the evidence adduced in Chapter III that the series He P" is really the F or D type, and is s" (1) f(m), should be recalled. The striking difference indicated by its value of N may be thus explained. Further the sequences in D', D" only differ from one another as representing one a satellite system of the other, and the same value of N should be expected. If the least square values are correct then the d, f sequences have the same N, and also the p, s in accordance with what is known as to their other similarities. The He systems therefore point quite definitely to the possibility that N is slightly different for different types of sequences. But even this must not be regarded as established with full certainty. The preceding discussion has shown that we cannot hope to determine exact values of N in the various series and elements from determination of formulae constants alone, but it has made it practically certain that the value in general is larger than Rydberg's value and closer to Bohr's limit 109738, and that changes in N in the different sequences should not be unexpected. Later when the properties of these sequences- come to be considered in detail it will be seen how important it is that in each case an accurate value of N shall be at disposal. It is then possible that when these properties become more fully established and further developed a method may be placed in our hands for the more complete determination of this important constant and its variations. This will be returned to in Chapter IX. CHAPTER V EFFECTS OF PHYSICAL CONDITIONS LINES related in type respond in a similar way to physical conditions. Con- versely in analysing a spectrum one of the first steps is to group together those lines which are affected in the same way by conditions of excitement or physical environment. Some of the most important of these will be considered in the present chapter in so far as they are applicable to our purpose. For this, by far the most important and definite is the effect of a magnetic field and it will be taken first. The effect of an electric field comes next. Although the Stark effect will, no doubt, ultimately be of the greatest importance in settling questions connected with atomic constitution, its value for analysing a composite spectrum has not proved so great as it promised to be on its first discovery. It is only in elements of low atomic weight that its effects are distinctive and even then they are not so quantitatively definite as those exhibited in the magnetic field. To these follow short descriptions of observations on the Doppler effect and on ionisation and radiation potentials. These do not exhaust the types of changes available, but they are the most definite. In dealing with individual spectra, the changes due to variations in excitement, temperature, gas-density*, line complexity, line character, and other effects should also be noted and used to separate lines into categories, but little is known as yet to correlate these effects with series types or other regularities. The Zeeman Effect. 1. In 1896 Zeeman discovered that when a source was subject to magnetic force, the frequency of the light emitted was modified in such a way that a single line became split into several components symmetrically disposed on either side of the original line. Led by certain theoretical views of Lorentz, he tested the polarisation state of these components and found that they were polarised in definite ways related to the direction of the field. Consequently the details of the effects observed depended on the direction in which the light was viewed relatively to the field. When the line of sight is at right angles to the field (transverse position), the components are plane polarised either parallel or perpendicular to the field ; when it is in the direction of the field (longitudinal position), those components which had their oscillations (electric displacements) perpendicular to the field now become circularly polarised, whereas those oscillating parallel have disappeared. Lorentz' theory was based on the sup- position that the free oscillations depended on accelerations produced by forces proportional to displacements, or, as they are called, quasi-elastic forces. Since * Commonly called the pressure effect. 88 ANALYSIS OF SPECTRA [OH. Rayleigh* pointed out that theories based on quasi-elastic forces give i> 2 directly, whilst the luminous frequencies require v as in theories based on the forces acting on electric charges moving in a magnetic field it has been generally recognised that this basis is inadequate. The theory, however, explains easily and directly all the phenomena for the case when a single line is split into a triplet of a certain magnitude. The theory correlates the different polarisation effects so directly that it serves to give a clear mental picture of the nature of the changes and is useful as enabling us to recall the polarisations without burdening the memory. For this reason the simple theory for the triplet is here indicated. In the case of a particle under elastic forces and freely oscillating in a period n, the force at a distance x from the point of rest is aj 2 x, where co 2nn. Take axes x, y, z with z parallel to the magnetic field H, and x, z the plane in which the observations are made. The vibrating particle is an electron of mass m and charge e. Then mx = ma) 2 x, my = ma> 2 y, mz = ma> z z. When the field H is applied the electron experiences an additional force per- pendicular to the directions of motion and of H and equal to Hev, v being the component velocity perpendicular to H. The equations now become mx = mw 2 x Hey, my = ma> 2 y + Hex, z aj 2 z. We can thus regard the motion as composed of a linear motion parallel to H and unchanged, and of circular orbits in the plane x, y in other words, treat any linear oscillation in the plane x, y as replaced by two equal and opposite circularly polarised vibrations and consider what happens to these when the field is applied. Suppose then the observer is facing the light and considering the clock directed or right-handed rotating orbit, with the field directed away from him. Then the field produces an inward force on the moving negative electron. Thus the cir- cumference tends to diminish without a change in the velocity. Hence its period is diminished, or the resulting wave length decreased, and we have a component displaced to the violet consisting of right-handed rotational movement. So, also, the other orbit is expanded, the period increased with the production of a component displaced to the red of left-handed rotational movement. At the same time the vibrations parallel to the field being end on, produce no effect. Hence the original line becomes split into two symmetrically placed components with equal and opposite circularly polarised light. If the observer is transverse to the field the vibration parallel to the field produces its full effect and, as its frequency is unaltered, we have a line in the original position, but now vibrating parallel to H (plane polarised perpendicular to the field). The two circular orbits now lie with their planes in the line of sight and produce light whose electric vector is perpendicular to the field. We shall, following the usual custom, define the light by the direction of the electric vector, using the symbols p, s to denote respectively the components vibrating parallel and perpendicular to the field. Thus the original line is split : * Phil. Mag. (5), 44, 356 (1897). v] EFFECTS OF PHYSICAL CONDITIONS 89 (1) When observed transversely, into a triplet whose central component is parallel, and external components are perpendicular to the field; (2) When observed longitudinally, into a doublet whose components are oppositely circularly polarised, the directions depending on the direction of the field as indicated above, i.e. the component on the violet side depends on rotation in a direction given by a screw screwed along the lines of force. The actual amount of the displacement is easily found, for in the circular orbit the disturbing force is Hewr and the elastic force mcu 2 r. Hence, if 1} be the new angular velocity =F HeQr, m I He ^" T 2^' since He/m is small compared with at. Hence the change in frequency is He/4:7rm. liv denotes the frequency and the wave length is A A.u. = 10~ 8 A cm. vel. of light _ 3 x 10 18 wave length A , He 3xl0 18 dA .'. dv = . -- = -- ;- 4-Trm A 2 If n denote the wave number, n = IC^/A. Hence with e/m = 1-772 x 10 7 E.M.U. dn 10- 10 e ^ = -^ --- - 10- 5 x 4-70. H 127T m This gives the shift in wave number per gauss. There are a very large number of observed triplets with this shift. Such a triplet is generally referred to as the normal triplet. All the magnetic shifts are small quantities e.g. in the case of A = 5000, it requires a field of 4250 gauss to produce a change d\ = -05 A. in this triplet. Ritz, following Rayleigh's suggestion, has supposed the light frequencies to depend on electrons moving in given internal magnetic fields, and that when the source is under the action of magnetic fields the internal is set parallel to the external. This theory is even simpler than that of Lorentz. For if H be the field 277^ = He/m, 27rdv = e/m x dH, or j? = ~ . (H = applied field.) On this theory the normal triplet has twice the spread of the former. Ritz has also attempted to explain the existence of other types. In accordance with general usage we shall refer to any triplet corresponding to the Lorentz as the normal triplet*, and denote the shift per 10 5 gauss of the * The question of normality as between one shift and another does not enter. It would be preferable to call it the standard triplet. 90 ANALYSIS OF SPECTRA [OH. lateral components by the letter a, but the value of this latter quantity must be that found by direct observation. 2. Not all lines are affected by the magnetic field, but of those that are, the types of the splitting are very varied, in number of components, in their shifts, in their polarisation effects, and in their relative intensities. The actual arrange- ment of the components in any given line will be referred to as its Zeeman pattern. In the vast majority of the cases observed the following relations are found to hold, and may be regarded as normal laws. (1) The shifts are accurately proportional to the field. (2) The shifts of the components in a Zeeman pattern can be expressed as multiples of a common quantity. (3) This common quantity is a sub-multiple of that of the normal triplet, or a. (4) The red and violet components are symmetrically arranged and corre- sponding components on the two sides are of the same intensity. (5) The centre of symmetry occupies the position oi the line with no field, (6) There is no s component occupying the position of the original line. (7) The shifts of the s components observed transversely and those of the corresponding circularly polarised observed longitudinally are the same. (8) Preston's law. Examples contravening these relations are known. They are to be regarded as anomalous and explanations of the anomalies are to be sought for. Examples will be given below. 3. From (1) it follows that if dn denote the change in wave number of any component due to a field H, dn/H is constant. The proof of the constancy of dn/H, as well as the determination of its value for a given case, are matters clearly of the first importance. The difficulty in determining its absolute value depends on the difficulty of measuring the value of the field with sufficient accuracy. We owe the establishment of the accuracy of the law chiefly to two independent investigations carried out at about the same time, one by Frau Stettenheimer* in Paschen's laboratory and the other by Cotton and Weissf , in both cases with special precautions to obtain measures of the field of an accuracy greater than that of the shift measures. Frau Stettenheimer observed the shifts of Zn S 3 (1) and of Cd S 3 (1), for fields varying from 10,000 to 35,000 gauss. These lines both give triplets in which the s-components have twice the spread of the normal triplet, i.e. are Ritz normal triplets, and the distances of the extreme s-components were measured. The following table gives the values of l0 5 dnjH for the various fields indicated. H ZnS CdS H Zn 8 CdS 9970 19-01 18-99 23640 19-10 19-06 10050 18-93 18-92 31700 19-04 18-97 10210 18-99 19-05 31720 18-93 18-92 23270 19-12 18-99 32010 19-00 18-99 23345 19-03 18-95 34910 19-07 19-08 23420 19-06 19-06 Mean I'(2), 5790 symmetric triplet moves to red : : H 2 (Gmelin)*; Cr, 5247 symmetric triplet moves to violet : : H 2 (Dufour)f. : (c) Hg/ - d 3 '" (2). 5789, and the - -081 companion to Cd S 2 (1) show the following quite anomalous splitting with one s-component in centre. Hg Cd Fig. 13 They are possibly due to mutual effects with neighbours. (d) Of the examples from Cr given on p. 92 (Dufour), 5204, line of symmetry displaced to violet, but intensity asymmetry in * of (3. 10. 15 : 25. 10. 11). 5206, no displacement and complete symmetry. 5208, no displacement and complete symmetry. Where intensity asymmetry in these and neighbouring lines is found, it is shown also by the longitudinal observations. (e) Dufour also adduces certain examples of intensity asymmetry from bands. Thus /2 2 18 18\ inCa 529M, 3.6/1.6/10; ( 2 ' 12. 18 8 ) red stron er 5293, 2/1. 3/5; red W6aker inSr 6362, 1. 3/? 8/? wYo red (/) In Th$ A = 3959, the shifts are - 1-42, 0, 1-23 / 1. 5. 15 - 1-, 0, 1-23 / 1. 5. 15 \ - 2-00, 80, + -98, +1-87 \l7T 1. ?/ * Here the extreme p and s components are bodily displaced -09 to one side, while the mid s-components are displaced the same amount to the other. A similar opposite displacement of s-components is indicated in Ba D 12 " (see below). In the present case it could be explained by the line being a close doublet -18 apart, one producing 0/6/5 and the other 0/7/4. With reference to (6), that there is no undisplaced s-component, this appears to be the normal rule. Deviations from the rule are comparatively rare although several examples are known. Many are given by Moore as occurring in Zr (one given above), and a few are known in other elements, e.g. 3587, 3733, 3865 in Fe (Reese). Also according to Miller the anomaly is present in MgZ> 2 "' and MgZ> 3 '". Paschen and Back find that H a has an abnormal triplet with centre containing both p and s. * Phys. Z. S. 9, 212 (1908). f c - R- 150, 014 (1010). % Moore, Astro. J. 30, 144, 178 (1900). v] EFFECTS OF PHYSICAL CONDITIONS 99 11. Soon after the discovery of the effect by Zeeman, an extremely important and fundamental law was postulated by Preston*, generalising from a few cases. It is that in all elements lines belonging to the same series show the same Zeeman pattern in a magnetic field. Its truth has been specially tested by Kunge and Paschenf as between corresponding S, P, D doublet and triplet lines in different elements and in Hg for different orders of the same series. In the S and P series there would seem to be few, if any, exceptions from the rule. It is found that the patterns for corresponding S and P lines are the same, supporting the con- viction already arrived at from general considerations that they belong to sequences of the same type. But the comparison further shows that the en- hanced doublet systems of group II have the same Zeeman pattern as those of the corresponding types in groups I, III. This result would hardly have been expected when the quite different conditions required for their excitation are considered and the further contrast in requiring a Rydberg constant quadruple the normal {. In the case of the D series the observational difficulties are increased especially in the satellite measures. There are also examples of apparently ano- malous behaviour, not to be unexpected when we remember the tendency of the d-sequents themselves to behave irregularly. The value of the rule in the analysis of spectra and the establishment of series is clear. For this reason the various patterns so far determined are collected here for reference, followed by a short discussion of the material. Doublets. S l9 Pi 9 1/3.5/3 DU\ 312.4.613 2 ; 0/1/1 S 2 ,P 2 ; 2/4/3 D u ; 0/3/2 F, observations wanting. Triplets. ^,P i; 0.1/2.3.4/2 S 2 ,P 2 ; 1/3.4/2 S 3 , P 3 ; 0/4/2 Z) 13 ; 0.2/1.3.5/2 Z> 23 ; 2.4/1.3.4/2 Z> 3 0/1.5/2 D u ; 4/7/6? Z> 22 ; 0/1/1 D u ; 0/7/0 F 13 - ? ^ 23 ; [0/5/4]? *V, 0/3/4 F 12 ; 0/5/4 FM', 0/1/1 F u ; 0/7/0 Singlets. S,P; 0/1/1 D; 0/1/1 * Phil. Mag. 47, 165 (1899). f Astro. J. 15, 235, 336; 16, 118 (1902); Sits. Berl. Akad. June 26, 1902. J The result follows naturally, however, on the quantum orbit theory. 72 100 ANALYSIS OF SPECTRA [OH. Combinations. p 2 '" (1) - s' (m) 0/3/2 p'(l) -d z '"(m) 0/7/6 Pi'" -d'(m) 3.6/4.7.10.13/7 p 2 "' - d' (m) 0. 4/7. 10/7 K" - # M 0/1/1 The components in italics are sometimes suppressed. It should be noted how in S" all the multiples 1 ... 5 of a/3 are comprised in the two patterns, whilst in S'" the S z , S 3 together give S 1 with the multiple 2 excepted. The actual measures for the D patterns present some difficulties in settling the actual Zeeman pattern formulae. The ratios of shifts are in general determinable, but the actual measures of the shifts suggest in many cases either aliquot parts of a slightly larger a than the normal, or the presence of Ritz shifts. The point may be illustrated by considering the data for the doublets. The following are the measures given by Runge and Paschen in Ca, Sr, Ba. D 12 D n Z> 22 1-09, -1-09 Ca Ba 1-45, -1-45 1-52, -1-52 1-12, - M2 H)9, -1-09 Q __+l 3 _ 1-41, - 1-41 1-53, -1-53 1-14, - 1-17 Ml, -Ml -0-2 -01 2-16, 1-44, -70, --78, -1-46, -2-06 1-51, -1-49 1-11, -1-12 In these measures, a corresponds to a value between 1-03 and 1-09 in the different sets of observa- tions. Here it is clearly 1-09. There is no difficulty with the D 12 f r l'^5 is 4a/3. Ba shows opposite shifts of centre in the mid and extreme s-components of about equal amounts. Allowing for this, the pattern for Ba is 3/2. 4. 6/3, which includes that of the other metals. This may be due to the fact that the two extra sets in Ba were too weak to be seen in the others or to a new effect in Ba. Tl also shows the more complete pattern of Ba. In Cu, Ag, the 2. 4 of the s are absent. In the D u the s-shift is less than 3a/2 which should be 1-63 if a = 1-09 10a/7 would give 1-56. In Ag the measure is exactly 9a/7. The patterns, being triplets, give no means of deciding directly whether a Ritz shift is present, but such would explain the irregularity. Either the pattern is 0/10/7 with an anomaly 0/9/7 for Cu, Ag, or there is a Ritz shift on the pattern 0/3/2. At least this latter represents the general nature of the pattern, and is so entered in the list. In D 2 they all agree in giving the s-shift somewhat larger than normal a, and in this Cu, Ag also agree. We have seen in Chapter III that Mg D" has a close satellite on the abnormal side of Z> n . This abnormality shows its effect here in that while Mg Z> 2 gives the normal Zeeman pattern that for Dj is 0/4/3. In other words the ^-component is the normal one for -D u " and the s-component that for D lz ". In D lz '" the material at disposal is meagre. The components are too weak to measure except in Hg where they are quite definite. The only other measures are by Miller in Cd, which are definitely 2/5/? in which the aliquot part is -38 in place of -54 in Hg. In Hg -Z) 12 '" the measures are not very regular, but indicate 2. 5. 8/5. 7. 9. 1 1/6*. But we have seen that the second satellite system in Hg'" is quite abnormal in that it gives satellite separations in the ratio 3 : 5 in place of 5 : 3. We should hesitate therefore to base the normal Zeeman pattern for D lz '" on it. The only other measures are by Miller from weak components in Ca, Zn, Cd which, allowing for consider- able observation errors, may agree with 4/7/6. This may be taken to indicate the nature of the Zeeman pattern. For Z) n "' Miller's measures for Ca, Sr, Zn, Cd definitely give 0/7/6, whereas Runge and Paschen's for Hg give 2/7/6. This difference in the p-component may be due to the fact * This deviates from the general rule that the relative shifts are the same. Here the relative p shifts are 3a/6 and the s are 2/6. v] EFFECTS OF PHYSICAL CONDITIONS 101 that the line 3650 or D n is like the Z> 12 not a normal D u line, or possibly, since the line is so far in the violet the zero p-component was absorbed, whilst as in the other satellites of Hg an additional and stronger ^-component has entered at 2/6. In D 23 '" Runge and Paschen give for Hg, 2. 4/1. 3. 4/2 for m = 2 and 2/1. 3/2 for m=3. For Ca, Zn Miller gives the same p-component and for the s a magnified a, but the readings are confused by the two close satellites. In Cd the pattern is 2/1. 3/2 and thus agrees with Hg. Sr shows an undisplaced p line with pattern 0/3. 2 quite definitely. The extreme Sr satellites would appear therefore anomalous. In Z> 22 "', Ca, Sr, Zn, Cd all agree but in Hg Runge and Paschen found 0. 2/4. 6. 8/5 for m=2 and 0/1/1 for m = 3. The two cannot be related, and again we find additional evidence of abnor- mality in the chosen mid satellite set in Hg for m=2. In TV" both orders of Hg give 0/1/2. So do Ca, Zn, Cd, but Sr shows an irregularity. The s-shifts in Sr are 1-59, -74, - -32, - 1-59. There appears to be a displacement of the centre of sym- metry of the mid components. Their mean is -53 or the true a/2. If this be taken, the formula 0/1. 3/2 contains the other. But again the extreme satellite set in Sr has evidenced some anomaly. Mg D'", being a non-satellite D series, may be expected to possess patterns different from the others. They are Z>j 0. 1/1. 2. 3/2 Z> 2 1. 2/0. 1. 3/2 D 3 0. 1/0. 1. 2/2. These all depend on the same aliquot parts a/2 as the extreme satellites of the other elements. Z> 2 , D 3 show the comparatively rare anomaly of an undisplaced s-component. One suspects an observational cause. For F" observations are wanting. The lines lie in the red in groups I, III and in the violet in group II. For F'" are observations by Moore in Sr, Ba only. The patterns given in the list are those of Ba. In Sr the satellites are closer, and the shifts as measured for the main lines may be confused by the presence of those of the next satellite of comparable strength. For F lt Sr has a shift 1-32 compared with 1-24 for F n and 1-38 for F 12 in Ba. As it is actually the mean, it may be taken as confirming the results from Ba. For F Z2 , Sr gives 1-21 as against 1-09 (normal) in Ba. The F 22 , F 23 lines in Sr are of equal intensity with d\ = '35 A. The numbers suggest therefore the normal for F 22 as in Ba and 0/5/4 (shift = 1-38) for F 23 . For F^, Sr gives 0/4/3. For the next order (w=4) in which no satellites are observed, Sr gives for each constituent 0/0 or no action. No effect for the higher orders is a frequent observation. The F'" patterns cannot as yet be considered as definitely established. The singlets all give normal triplets. These, as well as those of the combinations, are due to Runge and Paschen, Runge, Moore, and Wali Mahommad. The latter, s' - p z '" excepted, depend on a few instances only. These must be regarded as provisional. The above discussion illustrates the value of the Zeeman effect as an instru- ment in the analysis of spectra, not only in assisting in the allocation of series, but also as indicating where actual series lines are subject to some anomalous effect such as displacement from a normal but unobserved line. For this reason alone, quite apart from its more absorbing interest as a means of throwing light on questions of atomic structure and the origin of spectral lines, a more ex- haustive experimental study of the various patterns and their changes under conditions of field, displacement, or linkage (see below) is much to be desired. The fact that the patterns do not depend on the order in a series shows that they do not arise from modifications in the current sequence. The other fact that they are different for S and D and for D satellites further shows that they are also independent of the limit sequent. The fact that they are the same for the same type of series in all elements supports this and also shows that they do not depend on the atomic weight or atomic number, or indeed on the differences of the physical constitution of different atoms. The shift must be represented in the formula for the frequency by a third term which is fixed only by those 102 ANALYSIS OF SPECTRA [CH, conditions which determine the nature of the series type, but is independent of those conditions which settle the actual magnitude of the configuration changes*. The Stark Effect. 12. That the presence of an electric field affects the radiations emitted by an atom was first announced by Stark f in 1913. The phenomena are, however, by no means so regular and so definite as those in the magnetic field. In H and He the magnitudes of some of the effects are incomparably greater than those of the Zeeman. Stark instances this by the fact that, while for a wave length of 4000 A. in a field of 30,000 g. the components in the normal triplet differ by only -5 A., those of H y (4340) in an electric field of 30,000 volts per cm. differ by 13 A. These large effects are not exhibited by elements of larger atomic weight, nor are they sufficiently regular and distinct at least so far as in- vestigations have yet gone to afford much assistance in determining a priori types of observed lines. The effects may be classified under the following heads. (1) Components are polarised parallel and perpendicular to the field, and in general the p and s components show different displacements. Naturally those components which, when emitted transversely, appear as ^-components are not seen when observed longitudinally, whilst the transverse s-components are reproduced with the same displacements, but now unpolarised. (2) A line may be split into several components on either side of the original line. But this complex decomposition has only been observed in H, He, and a few other elements. (3) The original line is split into one p and one s representative and dis- placed either to the red or to the violet, but most frequently to the red. This appears to be the general type. (4) The displacement is normally proportional to the field. (5) In certain cases the electric field brings into prominence lines not other- wise observed or renders sharper certain lines which appear as very diffuse under ordinary conditions. With this occurs also considerable displacement. This phenomenon was first observed by Stark { in Li and by Koch in He. The displacement is proportional to the field and increases with the order. 13. Hydrogen. In H with fields of about 28,000 volts per cm., the lines split up more or less asymmetrically not only in position, but in intensity. When the field, however, is increased to 74,000 volts per cm. all traces of this asymmetry disappear, and the former components are resolved into additional constituents. Stark refers to the former as a coarse analysis, and to the latter as a fine analysis. * Thus on the quantum ring orbit theory it would depend simply on the nature of the change causing the light emission. It would not arise by a modification merely in the two levels between which an electron falls. The magnetic field causes a definite amount of energy to pass from some electrons to others or it adds a definite amount in some cases and subtracts an equal amount in others. These amounts will depend on the two kinds of initial and final paths, but not on the paths themselves. Further, if we may generalise from the equality of the patterns for the doublets in groups I and III, the effect is independent of the number of external electrons in the atom or possibly is the same for those atoms with an odd number of external electrons. t Ber. Berl ATcad. d. Wiss. 47, 932 (1913); Ann. d. Phys. 43, 965 (1914). I Ann. d. Phys. 48, 193 (1915). /&. 48, 98. v] EFFECTS OF PHYSICAL CONDITIONS 103 His results* for the coarse analysis of the first five lines may be represented as follows, using the same conventions as for magnetic decomposition. x 6563 4861 4340 4101 3970 d\ -3-15, +3-42 + 18 -4-01, +-89, +4-18 Intensities -6-23, -1-88, +1-53, +6-72 -4-18, +-89, +4-41 -9-1 6, -2-80, +3-56, +8-54 -6-72, -2 7 36, +1-90, +6-72 -11-3, +12-2 /7.MO\ V 6. 1. 8 ) /4.1.1. v 2. 4. 4 /2. 1. 1. 3\ \l. 1. 1. 2J (very small) For comparison the corresponding ineasuresf for dn in the fine analysis are given for H (4), or H^ : - 10-6, - 9-6, - 7-2, - 4-8, - 24, 0, + 2-4, + 4-9,^- 7-2, + 9-6, + 11-9 - 14-6, - 12-1," - 74, - 5-0, - 2-5, 0,~+ 2-5,"+ 5-6; +7-3, + 11-9, + 144 ' It will be noticed that the numbers of p and s components have increased from three to eleven and that all traces of asymmetry or displacement of centre have disappeared. Lately, however, Takamine J and Kokubu have found that with a field of double the strength of Stark's, the centre s-component of H (4) is displaced to the red by 1 A. The following diagram illustrating the fine analysis for H (4) is based on a similar one given by Stark. The number of components increases with the order of the line, viz. 11, 13, 14^-, and 11, 13, 16 5-components respectively f or m = 3, 4, 5. The beautiful order and symmetry exhibited by the Stark effect in this first element in- vestigated would naturally raise hopes that the electrical effect would place in our hands a very effective means for probing the con- H(4) P" Fig. 14 stitution of the atom and for the analysis of spectra. Unfortunately no other element responds in a similar way. It is only in He, Li, and perhaps Cu and Ag, that complex decompositions have so far been observed. 14. Helium. A similar difference between coarsl and fine analysis has been found by Stark and Koch in the two D series in He' and He". In this case, how- ever, there is considerable asymmetry in intensities accompanied by shifts to the red. Messrs Takamine, Yoshida and Kokubu have also investigated the effect for He by Lo Surdo's method, which has the advantage of showing on one plate how the displacements vary with the field. One of the most striking of their results is the way in which, in the D series that which gives a complex * Ann. d, Phys. 43, 1026 (1914). t Ib. 48, 193 (1915); Elektrische Spektralanalyse (Leipzig), p. 54 (1914). J Mem. Coll Sc. Kyoto, 3, 271 (1919). Mem. Coll. Sc. Kyoto, 3, 275 (1919). 104 ANALYSIS OF SPECTRA [CH. splitting the components seem to depend on detached original lines. As this is of great importance in connection with the constitution of these series their diagrammatic representations of the effect for m = 3, 4 in both He' and He" are here reproduced. X 4922 ='(3) X4388=Z>'(4) -20 -10 +10 +10 +20 V 10 10 L 10 10 Fig. 15. Scale of abscissae in A.U.; of ordinates in 10* volts/cm. X4472=Z>"(3) -10 * 70 10 15 L X4026=Z>"(4) o \\ 10 Fig. 16. Scale of abscissae in A. IT.; of ordinates in 10 4 volts/ cm. The existence of these detached satellites is clearly shown and they do not appear until the field has reached a certain strength, and then increase rapidly v] EFFECTS OF PHYSICAL CONDITIONS 105 in strength. They seem to be analogous to Koch lines. In describing the helium spectrum we have already recognised in the slightly different sequences appearing in D', D" at least two sequences in a satellite relation, which would account for these. The detached lines in D" for m = 4 are closer in than for m = 3, as they should be on this supposition. In D r there are two of which the outer closes in with increasing order whereas the inner appears to keep the same position. It would thus appear that the complex systems in He are only apparently so and have no analogy with those of H. They may be really due to the combination of Stark effects for neighbouring lines, of which the strongest shows components displaced to the red alone, whilst the other two (? Koch) have components displaced to the violet alone. Both S r and S" are displaced to the red by amounts increasing with the order and about the -same for p and s. A similar law is fol- lowed by P", but P', on the contrary, is unique in being displaced to the violet increasing with the order and about the same for p and s. The only similar effect hitherto observed (Koch lines excepted) is in Mg in the first line of the strongly accentuated type s' (I) p 2 r " (m). This suggests the inference that the He', He" are really analogous to the strong singlet series related to triplet series found in all the elements of group III. No triplet series have yet been found for He, but the other rare gases from A onwards have well defined representatives. Helium shows a further peculiarity in that for m = 4 both S' and S" (4437, 4121) have two p- and two s-components, both displaced to the red, whilst P' (3) (3964) has three p- and three s-, all to the violet. We should expect extra components for higher orders, but if so, they are too faint to be seen. Their diagrams also give the folio wing decompositions for 100,000 volts per cm. (p"(l)-p"(3) 4518 + ^-| Koch lines / (P" (!)-/>" (4) 4046 - Enhanced line N (1/3 2 - 1/4 2 ) 4686 This last is the only enhanced line which has been measured. These He en- hanced lines belong to the same type of atom as the radiating atom in H, and it is the only case where a similar symmetrical pattern has been found. 15. Neon. The Stark effect in Ne has been measured by Nyquist*. Lines towards the red end of the spectrum seem only slightly affected, 40 lines between 7059 and 5434 showing no displacement and little broadening. About 70 lines between 6206 and 4423 show varying displacements to the red, unpolarised, whilst about 20 show more than one component. Amongst the latter are several in which detached components on the violet side, mostly displaced to the violet. are developed by the stronger fields. The large number of Koch lines that is, lines only seen with strong fields is also a notable feature with this element. 16. Argon. Argon appears almost completely irresponsive to the electric field, at least for wave lengths greater than 4000. Bottcher and Tuczekf have * Phys. Rev. 10, 226 (1917). t -4t. d. Phys. 61, 107 (1920). 106 ANALYSIS OF SPECTRA [CH. examined a very large number of lines in this region, both in the red and the blue spectra, and have found no effect. Takamine and Kokubu* have also observed in the same region with fields up to 105,000 to 170,000 volts per cm. They could only find evidence of a slight displacement to the red in a few lines. With the exception of two, these all belong to the red spectrum and, moreover, in this spectrum, almost wholly to those of Rydberg's Type II. As the results may be of direct use in the analysis of these spectra the wave lengths are here given with indication of the special Rydberg type to which they belong. They are 4510 (A & ), 4335 (A 7 ), 4333 (A. 8 ), 4300 (C 2 ), 4272 (C 8 ), 4259 (4 9 )t, 4200, 4198 (C r 4 ), 4191 (B 6 ), 4182 (5 7 ), 4164 (Z> 8 ), 4158f, 4153, 4046 (6' 7 ). Blue spectrum, 4933, 4132. Of observed lines, only two belong to series already allocated (see Chapter X), viz. F > ^ 4348j bjue spectmnij no e g ect (Bottcher) 9 (9) 4933 to red (Takamine). The second is doubtful, as s 9 is a sequence in the red spectrum. It is desirable that the ultra-violet portion of the blue spectrum should be investigated, as it is here that the typical triplet series chiefly occur. 17. For our purposes the value of the Stark effect depends on its possible usefulness in indicating the series and other relations of the lines of a spectrum. For this reason it will be preferable to consider the data already obtained under the heads of the different serial types. The attached numbers in brackets indicate references given in the footnote on p. 108. Doublets. P. (1) Li. P (2) to red, p > s. (1) Na. P (2, 3) both to red very small. P (2), p < ; P (3), p > s. (1) Ca. PJ 2 (2) both very small to red. p > s. (1) Tl. P 1 (2) very small to red. p > s. (4) 0. P (3) no effect. Always a small displacement to red with p > s except Na P (2). S. (1) Li. S (3. 4) small to red increasing with order, p > s. (2) Cu. S (3) to red, S (4) to violet increases with order. S 2 > S . p = s. (2) Ag. S (3. 4) small to red increasing with order. S 2 > S 1 . In S v p = s ; in S 2 , p > s. (1) Mg. lg 2 (!) small to red. (1) Ca. S lf 2 (2) small to red. p > s. (1) Al. x 2 (1) small to red. S 1 >S 2 . p=s. Generally similar to P. S 2 > S except in the instance from group III. D. The decompositions are complex in Li, Cu, Ag, and are given in more detail. * Mem. Cott. Sc. Kyoto, 3, 281 (1919). f A+ lines according to Stark the only A+ given by him. EFFECTS OF PHYSICAL CONDITIONS 107 (1) Li. 58000/cm. 6103 4002 4132 3915 -3-43, --53, +1-24 Z>(4) D(5) -3-12, --53, -4-98, --71, +3-56 -4-63, --62, +2-98 +J^4 /. + 1-07 \G. 6. 1. 5. 4. - 7-21, -2-94, + 1-82, +6-41 -6^45, -2-22, +1-42, +6-27 (1. 1. 1. 1 \1. 1. 1. 1 (2) Cu. -09 ^11 (3), (2) Ag. -3-47,0, +2-53. )j -2-98,0, +2-70 ; -3-80,0, +4-23 -07' + 60 + -44 ; -10-3,0, +6-72 0, + 5-37T ; # (2), -10 -05 A-25300/cn, A, (3), + -46 + 33 #=33000/cm. ^(4), -2-51, +4-80 -2-49, +3-45 #=44000/cin. - 5-20, 0, + 3-33 -7-15, -1-77,0, +5-21, +11-04 _ 4 7 78> _ 1<40> _. 43 , o, +5-36 -, - - ; # = 50000/cni. - 5-00, -1-59, --69,0, +4-35, +13-00 -1-84, --84,0, +4-90 #=48000/cm. Complex systems are also shown by Mo 4157, 4284, 4529, 4582, 5243, 5204, 5367; Ni 3944, 4024, 5084 (Takamine). The complex systems shown in Li, Cu, Ag are quite distinct from those of the other elements. The Li systems are all shifted to the violet, the same happens in the first order of Cu and the second of Ag. In Li we have already seen that the principal series is probably dependent on the d sequent, suggesting that the diffuse depends on a / sequence. There are also peculiar difficulties in the D series in Cu, Ag, and the anomalies in the Stark effect may indicate that here we may be dealing with/ sequents. The Stark effect here shows some additional evidence that in Li at least the sequence system is quite different from that of Na and the other alkalies. ( 1 ) Na. A. 2 (3) to red. D^ > D 2 , p slightly > s. (1) Ca. DL 2 (3) to red. Z>!>Z> 2 , p>s. (1) Al. D lt 2 (2) to red. Z) 1 >Z) a , p>s; D t . 2 (3) to red and tine lines. (1) Tl. Z>j. j (2) small to red. F. The only observed definite F" line is Au F l (6) = 4128 by Takamine. It shows noticeable displacement to red with p > s. Triplets. P. The only triplet observed is that of (1) (3947) with indications only of shift to red. It is not certain that 0'" is the analogue of the triplets of group II. S. (4) Hg. S 2f 3 (1) both very small to red. p> s. Takamine (2) says S 1 (l) remains perfectly sharp. (4) 0. No noticeable displacement. 108 ANALYSIS OF SPECTRA [OH. D. (2) Mg. D! 2 3 (2) to violet increasing from D to D 3 . Stark (1) gives doubtfully to red and also D^ 2 (3) slightly to red. (1) Ca. All D (3) no noticeable shift. D\2) all small to red. (1) Hg. D! (2) all three to red, p > s. D 2 (2) all to red > D. p> s. D l (3) strongly broadened to red. (4) 0. Bottcher and Tuczek have examined 0"' (4 ... 8). They are all considerably displaced to red by amounts respectively d\ = -71, 2-0, 5-4, 7-6, 9-3. Also (1) 0'" (3) all to red D l > D 2 >D 3 . F. (1) Ca. F lm 2 3 (3), these and the L sets show no noticeable effects. (2) A. F (4), no effect. Singlets. P. (1) Ca. P (1) small to red. p > s. S. No observations. D. (2) Mg. D (4. 5) both to red. (3) Hg. D (3) to red. Combinations. s ' (!) - Pt" (!) ( 2 ) M g to violet. K"(2)-*'(2) (1) Hgtored. Lines produced or intensified by the field (Koch lines). He, see Chapter III, sect. 6 and Tables. Ne, a large number by Nyquist (5). Li, p p (m), to red, see Chapter III, sect. 15. Na, PJ_ p (m), to violet, see Chapter III, sect. 15. K, p l p (m), to violet, see Chapter III, sect. 15. (2) Cu. 4056 p 1 (l) -A (3) to violet - -62/ - -65 33,000/cm. 4015 ft (I)-/, (3) 47/-4S 3686 p 1 (l) -A (4) to red + 1-26/ + 1-40 44,000/cm. 3652 p 1 (l) -/ 2 (4) confused with D 2 (4). (2)Ag. 4226 to red +2-33/2-14 56,000/cm. 4206 +1-46/ + 1-28 55,000/cm. 4081 +-8S/ + -86 (4) 0. 4846 to violet - 1-4 4743 -2-1 4634 -3-5 4559 -4-5 It will be seen that the Stark effect affords comparatively little definite testing power for series types. The triplet with their allied singlet systems seem to respond very slightly, the doublet system rather more, with the exception (1) Stark and Kirschbaum, Ann. d. Phys. 43, 1017 (1914). (2) Takamine, Astro. J. 50, 1 (1917). (3) Takamine and Kokubu, Mem. Coll. Sc. Kyoto, 3, 281 (1919). (4) Bottcher and Tuczek, Ann. d. Phys. 61, 107 (1920). (5) Nyquist, Phys. Rev. 10, 226 (1917). v] EFFECTS OF PHYSICAL CONDITIONS 109 of Li, whilst the enhanced lines emitted by sources of the H type (single electron and point nucleus) show considerable and definite effects. Stark has put forward the hypothesis that the want of sharpness shown by certain lines is due to the effect of close inter-atomic electric fields, this accounting also for the "pressure effect." The Doppler Effect. 18. What is the nature of the radiating centres which emit a given type of line? Have they their seat in the molecule, the atom, or the atom ionised by the loss of one or more electrons? Stark and his co-workers* at the Aachen Institute have attempted to throw some light on this question by observations on positive or canal rays, and conversely their results and methods give the possibility of separating groups of lines in a spectrum as belonging to the same type. The ionised positive atoms of a gas in an excited vacuum tube move towards the cathode and when within the region of the dark space immediately in front of the cathode where the electric force is large are accelerated towards it. If per- forations are made in the cathode these, now quickly moving ions, shoot through and produce the effect of bright streamers behind. Here they can be subjected to the action of a strong electric field, either accelerating or retarding, between the cathode and a parallel wire net through which they pass into a zero field, and the light they emit can be spectroscopically observed either transversely or end on. In the latter case the Doppler effect is observed and the velocity of the emitting ion determined. If no disturbing influences Were at work the velocity of a particle would depend on its mass, its charge, and the potential difference through which it has fallen. The observed velocity would then deter- mine its charge. In reality, however, the matter is not so simple. The state of a given ion is constantly changing in its course through the field. During a part of the time it may have been an ion with the loss of one or more electrons, at other times it may have become a neutral atom or molecule. This is specially the case when the canal rays pass through the same gas or a gas with which the ion can combine. The result is that any observed line is the sum of the effects of a number of sources moving with different velocities, and the observed intensity is spread out and broadened towards shorter wave lengths. Also particles of the gas at rest are brought to emission by the impact on them of the moving positive rays themselves. The interpretation of the observations must, therefore, be subject to some doubt. Nevertheless certain broad conclusions can be deduced with certainty and probable indications be obtained as to the state of ionisation of an atom radiating a particular type of line. * (1) Stark, Fischer and Kirschbaum, Ann. d. PJiys. 40, 499 (1913). (2) Stark, Wendt, Kirschbaum and Kiinzer, Ann. d. Phys. 42, 241 (1913). (3) Stark, Wendt and Kirschbaum, Phys. Z. S. 14, 770 (1913). (4) Stark and Kiinzer, Ann. d. Phys. 45, 29 (1914). (5) Dorn, Phys. Z. S. 10, 614 (1909). (6) Wendt, Ann. d. Phys. 52, 761 (1917). (7) Friedorsdorff, Ann. iJ. Phy*. 47, 737 (1915 110 ANALYSIS OF SPECTRA [CH. The photographed image of a line on a plate is analysed as to its intensity at different parts, and the results represented by a curve whose ordinates measure the intensity at different distances across it. On this it is easy to mark points corresponding to the middle of the line emitted by atoms at rest or moving with velocities due to one or more positive charges falling through the given potential difference. After Stark we shall denote these as X + , X ++ , . . . atomions where X is the symbol for the element in question. Such curves are illustrated by Figs. 17, 18, which have been constructed by superposing the actual curves given for certain sets of lines in Al, Cl (see ref. 4). In Fig. 17 the four curves in thin line represent the intensity distribution in one doublet set in Al in S and D series respectively. The curve in thick line is that corresponding to a spark line A = 2621. The abscissae give the positions 2-6- 2-4 2-2 2-0 / ft-] 2621 D,(3) S,(3) O 7 2 3 * Fig. 17. In A1C1 3 vapour. Field 15,000 volts per cm. Abscissae 10 7 cm. per sec. R rest position of the lines; 1, 2, 3 positions for 1, 2, 3 velocities. corresponding to velocities of 10 7 cm. per sec. We note at orice the generally similar behaviour of the lines of the doublet sets of the arc lines and the quite distinct difference in that of the spark line. We can conclude with certainty that the carriers of the two types must be two different configurations and it is natural to conclude that the atom giving rise to the spark line has lost at least one more electron than that which emits the arc doublets. The doublets show maximum intensity near the position due to the Al + ion, but the displacement of the curve shows also the presence of a certain number moving with greater velocities. Stark has inferred that these lines have their origin in atoms which have lost one electron, or here in the A1+ atomion. At first sight, indeed, this would seem the most natural inference. But the effect is equally consonant with the supposition that the seat of the emission is the neutral atom, and that the lines are excited to emission by the recombination of the A1+ ion with an v] EFFECTS OF PHYSICAL CONDITIONS 111 electron. The energy thus gained is then radiated. Thus the A1+ atomion must be present if the doublet spectrum is to be emitted, but the emission is caused by the change to the neutral atom and is emitted by the atom in this neutral state. The thick curve due to the spark line 2621 shows a maximum for velocities due to A1+++. But in this ultra-violet line it is not possible to decide with cer- tainty as between the doubly or triply charged ion, that is, on the alternative hypothesis between the singly or doubly charged. Fig. 18 represents in a similar way curves for three different types of lines in the spectrum of Cl, but here the abscissae represent distance in -1 mm. across the lines. The curve in thin line is due to a line emitted in the positive column in the vacuum tube at low current densities and is denoted by Stark as of the 4740 ^4795 1 -2 -3 -4 -5 -6mm. Fig. 18. Cl rays in He. Field 17,000 volts per cm. R rest position. arc type. The other curves are due to representatives of different types in the "spark" spectrum, i.e. the spectrum shown by high current density. Of these the two curves in dotted line refer to types (sharp spark) which occur as sharp lines and become only slightly broadened with increase of gas density. The curve in thick line is due to a distinct type (diffuse spark) which broadens as the gas density is increased. The distinction in the behaviour of these spectral types shows itself at a glance. The arc type is clearly analogous to the arc doublet set in Al (Fig. 17). The spark lines all show the absence of resting intensity and a great preponderance of moving. Stark allocates the arc lines to Cl + , the sharp spark to Cl ++ and the diffuse spark at least partly to Cl +++ . On the alternative hypothesis the carriers would be Cl, C1+, Cl ++ . That different spark lines in Cl have their origin within differently ionised atoms is clear, but whether they can be divided into two clearly distinct types alone is not perhaps so evident from the figures. The possibility that the different electrons of an atom may not play precisely similar parts in the configuration of the atom should not be for- 112 ANALYSIS OF SPECTRA [CH. gotten, nor that ionised atoms of the same total positive charge may differ from one another according to the particular electron removed. These different ions would therefore have different chances for recombination. In (3) and S, I, N (4) the results are similar to those described above in Cl. In S together with the first spectrum (series) and the second (spark),' they also find a few lines 4157-9, 4152-9, 4151-0 which they distinguish as a second arc spectrum, and regard as not belonging to the other triplet systems. The difference in appearance between the intensity curves of this set and those of P'" (3) hardly seems to be sufficiently definite to justify this supposition. Moreover, the separations of the three lines are 29 and 11 which are the same within error limits as v 1 -\-v 2 = 29-17 and i> 2 = 11-21, and would indicate some relation to combination series with sequences p'" (m)*. In the spark spectra again two types of. sharp and diffuse are distinguished. They allocate the carriers thus: First arc spectrum S 2 + ; sharp spark S+ + ; Second S + ; diffuse spark S +++ . The behaviour of is precisely similar and the carriers were allocated on the same scheme. The first arc spectrum, however, belongs to the triplet series system. It is thus difficult to accept a molecular allocation which completely upsets analogy with series in other elements. As the results are difficult to interpret it would seem better provisionally to accept their source as in the atom, or + or S + . 19. Canal ray analysis has also been applied to lines in the following elements. The references are to those given at the commencement of sect. 18. He (1) . In helium the He" lines were originally allocated to the He+ and the He' to the He++ atomions, but Stark has since modified his view and now considers that both series depend on He+, that is, on our alternative theory, to the atom. Ne (5) . 6335 separated from the resting position. 6402, 6143, 6096 strongly broadened. 6507, 6383, 6267, 6164 slightly? broadened. A (5)(7) . Red spectrum. In none of Rydberg's A, B categories can a Doppler effect be established with certainty. In C, D almost all have it, and C to a greater degree than D. In the blue spectrum the majority show as + +. Hg< 2 >. Hg+ 2847. W(l)). Hg++ 4047, 3655, 3650. &,'" (1), D 12 "' (2), D u '" (2). Hg+++ 4916, 4347, 4339, 4109?, 4078. 8' (3), D' (3), p' - d z r " (3), 8' (4), p z '" - s' (2). Hg++++ 4797-4, 4707-2, 4486-8, 4398. Observed only in the negative glow and amongst the strongest there. They do not appear in the arc or spark spectra. The Hg+ is attached to the enhanced doublet series, the enhancement being due to the necessity of increased ionisation. The triplet series are the more easily produced and should belong to the least ionised atom. Further, the singlet and triplet series are so closely related, especially in the combinations of sequences from each and their appearances under similar conditions of excitation, as to make it difficult to believe that they depend- on different ions. That the con- * They also find on all their plates of spectra from the positive column, and on none of those from the canal rays, three other lines 4364-8, 4362-6, 4332-9 which they suspect to be due to impurities. Their separations are 56-9, 11-5 and thus close to 2 (v l + > 2 ) and v z . v] EFFECTS OF PHYSICAL CONDITIONS 113 figurations emitting the doublets in all the groups I, II, III are of the same type is clear from the similar build of their spectra and from their common Zeeman pattern. But the enhancement and the 4:N in place of N in group II shows that this similarity occurs between the atoms of the elements of I and III and the ionised atorns of group II. Stark's allocations in Hg, therefore, tend to throw doubt on those in other elements, although none can be felt about the classifica- tion of the types in different categories. The complication in the processes taking part in canal rays renders the interpretation of the data extremely uncertain. Al< 2 4) . A1+ 8 lf 2 (2 ...4), D lm 2 (2 ... 9) and 3057, 30502320, 23172319, 2315, with separations 76. A1++ 4663 ) . A1+++ 4480, 4513, 4529 f all8 P arklme8 - Also 3900, 3612, 3601, 3587, 2816, 2631, all spark lines but not distinguishable between ++ and +++. {B+ 2496 B++ 3451 spark. C+ 2478 C++ 4267 S 2 + 2882, 2529, 2524, 2519, 2516, 2507, 2436 all arc. S 2 ++ 4132 spark. 20. These investigations by Stark and his colleagues form the most complete set of observations on the Doppler effect. They depend, however, on the very complicated and uncertain conditions in positive rays. Gehrcke and Reichen- heim* have made direct observations on lines in the alkalies and alkaline earths emitted in the anode column where the conditions are much simpler. The velocities of the rays were directly determined by their deflection in electric and magnetic fields and compared with the Doppler effects. The lines dealt with be- long to the doublet sets in both groups. They definitely showed that in the alkalies the lines depended on sources moving with velocities due to a single positive charge, whilst in the alkaline earths they were due to two positive charges. The lines show no resting intensity and are bounded sharply on the violet side fading to the red. Their definite results under these simpler conditions are, therefore, conclusive that the group II doublets have their seat in ions which have lost an extra electron over those in group I. The alternative explanation of the neutral and singly positive ion in place of the singly and doubly holds here in the same way as before. Radiation and lonisation Potentials. 21. Considerations based on Bohr's theory of the production of spectral lines have led to a series of experimental investigations initiated by Franck and Hertzf, with results which also have value in the more restricted domain of spectral analysis. According to this theory there exist certain definite configura- tions of electrons around a central positively charged nucleus, or complex positive nucleus with more closely packed negative electrons, which behave as a single positive nucleus of smaller charge. In these configurations the electrons do not radiate, whereas if an electron passes from one to another at a lower level, the * Gehrcke and Reichenheim, Verh. d. Deutsch. Phys. Ges. 9, 474 (1907); Ann. d. Phys. 25, 861 (1908) (Li, Na, K, Rb). Reichenheim, Ann. d. Phys. 33, 747 (1910) (Ca, Sr, Na, Rb). t Phys. Z. S. 17, 409 (1916). H. A. s. 8 114 ANALYSIS OF SPECTRA [OH. gain in kinetic energy is transferred to the aether and radiated. The frequency v of the radiation is determined by Planck's relation Jiv = energy = E l E v , in which Ep may be regarded as equivalent to the kinetic energy gained by the electron in a fall from infinity to the pth level*. According to this view the various sequents must be regarded as proportional to energy gains from infinity or to the work required to set free an electron from the respective levels. In particular the limit term should be calculable from the work necessary to set free one or other of the external ( ? valency) electrons in other words, to ionise the atom. Franck and Hertz attempted to measure this work experimentally and to test the result against spectroscopic measures. Their work has been extended by several investigators in the United States and since the war by themselves in Germany and Horton and Davies in England. We shall here only give the results so far as they have a bearing on our immediate purpose. 22. If an electron collides with an atom it is reflected as if the two were perfectly elastic, provided its velocity is less than a certain minimum value. When it reaches this minimum value, however, it loses it on collision, its energy is transferred to the atom, which radiates it into the aether or it is used up in ejecting one of its electrons, i.e. in ionising it. This minimum energy of the col- liding electron then measures the work required to separate an electron from its normal position in the atom. In the experimental work the electrons are usually produced by the incandescence of a metal filament (say tungsten) in vacuo and are then accelerated by an electric field. After passing through a potential difference of V volts the gain of energy is eV. Thus observation of V determines their final velocity within a small error depending on the velocities with which they leave the filament. Consider for illustration the case of Hg, a metal whose vapour is indepen- dently known to consist of atoms only. Suppose a stream of electrons is shot into such a vapour and that their velocity is gradually increased. No effect on the vapour is produced until the velocity is that due to a fall through 4-76 volts. As soon as this occurs, the gas is found to emit radiation f, but no ionisation * Bohr's special theory takes these configurations as orbits described round the nucleus. It explains completely down to exact numerical details the spectra of the hydrogen type of atom, i.e. a single electron revolving round the nucleus. As the exact agreement in detail between theory and observation depends on the fact of motion, it is not easy to see how any other supposition for this type can be accepted, whilst acceptance for this type must carry acceptance for other types. But there are difficulties. For our purposes the more general form of statement depending on potential levels is sufficient, and involves no theoretical supposition beyond the now established Planck relation. In Bohr's theory the total energies of the electron in each orbit are considered, say - W p in the pth, and the difference - W p -( - WJ between the two values is radiated on transference from the outer to the inner. The two statements are equivalent. For types comprising more than one external electron mathematical difficulties so far have stood in the way of closer comparison between theory and observation. But even here the general dependence of ordinary series frequencies on the difference of two sequences is in consonance with the basis of the theory and is supported directly by the experimental evidence considered in this section. The theory will not, however at least without some fundamental modification account for all spectral lines. For instance, although the displacement effect (see later) might follow naturally, it would seem inapplicable to summation and linked lines. t Observed by the photo-electric effect produced. v] EFFECTS OF PHYSICAL CONDITIONS 115 occurs. As the velocity further increases, additional radiation suddenly appears at 645 volts, again without ionisation. lonisation is found to begin suddenly at 10-2 volts. In the first two cases the supposition is that the colliding electron has raised one of the atomic electrons from the lowest level to another which then descends to its former level and gives up the energy to be emitted as radia- tion. In the last case the energy has been wholly used up in ejecting the electron from the atom. By Planck's law, hv = eV, where h = 6-545 (1 -0014) 10~ 27 gm. cm. 2 /sec., e = 4-774 (1 -001) lO" 10 E.S.U.,. V volts = F/300 static C.G.S. units, v = frequency = nc = 3n lO^/sec., (n = wave number) whence n = 8104-6 (1 -0024) V. As the proportional uncertainty here is far less than that involved in the measure of V which is subject to errors of a few tenths of a volt -we may take n = 8100F. The three voltages above therefore correspond to 1st radiation ... n 38556 2nd radiation ... n = 52245 Limit n = 82620 If now we examine the spectrum of Hg we find the strong lines 2536, 1849 with nn = 39412, 54066, which are within error limits of the calculated radia- tions. These lines are respectively s f (1) p' (1), and s r (1) p 2 "' (1), in which s' (1) = 84180, again within error limits of that deduced from the ionisation potential. The reality of the identification is further sustained by the corre- sponding relations in the other elements of both sub-groups II. Working on direct lines, McLennan* and co-workers have shown, (1) that with increasing electron velocity a definite line (hv= eV) first comes out, and that with a still larger velocity the arc strikes and the complete series appears. They have shown that this latter velocity corresponds to the frequency of the series limit; (2) that in Mg, Ca, Sr, Ba, Zn, Cd, Hg, the same s' p' 3,uds'p 2 f " appear in the absorption series and further that the absorption is more pro- nounced with s' p' than with s' p 2 '". We have seen how his observations on the Doppler effect in positive rays led Stark originally to infer that the carriers of the series lines were the ionised atoms. The present results show that the actual carrier is the atom, but that the ionised atom (Hg + , etc.) must be present for the complete spectrum to be produced. In these cases the atom emits the spectrum in the process of being re-formed from the ion. Again in the alkalies the element exists in the atomic condition in the vapour. In these, as we know, the absorption lines belong to the P series, and we should expect therefore the radiation and ionisation potentials to refer to these lines. * Phil. Mag. 36, 461 (1918). 82 116 ANALYSIS OF SPECTRA [OH. This is found to be the case. For instance, in Na the radiation potential (2-12) and the ionisation potential (5-13 volts) correspond to P (2) and P (oo ) = s (I) respectively. 23. The limit of the absorption series is proportional to the work required to eject the electron from the lowest level in the atom. On the contrary the ionisation potential depends on the work necessary to produce this mutilated atom out of the gas, that is the work required to set free an atom from the molecule in addition to ionising the atom itself. In the preceding instances, the molecule is the atom and the ionisation potential should give the limit. This is, however, not the case in H, nor indeed in general. Here we should expect the ionisation potential to be larger. An indication is seen in Mg. Here the s' (1) p 2 " f (1) line does not appear as an absorption line, and here in contrast with the Zn group, the ionisation potential is larger than that calculated direct from the series limit by an amount greater than can be attributed to observation errors. We may surmise that Mg vapour is in the molecular condition although easily dissociated. Another instance may be taken from hydrogen. Here the radiation potential (10-5 volts, corresponding to n = 85060) is within 6* limits of the ultra- violet line N (l/l 2 1/2 2 ) for which the limit is 109678, corresponding to an ionisation potential of 13'54 volts. But the observed value is 16-9 volts. The difference 34 volts must be explained by the preliminary work required to split the molecule into free atoms. This value for the dissociation of H 2 is also supported by a direct determination of the heat of dissociation by Langmuir*. The value obtained by him is 84,000 calories at constant volume for two grams of hydrogen. Taking the calory as 4-18 x 10 7 ergs and the mass of the H atom as 1-66 x 10~ 24 grams, this gives 5'83 x 10~ 12 ergs as the work required to separate one molecule into two neutral atoms. The corresponding dissociation potential is 5-83 x 10- 12 x 300/e = 3-66 volts and is thus in good agreement in order of magnitude with the value deduced above. The observed radiation potential in H is only slightly larger than (but within observation errors equal to) that deduced from the line frequency. This is rather difficult to explain. No radiation effect can be produced in the gas H 2 until the atom is produced, requiring say, a velocity due to v l volts. Suppose the real radiation potential of the atom is v 2 - Then if v 2 > Vj_ no atom present can be made to radiate until the velocity has risen to v a , and then only an ex- tremely small fraction of the already small proportion of atoms in the whole gas will be struck and made to respond. Whilst therefore radiation of a few atoms might begin at v 2 we should expect the effect to be far too small to be observable. No measurable amount would appear likely until the velocity is increased to that due to Vj_+ v 2 , when every colliding electron can dissociate one molecule and excite one of the atoms simultaneously. In other words we should expect the observed radiation potential to be the sum of the dissociation * Jmarn. Amer. Chem. Soc. 37, 451 (1915). v] EFFECTS OF PHYSICAL CONDITIONS 117 and the true radiation potentials. Nevertheless in H as we have seen, the ob- served value is only slightly larger than the true. The observed ionisation is, however, the sum of the dissociation and true ionisation. There is also increased radiation at 13-9 volts, and another ionisation between 13-1 (Mohler and Foote), and 14*4 (Horton and Davies). It may be suggested that in H, as the radiation potential is about three times that for dissociation, each electron when the potential has reached v 2 has been capable of dissociating three molecules. There will thus be a very considerable number of atoms present when the true radiation potential is reached and conse- quently some of the electrons may cause a sufficient number of atoms to radiate, to produce a measurable effect. Even thus there should be a great increase in radiation at v l + v 2 or 13-75 which is observed Davis and Goucher (13-6), Horton and Davies (13-9), Franck, Knipping and Kruger (13-6). The smaller ionisation would be explained by the ionisation of the few atoms produced as suggested above. Compton and Olmstead* suggest that the atoms present at the lower voltages are produced by the action of the hot filament. 24. Although the true potentials may be masked by the dissociation effect, their difference should give the correct value of the first current sequent. So far as our present experience goes Rydberg's N can only vary very little from 109,700, except in enhanced series where 4N enters. Also, no cases are known where a sequent has a denominator less than unity "(". It follows therefore that in the first case no limit frequency can be greater than N nor in the second case than 42V. In other words no true ionisation potential can be greater in the two cases than 13-54 or 54-1 volts. If such be observed, there must be some special cause requiring elucidation. As a fact it is only in H and other gases that greater values have so far been found. In the case of H, N, the cause can be attributed to the dissociation effect. But this cannot explain the abnormal effects in He, Ne, A since the molecule is already monatomic. Nor does the 4N alternative fit all the conditions. In He there are two ionisation potentials 25-6, 80 differing by 54-4 volts, and one radiation 20-4. Now if in the enhanced series, the limit is 4A r /l 2 , it corresponds to 54-1 volts. This should measure the work required to eject the second electron from the previously ionised atom He + . The close agreement of this with the difference of the two ionising potentials suggests that the second corresponds to the enhanced type of line, that emitted in the He + atom, and the smaller to the series emitted by the He atom. This also has been definitely proved by Messrs Horton and BaileyJ who found that under 25-6 volts no lines could be photographed whilst at 25-6, and over, all the He' and He" systems were present. The first enhanced sequent would be 42V/2 2 = 109,700, or 13-54 volts. We should therefore expect an observed radiation potential at 54-1 13-54 = 40-6 volts. None of the observers have noted a special radia- tion at this point, but it corresponds closely to double the observed radiation at 20-4 volts, and may easily have been attributed to the increased radiations * Phys. Rev. 17, 45 (1921). f On the quantum theory, also, this cannot occur. But see Chap. XI, sect. 13. % Phil Mag. 40, 440 (1920). 118 ANALYSIS OF SPECTRA [CH. produced at multiples of the first. Failing a knowledge of the type of lines of the He atom spectrum represented by the radiation potential we cannot a priori determine the true radiation and ionisation potentials from observed lines. The rare gases from A onwards* (see Chapter X) certainly show the triplet type as in the elements of group II. If the analogy with group II holds, the type represented would be s' p', s' p 2 '", with s' large. In He the first sequent (25-6 - 204 volts) is 42120 = N/(l-612) 2 , and is probably not within observation errors of He" s (1) = 38454-5 and certainly not of He' s (I) = 32034. The 20-4 volts treated as a true radiation potential correspond to a wave length 606-5. Lyman and Frickaf have investigated this region with special care and have found a definite He line at A = 585, which they suggest is the representative of the line corresponding to 20-4 volts. It would demand a radiation potential of 21-13 volts and would seem considerably outside possible observation errors either in A or in voltage. Further it cannot belong to the He system since its wave number 170940 is greater than N, though it may belong to He + with its &N, or to a summation line. It has been assumed that the lines represented in these effects should be the two so-called principal series P' and P". But there are objections to this assumption: (1) There is no evidence that the type repre- sented in group is the principal series ; rather the fact that the type in group I is P (m) and in group II they are the singlets s' p' , s' p 2 '" would give a pre- sumption that the P (m) would not be the representative in this group; (2) the series usually represented as He" P is not a principal series type; (3) if these suppositions were accepted the 38454 above (or 42120 from voltages) would be a limit and not a current sequent, that is, it should require an ionising potential of 4-7 + preliminary volts. 25. The uncertainty as to type, however, does not affect the reality of the abnormal character of the high ionisation potentials of the monatomic gases He, Ne, A, which correspond to frequencies of 207380, 135300, 122325 respec- tively. It would seem to indicate that the atoms of these gases in their normal condition are not capable of radiating, but that some preliminary work has to be done on them to change their configurations into one of the radiating types. The following mechanical model will serve to illustrate the nature of such an effect. Suppose a nucleus is surrounded by a rigid spherical shell on which rest under the attraction of the nucleus one or more (in He, say two) electrons. Before this is capable of radiating, these electrons have to be removed to say the lower level of the radiating systems. The electrons are now capable of playing the part which valency electrons take in other elements. A certain amount of work has to be done, therefore, as a preliminary. That the normal He atom is not capable of radiating is also indicated by the fact that the gas does not absorb light of the frequencies of the spectra. The explanation would also account for the great stability of these atoms and the want of affinity either for their own atoms or for those of other elements. That this preliminary work diminishes from He * There is some reason to think that the spectra of He and Ne differ in type from those of the other rare gases, but it is advisable to test the data as if the types were the same. t Phil Mag. 41, 814 (1921). v] EFFECTS OF PHYSICAL CONDITIONS 119 to A is easily explained by the fact that Ne, A possess additional internal electron systems which are not close in to the nucleus. Hence the total attraction is not that due to a single charge equal to the algebraic sum of the charges, but the repulsive effect of the internal electrons on the outer is greater than if they were concentrated at the nucleus itself. For the He+ radiation an additional and larger preliminary work would be required. If we assume that the He radiations correspond to triplet systems as is known to be the case in the rare gases from A onwards, the radiation and ionisa- tion potentials will be those corresponding to s f p' and s' p^'", and s' p' would be the strongest line in the system. This is without any doubt He P" (1), n = 9230. Assuming this to be s' p', as indeed its Zeeman pattern = 0/1/1 indicates, the true radiation wave number is 9230 and the true ionisation 38454 or 1-14 and 4-75 volts. The observed ionisation corresponds to n = 207380. Thus the first preliminary potential is the equivalent of 207380 - 38454 = 168926 or 20-8 volts. For the He + spectrum, the strongest observed is the 4685 or m = 4 in 4N (1/3 2 - 1/w 2 ), suggesting the first line m = 2 or the first of 4N (1/2 2 - 1/w 2 ). This is the line 1640-2, n = 60968-2, observed by Lyman, equivalent to 7-4 volts. It gives the limit 109720 or 13-5 volts. The observed is 648000. Hence the sum of the two preliminary potentials is 648000 -- 109720 - 538280 or 66-5 volts. Thus the first preliminary is 20-8 and the second 45-7 volts. The second is thus rather more than twice the first, which is to be expected as it is subjected to an attracting charge twice as large. The observed potentials should therefore be He ... 20-8+1-14 = 21-9 20-8 + 4-75 = 25-6 He+ ... 66-5 + 7-4 =73-9 66-5+13-5 = 80 No radiation potential for He+ has been observed, but it may possibly exist at 73-9. It may be noted that in He, as in H, the actual observed is somewhat less than the calculated. At present the above explanation can only be held as tentative. 26. Neon also possesses two radiation potentials (see table below), but is peculiar in exhibiting three independent ionisation potentials. The sequents, as calculated from the two radiation, and from the first and third ionisation are the same within error limits, viz. 4-9 and 5 volts. Five volts correspond to a wave number of 40100, within error limits of 39696, which, as Horton and Davies point out, is the value of a known sequent s 5 (1) (see Chapter X). They (11) have attempted to throw light on the triple ionisation values by observing the changes in the spectrum as the electron velocities are gradually increased. No lines are observed when the potential of 16-7 is reached, from which they conclude that probably the corresponding spectrum lies in the ultra-red. On the contrary, the two other ionisation potentials are related to two different types of observed lines which have been allocated by Paschen respectively to P, S and to I) series. These special results will be discussed in more detail in Chapter X under the neon spectrum. But the existence of the three ionisations raises questions quite apart from their relations to the lines of a special element and may best be 120 ANALYSIS OF SPECTRA [OH. considered here. An ionisation potential measures the work required to separate an electron from the atom (or the molecule). We should expect therefore to find as many ionisation potentials as there are separable electrons. But Horton and Davies do not consider that the potential required for the removal of the two electrons was reached in their experiments, because when Ne was first entering the apparatus no indications of the 11-8 radiation and 16-7 ionisation were obtained, whilst the others were plainly shown. The latter could therefore not correspond to additional work required to eject the second electron from an already ionised atom. Nor is it to be supposed that the 16-7 corresponds to the ejection of one and the 20, 22 to the simultaneous ejection of two, for it is very improbable that the double ionisation would give a considerable current when the simple did not give a measurable effect. Also it is very improbable that the work done to separate the second electron (22-8 20) would be less than that required for the first. This latter difficulty might, however, be explained by the considerations adduced above, under He, which require preliminary work to be done on an atom before it is capable of radiating. Thus if in Ne this pre- liminary voltage were 13 volts, the additional for ejection of one electron would be 16-7 - 13 = 3-7, with 22-8 - 16-7 = 6-1 extra for the second. But there is the additional objection to the higher potential referring to doubly charged ions, in that the lines observed to correspond to the higher potentials do not appear to be of the enhanced type. The existence of two ionisation potentials for a singly charged ion would be easily explained, as they point out' on the supposition that the two separable electrons play independent and different parts in the atomic configuration, and require different amounts of work to eject them. The different ionisation poten- tials would then refer to the ejection of different electrons. This, if justified, would lead to the very important conclusion that the P series depended on one and the D on the other. Indeed, configurations being regarded as orbits, this would be in accordance with Bohr's theory of emission. With three ionisation potentials in an atom such as Ne with only two separable electrons, this kind of explanation would require the existence of a third possible stable arrange- ment in the unexcited stable atom. This would point to the existence of a kind of atomic allotropy, a supposition which seems improbable. But in the present case the facts (1) that the first set of radiation and ionisa- tion potentials refer to the same sequent value as the set 17-9, 22-8, viz. 5 volts or n = 40100, (2) that apparently they do not appear when the gas first begins to flow through the apparatus, suggest the possibility of another explanation. The hypothesis that the ordinary neutral atom requires preliminary work to be done on it in order to change its configuration into one capable of radiating carries with it the necessity that this configuration shall be one of considerable stability, and that when produced it subsists for a considerable time as mole- cular time intervals go. Thus when the gas first flows in none of these readjusted atoms are present. After the higher potentials have been acting, and the adjusted atom produced by recombination, they exist in considerable proportions. When this state has been attained, the lower set of potentials, here 11-8, v] EFFECTS OF PHYSICAL CONDITIONS 121 16-7, can produce the radiation and ionisation effects from them. These are the same precisely as the higher ones produce at once from the original unadjusted atom. The fact that no lines were observed with the lower set is easily accounted for on this basis by the smaller proportion of adjusted atoms present with consequent small intensity of emitted lines. A difficulty, however, still remains in this case, in that the lowest ionisation potential corresponds to a wave number 135270 and so greater than N. 27. In A only a single pair of potentials have so far been recognised. The corresponding first sequent is 29164 close to d'" (1) which is 27832. In spite of our present ignorance of the type of lines represented by these potentials in this group it may be well to see if it is possible to fit in observed lines with the sup- position that the types are to be the same as those in group II since A, Kr, X, Ra.Em all possess the corresponding triplet series. In other words, are there lines corresponding to types s' p' ', s' p 2 r ", allowing for the preliminary voltages referred to above? In group II the p' ', d', and d'" (1) are of the same order of magnitude. The nearness of the 29164, 27832 above would therefore point to the voltage line as depending on s' p'. The observed radiation potential is (s f (1) - p' (1))/8100 + preliminary volts and s' (I) must be less than 109700, i.e. the actual frequency of the line less than 109700 - 29164 or < 80500. The value of p 2 '" is 51912-28 and the line s' - p 2 '" must therefore be less than 57790. Moreover, these singlet lines are amongst the strongest. Now Lyman* has measured the A spectrum between nn = 53000 and 74950 and has found a number of very intense lines. Amongst these are 53367-20 intensity 10 and an isolated group of three at the extreme ultra-violet observed, of which the last is 74950-7 of intensity 5, and therefore high as the last line observable. The first as s' - p 2 '" would require s' = 53367-20 + 51912-28 - 105279-48. Using the value of p' = 29164, calculated from the potential differences, the s' p' should be 76115, which is within error limits of 74951 (voltage error = -14 volt). With this value of s' the "preliminary" potential would be that due to a fre- quency 122325 - 105280 = 17045 or 2-1 volts. We thus find a set satisfying all the conditions, but it can have little weight unless sustained by similar agreement in the as yet uninvestigated heavier gases. These potential investigations are as yet only in their initial stage, and their complete relationships not yet fully understood. Ultimately with a fuller knowledge of these conditions and more accurate determination of potentials they should prove a valuable addition to our analytic tools. 28. The following table gives the experimental values so far determined. The references are to those investigations whose data have been adopted. The numbers in italics are values deduced from observed lines. * Astro. J. 33, 107 (1911). 122 ANALYSIS OF SPECTRA [CH. '-:. (-.- * Element Radiation \AMJUWUIWH, I lonisation 11 Wi LUIVIjSUiillA W. jit, r viviwwuis N Radiation lonisation ( 10-5 H (1 > \10-15 14 13-6 13-54 16-9 85060 82239 116654 109678 He (2 > 20-4 25-6 80 165260 207380 648000 Ne (3) 11-8 17-8 16-7 20-0 22-8 95590 144180 135270 162000 184680 A (1 > 11-5 15-1 93161 122325 Na (4 > 2-12 -06 2-09 5-13 5-117 17170 16956 41550 41449 K< 4 > 1-55 1-60 4-1 4-32 12555 12985 33210 35006 Rb<*> 1-66 1-59 4-16 4-16 13446 12816 33696 33687 s< 5 > 1-48 1-45 3-96 3-87 11989 11731 32080 31402 Mg<> 2-65 2-70 .:( . T , 4.42 7-75 7-61 21467 21870 35806 35051 62750 61670 Ca (7 > 1-90 1-88 2-85 .;<- ,..-..' ...... 2-92 6-01 15390 15210 23085 23652 48680 Zn< 8 > 4-18 4-01 5-65 5-77 9-3 9-35 33858 32500 45765 46243 75330 757tf3 Cd< 8 > 3-95 3-78 5-35 ... | ; 5-39 9 8-95 32000 30655 43335 43691 72900 72535 Hg< 8 > 4-76 6-45 6-67 10-2 10-39 38556 39411 52245 54066 82620 84179 Tl (t) 1-07 1-07 7-3 8668 8683 59137 22786 ,Pb (7) 1-26 7-93 10206 64143 ..'. N ( > 8-25 -1 16-9 -5 66858 810 136800 4000 P 4-7 11-5 38070 93150 Q(,io) 7-91 -1 15-5 -5 64070 125650 4000 S (lo > 4-78 12-2 38720 98820 Ido) 2-34 -2 10-1 -5 18980 81810 P(l),P(oo) P(l),P(oo) P/' (2. 2)? v] EFFECTS OF PHYSICAL CONDITIONS 123 References. (1) Horton and Da vies, Proc. Roy. Soc. 97, 23 (1920). See also Mohler and Foote, Phys. Rev. 15, 555 (1920); Davis and Goucher, Phys. Rev. 10, 101 (1917); Franck, Knipping and Kriiger, Ber. d. D Phys. Ges. 21, 728 (1920). (2) Horton and Davies, Proc. Roy. Soc. 95, 408 (1919); Phil. Mag. 39, 592 (1920). (3) Horton and Davies, Proc. Roy. Soc. 98, 124 (1920). (4) Tate and Foote, Phil. Mag. 36, 64 (1918). (5) Foote, Rognley and Mohler, Phys. Rev. 13, 59 (1919). (6) Foote and Mohler, Phil. Mag. 37, 33 (1919). (7) Mohler, Foote and Stimson, Phys. Rev. 14, 534 (1920). (8) Mohler, Foote and Meggers, Journ. Opt. Soc. Amer. 4, 364 (1920). (9) Mohler, Journ. Opt. Soc. Amer. 4, 49 (1920). In Bull. Bur. Standards, 16, 669 radiation potential is given as 8-18 -1. (10) Mohler and Foote, Bull. Bur. Stand. 16, 669 (1920). (11) Horton and Davies, Phil. Mag. 41, 921 (1921). Notes to Table. H, He, Ne, A. See text. Hg. Davis and Goucher, Phys. Rev. 10, 101 (1917), give values 4-9, 6-7, 10-4 much closer to the calculated values. Tl. This is the only element observed in group III. We should expect to find here the first P line and the limit s (1), as in the analogous doublet sets of group I. Indeed the P lines are strongly reversed in the spectrum. The observed radiation potential gives PJ (2) with extreme closeness instead of P (1), but P (1) is a negative W.N and is really 8 (2). It will be seen in Chap. XI that there is probably a -8 (1) line, i.e. a +P (1) with * (1)= 95878. This should produce a parallel P series s (1) -p (m) far down in the ultra-violet, so that the usually accepted P series is s (2) - p (m). The first line of this s (1) -p (m) would require a radiation potential of 6-7 volts, and ionisation potential of 11-8. The limit for the P/' (2) belonging to the observed radiation potential is 22786 requiring an ionisation potential of 2-81 volts instead of 7-3. The question is complicated by the fact that the Tl vapour may be T1 2 requiring 7-3 - 2-8=4-5 volts for dissociation. But if so 1-07 cannot refer to a line resonance and might be a radiation due to the molecule. The balance of evidence is in favour of the vapour being monatomic. The question is further considered in Chap. XI, sect. 12. Pb. Mohler, Foote and Stimson suggest that the radiation potential corresponds to the strong line X = 10291, TO = 9717, requiring a voltage = 1-20. N. The observers suggest that the radiation potential corresponds to the strong doublet XX 1492-8, ... 4-8 or nn = 66998, 66898. But no allowance is made for the dissociation effect made evident by the large ionisation potential. P. The authors say that at 300 the vapour is P 4 . 0. In the Phys. Rev. 15, the authors give 7-87 and 15-4 in place of 7-91, 15-5. S. The observers say the vapour is probably S 8 . 1. The radiation potential might represent the strong doublet XX 5345-27, . . . 38-31 or nn = 18703-02, 18727-43. CHAPTER VI THE OUN 1. We have already seen how the doublet and triplet separations in different elements of the same group appear to depend in some rough measure on the squares of the atomic weights. This problem of the relation between the separa- tions and the atomic weights meets us therefore at the threshold of any investiga- tion on the analysis of spectra. As these separations have their immediate source in the mantissae of the different sequences, they depend on the difference of these latter quantities. This difference is denoted by A. The investigation has therefore to deal with the manner in which these A depend on the atomic weight. The first step clearly is to express these quantities in terms of the square of the atomic weights say A = Aw 2 . If the data for doublets in groups I, II, III be treated in this way, it is found that A is not a constant. A closer inspection, however, shows that the A are all multiples of a certain constant whose value is close to 362. This suggests that the A are of the form mqw 2 , where m is an integer, q a universal constant, and w the atomic weight. If, however, we now proceed to apply the same considerations to the triplets of group II, this is found to be no longer the case, but a similar rule appears to hold with a constant equal to one-quarter of q. As an instance may be given the Zn triplets in which the observed lines are measured with great exactness. It is convenient to use in place of the atomic weights themselves, their values divided by 100. The A l5 A 2 for Zn expressed in this way are A x = 16845-62w 2 , A 2 = 8151-93w 2 , and further, ^ = 31 x 543-40w 2 , A 2 = 15 x 54346w 2 . But 5434 is not a multiple of 362. The difficulty is met, however, when it is noticed that 543-4 = 6 x 90-5 and 362 = 4 x 90-5. The same constant 90-5 is found to meet all the other cases, so that apparently the A are multiples of a quantity q w 2 , where q l is of the order of magnitude 90-5. The same law is also found to hold for satellite separa- tions. The general law was first* discovered in this way. The law, however, is subject to a restriction, which though small, is quite definite, although it is not observable in the case of Zn just considered. It is found in the triplets of group II that the q as determined from A x and A 2 never quite agree, but that if deter- mined from A! + A 2 they are the same for all elements within error limits. The law is so important that a full discussion of the evidence in support of it is necessary. In the original paper (1913) the method outlined above was followed. Since then, however, the accuracy of the observed wave lengths in the spectra of many elements has been very greatly increased, and the discovery of summation lines has given the ability in very many cases to determine series limits very much more closely. We shall present the evidence therefore in another * [in.] CH. vi] THE OUN 125 form by adopting a more accurate value of q, tabulating the atomic weights deduced from the spectral measures and contrasting them with their observed chemical values. In the older method, that of comparing the values of q in each individual case, the deduced q involved the combined errors due to both spectral and chemical measures. In the presentment here adopted, the two uncertainties are kept apart, and the spectral atomic weights with estimated spectroscopic uncertainties directly compared with the chemical values and their estimated uncertainties. At the same time q must ultimately depend on chemical measures, and for this purpose it is determined in relation to silver* whose atomic weight is thus regarded as a standard. The A in Ag can be found with extreme accuracy and gives with w = 1-0788 the value of q as 361-78 -05f. The values of the deduced spectral atomic weights are given in the subjoined table. Each indi- vidual determination depends alone on the observed separation v, and the series constant S (oo ). The first is subject to observation errors in two lines, and the latter to those on a whole series, as well as defective methods in deducing limits. The errors are therefore due to dv on the separation, and on the limit adopted. For the smaller separations it is not possible to determine A to the same degree of accuracy as is obtainable in v, by the use of 7-figure logarithms only. If the full attainable order of accuracy is desired, it is necessary to use 9-figure log- arithms, or a better method to determine the A by a formula of approxima- tion. Thus, if v be the separation and n the wave number of the limit, and D denote the denominator, n = N/D 2 and - 2N 3N = (A + whence, inverting with y = vfin> A = Z> {*/ - f */ 2 + f */ 3 - Since D has always to be found for other reasons, log n and log D are included in the work, whence log y and the powers are easily found, the characteristic in each case showing at once how many terms of the series (up to 8) must be retained. For exceedingly large values of v such as in Tl, the series converges very slowly and it is best then to calculate with n as the mean of the two limits, when with y = v/4n \ = W{y + f + fy + ...}. It is possible to estimate limits of uncertainty in dv, in each case and thus to obtain information as to possible variations in the deduced w. The further * Phil. Mag. 38, 301 (1919). f This value expressed as a change in a denominator is 361-78 x 10~ 6 or 361-78 x 10~ 10 in terms of the real atomic weight ratio to H. It has zero dimensions and if dependent on the fundamental 4 / e 2 \2 atomic constants must be a function of e*/kc. Its numerical value is close to _ ( =-- } . O X O \ IT llC J 126 ANALYSIS OF SPECTRA [CH. assumption has been made that the value of N is the same for all the ^-sequences, and, in dealing with the satellites, for all the d and/. It should not be lost sight of that this assumption has been made. The fact that, making it, the law of constant q holds to at least a first approximation, shows that the assumption is justified to at least the same degree. The fact that the value of N used may not be correct does not affect the argument although the assumption of its constancy does. For suppose the true value is N (1 + ) 2 a nd the two limits have been calculated as N/D 2 , N (D A) 2 . Then the true values are or p.-A> 2 the third the deduced A, the fourth the oun and its multiple, the fifth the deduced atomic weight \/{8/361'78}, and the last the chemical atomic weight. The numbers in brackets on the right of each number give the estimated uncertainty in the last digits of the corresponding quantity. Thus v in Li is -338 -002, or in K m8 = 53 (55-259 -054). The estimates of dv, % on which these maximum variations are based, are given in the notes to the table. They err rather on the side of being too small rather than excessive. The values of the chemical weight are those of Brauner* except where otherwise noted, and their estimated possible errors are based on his indications. * Abegg, Handbuch der anorganischen Chemie. VI] THE OUN 127 Element V A m x 5 Spectral atom. wt. Chemical atom. wt. He 1-007 33-37 58 x-5753 3-985 3-99 A 179-50 75-60 255-10(100) 2519 1057 3576-89 43| x 57-59 18} x 57-91 62 x 57-70(23) 39-94(8) 39-88(?) Kr 786-45 309-20 341-16 ( 1095-65 11127-61(70) 10969 4244 4680 15213-56 15650-21 44 x 249-30 17 x 249-63 18f x 249-63 61 x 249-40 1 /17 , 62f x 249-40 j (1/ 83-029(27) 82-92(?) X 1777-90 815-05 2592-95 24893-14 10996-29 35889-43(158) 40f x 610-87 18 x 610-89 58| x 610-88(30) 129-94(3) 130-20(?) Ra.Em 5371 2649 8020(1) 72824 36160 104984 40f x 1787-09 18 x 1786-66 58f x 1786-96(25) 222-247(15) 222 to 222-4 Li 338(2) 11-58(7) 6 x 1-782(1) 7-017(20) 7-03 Na J 17-175 P { 17-260 8 742-37 746-03(25) 39 x 19-035 39 x 19-134(6) 22-938 22-999(4) 22-998(2) K 57-68(1) 2928-7(15) 53 x 55-259(54) 39-082(12) 39-097(3) Rb 237-60(3) 12937-3(50) 49 x 264-03(9) 85-428(15) 85-448(5) Cs 554-00(2) 32565(4-6) 51 x 638-53(10) 132-852(11) 132-823(7) Cu 248-444(4) 7307-087(150) 50 x 146-1419(30) 63-5569(60) 63-56(1) Ag 920-433(5) 27789-10(30) 66 x 421 -0473(45) 107-88 107-88 Au 3815-56(2) 113934-9(60) 81 x 1406-604(70) 197-180(19) 197-20(7) Mg'" 40-67(7) 20-08(1) 60-75(7) 848-8(14) 418-6(2) 1267-4(14) 39 x 21-489 19|x 21-467 59 x 21-481(23) 24-367(11) 24-362(2) Mg" 91-50(3) 8 92-45(3) D 1211-0(5) 1223-6(5) 56^x21-53 57 x 21-47 24-39(4) 24-36(4) . ^ Ca"' 105-883(10) 52-188(10) 158-071(10) 2791-58(75) 1371-14(50) 4162-72(100) 48J x 57-857 23} x 58-346 71f x 58-017(14) 40-046(4) 40-07 Ca" 222-88(1) 3951-58(80) 68 x 58-112(15) 40-08(1) Sr'" 394-22(2) 186-83(3) 581-03(1) 11829-0 5528-7 17357-7(16) 42| x 276-703(40) 19f x 279-933(70) 62x 277- 726(33) 87-616(51) 87-66(3) Sr" 801-88(1) 16119-3(7-4) 58 x 277-920 87-645(190) . Ba'" 878-14(6) 370-56(6) 1248-70(6) (29344-6 (29518-7 (11992-9 1 12062-37 (41337-5(40) 141581-5 43 x 682-432 43J x 682-506 17jx 685-311 17f x 689-298 60l x 683-265(67) 60| x 684-468 137-427(7) 137-548 137-43(6) Ba" 1690-93(3) 38608-3(180) 56J x 683-332(320) 137-433(36) Ra'" 2050-26 832? 2882-26(?) 225-97 to 226-^ 128 ANALYSIS OF SPECTRA [CH. Element V A mx5 Spectral atom. wt. Chemical atom. wt. Ra" 4857-11 111056 60 x 1850-93 226-201 Zn'" 388-894 190-097 578-991(10) 7204-19 3486-29 10690-48(100) 461 x 154-929 22* x 154-946 69" x 154-934(12) 65-4413(20) 65-40(3) Zn" 872-8(10) 9135(13) 59 x 154-87(23) 65-427(45) Cd"' 1170-842(8) 542-00(15) 1712-84(15) 23105-83 10370-33 33476-16(300) 50f x 455-278 22f x 455-839 73! x 455-458(60) 112-2023(80) 112-3(1) Cd" 2481-7(6) 27348(15) 60 x 455-48(25) 112-200(28) Eu'" 263 0-30 2W 3-21 100 3-87 100 4-06 363^^(16) 512 26 1832* 69 550 b9 604 fill 832-92 D1 * x 833-83 21| * 852-H ft o v 837-92 x 838-60 152-187, 7m 152-248 1 m * 152-249* Eu" 5342-5(10) 61207 73 x 838-45 152-24(10) Hg'" 4630-467 1767-279 6397-746(10) 87819-08 30008-03 117827-11(10) 60f x 1445-581 20! x 1463-806 8l|x 1450- 180(100) 200-211(8) 200-3(3) Hg" 9831- (?) Al 112-038(10) 1752-07(30) 66 x 26-546(2) 27-088(2) 27-10(5) Ga 826-04(5) 13540-7(180) 77 x 175-857(240) 69-720(40) 69-9(3) In 2212-61(30) 37687-5(80) 79 x 477-056(90) 114-831(11) 114-8(5) Tl 7792-40(30) 134153-46 89 x 1507-342(150) 204-119(10) 204-04(5) Sc 321 (?) 6407 (?) 91 x 70-41 (?) 44-114 (?) 44-l(5)f 3-65(3) 2-03(2) , 5-68(3) 171-0 94-1 265-07 18^ x 9-242 lOJx 9-180 28| x 9-220(40) 15-966(40) 16 S 17-96(15) 11-21 29-17(20) 1044 651 1695(12) 28 x 37-28 17! x 37-20 45-| x 37-25(20) 32-088(100) 32-07 (?) Se 103-680(150) 44-66(250) 148-34(25) 6390 2736 9126 28^x226-16 12 x 227-98 40^x227-34 79-270(280) 79-2 (?) Mn 173-604(50) 129-263(50) 302-864(50) 3420 2533 5953-32 31 J x 109-44 23} x 108-95 54! x 109-235 59-9512(63) 59-93 Notes to the Table. Group 0. The separation of 1-007 for He'" is that given by Paschen from consideration of all his measures. But it is doubtful if it is a true 8 doublet separation and does not belong rather to a satellite or F type. The data for the other rare gases are taken from [v. p. 313]. They are not the final and more accurate values there given, which are obtained from other pro- ' perties, but are calculated direct from the observed separations and the limits found, so as to be comparable directly with the other elements in the table. The data there given for Ne are based on analogies with the other gases and are omitted pending a further discussion of Paschen' s allocation of series in this element. * Jaensch. f Honigschmid gives 45-1. Z. S. f. Electrotech. 25, 91 (1919). This requires 87 x 73-64 and gives w = 45*12. vi] THE OUN 129 Li. v is mean of -336, -340, -339 Kent's values for P (2), S (2, 3), d/ = -02. Limit asymptotic from Sevan's high orders of P and 8 (oo ) =p (1); =1. Na. v from Fabry and Perot's interferometer measures of P 12 (l) supposing d\ = -001. There would seem, htowever, some difficulty in adopting this as the separation on S (oo ). For S (2) Meggers has given measures in I.A. to -01 with estimate of probable errors -03, which agree within his probable errors with the measured separation by Kayser and Runge. Both require the multiple 39. The mean of Meggers and of Kayser and Runge is taken for the second. The difference between the P (2) and S separations would appear to be real. Limit is based on asymptotic P (oo ) from Wood and Fortrat's measures of P (m). % is thus too small to affect the results. K. v. The mean of Meggers, Meissner, Burns, Hermann, Saunders for P (2) is the same as that observed by Burns. Meggers' from 8 (3, 4) gives 57-69, 57-68, which agree with the means of Eder and of Schillinger dp is taken as -OL Limit asymptotic from Bevan's P (m) with =2. Rb. v by least squares from Meggers' P (2), S (2, 3) with his estimates of possible errors, dv = -03. Limit asymptotic from Bevan's P (m) with = 2. Cs. v from Meggers' P (2), S (2, 3) with dv = -02. Bevan's P measures are not good. The asymptotic limit is quite clearly too large as the calculated values deviate too largely from the observed. The formula in a/(m -) for S gives a limit 3-2 less and agrees well with observed S. Further, there are summation lines for P (3, 4), both giving limits close to the latter. Hence 8(at>) = 19670-41 1. Cu. The limit is determined very accurately from summation sets; taken as -5. Ag. = -3. This gives the standard q by making the spectral and chemical weights agree. Au. dv = -02. The limit is deduced from summation Z> lines and is very accurate. Mg'". Nacken's in I.A. to -001 from 8 (2. 3. 4) give means 40-743, 20-076, 60-820. Rowland's from D (2) in the sun 40-67, 20-08, 60-75 adopted 60-75 -07. too small to be effective. [Note. Just before going to press Perot has published interferometer measures of 8'" (2) which give ^ + 1/2 = 60-74. With d\ = -001 on a single line and = 1 this gives 5 = 21-477(8); w = 24-366(4), variation wholly due to .] Mg". It is difficult to be certain here. The limit is determined indirectly from F which gives a very close agreement with observation up to ra = 10. The deduced D (oo ) is therefore good, but, as applied to the S, it gives for 8 (3) clearly too large a limit. It is therefore incorrect to take it for S (oo ). With D (oo ) should go its observed separation which is distinctly larger than in the 8 series, but it is difficult to say what it should be as an abnormal satellite is present. The observed v is 92-45. If this is used the deduced A is 1224, as against 1211 with the S separation on D (oo ). Further, if the S (2. m) series be considered with its directly deduced limit 40618 arid v =30-5 both subject to considerable possible errors the deduced A is 1234 ?, which indicates that 1224 should be nearer the truth than 1211. The S (oo ) should be considerably less (at least 10) to satisfy 8 (3). A = 1211 as 565 gives w =24-39, and A = 1224 as 575 gives w = 24-36. The latter thus gives the same value within limits as that from Mg"' and as the chemical. It depends also on a multiple of 5 in agreement with all the other doublet series. This would seem the preferable assumption, but the actual result must be regarded as undetermined. It is possible that both are correct and that the 8 is abnormal in being displaced by two ouns. Ca'". v by least squares from measures by Crew and McCauley, and by Hoist. Limit not so good =4. Possibly dv has been taken too small. Ca". The limit is difficult to fix and as in Mg" the F separation is greater than that of the D satellite. The D asymptotic condition would seem to require from 6 to 10 larger, but the observation errors are too large to make this certain is taken as 10. Brauner's value of the atomic weight is 40-124. Later Honigschmid and Richards* have determined it as 40-07. Originally the multiple 48 was taken for A t giving 5=58-220, and w= 40- 115(4), true A 2 = 1368*1. These agree best with other spectral data and with Brauner's value with which the Ca" and Ca"' spectral weights agree. Sr'". v from Meggers' S (I) and Hampe's S (2), dv 'Ql, very small. * J. Amer. Chem. Hoc. 32, 1577 (1910); Wien. Ann. p. 318 (1910). H. A. s. o 130 ANALYSIS OF SPECTRA [OH. Sr". The same difficulty as to the limit as in Ca". The F separation is again larger than that of the D satellite. The evidence appears to point to the S (oo ) as about 64322, but the uncertainty must be large =20. Ba'". | = 1. We have here the complication referred to in Chapter III, sect. 2*7. The data for the two alternative limits 28629-20 and 28514-8 are both entered, that for 28629 coming first in each case. It is to be noted that the Ba" and chemical weights support the former limit in Ba'" and that with the latter the 8 from v lt v 2 show an excessive divergence. Ba". v from Schmidt, ^ = -03. Limit determined from$ makes the D roughly asymptotic, but actual allocation of lines not certain. = 20 but may be 100 in error. Ra'". The v z is not well supported; cf. [in. p. 64.] Ra". v from S (2, 3), probable error <-05. The limit calculated from S (1, 2, 3), but the 8 t (3) is possibly not correctly allocated. Zn"'. The limit calculated from S gives good agreement for the D and is sustained by D and P lines. =2. Zn". v very uncertain. 8 (1) gives 871-5 1-2, S (2) 873-34 -8. Limit is calculated f rom S (I, 2, 3) of which 8 (3) is doubtful. = 20. Cd'". v t is very exact, but not v 2 , dv = 15. Limit calculated from S is good. = 1. Cd". The limit is very uncertain. The uncertainty in the oun depends chiefly on this; = 20. Eu"'. There seem to be two sets of v. Eu". A good F series gives d (2). Thence D (oo ) from the D lines; = 30. Hg'". Limit from formula agrees well up to m 13; = 2. Hg". The presence of displaced sets makes the series as known quite indeterminate. Al. The limit is good; = 1 for 8 doubtful for D (oo ). Ga. Relations uncertain; =40. In. Limit from formula fairly good; =2. Tl. =2. O. Limit goes well with 8 and makes D asymptotic, but is immaterial here. S. v from 5(4), means P (2) and 4, 5 in 8, D give v = 18-20, 11-30, requiring m = 46, and same W. Mn. Limit and separations both good; =2, dv = -05. Consider first the doublets of groups I, III. It will be noticed that all the A are multiples of 8 with the exception of Li in which the allocation of the P series has appeared doubtful. A comparison of the spectral and chemical atomic weights, with their respective uncertainties, brings out the remarkably close agreement between the two. In order to show that the agreement indicates a real law we may find the changes in the deduced spectral weight if the multiple is altered by unity. If this multiple be m, the change in S is roughly 8/m and in w is w/2m. In the following list the first line of numbers gives w/2m. The second line expresses them as multiples of the possible spectral errors and the third as of the chemical uncertainties. Na K Rb Cs Cu Ag Au Al Ga In Tl 3 -38 -9 1-3 -6 -8 1-2 -2 -45 -72 1-15 19 24 60 12 100 60 10-3 11 7 115 150 130 180 190 60 17 4 1-5 1-4 23 It is seen that in every case without exception a change of the multiple would completely upset any connection with the chemical atomic weight. The enhanced doublet series of group II are not at present determinable with sufficient definiteness to afford secure evidence on which to base the proof of such a fundamental law. This is unfortunate as with the very large separations involved, and the smaller ratio of mantissa change to observation error, they should be capable of giving spectral weights with extremely small possible errors. The observed lines are, however, so few and so far in the ultra-violet that, with vi] THE OUN 131 the exception perhaps of Mg, the limits can only be obtained very roughly. Nevertheless the numerical agreement as it stands is even more strongly in support of the law. The individual cases are considered in the notes. It is quite possible that the uncertainties adopted may be too small. The whole multiple of 8 is again sustained for these doublets with only the possible exception of Ba, whose limit is so uncertain that its result has little value. A similar support of the law is afforded by the triplet series of groups 0, II, except that the quantity now involved depends on J8, and the values are de- duced from the A x + A 2 . For the present purpose, He, A must be set aside ; He because its separation is so small that observation errors are a considerable fraction of the whole amount, and A because its observed separation has large uncertainties. It may, however, be stated that other considerations* developed later, show that the oun for A here deduced is very close to its true value, and that its spectral atomic weight is 40 within very narrow limits. Again the agreement between the spectral and chemical weights is very close. It may be illustrated as in the case of the doublets, only here the change will be w/Sm as we are now dealing with multiples of 8 X and m refers to 8. The resulting numbers are as follows : A Kr X Ra.Em Mg Ca Sr Ba Zn Cd Eu Hg O S Se 08 -17 -28 -5 -05 -07 -17 -3 -12 -17 -23 -3 -07 -09 -18 169 33 1 20 3 5 60 20 3 40 3 1 -64 ? ? ? ? 20 ? 5 5 4 1 10 1 ? ? ? The changes are necessarily smaller than those for the doublets. On the other hand the observational measures are in most cases so much more accurate that their ratio to possible variations remains of the same order as before. An excep- tion must be made of the elements of group VI, which have no evidential value. 3. For convenience of comparison, the various multiples are here collected. Triplets Doublets n {Na 39 j'A 43| 44 18* I8f, 17 Rb 53 49 ! x " 40f 18 Cs 51 1 Ra.Em 40| 18 {Cu Ag An 50 66 81 /Mg 394 194 . 57 / M o Ca 2 48i 231 68 . 'Sr 42?- 19* 58 Ba ^^4 43 174 56 j (Ra "": 60 \ /'Zn 464 224 59 Cd iv2 50| 60 JV^U 614 214 . 73 IHK ***i 60 204 . CAl 66 r'O 18 10| 77 S 28 17 TIT(ft) ]ln 79 [Se 28 12 ITI 89 Mn a* 23^ ITT (a) Sc 91 * See [v]. 9 2 132 ANALYSIS OF SPECTRA [CH. These multiples must depend in some definite way on their group number and their ordinal position in their group. The definite law of their constitution is not, however, clear, but certain features are at least evident : (1) The doublets are multiples of 8, the triplets of 8 X . (2) The multiples are quite independent of the atomic weight or of the atomic number. This is clear from the way in which they vary. (3) The multiples of A 2 are all of the same order, close to 20 for all the elements and markedly so for the rare gases. (4) There is a distinct contrast in type between the march of the multiples in the first and in the second sub-groups in I, II, III both in triplets and doublets. In those of I (a), II (a), there is first a considerable rise and then a small fluctua- tion. In those of I (6), II (&), III (6), on the contrary, there is a continuous rise. In the rare gases there is a decrease to equal values for X and Ra.Em. (5) In the doublets of I, they are all close to square numbers. Thus I (a) 6 2 + 3, 7 2 + 4, 7 2 , 7 2 + 2. 1(6) 7 2 +l, 8 2 + 2, 9 2 . (6) The A of the doublets and Aj of the triplets of the first element in each group may be written as follows : A ? Na Cu Mg Zn So* Al S 1755J M (2d ) 52x35 1 50x45! 39^5 31 x 65 X 52 x 13 1 33x85j SxWS^?) This seems to indicate a rule that the first lines in the two sub-groups of group n should be multiples of (2n + 1) 8 1? and (2n + 2) 8 X . Mg is the only exception which may possibly be explained as below. Its multiple should be 32 x 58 X = 408. The enhanced doublets are not subject to this relation. 4. The curious difference in the values of the oun as calculated from A x or A 2 , except in the rare gases, has already been referred to. The true oun is that calculated from A x + A 2 . The systematic way in which the oun from A x is less than that from A 2 , and the impossibility of making them proportional to the square of the atomic weight, whilst that from A x + A 2 agrees in all cases so closely with the relation, give additional evidential value to the latter result. The effect is real though small. It may be expressed as a transference from the true A! to the true A 2 . Here the "true" value means that calculated from the true 8 using the same multiples for A x , A 2 as those shown in the tables. From the nature of the test a transference of a quantity larger than one oun would not put itself in evidence the effect would be merely to alter the relative multiples. In estimating this transfer, therefore, this ambiguity must not be forgotten. If m. n denote the multiples of AJ , A 2 the transfer is mS Aj or A 2 n$. It is easy to show that this quantity is almost independent of f and depends on dv much less than does 8. Calculated in this way the transfers are found to be as follows: Mg --3 -4 Zn -27-18 Ca 7-67 2-3 Cd 8-66 1-3 Sr 43-6 -66 E (293 Ba 35-8 -7 (279 Ra 87? Hg 279-3 -2 * This arrangement is upset if Honigschmid's value of w (see footnote, p. 128) is taken. vi] THE OUN 133 The source of the modification must lie in the limit sequences alone, since both S and D series depend on different second sequences and yet possess normally the same separations. Further the modification must take place either in the S 2 limit, or on both the S l9 S 3 simultaneously. The fact that when cal- culated from A! + A 2 the ratio of 8 to w 2 is the same as in all other cases would seem to indicate that S l} S 3 behave in the same way as in other elements, and that the change is in S 2 (oo ), showing itself as a shift in its mantissa. This may be due either to an actual shift or to, say, a change in N for the middle limit of a triplet, or to a common change for the extremes. If the shifts be real, their values as given above do not show any evident signs of regularity. A rough relation to the atomic weight is shown if the real shifts are supposed to be two ouns extra for the first, one oun for the second and fourth elements in each sub-group. Thus Mg(25 1 ) Ca^j) Sr Ba (SJ Ra 10-74l-4 22-172-3 43-6-66 206-6l-92 87? (44-1 5-8) w (55-35-5)w (60 -7) to 3(61-4)o (38-5?)u> Zn(2d 1 ) Cd(8j) Eu Hg ( t ) 77-47'22 122-4l-33 !?*'o 7 924 2 Loo'Z , (118-3)tt; (109l-2)w (^4-6^ w 3 (105 -3) w or 2(59-l)to 2 (54-6 -6) w 2(502)w 6(52-5-l)w; Whether the relations indicated correspond to reality or not there is no evidence to show. If these extra ouns are really transferred the true values of A 2 would be considerably altered. The discovery of other independent data for determining A x and A 2 would therefore place at our disposal a means for testing this sugges- tion. This will be dealt with in Chapter IX. Meanwhile it is interesting to note that the transference of the two ouns in Mg makes its true multiple in A x equal to 40 or 32 x ^ and thus to fall in step with the relation (6) of these multiples*. The similar change in Zn, however, would upset the relation for this element. 5. We pass now to the consideration of the satellite separations. The man- tissae differences here, the inert gases excepted, are considerably smaller than those just considered, but the effect of on their values is negligible unless is very large. Consequently in the data which follow, the uncertainties depend only on the observation errors of the lines involved. In the doublets of group I, Cs D only shows definite satellites. Mg has indications too small for evidence. The data are here collected from Table V in the Appendix, and the mantissae differences alone given, together with the uncertainties in the mantissae from which they are derived. Under each mantissa difference is put the nearest oun multiple, the values of the oun being those obtained in the previous table except in group where the more exact values from [v.] are used. Orders above the second are in general excluded as the changes due to observation errors are comparable with the oun itself. They serve to give the oun multiple, when the law is established, but they are of no weight in establishing the law. * Several alternative explanations are discussed in [m. p. 333]. 134 ANALYSIS OF SPECTRA [CH. Table of D mantissae differences in the triplet systems. [The first column gives the element with its oun beneath, the second the order m of the set, the third, fifth, and seventh give in brackets the maximum possible errors in the respective mantissae, the fourth and sixth the two mantissae differences with the corresponding multiples of 8 beneath, and the last the sums of these two differences.] A 14-480 (1) 4139 71J =4138-0 (1) 39 = 2258-9 Kr 62-384 X* 152-752 3 (?) (6) 2 (10) 7683 132f = 7689 40 = 2316-8 A4 As 4109 (6) 2433 (6) 24954 16-1=4117-3; 9f=2433; 100 = 24953- As A (10) 6984* (10) AT (6) As 23345 (5) = 23331-0 3146 56075* (10) 12|=31l9-2; 28 = 6987 222|=56083-2 * Differences estimated from Z>, , . (78) (?) 46435 76=46436-2 (6) 18187 (?) 11007 29| = 18177-5 18 = 10992-8 (78) 17134 (78) 10037 28 = 17108 16$ = 10081 () 74679 (?) 44924 122$ = 74695-9 73$ = 44909-2 (?) 75276 (?) 45720 123^ = 75306-9 74^=45672-7 9946 9947-9 54841 54834-9 29194 29170 27171 27190 119603 119605-1 167431 167415-8 * Two independent D sets. The two Z> n (GO) have mantissae differences =8547 = 145 -7. Ra.Em* 1 (7) 60752 (12) 36191 96943 446-756 34 = 60758-8 20^ = 36187-2 96946-0 1 (12) 55841 (5) 31788 (10) 20935 (7) 108564 31 = 55844-3 18 = 31719-5 1 If =20997 108560-8 * Two independent D sets. The two D n (GO ) have mantissae differences = 41992=23^5 -2-06. In this group the values of the oun used must be regarded as exact, so that any adjustments in data as they stand depend only on observation errors in two lines. The differences show remarkably close agreement with the respective oun multiples and in the two cases where there is a suggestion of a triplet modi- fication of the same nature as in A 1? A 2 the sum remains the correct multiple oun within very small error limits. Ca 14-50 , (730 * 464 (746 (16) 450 12$= 727-8 8= 465-6 12|= 742-3 7f= 451-1 (3) 746 (6) 495 12|= 742-3 8$ = 494-9 (11) , 846 (11) 536 14$ = 844-2 9= 538-3 (26) 1134 (?) 776 19$ = 1135-3 13J= 771-4 Z 3 calculated from Z) 22 > clearly one oun displaced in mid sequent. (24) (6) (20) 1194 1196 1193-4 1241 1237-2 1382 1382-5 1910 1906-7 VI] THE OUN 135 Sr 69-5 Ba 171-15 Cd 113-87 Eu 209-0 Hg 302-54 B&F 2 Zn 2 38-74 (7) (7) (10) (2) (2) (9) (3636 * 2141 * 13640 (8) 2137 (5) 13=3614-0 7| = 2154-5 3355 (7) 2185* (3) 12=3336 8=2224-0 4142 (10) 1656 (100) 15=4170 6 = 1668 . * Calculated from D a2 (2), A* (2). 10646 (6) 5012 (3) 5^ = 10612-6 7 = 5135-1 9223 (2) 3 = 9243-4 7534 (9) 3719 (90) 11=7530-8 5= 3767-4 4793 7=4792-3 (30) LR. (27) 2029 K. R. give 489, 418. E.V. 569, 378. K.R. (1274* (1234 4 = 2049-6 2| = 1252-5 (150) 2175 (150) 1694 (49) :.v. s (40) 4|=2163-0 3| = 1707-9 * Calculated from D 3 (40) (4) 11932 14^ = 1 1914-2 ( 3996* 14032 (40) (4) 7126 = 7106-7 6897* 6861 (14) 2f = 3988 (6067* '6052 4| (14) = 6888-2 6521* 6467 4 = 6163-3 4 i = 6525-8 (00) 6939 4?- = 6888-2 (60) 6281 = 6163-1 (99) (84) (150) (40) (4) (14) (60) 5777 5768-5 5576 5540 5560 15658 15747-7 11253 11298-2 Z> 3 give 526, 369 3303 3263 3302-1 3869 3870-9 19058 19020-9 10893 10893 10876 12588 12519 12689-1 13220 13051-3 Calculated from Z> Of the above Zn must be omitted as the measure uncertainties are larger than the oun. With the others a tendency towards a modification between the two constituents (o^ , o- 2 ) of a triplet is shown precisely analogous to that we have seen to occur in the series separations (v , v 2 ). It is much less marked and largely disappears when the d 2 , d 3 are determined from Z) 22 , D^. In Ca D (1) the rela- tion holds within limits which, however, are larger than the oun. Ca D 12 (1) is given by Paschen as double. One is the D line and the other probably a P. If calculated from Z) 22 the a agree more closely with the F separations. The F series show the effect of close unobserved satellites and the true separations must be found from the high orders in Ca with good measures. Those from m = 7 give 21-69 -f 13-77 = 35-46. Those, regarded as the true a, give mantissae differ- ences of 730, 464, sum 1194, which agree precisely with the oun multiples. Sr D (1) shows quite definitely the triplet modification with a correct sum. We cannot here compare with the F separations as these are not sufficiently definite, 136 ANALYSIS OF SPECTRA CH. The material from group II thus supports the multiple relation very closely except the cases of BaZ)(l) and HgZ)(2). In HgZ) 12 (2), the measured v separation is -56 too large. Either something has happened, or the assigned error limits (dX = -005) have been taken too small. If we suppose Z) 22 (2) corrected by d\ = -008, and D 12 (2) by dX = -04, the v separation becomes correct and the mantissae differences are now exact oun multiples. We return later to Ba D in sect. 8. Doublets. m m Cs 2 (23) 7413 (22) Ca 2 (1) 859 (1) 159-63 11$ = 7341 14-50 14f= 858-8 3 (2) 8596 (2) 3 (1) 829 (1) 13|=8620-1 14= 829-7 4 (9) 8870 (8) 4 (9) 525 (12) 13f = 8779-4 9= 524 5 (54) 8791 (231) 13f =8779-4 Sr 2 (12) 4598* 4580 (16) Cu 2 (1) 835 (15) 69-43 161=4582-3 36-53 5f = 840-03 880* 3 (3) 4308* 4287 (3) 3 (100) 976 (100) 15^ = 4304-6 6 = 876-8 4 (100) 4103 (3) 6f= 986 14f= 4096-4 * Calculated from D 2 . * Calculated from D 2 . Ag 2 (D 2425* (-6) Ba 2 (0) 12835 - 256 (0) 105-26 5| = 2421-0 171-15 18| = 12836-2 3 (8) 1579 (9) 3 (1-5) 10592 (1-5) 3f = 1579 15$ = 1061 1-6 . * Calculated from D 2 . 4 (7-6) 10505 (8) 15J = 10440 Au 2 (6) 10208 (6) 351-70 7$ = 10199-3 Inverse D sets Cu 1500 4 Ka 2 CO 35667 CO 10^ = 1497-9 463-3 19^ = 35676 4 /. 26383 CO Ag 3053 4 141=26410 7^=3052-4 1509* Au 9578 4 Zn 2 (27) 1531 (27) 6| = 9495-9* 38-72 9| = 1510-2 * See sect. 8 below. 10 =1548-9 Al 2 (4) 110 (4) * Calculated with o- = J^sc p. =51-07. 12-14 3 (16) 4= 112-9 823 7|= 823-6 (16) Cd 113-87 2 (22) 4314 - - 91=4324-8 12 (22) In 119-26 2 (50) 2405 5=2385 (50) Eu 209 2 (18) 7910 - 9$ = 7942- 78 12 (18) Tl 2 (40) 9047 (40) Hg Undetermined 371-84 6 = 9044 3 (?) 10091 (?) 6f = 10174-6 vi] THE OUN 137 These doublets, with d 2 calculated from Z> 22 , give very remarkable support to the rule with the following exceptions; Cs D (3), inverse Au D, Ba D (3). In the last the deduced mantissa difference is close to an oun multiple, but the observation errors must be taken as quite negligible and the D satellite and F separations agree. The value of here may be very large. The other two cases are more serious and will be returned to later. It may, however, here be mentioned that Cs D is certainly in some way anomalous, for it shows itself hopeless to fit with a series formula. The general agreement of all the data with the rule together with the system- atic nature of the deviations where such occur point to the conclusion that at least to a close first approximation the law of oun multiples is correct. Where, therefore, the few deviations occur, greater than are permissible by observation errors, it must be our object to discover the source of these deviations and their laws. To this we will return shortly. Meanwhile it should be borne in mind that up to this point the actual values of the ouns have been estimated by direct comparison with the chemical values of the atomic weights which vary very greatly in the degree of accuracy with which they are known. If, however, the law is a real one, it should be possible to determine the oun values direct from other spectroscopic data in combination with the A. Later further relations will be brought to light which will give much more accurate values in this way. Displacement. 6. In the foregoing we have seen how all the constituents of S and of D sets are to be regarded as modifications of one of them. Such a modification we shall call displacement, and a displaced line a collateral. When an oun multiple is added to or deducted from the limit mantissa, it may be indicated by writing the multiple to the left of the line symbol, and when to that of the sequent by writing it on the right. Thus, if S (m) denote a line of the $! series, and S 3 (m) = ( - A 2 ) S 2 (m) = (- A x - A 2 ) S l (m). If the law is correct, A! = #S, A 2 = ?/8 and it may be written S 2 (m) = ( - xS) Si (m), etc. or, we may regard S 3 as the normal line and then S 2 (m) = (y8) S 3 (m), ^ (m) = (x + y. 8) S 3 (m). So, again, if the satellite separations are produced by displacements of pS, qS and D 13 (say) be regarded as the typical D line of the set, the whole system consists of displaced lines represented by the scheme D 13 (m) ( - A,) D 13 (>n) ( - A! - A 2 ) D 13 (m) 138 ANALYSIS OF SPECTRA [OH. If this were all, such a notation might be considered an unnecessary complication. As a fact, however, these displacement effects are found to be a very common phenomenon, and the changes shown in the above schemes of S and D lines are only special examples of a very general rule. Displacements on a single sequent such as those in the S sets are common, but apparently double displacements would seem to be the rule. In other words a displacement in one sequent seems to encourage displacement in the second. At present the only evidence that such displacements occur must be based on coincidences between observed lines and the calculated collaterals. Such a coincidence in a special case is no proof that the lines are in reality related in the way supposed. When, however, a very large number of very exact agreements are found to occur we are bound to recognise the existence of the effect as a general relation. With double displace- ments with two multiples to manipulate it is much easier to arrange a given coincidence. Consequently such coincidences can have little weight unless sustained by at least double conditions and applied to cases where observation errors are very small. The following are a few instances which will serve as illustrations. (a)* The Ba S'" (5) lines show a deviation in wave number from the cal- culated values of about 65, and far in excess of that ordinarily shown by C values for this order. In addition, S 1} S z show a diminished separation of 875-79, instead of 878-14, whilst S 3 has not been observed. The shift of 65 corresponds closely to that due to a displacement of ISSj in the limit. We proceed to test this supposition. First as to the degree of accuracy of the observations. Those of $j (5) are due to Schmitz and are given to -001 A. Allowing a possible error of dX = -005, the possible dn is .-08. S 2 is by Saunders who allows a possible error dX = -2 or dn = 1-4. Even these maximum errors taken in opposite direc- tions cannot change the observed separation to the normal value 878-14. Some- thing then has clearly happened to the set. A displacement of 13S X in the limit (28629-20) diminishes the wave number by 64-96. The value of S (5) given by the formula is 25214-15, and consequently (13SJ S (5) is 25149-19, whilst the observed is 25147-84. The difference 1-35 (dX = -2) may well be ascribed chiefly to formula defects. But further a displacement in the S 1 (oo ) necessarily produces a change in the v separation. Here it produces a diminution of 3-01 and consequently a separation 878-14 3-01 = 875-13. This explains the observed abnormality in the separation since the observed and calculated agree within one-half of Saunders' estimated possible error. In addition, the normal S { (5) deduced from observed (ISS^ S 1 (5), is sustained by a possible S x (5) in A = 3119-654, n = 32045-57 since the normal S (5) = 25147-84 + 64-96 = 25212-80 and 25212-80 + 32045-57 = 2 x 28629-19 = 2 x limit. It is this independent support especially that of the modified ^ which gives weight to the suggested explanation. Saunders' value for S (6) also shows a large C of 54-2, which * This example is based on the limit 28629 and the old arrangement of S (2), with Saunders' original measures of S (4). vi] THE OUN 139 may be the same 138 X displacement within observation errors, but as it stands is a 118! displacement. A similar example is found in Au S (6). (&)* In the copper spectrum there appear together with the S (2) doublet three neighbouring sets clearly related. They are in W.N. 8(2) (10) 12353-36 (-03) 248-43 (10) 12601-79 (-02) (2) 12320-73 (-03) 32-63 33-18 (2) 12386-54 (-05) 133-42 (2) 12486-78 (-03) 24774 249-10 250-92 (2) 12568-47 (-03) (1) 12635-64 (-05) (1) 12737-70 (-05) All the measures are by Meggersf with probable errors given in brackets after each wave number. The separations of the first of each doublet from the Sj_ are given in thick type on the same line and the doublet separations between. With reference to these values, it may be safely taken that the probable errors in the separations are much less than those of the individual lines. This is clearly shown by a comparison with other observers. Eder and Valenta, and Meissner agree in making S (2) larger by -04 A. whilst in S 2 (2), Eder and Valenta make it -05 larger and Meissner -04. They all agree therefore within -01 in making the separation the same. Calculation shows that the lines in question belong to the doublet systems (1218) (1218), (-118)S(-9S), ( - 428) S ( - 328). The observed and calculated separations and shifts from S are as follows : Calculated v Observed v Calculated shift Observed shift 247-74 247-74 -32-40 -32-63 249-09 249-10 33-29 33-18 250-91 250-92 133-47 133-42 It is seen that the separations agree with exactness within -01 and the shifts are very close. The differences in the latter are possibly due to an error in Meggers' S. Both Eder and Valenta, and Meissner agree in making it -04 A. larger or dn = -06 smaller. These would show shifts of 32-57, 33-24, 133-48 in still closer agreement with the calculated. (c) Another very striking instance of double displacements is afforded by lines related to Kr$(l, 2, 3){ given in more detail in Chapter X. Here the evidence of double displacement is especially strong because whilst separations due to displaced limits remain the same for different orders, those depending on displaced current sequences alter in a definite way from one order to the other. For details see I.e. (d) There is evidence for a long X D u series extending up to m = 15. Together with this there exist two other series corresponding respectively to (28 X ) D ( - 28 X ) and ( - 28J D (28J& (e) The F series seem peculiarly subject to displacement. Frequently a whole normal order will even disappear and be represented by displaced or other- * Phil. Mag. 39, 471 (1920). f Butt. Bureau of Standards, Wash. No. 312 (1918). % See [v. p. 349]. See [v. p. 399]. 140 ANALYSIS OF SPECTRA [CH. wise related lines. For instance in the alkaline earths the first triplet splits up into two sets, one corresponding to a doublet representing the first two lines of a triplet and another doublet shifted from that representing the last two of the triplet. Thus in Sr (see Table III) for the first order occur *i (2) *, (2) Perhaps some of the best established displacements of this kind are afforded by Kr F*, supported not only by complete sets in each case, but by summation lines as well. It will be sufficient here only to indicate the summational evidence for the F lines. m 2 3 4 (2) (7A t ') F t JF(oo) FI (1) 17321-51 30677-82 (44034-13) (-35 X ) 44028-04 (In) 23353-84 ...77-27 (2) 38000-71 (2n) 26067-66 ...77-16 (6) 35286-68 (5) 17594-17 ...77-76 (1) 43761-38 FI (2) (7A 2 ') (6) 17747-14 ...77-73 (1) 43608-33 FI (2) (10A 2 ) (2) 17972-78 . . . 77-70 (1) 43382-63 Fj_(2) (16A 2 ' + A, The central column (in italics) gives the limits determined as the mean of the corresponding F and F lines. It should be specially noticed how F (2) which we should expect to be the strongest line of the series is very weak and all the energy appears as transferred to the well-marked displaced sets. In X also are found F (2) (10A 2 ), F^ (2) (10A 2 ) and others. 7. Returning to the displacement schemes for S and D triplets above, it may be interesting to compare the normal change of intensity with displace- ment. Certain theoretical considerations with which, however, here we have nothing to do suggest that the actual energy emitted by a given configuration is proportional to its wave number f. Consequently the energies per configuration in a doublet or triplet set of the same order would be practically the same, and the ratio of the intensities observed in a spectrum would be a rough measure of the number of corresponding configurations taking part in the emission. Let us suppose that the normal S line of any order is the first or S^ J. The rule is a descending order of intensity from /S x to $ 2 to S 3 . We should conclude that the normal configurations form the majority of emitting centres. A certain pro- portion, however, of the normal ones readjust themselves to one corresponding to a A! displacement on the limit and a smaller proportion still to that of an extra A 2 . The negative displacement has been concomitant with diminished intensity. In the case of a D set, let us suppose D 13 to belong to what we may call the normal configuration. When it is forced to emission however by far the larger proportion break up into others. At first, say, it breaks up in the same manner as in the S, resulting in A 1? A 2 displacements in the limit, and showing intensities diminishing from Z)j to Z> 2 to D 3 . In certain elements no further change takes place. In the majority, however, further changes intervene. * See [v. p. 380]. f Energy = hv, h = Planck's constant, v frequency. J The illustration is not affected by the particular line taken as normal. vi] THE OUN 141 The Z> 3 set remain stable, but the greater proportion of the others alter their con- stitution in a way which causes displacement in the ^-sequent and we get strong lines Z) 12 , D 22 , leaving Z) 13 , D^ weak. The Z) 22 centres remain stable, but the Z) 12 are still easily upset and the large majority change to Z) n which becomes the strongest, i.e. the most numerous, of the whole set. In all these changes a positive displacement, quite irrespective of the sequent in which it takes place, goes with an increase of intensity and a negative with a decrease. The same rule is exhibited also in F series. There seems a general tendency for it to hold in other cases, though other conditions may modify it. For instance a usually stable configuration may, under certain conditions of excitement, entirely break up and give place to one or more collaterally displaced. As an example may be cited Cd S'" (6, 7). Kayser observed ( - 68J S l (6) and not S 1 (6). Huppers has since observed S l (6) and not ( 68-J S^ (6), but he has also observed ( - 68j) $! (7) and ( - 68^ S 2 (7). The number of instances of this kind, where, of collaterally related lines, one is seen by one observer and the other by another, is very large. The difference must be ascribed to differences in the excitation used by the two observers. 8. After these remarks on displacement in general showing definite instances of its real existence, we may return to the consideration of the few apparent exceptions from the oun multiple law, viz. the inverse Au D set, the Cs D, BaZ)'"(l). (1) The mantissae differences for the inverse D sets in Cu, Ag, Au cannot be in error by more than three units at the outside, whilst the values of the oun multiples are correct to a few decimals. Consequently the exact agreement of the two in Cu and Ag is very striking and leads to a suspicion that some change has happened in Au which has hidden, but not destroyed, a similar agreement in it also. If so, this can only have occurred in the other sequent D 1 (co). It is therefore natural to see if any displacement on it can explain the anomaly. It is found* that a + 28 displacement does so. This displacement diminishes the limit by 85-74. Consequently the true d sequent calculated from it must be 85-74 less. The new denominator corresponding to this is 1-503812. It alters the mantissa difference given in the table to 10905. Now 7|8 = 10901-2 and the difference of 3-8 corresponds to dn = -24, and is within observation error limits. We thus find again exact equality in the three cases where errors are practically negligible. It may be noted that in Cu, Ag the D u lines are abnormally weak, whilst Au Z) u is of normal intensity an instance where a positive displacement has increased intensity. (2) Cs D. This is a case where the D series in itself shows quite exceptional anomalies in being quite out of accord with any of the usual formulae. With D (oo ) = S (oo ) the d mantissae converge asymptotically so that it must be the proper limit for the normal series as a whole. The formula calculated with it from the first two lines m = 2, 3 gives large errors for all the others, in fact for * Phil. Mag. 39, 470 (1920). The 25 given there is correct but the numerical details are in error. 142 ANALYSIS OF SPECTRA [OH. m = 4, 5 the C are dn = 16 and the calculated Z> u (5) is the observed D 12 (5). Calculated from m = 3, 4, i.e. allowing for some anomaly in Z) (2) the formula agrees much better, but still with outstanding errors of the order dX = -5. It is clear that some changes from normal conditions occur. The F limit, calculated from good measures for F 9 is very close to the value of d l as calculated from Z) n (2) and Z)(oo) = $(oo). This would seem to show that there is no change in the limit for D u (2) and any changes must have taken place in D 12 . It would seem hopeless to settle with certainty the seat of the anomaly. The following results of calculation may, however, be of interest. If the observed is really (28 X ) D u the d mantissa is 404 larger and the difference in question becomes 7817 in place of 7413, and is now close to 12|8 = 7822-0, but the satellite separation is now 5-32 larger than the observed F separation, so that displacement in the d sequent must also take place, either in Z) u or D 12 . Treating the observed line as (28 X ) Z) n (2) (2S X ) makes the a = 99-08 against the observed F separation of 98-03. If the Z) 2 are the seat of the anomalies, they will be ( - 2S X ) D 2 (2) ( - 28!). The matter cannot be settled until the constitu- tion of the Cs D series is better known. For our immediate purpose the impor- tant fact emerges that the numbers given in the table for the mantissae differences are unreliable and have no evidential value. (3) Ba D'" (1) shows an anomaly also in the ratio of its separations. Another set is indicated far up in the ultra-red beyond the observed region by a dependent F series which gives the normal satellite ratio of 5 : 3 and mantissae differences which are oun multiples in step with those of Cs and Sr, but the measures are too uncertain to serve as evidence for a law. An explanation of the anomaly by displaced limits on one of the D is not tenable, for the satellite separations are sustained as correct by the corresponding separations in the F (GO). A. displace- ment of the whole set of -D (1) by about 1700 would make the mantissae differences exact 168, 7|S. This would be attained either by a displacement of 6A 2 in the limit (shift 1701) or a linkage to a true D (I) set by a + b links (shift 1717 see Chapter X). But neither of these explanations is permissible since the F() calculated from the associated F series agrees too closely with the d(l) calculated from D (1). This anomaly, together with that of the exceptional satellite ratio, indicates that some as yet unknown effect has operated, with the consequence that the set is not available for drawing conclusions from as to normal laws. 9. The fact that the oun enters as a definite discrete quantity in the con- stitution of the spectrum of an element may be regarded as established not only by the foregoing evidence from the v and a separations, but by the way in which it explains a host of details in the more complicated systems so far as any analysis of them has been attempted. Formally the oun in each case is deducible from the data of the spectrum itself. The result is independent of the definite relation to the square of the atomic weight, although this relation was the means through which its existence was first discovered. The foregoing discussion would seem to afford conclusive evidence in favour of the relation in question. Never- vi] THE OUN 143 theless it involves a difficulty arising from the more recent discovery of the existence of isotopes. This difficulty arises in two ways; (1) if an "element" contains two or more isotopes always in the same proportion, the chemical atomic weight is the proportional mean of those of the isotopes. For instance, if Cl* consists of isotopes of weights 35 and 37, the observed 35-5 has no real existence and an oun depending on (35-5) 2 would be meaningless. (2) If an element consisted of several isotopes, we should expect its spectrum to be com- posite consisting of lines belonging to each isotope. At present, however, the first difficulty does not arise, for the spectrum of Cl has not yet been analysed, even into series lines, and elements with non-integral atomic weights where series are known, such as Cu and Ag, have not been investigated for isotopy. The second difficulty is more serious and it is necessary to see quite clearly how the matter stands. Isotopy is supported by two sets of investigations, one from radioactive considerations by which it was discovered by Soddy and his col- laborators, the second by observations on positive rays by Aston. Let us con- sider these in order. The emission of an a particle reduces the atomic weight by about 4, and the new element takes its place in a group two lower than that of the original one. Soddy supposed that after the emission of a j8-ray, the new element is raised into a group one higher than the old one, but with its atomic weight practically unaltered. It may thus happen that the same place in the periodic table is occupied by two elements of different weights to which he has given the name of isotopes. It is found that in all cases investigated isotopes are inseparable by chemical reactions and that they have the same atomic volumes. In other words, their chemical properties are dependent only on their position in the periodic table, which may also be defined by their atomic number, that is, their ordinal position in ascending weight. This is usually assumed, perhaps without sufficient evidence, to count from He as twof . If any doubt were possible as to this explanation it would be removed by the direct determination in one particular case. Lead occupies the position of several such isotopes, originating after a series of corresponding transformations respectively from Ra, Th. X, and Ac. X, as well as possibly ordinary lead if itself not a mixture of the others. Pb is reached from Ra after five a emissions and from Th after six. Consequently the atomic weight of Ra.Pb should be 226 20 = 206, and of Th.Pb 232-4 - 24 = 208-4, if Th contains a single element. Values close to these have been experimentally obtained, but it is difficult to find U or Th minerals free the, one from Th and the other from U. Determinations from pitchblende give values about 206-5 -2, the purer the mineral the lower the value. Honigschmid and HorovitzJ, with material from very old geological formations, have found 206-046 -014 (Morogoro, E. Afr.) and 206-06 -008 (Moos, Norway). Richards and Wadsworth have found 206-08 (Cleveite, Langesund). For Th.Pb, Soddy and Hyman|| using a Ceylon Thorianite found * Aston, Phil. Mag. 39, 611 (1920). f Those who regard He as built up of H atoms must take its atomic number as four. j Monatsh. f. Chem. 36, 355 (1915). J. Amer. Chem. Soc. 38, 2613 (1916). || J. Chem. Soc. 105, 1402 (1914). 144 ANALYSIS OF SPECTRA [OH. 208-4 -1, whilst Honigschmid* found from Thorite 207-90 -013. The experimental results thus fully support the radioactive deductions. Thus the plausible explanation of the general effect has been directly estab- lished in at least one particular case, and it must be taken as a definite fact that elements exist with different weights but identical chemical qualities. It has, however, been further asserted that such isotopes exhibit identical spectra. The only direct observations bearing on this are comparisons of the spectra of the two isotopes, lo and Th, and of lead isotopes. lo has never been obtained free from Th. Exner and Haschekf, using an impure mixture, found no new lines due to lo. About the same time Russell and Rossi J, using a preparation con- taining from 10 to 16 per cent, of lo which they had purified from other elements except traces of Scby the greatest care, photographed its spectrum as well as that of pure Th on the same plate between 5000 and 3800 A. They found no difference either in the lines present or in their relative intensities between the two spectra, except that in the lo preparation five of the strongest lines of Sc were present. They found that the presence of 1 per cent, of Cr 2 or U 3 8 could be detected with certainty and that -1 per cent, of U 3 8 was just on the verge. No statement was made as to whether the supposed pure Th was tested for the presence of lo. There is also found agreement between the spectra of ordinary lead and of that of radioactive origin. Merton has found practically exact agreement in the case of seven of the lines. More recently Aronberg|| found a slight difference in the line 4058. Merton^f has confirmed this and has definitely proved the existence of small shifts in this line for ordinary lead, lead from Ra, and lead from Th. For Ra-lead the wave length is -0050 -0007 larger than that for ordinary lead and for Th-lead -0022 -0008 shorter. These are in the same order as their respective weights. Later** he has extended the investigation to other lines of Pb and has found for the wave number differences of ordinary lead over Ra-lead the values 4058 -065 -005 3640 -052 -002 3740 -053 -008 3573 -037 -004 3684 -035 -005 [Of these, 3740, 3573 belong to the first set of Kayser and Runge's type II. The Zeeman patterns are 0/5/4? ; 2/4/3 ; 0/3/2 ; 0/10/7 ; 0/5/4, so that probably none of the lines are analogous.] All the relative shifts are more reliable than the absolute values given. He points out that the shift for the first is 200 times as great as that calculated from * Z. S. Elektroch. 25, 91 (1919). See also Maurice Curie, C.R. 158, 1676 (1914); Honigschmid and Miss Horovitz, ib. 1796; Monatsh. 34,283 (1913); Richards and Lerahert, C. R. 159,248 (1914); Richards and Wadsworth, J. Amer. Chem. Soc. 38, 221 (1916). t Wien. Ber. 121, 1075 (1912). J Proc. Roy. Soc. A, 87, 478 (1912). Proc. Roy. Soc. A, 91, 198 (1915). || Astro. J. 47, 96 (1918). j[ Proc. Roy. Soc. A, 96, 388 (1920). ** Proc, Roy. Soc. A, 100, 84 (1921). vi] THE OUN H5 Bohr's theory that the true value of N is (1 m/M) N^ referred to in Chapter III, sect. 7. 10. These are definite facts. How can they be squared with the other fact, that the spectra so far analysed depend directly on the oun, itself dependent on the atomic weight? Unfortunately at present the question cannot be dealt with directly, for in neither Th nor Pb have series been discovered and the ouns determined. Granting that the whole of the spectra in Th and lo are the same, it might be suggested that the reason was due to the fact that the substances used were not pure but mixtures of both and that the observed spectrum in each case was the sum of two. This would be quite in accordance with the fact that Th has a very crowded and complicated spectrum. But a similar explana- tion is doubtful as applied to lead. For Aronberg's and Merton's results show that each isotope in at least one instance possesses its own representative of a typical line slightly different but quite definite. In each spectrum this special line appears single and points to the purity of each, as well as to the existence of ordinary lead as another pure isotope and not as a mixture. Even this conclusion, however, is not certain in its entirety. For the different lines are close, and the observer measures the position of maximum intensity, which would depend on the proportions of the various isotopes present. The experimental evidence for the identity of the spectra cannot yet be regarded as absolutely conclusive. In spite, however, of its incompleteness it must be confessed that it points provisionally to practical equality in all the isotopes belonging to the same atomic number. If so, there must be some ex- planation for the two apparently irreconcilable facts. Amongst the possibilities is the supposition that of the different isotopes one alone is of normal type, that it alone is capable of emitting a spectrum, and that half He-atoms or H must be added or ejected in the others during the excitation before they can emit radia- tion energy. It is indeed a fact that isotopes in general differ in atomic weight by two units or one, 11. We next consider Aston's observations. These relate to Hg and gases of which the spectra of Hg, the rare gases, H, He, and have been analysed and series determined. He finds that H, He, C, N, 0, F, P, S, As, I are single elements without isotopes so that here the difficulty does not enter. In the rare gases he finds Ne ^ two _ 20> 22 Also ^ ^ ^ Br A has one, 40, with possibly a few of 36, Kr has at least five, 80, 82, 83, 84, 86, X has five, 128, 130, 131, 133, 135, also Hg besides 200 has a strong proportion of 202, and a number of others in small proportion. The spectral atomic weights* are A Kr X 40-0141 -0006 83-054 -0006 1 29-963 -0002 * [v. p. 34-2 1. H. A. S. IO 146 ANALYSIS OF SPECTRA [CH. in which the possible errors given are somewhat too small as no account was taken in their estimation of the true value of N in the d- and /-sequences, a point considered later in Chapter IX. They all point to whole numbers, the values given in the table in sect. 2 even more definitely. Also Hg = 200-21 '01. On the other hand no evidence has yet been adduced to show that the spectra are not composite. The presence of sets of separations of the same order of magnitude but definitely different might indicate such compositeness, and the spectra, especially that of X, are very crowded. We cannot say decisively that this is not the case, but the writer believes it is very doubtful. On the other hand while Aston's experimental work must be accepted it is possible that the conclusions drawn from it, although the most natural at first sight, may not be justified. It is very suspicious certainly that in Kr and X with such large numbers of supposed isotopes, the atomic weight should come out in both cases not only whole numbers but to numbers in the usual relations to the weights of surrounding elements in the periodic table. It may be that the drastic electric conditions to which the atoms are subjected in the actual experiments may eject or add He or half He, or H atoms which are generally supposed to go to the constitution of elements. At least this is a possibility which should be tested. 1 2. The evidence given in this chapter for the dependence of the oun on the square of the atomic weight would seem so conclusive as to exclude the supposi- tion of any other relation. But the difficulty referred to above would be avoided if it could be shown that the oun depended on the square of the atomic number, and as this last is very roughly proportional to the atomic weight it might be thought a priori that the same law might be applicable to it within error limits. The weight relation is so closely followed, and so many regularities are brought out, especially in the doublet series, where the quantity in question is the large 8 or four ouns, that this is scarcely probable. Nevertheless the question is so important that it is desirable to test the data on this point. At least if it is found impossible, the impossibility of making the data fit will greatly add to the con- fidence felt in the positive result for the weight. For the purpose of comparison with the weight discussion it will be convenient to deal with the numbers 22V/100 = n where N is the atomic number. Also we shall assume that N is measured from He = 2. We begin with Zn where A 1? A 2 are known with great accuracy and where AJ 2A 2 is a small quantity and therefore is a small multiple of the oun. The atomic number of Zn is 30. Then A! = 7205-14 = 20014-28 2 == 31 x 645-622^ 2 , A 2 3486-71 = 9685-305H, 2 = 15 x 645-687w 2 , A! + A 2 - 10691-85 -f- -lp = (29699-583 + -28p) n 2 = 46 (645-643 + -006^) n 2 . Hence, 645-643 must be a multiple of q the oun constant. In other words, q must be one of 645-6, 322-8, 215-2, 161-41, 129-13, 107-6 .... Of these the first vi] THE OUN 147 three are multiples of the fourth and sixth, and it will only be necessary to consider the last three. But further, the true oun must enter also in the satellites and the enhanced doublet separation. The satellites of Zn are not known with sufficient accuracy to serve. For the doublet, with p 2 < 1, A - 9135 + I3p = (25375 + 36-lp) n*. Now 25375 + 36j9 = (157-21 + Vp) 16141 = (196-51 + -28p) 129-13 = (235-81 + -33^) 107-61. The numbers in brackets must be integers. The second is therefore definitely excluded in spite of the large possible errors. The first is just possible and the third possible with two-thirds the maximum error. There remain for further testing 161-41 and 107-61 or for 4S l5 645-643 -006, 430-428 -004, corre- sponding to the " weight " value of 361-78. With these the corresponding multiples for the triplets (A x + A 2 ) are respectively 184, 276 and for the doublets 157, 236. The oun values deduced by dividing the A t + A 2 and A by these multiples are then q ...... 161-41 107-61 Triplets ... 232-431 154-95 Doublets ... 232-74 154-84 These make the atomic numbers deduced from the triplets and doublets the same within 1 in 1500, and 1 in 3000 as compared with equality in weights given in the table of 1 in 3500. Take next the case of Ag with accurate measures for v and &. The atomic number is 47 A 27789-10 + -30^ = (314'49-86 + -33p) n\ 31449-86... 48f (645-125 + -007^) = 73 (430-82 + -004^). Neither the 645 nor the 430 can be brought to agree with the Zn value without allowing errors 45 or 100 times the maximum possible. But it might still happen that in different groups the q might vary slightly. Let us then test further for the satellite and the inverse D. The above give for the 8 respectively 570-033 and 380-673. Also 5 Sat. diff. Inverse D 24251 30534 570 4|5=2442 55= 3012-6 380 6^5 = 2379-2 85 =3045-4 Atomic weight of 5 = 2421-0 7^5=3052-4 These are sufficient to show that the atomic number does not fit in with the conditions. It has also been tested on other elements with a similar result, definitely against the theory in spite of naturally a few coincidences. Further the doublet series requires the oun itself or 8 l5 whereas on the "weight" theory all the doublets with the doubtful exception of the enhanced Ba depend on the larger quantity 8. It is in fact this large quantity which makes the evidence in 148 ANALYSIS OF SPECTRA [OH. vi these series so conclusive. This statement may be illustrated from the alkalies, with atomic numbers 11, 19, 37, 55. Here Na A = 744+2p =(15372 +41 p) n* K A = 2928-7 +# = (20282 + 13-8p) n z Kb A = 12937+5p =(23625+9-1^) n 2 Cs A =32565 + 4-6^ = (26913-2 + 3-Sp)n* whilst 15372... =23f (647-25 + -57p) = 35f (429-99 + 1-16^) 20282. ..=31^(643-86 + -4p) =47 (431-52+ -2Sp) 23625... = 36 (647-26 + -25p)= 55 (429-54+ -16p) 26913... =41| ( 644-628 + -lp)=62i (430-61 The multiples are those which produce quantities as near as possible to 645 and 430. It is seen at once not only that it is impossible to make them agree amongst themselves or with the value from Ag or Zn, but that it is necessary to have recourse to the 8/4 to get even a rough agreement. Compare these with the corresponding quantities for the "weight" theory with q = 361-78 -05: 744 =(14067+39^?)^ =39 (360-68 +^-06) u? 2928-7 = (19160 + 13p) w 2 =53 (361-51 + -25^ -06) u? 12937 = (17718-6 + 6-Sp) w* =49 (361-604 + -14^-04) w z 32565 =(18458-84+2-6^) * = 51 (361-938 + -05j9-04) w 2 in which the uncertainties are due to estimated uncertainties in the atomic weights. CHAPTER VII LINKAGES 1. In the preceding pages it has been seen that flame and arc spectra, so far as they have been analysed, are constituted of lines either themselves be- longing to series or directly related to them by displacement. As the conditions of excitation become intensified, such as by increase of electric potential in the spark, these direct series lines tend to diminish in number and decrease in intensity, whilst new lines appear, or in certain cases (the enhanced series in He and group II) old lines are intensified. In so far as the terms "arc spectrum" and "spark spectrum" are used to denote the sets of lines appearing in a given element in the arc or in the spark, they are convenient. In truth, however, it is doubtful if it is possible to draw a sharp line of distinction between the two. Certainly spark spectra of the same element differ very greatly with the con- ditions of the spark, in certain cases even the slight changes by different experi- menters produce differences in the lines observed. Under the same conditions of excitation, the nature of the spectrum series or otherwise depends chiefly on the element in question, its group in the periodic table and its position in the group. With increasing atomic number, in other words with increase in the number of electronic and other constituents of the atom, the spectra become increasingly crowded, both in arc and spark. It is natural to correlate this with the larger number of configurations possible with the increase in complexity of the nucleus and surrounding electrons. The emitting centres are to be con- sidered as different from the normal atom, either in the configuration of the constituents or by the absence of particular individuals. These abnormal centres are produced by the disturbing effect of the excitation. It is natural to suppose that with a given element the arc would produce one type of change and the more drastic spark other types. At the same time a type produced by the arc in one element might require the spark for production in another. The view at present current is to regard the energy emitted as dependent on its frequency. If this is the case, intensities of observed lines, especially in the same region, will depend chiefly on the number of each abnormal configuration present under the given conditions. These remarks are purely hypothetical and though they serve to give some clearness to our conceptions and to help in visualisation, we must here regard them only in that light. As a fact the spark tends to intro- duce new sets of lines in great number, which with few exceptions show none of the ordinary series relationships. Until lately little was known of their con- stitution beyond the fact that they exhibited considerable numbers of pairs showing the same separations, apparently without relation to those of the doublet or triplet series. In [iv. v] an attempt was made by the author to throw some 150 ANALYSIS OF SPECTRA [CH. light on this question. Only a beginning has been made, but certain important conclusions have been arrived at which also have valuable application in the general analysis of spectra. The present chapter is based chiefly on these two papers. The general result is that, in certain elements at least, the spark spectra consist almost wholly of long sets of lines differing from one another in succession by certain special separations which can be calculated directly from the ordinary series limits and A. These separations may be called links, and a complete set a linkage. These linkages appear to start from ordinary series lines. While then the terms flame, arc, or spark may be usefully retained as referring to the mode of production of a given spectrum, when dealing with the emission of an element as a whole, it will be preferable to divide the types into series spectra, enhanced series, linkage spectra, band spectra, or others which may be discovered in the future. 2. The evidence for the existence of these linkages depends on the presence of a large number of separations of a given value. On account of observation errors no exact value can be expected, and in searching for a given link separation I it is necessary to take account of all within a small variation x, or say values I x, where x is small. As the spectra in question contain a very large number of lines it is certain that at least a few coincidences will be found, even if the lines constituted a purely chance arrangement. Before any conclusion therefore can be drawn as to the existence of a given link, it is necessary to know how many coincidences are to be expected on a pure chance arrangement. Let us suppose that there are p lines between wave numbers n 1} n 2 . The average interval between the lines is (n 2 n-^j(p 1), and the chance that a line falls within the range 2x is 2x (p l)/(n 2 %). This therefore is the chance that, starting from any given line, another will be found I x ahead. Hence with P lines the number of probable coincidences is 2Px (p l)/(n 2 n-^. We begin with the line % and take each in order, but it is clear that when we arrive at n 2 I no line beyond can give the separation I. The probable number of lines in this region is I (p I)/ (n 2 %). Consequently P = p - (p - 1) l/(n 2 - ni ) = p(l- l/(n 2 - nj) since p is large. Hence the probable number of coincidences is n 2 ~ fa If, however, we know beforehand that the arrangement is wholly based on links, no separations other than those or than those compounded of sums or differences of links can enter. Thus in a spectrum in which links preponderate, chance coincidences for a value other than a true link would be considerably less than that given by this formula. 3. In searching a spectrum for a given link, values differing by one or two units are included and a list made of all observed values. These are then treated graphically as follows, On squared paper the separations are plotted on a line of abscissae at distances corresponding to -1. On the ordinates to each, dots VII] LINKAGES 151 are placed for each representative. Then for a given abscissa the number of dots within a distance x on either side is counted and entered as the corre- sponding ordinate. In this way a curve is obtained whose ordinates represent the number of separations within x of the corresponding abscissa and which gives a visual representation of the frequency of occurrence of the separations in the neighbourhood. This curve we shall call an occurrency curve. On this a dotted line is drawn tfo represent the occurrency on the supposition of pure chance. Some of these are represented in Figs. 19-22. Figs. 19, 20 give those for the ordinary doublet separations in Ag, Au, Fig. 21 that for the t'-link in Kr, and Fig. 22 for the v-link in Au. In general they do not rise to a single peak, the cause of which we shall consider later in sect. 6. In Fig. 22, the range has been considerably extended to see how it behaves when at a distance from the true link. It is clear that here the chance occurrences are far fewer than those given by the probability formula above, in accordance with the remark that it gives a maximum estimate. 152 ANALYSIS OF SPECTRA [OH. 4. The clue to the source of one such link was found in the spectrum of copper in which a separation of 1000 was found to be very frequent. It is close to 4v, where v = 248-4 is the series doublet separation. As v is formed by the displacement A on p (1), it suggested that the 1000 was formed by a dis- placement of 4A, viz. j x ( 4A) p . But the value of this was too large. It was found, however, that p ( 3A) p (A), or, say, p 2 ( 2A) p 2 (2A) was equal to 999-75, a practically exact reproduction' of the 1000. The inter- mediate separations proceeding by steps of A were also found, as well as those depending on the s sequence, s s (A), s ( A) s. They were tested in Ag, Au, where the quantities involved are much larger and the evidential value greater. They are sustained also by the corresponding quantities depending on A x in the triplets of the rare gases. As these links enter fundamentally in the constitution of these spectra, it is convenient to denote them by special symbols. The following are adopted : P 1 -p 1 (&) =a ^ 1 (-2A)-^? 1 (- A) == c Pl ( - A) - Pl = b Pl ( - 3A) - Pl ( - 2A) = d s s (A) = u s ( A) s = v in which it will be noted that b represents the v separation regarded as a link and e = a j rb + c-\~d. The values for Cu, Ag, Au and the rare gases are given in their tables of series in the Appendix. There are also certain others* depending on the d-sequence and satellite separations, and indications have been observed in the triplets of the rare gases of links depending on A 2 . These still await investigation. When a line is formed from another by the deduction of a link, we shall represent it by writing the link symbol on the left of the latter and when by addition on the right. Thus in the set of lines (3c) from the Kr S system given below in sect. 5 the lines are represented thus : u. S (2). 2e e. S (2) S (2) S (2). e S (2). 2e e. S (2). v S (2). u S (2). 2e. v 5. The work of analysing a given spectrum for the isolation of its linkages is a matter requiring some patience, especially when, as is the case in X, the spectrum is very rich in lines. A list of the wave numbers in order is first ex- amined, line by line, for each supposed link allowing for variations of from one to two units. When such a link is found, the two wave numbers involved are joined by a pencil line with indications of the link in question. The result is a maze of lines forming a complicated network stretching throughout the whole list. The next step is to start from any one wave number and follow up all the connections on a new list. In this way a set is isolated from the general list, all connected together in parallel and series groupings, but showing no connection * E.g. [iv. p. 386]. In Au depending on d (1) analogous to v on (1). [v. p. 348]. In Kr S (2, 3), p 2 ( -3A 2 ) -p 2 (A), say c a . vii] LINKAGES 153 with other wave numbers in the spectrum. This list is then arranged in a map so as to show as simply and clearly as possible the structure of the network. Some of these maps contain a very large number of lines. One example of medium size is shown in Fig. 23. It represents the linkage starting from Ag S (3). We return to the discussion of these maps later. It is first necessary to consider the evidence for the real existence of these links. 2620-34^ 961-1S (1) In all the 'elements so far investigated, the occurrency curves all show a considerable excess for all the above links over the numbers to be expected as due to pure chance. In general, however, they do not rise to single peaks* see, e.g. Fig. 20 above. Their form seems to indicate the presence of a dis- turbing secondary effect which modifies some of the apparent individual links. The evidence from the occurrency curves does not depend on that of a single link in a single element. For if such a curve be drawn for some actual pure * For an example of a striking single peak, see XF [v. PI. II, fig. 3]. 154 ANALYSIS OF SPECTRA [OH.- chance arrangement, it would not be the straight line given by the probability formula, but a ]agged curve of which that line would be a kind of mean. In a given case, then, our observed occurrency curves might happen to occur on one of these chance peaks. When, however, in all the observed cases for all these links, we find the occurrency curves rising up at the link value to about double the pure chance values we are compelled to take them as evidence for the real existence of these links. This collective evidence again in favour of the link arrangement increases the evidential value of each curve, because the presence of the link effect being allowed, the value of the chance occurrence is less than that given by the probability formula, or the dotted line should be lower in each diagram. (2) By far the most conclusive evidence is furnished by the very large number of regularities, repetitions, collocations of links and meshes. When four lines are related in the manner X, X + x, X + y, X + x + y, their representation in a linkage forms a parallelogram, and is called a mesh. There are an enormous number of these, especially where one of the links involved is the long e-link. Examples of these regularities are given in Fig. 24 taken from [iv]. The prob- ability of the chance existence of any one of these is extremely small, whereas, as a fact, they are extremely numerous. (3) The existence of links modified by some effect is shown by the presence of sequences of separations differing from the normal link by more than observa- tion errors. As illustrations may be taken (a) 30514 2460-39 2460-84 2461-00 2457-26 40353 (&) 15293 5634-92 5633-23 5631-12 5635-29 5639-46 44097 1886-73 24062 3183-70 (2) 3183-38 3183-11 1940-68 1884-03 194093 (a) is from Ag in which u = 2458-64; (6) from Au in which d = 5634-93; (c) from Kr in which e = 3183-34, u = 1884-03, v = 1942-44. (a) shows clear signs of a modification real or apparent in a u link. The mean of the links in (6) is 5634-80 or a true d, and each of the e-links in (c) is a true e. Many such examples may be seen in the maps given in [iv], as also in that of Ag S (3) given here. (4) A very common irregularity occurs where a slight change in the wave number of one line makes all the links surrounding it normal. In cases where there are several converging links the effect is striking, and gives direct evidence for the real existence of the link effect. As the effect should be capable of throwing light on the cause of the link modification, it will be well to give several illustra- tions, premising that the number of such instances is very large. (a) Taken from I in Fig. 24. The lines belong to the Ag P linkage. The line 42203 differs from two preceding lines by 964-89, 2618-83 and from two of larger wave number by 959-62, 2456-44. If the line be altered by 2-30 the differences become 962-59, 2616-53, 961-92, 2458-74 or practically the exact links, c = 962-54, v = 2616-61, u = 2458-64. LINKAGES 155 ./ > .<_. Fig. 24. The links arc represented in diagrams as follows: 6 - I 964-Z9 Z456-44 42203 2618-83 959-62 Large dots represent observed lines. The small circles one line in each diagram whose wave numbers are given below. References are to maps in [iv]. (a) 43720 in the Ag P linkage, two meshes on one link. (b) 25933 in Au Xii \ (c) 38457 in Au Xiii Y showing complicated congeries of meshes. (d) 42068 in Au Xiv ) (e) 39150 in Ag Pii\ ( f ) 30029 in Ag Pii \ showing complete cycles of links. ( 22 (1) (28 1 ).e.v, giving for D (1) 2735-49 3815-01 6550-50 Also, next to 38757-29 there is 38746-77 or 10-52 behind, i.e. another S x displacement. It would make Z> 22 = 6549-39, the true value. Also another line 34898-53 is 46-72 behind 34945 and 58 X on sequent shifts 46-40. These examples illustrate the occurrence of other displaced D (I) sets in this neighbourhood. CHAPTER VIII THE p AND s SEQUENCES 1. Before any definite knowledge as to the essential properties of the different sequences had been attained there was nevertheless a general agreement by different observers in the allocation of series. When a series consisted of sets whose separations diminished with increasing order, it was assigned to the P system. If a series consisted of sets with constant separations in which the first sequent approximated to the limit of the P or vice versa, it was assigned to the S system. An independent series with the same limit as the S and the same separations was assigned to the D. Also in the majority of cases the D nature of a series was supposed to be indicated by its satellite system. But it was found that a similar satellite arrangement, though on a smaller scale, was also exhibited by yet other series with the distinction that the constant separations were equal to those of the satellites of the first D set, and that they ran down to limits equal to the first cZ-sequents. This latter property differentiated the F series from the D. This classification was based on the external form of the different series and was not always applicable. The first definite test of essential likeness between corresponding sequences in the different elements was afforded by the discovery of the Zeeman effect. The distinct Zeeman patterns obtained showed that the p and s sequents in the doublet series of all the elements (Li excepted) belonged to a single category with the same characteristics. A similar result was exhibited in the triplet systems, but with no indications as to any connection in. p or s properties between doublets and triplets. So also the D doublets and the D triplets were respectively co-ordinated. All these sequent pairs are subject to their respective Zeeman patterns in all cases where the latter have been observed. But all lines which show these patterns do not necessarily come into the succession of a normal series. It must be considered that they nevertheless have some intrinsic relation to them. The only indication of the physical cause of the difference between doublets and triplets is that afforded by observations of Stark on the Doppler effect in canal rays. These, as we saw in Chapter V, at first sight seem to show that the sources emitting doublets have lost one electron, whilst those emitting triplets have lost two, but this distinction cannot be upheld. In this and the succeeding chapter an attempt will be made to obtain some insight into the nature of the similarity of the corresponding sequences in different elements and of their constitution. This can only be accomplished by a com- parative study of each sequent in each element. Rydberg, as we have seen, was the first to attempt this in his great memoir. 166 ANALYSIS OF SPECTRA [OH. Not only did he bring to light the existence of definite sequences, the constant N, and the relations discussed in Chapter IV, but he also attempted a comparison between the magnitudes of the various /x's in the different elements. His results- were combined in the following statement of regularities, where /z, S, a denote the- jit's respectively of the d, p, s sequences. 1. The sum 8 + a has approximately the same value amongst the different elements of the same group. II. The difference 8 a possesses approximately the same value in corre- sponding elements of groups II and III. III. The values of the difference ^ a in all the elements examined lie between the limits -32 and -48. IV. The difference 8 JJL has very similar values in corresponding elements of groups II and III. The last rule is a consequence of the second and third. These statements are, however, in view of our present more accurate measures, only very roughly true. But he made a very interesting application of them to the case of gallium of which at the time only the doublet S (2) was known. This element lies between Al and In in group III. He thus obtained estimates for the constants of his formulae and deduced for Si (2, 3,4) 4189-5, 2747-2, 2436-1 />! (1,2,3) 6791-9, 2965-9, 2504-9 His deduced Sj_ (2) = 4189-5 corresponded to the then measured 4170, or the now known 4172-2. The others were not then known, but may be considered as representing the now known doublets whose first lines are 2780-2, 2481, 2943-7, 2500-2. A glance through the formulae tables will show that in all cases in the p, s sequences the a is negative. In other words the mantissae increase with the order. This result is true both for doublets and triplets. The exceptions in He" and Li have been already referred to and form part of the evidence that the series in question have been wrongly allocated to the P series. On the contrary the / sequence has its a positive in both, or, in all* cases its mantissa decreases with increasing order. So also the d has a positive in all doublets with the exception of Cu, Ag. In the triplets it is positive in group VI and negative in 0, II. It may be suspected that the normal d sequence also requires a positive, but that in certain groups this has been modified by some special cause. We may postulate the rule that the p, s sequences are characterised by increase of mantissa and the/ by decrease as the order increases. The d sequence, however, does not appear to follow any definite rule in this respect. 2. Taking for the present p (m) to denote that sequence which produces the P series, there are two different functions p , p 2 for doublet series and three Pi,p 2 , Ps f or triplet. We know that the first orders in each are related in the way * The formulae given under X F, Kr F are probably not for normal F, but are related to a special kind of series the 1864 see Chapter X. VIIl] THE p AND 8 SEQUENCES 167 that they are displacements one from the other by the oun multiples A or A x , A 2 . The first question then that meets us is that of the general relationship between the sets of the same order for orders above the first. For this purpose we calculate the mantissae for the first four or five orders and determine the differences for p l , p 2 or p^p^p z . With the higher orders the changes produced by observation errors become considerable and so large that definite conclusions are not possible. The data are restricted because P series have only been measured in the doublets of I, III and the triplets of Mg and the Zn sub-group of II, whilst Ag, Au show only two orders and Cu one. The results are given in the following table*, in which also in the triplets the sum of the differences in each order is given in a third line. Na 742(1) 769 802 928 1563 K 2929(2) 2975(28) 2990(90) 3167(200) 2593(1100) Rb 12939(5) 12962(28) 12995(150) 13699(300) 12415 (?) Cs 32565(5) 32104(45) 32155(230) 32025(1100) 1313 Al In Tl 1752 (0) 37687 (5) 134154 (5) 1329 (78) 27236 (45) 94018 (35) 1377 (23) 26959 (24) 91195 1380 (50) 28048 (450) 90615 26799 92157 Zn j 7205 (6) 3486(1) 10691 5355 (28) 2525 7880 5191 (9) 2414 7605 5154 (30) 2375 7529 5026 (60) 2283 (60) 7309 Cd - 23106 (0) 10370 (2) 33476 17423 (25) 6980 (25) 24403 17649 (80) 6541 24190 17109 (25) 6407 23516 17160 (60) 6249 23409 Eu j 51301 18334 69635 41809 15087 56896 43789 14879 58668 31758 13290 45048 41976 13670 55646 Hg | 87908 (0) 29918 (0) 117826 71967 24779 96746 71364 23817 95181 96518 96451 The observation error changes in brackets are those for a single line. With the exception of the alkalies these show a sudden diminution in the second order and then a slow further decrease to a limiting value. In Na, K, Rb on the contrary we find a gradual increase to a maximum and then signs of a decrease. This effect is most marked in Na, whilst Cs behaves like the other elements though here they may remain constant after the first fall. The sodium data are very accurate so that the abnormal behaviour shown is a real effect. It is clear that the p and p 2 cannot both be represented by formulae involving even a/m + j8/m 2 . On the other hand, the mantissae differences are all oun multiples within error limits. The value of the oun, however, in Na is so small 4-76 that deviations of J8 t or 2-38 might be explained by the usual errors, so that the conclusion cannot be regarded as established thereby. A similar relation with oun multiples holds in the other three elements, but here, although the ouns are much larger, unfortunately the errors are also large, so that a * Taken from [n. p. 51] with Cd P (3), Hg (1) corrected as in Table III, and Eu added. 168 ANALYSIS OF SPECTRA [OH. definite conclusion again eludes us. The actual changes from the first order A are Na 5Si + 2, 128! + 2, 39^ + 0, A + 48 + 0, 308 K 38! + 4, 4S 1 + 6, ITSj + 3 Rb + 23, 8i-5, 128-32 Cs -(38! -17), -(38J- 68), - (3Si + 61) Expressed in this way it is clear that the anomalous effect decreases in influence in the elements from Na onwards until in Cs it appears evanescent. If the measures were sufficiently accurate to establish the oun multiple effect as indicated, the functional form difficulty as to the two p , p 2 would be avoided, and the p 2 (m) would become like the first order, merely displacements on the p . Similar indications in favour of the displacement relation are afforded by the doublets of group III. The measures are more reliable than in I (Na ex- cepted) and the evidence is the more striking. The differences are given as multiples of 8, the first being A : Al 668, 50 8 + 1, 52 8 + 4, 52 8 - 1 In 798, 57 8 + 44, 56J8 + 3, 58|S + 21 Tl 898, 62|S - 191, 60J8 + 0, 60 8 + 174 These are all within error limits except the two in Tl which deviate by as much as |8j . The deviations appear far greater than can be allowed for by mere ob- servation errors on the lines involved. With this exception, important from its large oun, they are all close to oun multiples. But there is a possibility of the presence of some disturbing cause in Tl, for the deviations from the calculated values are greater in this P series than in any other known. The first exception is in a line used for calculating the formula and the second is one in which the C value is exceptionally large. The evidence from the triplet systems is extremely meagre, being based only on Zn, Cd, Eu, Hg. Of these also the P series of Hg represents many difficulties as we have seen in Chapter III, whilst it shows no P 2 lines after the third order. On account of the triplet modification, we deal first with the v l + v 2 separations or compare p 1 and p% . Again is evident the large decrease in the second order to values of the same magnitude for higher orders. This, as in the case of the doublets of group III, is roughly f (A a + A 2 ). This rule, that the mantissa differ- ences after the first order in a P series are roughly from 7 to '8 those of the first is a useful one to apply when searching for P series in a spectrum. It holds not only as between p 1 and p 3 but with p 2 as well. In general the differences after the second show a slow rate of decrease with ascending order to a value which becomes the same at about m = 5. The data afford little opportunity for testing the question of the oun relationship as was done in the doublets. In Zn the oun is too small compared with possible observation errors to give definite results. In Cd the differences for m=2...5 are respectively 53|8 + 7, 538 + 41, 51|8 63, 51J8 56, the last two being possibly equal within errors. In Eu the data for m = 2 are unreliable as deduced from supposed displaced P lines. vni] THE p AND 8 SEQUENCES . 169 Similarly m = 5 gives an uncertain p 3 . The other two which are good data give 708 + 14, 53|8 + 10 with 8 = 837-92 and the same multiples - 34 and - 23 with the alternative 8 = 838-60. This is striking evidence in favour of the relation since the oun (209) is so large. In Hg the difference f or m = 2 is 66 J8 +16, practically an exact multiple, but the lines involved are a too doubtful P (2) set to base certain conclusions on them. For m = 3 the difference 95181 with extremely small possible errors is not in step with the differences before and after. The lines on which it depends are established as belonging to the P series by the existence of a corresponding complete P triplet, with the exception that one of the two lines for p 1 is subject to a 8 X displacement on the limit. In the table this displacement was originally assigned to P x (3) in the absence of anything to show which was the displaced. The present anomaly would seem to point to the P 1 (3) as the displaced. If this be assumed, or which is the same thing pi determined from P 1 (3), the mantissa of p 1 is increased by 1852, and the difference (p lt p 3 ) to 97033 = 66f x 1453-6 or 66|8, within the uncertainty of 8 itself. The values for m = 5, 6 are equal within possible errors to 96670 or 66J8. If better measures would prove the equality of these two differences, it would be almost conclusive evidence that^and^g are related by displacement. The hypothesis that the different p sequences, like those of the d, are related by displacement may then be adopted provisionally as a working hypothesis. 3. The further question arises whether the curious triplet modification shown in the first order continues in the others. The most accurate values in Zn are those f or m = 3 with possible errors 9 in each mantissa of the triplet. The observed values of the differences are 5191, 2414 or 33J8 + 2, 15J8 + 13. These as they stand show a slight transference from the large to the small differences, but this may be zero within easy error limits. This is the case for instance if the errors in P lt P 2 , P 3 are respectively dX = -008, -005, - -012. In the first order, however, Zn shows a negligible transference, so that it offers no evidence for or against. In Cd, the corresponding quantities are m = 2 17423, 6980, 50; 38J8 - 19, 15J8 + 26 m=3 17649, 6541, 160; 38|8 + 2, 14J8 + 48 m = 4 17109, 6407, 50; 37f 8 - 86, 148 + 23 As they stand, they seem to show the systematic transference from the AJ to the A 2 , but it is only definite in the case of m = 4, if the possible errors shown are really maximum. In Eu the corresponding quantities for m = 3, 4 are 52|8 + 4, 17|8 + 4 and 388 - 86, 15|8 + 91. The second shows a transference, the first only if the transference is about one oun. The data of Hg are of no use, not only for the doubtfulness of P (2), the uncertainty in P (3), and the absence of P 2 (4, 5), but because the value of 8 is not known with sufficient exactness in the last digit. The result of the comparison is that a systematic transference is shown in the one element capable of giving evidence but that it is only definite in a single triplet. It is slight evidence on which to build an important general- isation, but taken in combination with its proved existence in the first order, 170 ANALYSIS OF SPECTRA [OH. we are justified in concluding that the transference modification exists in all orders. It is what should be expected, e.g. on the supposition that it is caused by a change $N in the middle sequent p 2 . 4. In the preceding, there is little to show which of the sequences p 1 , p 2 is the normal type from which the other is displaced. If the positions of the first S lf 2 lines be compared amongst the elements of the same group, it will be seen that the S 1 occupy corresponding positions whilst the S 2 are pushed further and further to the violet with increasing atomic weight. This leads to the suspicion that the S 1 lines (limit p l (1)) depend on the normal sequence whilst the p 2 (the S 2 limits) take the displacement on p . On the contrary we might be dis- posed to regard the p 2 as the normal at least in triplets from the fact of the existence of the curious p 2 " s' (m) singlet series without any trace of lines depending on p or p 3 . Also the important e-link appears as depending on equal and opposite displacements (2A) on the p 2 sequent. In ohe case of doublets the matter would appear to be settled in favour of p 1 by the following considerations. If the sequences are compared in the different elements of the alkalies, the mantissae of the p l , p 2 are Pi Pz Na ... -116873(0) =2 x -058436 -116130 = 2 x -058065 K ... -234671 (100) =4 x -058668 (25) -231736=4 x -057934 Rb ... -292314 (110) =5 x -058463 (22) -279377=5 x -055875 Cs ... -361277 (115) =6 x -060213 (19) -328729 = 6 x -054788 The remarkable relation indicated in the second column under ^ , and the distinct deviation from it under p 2 clearly point to the fact that, in group I at least, p l is to be regarded as the normal type from which p 2 is displaced by oun multiples. 5. The curious multiples 2, 4, 5, 6 in the different elements are reproduced in their atomic volumes. In [i] the values of the densities given in Landolt and Bornstein's tables were used giving values of the atomic volumes which could be written as 2 x 11-80, 4 x 11-15, 5 x 11-21, 6 x 11-76. The two sets show so great a parallelism as to suggest that the mantissae of the first orders are proportional to the atomic volumes. The values of the latter as given by (atomic weight)/density are supposed to represent quantities proportional to the volume of the molecule. That they give an approximation to relative values of molecular volume in these elements is certain, but their values depend on the temperatures at which and the physical conditions in which the densities are determined. If the atomic volume enters in the constitution of a sequence it must in each case be a quite definite quantity for each element, either a volume, or a certain linear magnitude which enters to the third power. Of this at present we can get no absolute determination*, and we must be content with the approxi- mate relative values given by (atomic weight)/densityf. In this case we should probably get more accurate ratios by taking the densities under corresponding conditions. For instance in the above the melting point of .Cs is about 26, so * In gases perhaps from the kinetic theory. f It must be remembered, however, that this gives molecular volume, whereas the light emitting source appears to be the free atom. vin] THE p AND s SEQUENCES 171 that its density was determined close to its melting point. It would then be abnormally low compared with the other elements or its atomic volume com- pared with them should be lower than 6 x 11-76. In any case the agreement in the march of the mantissae and atomic volumes is so close as to necessitate a closer discussion in order to see if it can be made exact within limits of variation which appear reasonably possible. For this purpose we shall replace the data used in [i] by later and more extended ones by Hackspill*. At the outset it is to be remembered that we are now dealing with the absolute properties of a mantissa and not with differences in the same order. Consequently the true mantissa is that found when the correct value of N is used. Rydberg's value of N is almost certainly in error by a small, but not negligible, amount. If the true value be N (1 + ) 2 the true value of the mantissa of p (m) is w + fji (1 + ) where ^ is the mantissa calculated with Rydberg's A T . In the present case m = 2. We shall assume also that is the same for allj. We can deal with the old measures by supposing the scale to be that of the old N, so that the mantissae to be compared are /* + 2/(l + )> or Sa 7 /* + 2'. The largest deviation in N yet found is that required for He P' where &N = 139. With 8N = 200, = -000900 and ' = within a unit in the last digit of a mantissa. In comparing then the mantissae with the atomic volumes, we must suppose 2 added to the former and then determine to make the agreement as close as possible. The errors due to uncertainty in limits (f ) and measures (dX) are, for this purpose, negligible. Hackspill* gives the densities to four significant figures at C., the co- efficient of expansion up to the melting point, and the dilatation on melting. In the liquid state the physical conditions are simpler, although the tempera- tures are very different, as in the solid we may get complications through crystalline form, porosity, etc. It is advisable therefore to consider the data under different conditions, and for this purpose take the densities (1) all at C., (2) all at a temperature TT f their absolute melting points, corresponding to Cs at C., and (3) in the liquid state at their melting points. As the temperatures of these are different, they are also compared at 120, well above the M.P. of all. According to Hackspill's data the atomic volumes are Na K Rb Cs 0C 23-650 45-515 56-039 69-880 91 M.P 23-976 45-879 56-190 69-880 Liquid at M.P. ... 24-506 47-338 57-910 71-958 At 120 C. ... 24-629 48-024 59-189 73-924 * C. R. 152, 259 (1911). Density at Co. expans. solid Dilatation Co. expans. liquid . -000 at M.P. -000 Na ... 0-9725 216 -0150 275 BSESft Rb ... 1-5248 27 -0228 339 Cs ... 1-9029 291 -0232 341 (28 50) 348 (50 125) f Even on Bohr's hypothesis this is practically true. 172 ANALYSIS OF SPECTRA [CH. If 2 = x, the procedure is then to express each mantissa + x in terms of its particular V and determine x so as to make the coefficient of F as equal as possible. The value of x will depend on the ratios of the F, none of which are really correct, and which vary under the four conditions taken. The coefficient of F obtained will of course depend on the physical conditions or, in other words, on the unit in which F is measured. The results are given in the following table, which also contains those derived from values of the atomic volume given by Richards and Brink*, that for Cs being omitted when determining x as being too near the melting point. Liquid at M.P. 010251 005187 F 0051 74 F 005225 V 005163 F 5187 f In this, Cs has been weighted as 0. The variations in the value of x are due to the fact that the different physical conditions produce different ratios of the F. The ratios should be expected to approximate to true ratios of F when the temperatures at which the densities are determined are as far below the melting points as possible. For this purpose it might be preferable to use Na and K alone to calculate x. The results with these give x = -010797, mantissa = -005398 F x= -011927, = -005434 F 9 M.r. x 009833 012150 Na ... 005357 F 005381 F K 00537 IF 005380 F Rb ... 005391 F 005418 F Cs 00531 6 F 005350 F Mean ... 5359 5385 Richards and 120f Brink 007149 012344 005029 F 005452 F 005027 F 005443 F 005031 F 005460 F 004959 F 005262 F 5029 5404 Hackspill at C. Richards and Brink at 15 0. Both are clearly subject to observation errors in addition to physical, for, com- paring the densities in the two sets and reducing Richards and Brink's to by Hackspill's values of the dilatation, we find for Hackspill and for Richards and Brink respectively -9725, -9731 for Na and -8590, -8647 for K. Observation errors therefore do not admit of a closer approximation than that x is near 11300 and the mantissa about -005416 F. In the latter F is supposed to be the value of w/p when p or the density is measured at C. In other words, the unit of measurement of F must be such that the true F of Na is 23-650 such units. When the F of other elements is to be determined by w/p, the p must be measured at C. If means could be found to determine states corresponding to Na at C., the density measured in these states would give true values. Failing this we must take C. and be prepared to admit small errors. It should be noted that the data for 120, where the physical conditions are probably more similar, make the F coefficients for Na, K, Rb equal. . m The preceding discussion may seem unnecessarily elaborate. The importance of the problem, however, deserves it. It also enables a judgment to be formed on the extent to which the constants involved depend on the data. Provisionally those of Richards and Brink reduced to C. by Hackspill's values of the dila- * J. Amer. Chem. Soc. (1907), p. 117. vm] THE p AND 8 SEQUENCES 173 tations will be used as they give a better agreement with Kb, whilst the deviation in Cs is in the direction to be expected owing to its closeness to the melting point. Under these conditions the value of x is -012060 and the mantissae are Na -987940 + -005458 F = + -002729 x 27 K + -005458F - + -002729 x 2F Rb + -005477F = + -002738 x 2F Cs + -005281F = + -002640 x 2F [Note. To bring Cs into line the true atomic volume should be 68-40, as against Richards and Brink's w/p = 70-69 and HackspilTs 69-80. There is possibly an error in Richards and Brink; also the observed w/p should be > 68-40 as being so near the M.P.] 6. The possibility of making such an exact agreement within the uncer- tainties of data is strong evidence in favour of the dependence of the p mantissae on a quantity of the nature of the volume of the atom. If the dependence is real in the alkalies it ought also to be found in other elements. In group III the relation is found in the s sequence. In [III] the first lines known at that time were S (2). The result below was obtained using 2 = -043761. In Chap. XI however it will be shown that lines for m = I exist. With densities Al = 2-583, Ga - 5-95, In = 7-26, Tl = 11-85 the denominators may be thus written Al 1 + -956239 + -002751 x 8F Sc + -002750 x 90-0 Ga + -002752 x 8F In + -002758 x 6F Tl + -002761 x 5F The practically exact agreement of the coefficients must be due to chance, as the densities are not sufficiently exact for this degree of precision. Also Al, Sc belong to the high M.P. and Ga... to the low M.P. sub-group of III. If in Sc the descending multiple 7F be taken, the resulting density for this element is 2-11. That of Al is 2-58 and the next, Y, is 3-8, so that the march of densities would be the same as with Mg, Ca, Sr, viz. 1-72, 1-57, 2-54 or with Na, K, Rb, viz. 97, -86, 1-52. In the Cu sub-group I (6) there is still some uncertainty as to the actual theory of the S and P series. The limits calculated from the lines differ from the real D limits by amounts not explicable by observation errors*. Moreover as both the p and s sequences have m= I for the first order, it is not clear which is to be taken for p. If the p sequence give the S series, i.e. P (oo ) = p (1), the mantissae calculated with the D limits are -002707 x 17 F, -002758 x 12 F, 002727 x 9F respectively for Cu, Ag, Au. But we should certainly expect * Shown also by irregular march of the a. 174 ANALYSIS OF SPECTRA [OH. the p (m) to be analogous with those in I (a), i.e. give the P series and the form 1 + (1 - 2) + 2 + /* for the denominator in p (1). If 1 - 2 < -86, this would also explain the fact that the calculated /x is so large (-9) compared with the alkalies and that the integral part is 1 instead of 2. For instance if 1 2 = -807000, the denominators of p (1) are Cu 1 + -807000 + -058248 =1 + -807000 + -002734 x 3V Ag + -084869 - + -002757 x 3F Au + -122155 = + -002992 x 4F This arrangement brings the p sequence into line with that in the alkalies. There is other evidence that the strong set taken for Au P (1) is not the normal set. In the enhanced doublets of II (a), there may be considerable uncertainty in the limits. The following results have been given as illustrating connection with atomic volume* : Mg 5(2) mantissa = -002710 x 24F Ca p 2 = -002762 x 7F Sr p 2 = -002828 x 6F Ba p 2 = -002730 x 7F Ra p 2 = -002740 x xV where in Ra, density = (-94 ) x. Here Sr is outside the rule. Further there seems no evidence for any considerable group constant, and the relation appears in the p 2 sequent instead of the p . The enhanced doublets of II (b) are not defined sufficiently to enable absolute conclusions to be drawn from them. 7. The triplet systems also afford clear indications of dependence on the atomic volume, taking the sequent giving P (oo )j\ In the Zn sub-group with densities Zn 7-01, Cd 8-65, Hg 13-55, the mantissae are Zn -227900 = -002715 x 9F Cd -282353 = -002715 x 8F Eu -244131 = -002720 x 89-75 Hg -241297 = -002725 x 6F The very close agreement for the three elements must, in view of the uncertainties of atomic volumes, be largely a matter of chance. The essential things are that the volume connection is strongly supported, and that for this sub-group no group constant seems to be called for. If a similar connection holds for Eu it is natural to suspect that its multiple falls into line with the others and is 7. This would give for the density of Eu a value close to 11-85. It has not been directly measured, but this value is about the magnitude to be expected from its position between Cd and Hg, viz. 8-65 and 13-55. * Proc. Roy. Soc. 91, 462 (1915). f For reasons given on pp. 64 and 82. vm] THE p AND^s SEQUENCES 175 When we attempt to apply similar considerations to the alkaline earths, we are met with the difficulty of the impossibility of satisfying all the lines with formulae in a/m only, and it is not possible, owing to the absence of observed P lines, to determine the true s (I) as the P limit, except in Mg. As they stand, however, in the tables, they give with densities 1-72, 1-57, 2-54, 3-77 for Mg, Ca, Sr, Ba: Mg -314542 = -002776 x 8F Ca -480424 * -002686 x 7F Sr -544308 - -002629 x 6F Ba -611624 - -002783 x 6F Ra -607138? = -002770 x 219-2 It is not a satisfactory agreement, but the limits are subject to great uncertainties. The data do, however, indicate the multiples of F which enter. If x denote the corresponding multiple for Ra its density should be 226&/219 = l-02x or, allow- ing uncertainty of 50 in the -002770, p = (1-02 -02) x. This gives p = 5-10 -1 with x = 5 and 6-12 -12 if x = 6, either, especially 5-10, in step with the corre- sponding quantities for the other elements. They agree within errors with those deduced from the doublets, viz. 5-64 with x = 6. Taking account of the combined evidence from the whole of the series there can be no doubt but that the true p sequence both in doublets and triplets, depends directly on a quantity equivalent to the volume of the atom. This general con^ elusion is not affected by the certainty that further investigation may modify some of the foregoing data. This relationship is the sought for criterion which distinguishes the p, and as we shall see shortly the s, from the d or/. The mul- tiples found under the different groups are here collected for reference. II III i Mg Ca Sr d ? 7 6 t 8 7 6 Zn Cd En d f ? T ^ t 9 8 7? Na K Rb 2 2 2 Cu Ag AU 3 3 4? Al 8 Ga 8 Sc 7? In 6 Tl 5 Cs 2 Ba 7 6 Hg ? 6 Ra? 6 or 7 5 or 6 The columns under d, t refer to doublets and triplets. 8. Returning to the consideration of the p sequence in the alkalies, it is found that the ratios of a//z with 2 for the four elements are -195, -197, -195, 194 pointing to a common value. If this be calculated from the accurate /x, a in Na, but with the approximate 2 = -012060, we get p (m) = NJ{m + -987940 + -0067794F ( 1 - 19491\| 2 m )} in which V is determined from densities measured at C. 176 ANALYSIS OF SPECTRA [OH. With atomic volumes for Eb calculated from the mean of Richards and Brink and of Hackspill and for Cs from Hackspill, this gives the following formulae for p (m) for the alkalies : K =N/L + 1-294437 - /{ m ) + 1-365552 - + 1473202- I . m } For Na it is necessarily the same. Using the old limits the values of C for K, ~Rb(m= 1 ...4) are K -29, --9, -47, --33 Rb --3, --09, --01, --08 These could be slightly diminished by admissible changes in the limit of about unity. For Cs the observed V is admittedly out of step. If the theory here developed is correct, and if it were possible to determine the true value of 2 by some independent method, the observed mantissae would give data for the relative values of the atomic volumes to about 1 in 100.000. The corresponding densities, w/V, where V is determined to make the formula give the observed mantissa, are Richards Hackspill and Brink Calculated at at Na ... -9725 -9725 -972 < at 15 -9724 < 2) at -9743 (3) at 10 K ... -8636 -859 -868 -867 (1 >atl5 -875 (3 >atl3 Rb ... 1-5301 1-5248 1-5220 {4) at 15. Cs ... 1-9391 1-9029 2-366 < 5 > 2-400 <> (1) Gay Lussac, (2) Schroder, (3) Baumhauer, (4) Erdmann and Kothner, (5) Bekeloff, (G) Menke. Taken from Hackspill' s paper. These densities should be progressively greater than observed values as the melting points fall to that of Cs. The observed 24 for Cs are clearly excessive, but serve to show that Hackspill's may be underestimated. The necessity in any case of admitting a correction in the form 2 to allow for the true N has been already referred to. The values, however, obtained for the two doublet groups I (a) and III are far too large to be accounted for in this way. For instance in the alkalies 2 = -012060 would require a dN = 1326 and we have seen in Chapter VI that the agreement amongst the oun values shows that dN cannot amount to more than 200 at the outside as between different elements. Thus it would appear that a group constant is required in addition to a true 2 depending on dN. But a further complication arises with dN in that the old /A, a, calculated with the old N from the first lines, now become /A (1 + ) + 3 and a (1 + ) 2, here being the value required by dN (see p. 84). The vm] THE p AND * SEQUENCES % 177 ratio a/fj, becomes (a 2)/(ju, -f 3). It is thus conceivable that, given accurate measures of the atomic volumes of the four elements, reliable estimates of dN might be obtainable by imposing the condition that this ratio is constant. Treating group III in the same way with the group constant -956239 the values of a/p come to Ga -23014 Tl -22856 The numbers suggest that with correct values of volume and series constants equality might result. With present data it is useless to attempt to go further. 9. The s sequence. The fact that the mantissae differences of the p and s sequences are for the majority of elements quantities in the neighbourhood of 5 has long been recognised. Ritz definitely adopted the theory that in the s sequence the order must be taken as m -5 so that his formula runs s (m) = N/{m - -5 + p. + p/(m - -5) 2 } 2 , and Paschen has adopted the supposition in his notation (Chapter II, sect. 13). The formulae for the alkalies in the tables are also calculated with a/(m -5) as it seems to give better agreement than with a/m. The actual values of the mantissae differences for the first order of the p l and s sequences are given in the following table*. Na -4901 Cu -4734 Al -4893 Mg'" -5025 Zn'" -5283 K -4646 Ag -4609 In -5304 Ca'" -5990 Cd"' -5263 Rb -4878 Au -3833 Tl -5949 Hg'" -6036? Cs -4923 In the enhanced doublets the P series are too far in the ultra-violet to be observed. But since S (oo ) = p (I) the first p mantissae can be found. They give Mg Ca Sr Ba Zn Cd 3631 -3572 -3891 -4021 -3825 -3865 The numbers for the enhanced doublets show a remarkable deviation from those of the other doublets and the triplets which are all. of an order of magnitude of -5. If in the alkalies the sequences are compared as to their formulae constants when p takes a/m and s, a/(m- -5), it is seen that the a in the s are of the order of one-half their value in the p, but slightly larger. This fact alone is sufficiently definite to disprove a theory which regards the p and s as the even and odd members of a single sequence with AN in place of N, as in this case the a should be equal. The differences of fjL p and /z s as given in the tables are Na K Rb Cs p^-8 ... 495411 472590 493067 493789 Pt -s ... 496300 469582 482068 462192 It will be noted: (1) In agreement with the conclusion already arrived at, the march of the numbers points to p l as the normal sequence. (2) The great deviation of the value for K from those for the others, which suggests some special cause. (3) The rough equality of the values for Na, Rb, Cs, which raises the question * Based on [n. p. 51]. H.A.S. 12 178 ANALYSIS OF SPECTRA [OH. as to their possible real equality. To answer this we may take the case of Cs. Whilst in both p and s the value of /x -f a is subject to small uncertainty, the individual //, and a are not so definite for two reasons, (a) the observation errors and indeterminateness of have considerable influence on the ratio //>, ; (6) the functional form, e.g. whether a/(m -5) 5 a/(m 1) or a/(m f), has a considerable influence on the value of a and thereby on that of /x. We will con- sider these in order. Under (a) the limit is determined from the highest orders of P lt and f, which on this method is small, may here be as large as 3 in fact in Cs it is 3 larger and has been modified to suit S conditions. P (I) has small errors which are negligible, P (2) has d\ = -Q5p; S (2), 1-5^; S (3), -03^ 2 . The resulting change in p v ju s is 223f + 90p + 118^ 27jo 2 , or, say, a maximum possible of 669 235 or 900. Under (b) failing definite knowledge as to the true functional form, we will suppose as an example that the a of s is exactly one-half that of p. This would change p, v ,u s by + 10600 supposing no changes in a v . It is clearly excessive, but the example is sufficient to show that this cause could produce considerable changes. Under (a) also the value in Na is subject to uncertainty of about 240. These "(a)" uncertainties might make the fjL P fjif. within 480, of equality which might quite possibly be explained by functional defect. Thus it is quite possible that the differences of the /z for p and s may be the same in Na, Rb, Cs. But the evidence is not sufficiently positive to base any further conclusions thereupon. The greater accuracy in Na, and the smaller changes produced under (b) above with its small a, render a closer discussion for this element desirable. The nearness of 495411 to the half of a possible 1 x of the p discussion above suggests that while the "true" w-f/z of the p is m + c + kV, that of the s is m + Jc + kV. We have seen that the true c, i.e. the constant determined with correct N (1 -f ) 2 > is 1 - a? + 2. Hence i (1 - x + 2) = 495411 + 240p, 240^ being error term in the observed difference. This gives 2 - x + 480^ - 9178. The value of x as determined from the atomic volumes above varies from 12400 to 9880, or, say, = 11140 1260 . . . 2 - 480j? + 11140 1260 - 9178 - 1962 1260 + 480^. A correct ratio of two atomic volumes, and accurate measures for Na S (2, 3) would thus give data for finding 2f , or the true value of N. Using HackspilFs values at for all four elements, it was found that x = 9883. This would give 2 = 705 with p = 0, N = 109752. It is of the order of magnitude to be expected, but at present is only to be regarded as an illustration of method whereby with further accuracy in data a reliable measure of N may be obtained. The present theory suggests that the two se- quences are of the form possibly for Rb, Cs as well as for Na. vm] THE p AND s SEQUENCES 179 10. The curious multiple relation in the mantissae of the p in the alkalies has suggested an alternative correlation of the regularities. It is given in [n, in]. It will be sufficient here simply to give the general results. In the alkalies by adding J A (1 l/m) + |A (1 l/m) and writing the mantissae 1 | A (1 l/m) + ju, a/m, the a//x are found to be about the same for Na, K, Rb. The quantities are Na m + I - JA (1 - l/m) + 2 x -074229 (1 - -21276/m) K + 4 x -074401 (1 - -21145/m) Rb + 5 x -074431 (1 - -21455/m) ( m + 1 + 6 x -074972 (1 - -19687/m) {or m + 1 + 63 + 6 x -074334 (1 - -19856/m). In the triplets A 2 , which is about |A X , is to be taken. Then Zn m + 1 - A 2 (1 - l/m) + -003461 x 9F (1 - -21558/m) Cd + -003461 x 8F (1 - -21537/m) Eu + -003461 x 6 x 14-07 (1 - -21534/m)* Hg m + 1 + + -003496 x 6F (1 - -21409/m). * Depends on value of limit. In the alkaline earths it is found necessary to introduce an additional term j8/m 2 to obtain agreement between observation and formula. The corresponding ratios then seem to require /? (1 l/m) + j8 (1 l/m). Thus Mg m + 1 - j8 (1 - l/m) + -382462 (1 - -21533/m) + /m 2 , j8 = 20A 2 Ca + -574797 (1 - -21572/m) + 0/m 2 , ft = 14A 2 Sr m + 1 - 2 (1 - l/m) + -676156 (1 - -21404/m) + 0/m 2 , )8 = 3A 2 . Here the coefficients of the terms (1 -215/m) are, with the atomic volumes already given, -003389 x 8F for Mg, -003214 x 7F for Ca, -003265 x 6F for Sr. The volume coefficient for the alkalies was -003382. In group III the presence of the group constant found necessary for the volume relation gives the ratio -215 for Al only, viz.: m + 1 - -043761 + -003500 x 8F (1 - -21527/m). These two attempts are not necessarily mutually exclusive. They appear rather as the attempts of incomplete formulae to fit themselves to actual rela- tions. They are sufficiently promising and suggestive as to call for a more exhaustive discussion, and the provision of more accurate measures. A first requisite is the accurate determination of limits, as the change in a due to , though small, is a considerable fraction of a itself. Also the true value of N is indispensable. For instance if N = 109700, it will be found that in the alkalies the common factors for Na, K, Rb, all agree with -074570. Conversely, if the true form could be known, data would be provided to determine or N. 12 2 CHAPTER IX THE d AND / SEQUENCES 1. In contradistinction to a great stability in form shown by the p and s sequences, those of the d and / seem to be more protean. They are far more subject to displacement than the former, and the electric field exerts a much greater influence on them, not only in splitting lines into components, but also in shifting and intensifying certain combinations. In fact the diffuseness of the Z), as well as of other nebulous lines, has been explained by Stark as due to the mutual influence of the electric fields of neighbouring centres of emission. This instability of form, or deviation from apparent normality, is more pronounced in the elements of higher atomic weight in each group. It is exhibited in several ways of which the following examples may serve as some illustrations. (1) The march of mantissae with increasing order in certain elements is abnormal. The case of Ca has been referred to in Chapter II, sect. 18. The same effect is also strongly shown in the singlet series of group II. (2) In triplets the normal rule in D series is two satellite separations in a ratio very close to 5 : 3. The closeness to this ratio in actuality is in strong con- trast to the corresponding ratio for v separations which varies between 2 and 2-5 in each group. In Hg there is a case of 3 : 5, and the first D line shows evidence of a considerable number of associated satellites. The latter effect is very noticeable in Kr, X. (3) In the rare gases, especially, are found several individual D series based on displaced limits and displaced sequents. One example in X has been worked out in some detail in [v. p. 399]. (4) There appear many instances of two sets serving for the first order D lines. Thus in Ba'" there are two, one set with separations 260, 157 (due to 158, 98) in the normal ratio 5 : 3 = 1-66 and a d 3 sequent conforming with a rule deduced later, the other set with separations 380, 180 in the abnormal ratio 2-11. To these two correspond two sets of F lines with the respective separations. A similar duplicity is also shown in Ba". So also in X there appear two typical D (I) sets, each showing satellites with different separations, but here both in the normal ratio 5:3. (5) In general there is exhibited a very large difference in the sequence mantissae of the first two orders compared with those between the higher orders. The inverse D sets in the copper group of elements have a mantissa about -5 less than the normal d (1) and suggest sequent forms related to the d in a similar way to that in which the s stand to the p. But if so there is little evidence for their existence beyond m = 1. A similar relation is also shown by the sets in the alkaline earths with mantissae about -5 less than those of/(m), and again with no representatives of higher orders. OH. ix] THE d AND / SEQUENCES 181 (6) In many cases the separations in observed D sets are abnormal, and when this is so they are not reproduced in the related F series. This is a very common abnormality in the rare gases. It is due* to the fact that the sequents in a given triplet (or doublet) are not the same for the three (or two) lines, but at least one has suffered displacement. As examples may be taken Kr Z) 6 . The separations are 78840, 308-82 compared with the normal 78645, 309-20. The modification is due to a noun displacement on the sequent in the middle line D 26 . Also X D (2) has separations 1778-21, 810-38 compared with normal 1777-90, 815-05 and due to one oun on the sequent of the third line of the triplet, D^ . A similar effect is seen in several of the data in the table in Chapter VI, sect. 5, e.g. in Ca D (1). (7) In the F it almost seems a general rule that the low orders are extremely unstable. Examples have already been given from the alkaline earths, in which it seems that the first order sets are disrupted into at least two parts. There are many instances of associated sets with displacements in the / sequent of large multiples of A 2 . When such displacement occurs, the normal line is in general much weakened, and indeed in some cases disappears entirely. The even orders seem particularly subject to this effect. Thus in goldf, of the normal set for m = 4, only F (4) has been observed, whilst a set with a displacement 10JS on the sequent is seen in both F and F. Their wave numbers are F l (4) (10J8), (3n) 22001-67 26485-93 (5) 30970-20 F (4) (10J8) F 2 (4) (10JS), (2n) 22253-23. The mean gives the normal F 1 ( ). So also in CuJ there is no representative of F (4) but a set, displaced 128 in the limit, has been observed, viz. (128) F l (4), (4n) 23929-06 28334-41 (In) 32739-77 (128) F x (4). The mean is the (128) F l (oo ), within small observation errors and giving ^(00) = 28381-98 the true value. The half difference gives the common/ (4) sequent and this conforms with the value calculated from the formula. This curious instability for m = 4 is shown also by absence of the Ba F" (4) lines in the F series related to one of the D" (1) sets referred to above in (4). When such disruption occurs, a normal set is not necessarily replaced by a single collateral. In general the normal set is represented by a congery of such collaterals and the spectrum in the region in question contains a large number of lines giving nearly the same separations, especially chains, apparently of links, but in reality formed by successive displacements on the normal sequent or limit. This effect, especially in rich spectra, is so common as to give the impression that it is a characteristic feature of the / sequence. Less frequently a similar effect is shown by the d sequence. For instance the large number of separations in the Cu spectrum of about the same values as that of the doublets, which was first pointed out by Rydberg, are probably due to collaterals of D lines. * [v. p. 363]. t Phil. Mag. 38, 20 (1919), corrected as shown. J Phil Mag. 39, 409 (1920), corrected as shown. Astro. J. 6, 239 (1897). 182 ANALYSIS OF SPECTRA [CH. 2. Whilst in the p and s sequences the mantissae appear to be in general either small or of order of magnitude -5, those of the d, f the d' of II (a) ex- cepted have large values in the neighbourhood of -9. The apparent exceptions with very small mantissae, such, for instance, as occur in the alkaline earths (see D mantissae tables) have in reality values slightly larger than unity. For instance the denominators in Ca D u "' run 1-9469, 3-082, 4-089, . . . , clearly indi- cating mantissae -94, 1-082, 1-089, . . . becoming again less than unity after m = 5. In the exception made above of d' the march of the mantissae with increasing order is remarkable for the way in which they continuously decrease from large values to very small. For instance in Sr D' they decrease from 1-127 for m = 1 to -349 for m = 10. For other instances see data for Mg, Ca in Table V. In many groups the mantissae in the different elements are very close to equality. For example in Cu, Ag, Au they are f or m = 2 respectively 979094, 979830, 980714. In the F series of the low melting point elements of groups II and III so close is the resemblance that the differences between them appear to be almost wholly due to the difference of the limits, i.e. of the values of d (2), whilst the/(3) are almost the same. To show how closely they agree, the mantissae for m = 3* to four places of decimals are collected here, and for comparison those of the alkalies : Mg -9621 Zn -9785 Cd -9703 fiu -9717 Hg -9756 Al -9708 Ga ? In -9693 Tl -9736 Na -9979 K -9928 Rb -9878 Cs -9773 3. Hicksf has attempted to discuss the properties of these sequences in the same way as those of the p, s by comparing their denominators as calculated from the observed wave numbers and series limits. The general results may be expressed in the two following laws. I. The differences in the mantissae of successive orders are multiples of the oun. II. The mantissae of one of the first order of the d and of the / sequents are multiples of A for doublets, or of A 2 for triplets. From these two statements combined it follows that any d or / sequent must have its mantissa a multiple of the oun. Thus these sequences differ essentially from the p and s which depend on the atomic volume. It is not possible to prove the first statement for all orders, as changes produced in these by observation errors and small uncertainties in the limit are comparable with the oun itself. But the proof seems to be definite for the first two orders, and for the second and third in the case of large oun values or very exact measures. For these the agreement is complete for all the elements tested. The second law is not susceptible to direct testing for elements of low atomic weight, since the multiple required is larger than, or comparable with, the value of A itself. Consequently a unit change in the multiple alters the required value of A by an amount less than its possible error as determined directly from the doublet or triplet separations. For the other elements so large a proportion conform * m=3 chosen in order to get observed representatives of all. f [in.] ix] THE d AND / SEQUENCES 183 so closely to the law as -to give conviction that it corresponds to reality. The exceptions were all in elements in which the lowest order D lines were those for m = 2. In the copper group and the gallium indium group this multiple law was clearly disobeyed. The sequents, however, here conformed to the deduced criterion that they should depend on oun multiples. Since the publication of his first paper on this question, he* has shown that in all three metals of the Cu group, there exist sets of D (1) lines in the farthest ultra-red. The data have been indicated in the foregoing chapters (pp. 61, 163). The sets are beyond the observed regions, but their existence is proved and the sequence values determined by the presence of summation lines, by sets of combination lines, by sounding, and by the existence of F series depending for their limits and separations on the d (1) sequents. This fact also explains why only a few F lines depending on the old d (2) limits exist. It is then found that these new d (1) sequents completely satisfy the second law. In group III (6) lines corresponding to D (I) sets should come in the red and near ultra-red where arc observations have not been ex- tensively made. There are, however, indications of such D (I) lines in which the d 2 (1) sequents obey the law. There is also evidence for corresponding F series. They are considered in Chapter XI. In all these cases the A are large numbers with corresponding small multiples, and the closeness of the agreement in practically all elements proves that the second law holds with a very close approximation. Nevertheless in the discussion given in [m] an important over- sight was made which, while not affecting the approximate truth of the second law, left out of account certain considerations which could afford possibilities of producing exact agreement and thereby diminish the value of any evidence for such exact agreement as might be otherwise adduced. The oversight con- sisted in the neglect to consider the effect of using an incorrect value of N in determining the numerical values of the mantissae. Any resulting error will be small and will not affect the proof of the law as being approximately true. We shall therefore first deal with the data calculated from the old value of N = 109675, see how closely they support the laws, and afterwards consider the effect of small changes in N. That such changes must be a very small fraction of N we already know from the general exactness of the ratio oun/w 2 in all elements. All the numerical data are collected in the table below, taken from those given in the D mantissae tables. In testing for law II the question naturally arises, What value is to be taken for A 2 when triplets are compared? Are they the values directly determined with uniform N from the observed v 2 or, as we should rather expect, are they the values calculated by multiplying the true 8 determined from v l + v 2 by the multiple found from v 2 ? In the table both values are inserted. They appear in the first line under each element, the second number being that calculated from the true 8 with the corrections due to and dv, these being the same for both. In group II the second set of data belong to the enhanced doublet series. The terms in p correspond to possible observation error effects, in which p 2 < 1. The terms in X denote the mantissae differences of the first two orders in the d v * Phil. Mag. 38, 1; 38, 301 (1919); 39, 457 (1920). 184 ANALYSIS OF SPECTRA [OH. A 1057; 1053-1 --030?+4di>, dv, dv<-l. A 2 =4681-80; 4676-31 --121? + 3-3dj>. - 28-21? =197 (4243-188 -0 - -021?). d 3 (1), 884207 - 4p - 30-5? - 30^ = 189 (4678-343 - -02lp - -161? - -161^). / (2), 865448 - 16^ - 107-26? = 185 (4678-098 - -086p - -580?). X(l, 2), 3257 -79-6? 86, 136=3242-2. X (several D) 10996-29; 10995-91 --31? + 4-4cZ/, dv<\. I. d a (l)*, 769890 -2-5^-25-27? -25^ =70 (10998-43 - -036^ - -361? - -357^). II. d 3 ( 1 )*, 868846 - 5-5p - 29-75? - 29-75- 1-07?). The two d are, calculated from 22079-34 as Z> 23 and 16725-1 as D 13 . The difference 440 corresponds to a sequence displacement of one oun, 5 1 =4A7. The dv depends partly on observation errors (1-0) and partly on allocation of the real v between a few possible values differing from one another by about 3. I Na 746-03 - -0450? + 43-2^, dv < -01. d(2), 989028-5^-121?. X (2, 3), -2541 -168? 49, 3A + 166 = 2534-23. K 2928-7 --200? + 50- Qdv, ?<2, di><-Ql. di (2), 853474 - 38p - 106? = 291 A + 225 + 7 - 48? - 38^ 145. Z(2, 3), -57540 -143? 260, 20 A -205=57469 -4?. Rb 12937-3 - -925? + 54^, ? < 2, dv < -03. d 1 (2), 766177 - 48p - 96-5? =59A + 115 -27 -42? -48^ 88. X (2, 3), - 60908 - 135? 60, 4A + 34f5 = 60924 - 4?. Cs 32565-4 - 2-45? + 57d, ? ?, dv < -03. d 2 (2), 547238 - 22-5p - 75-33?. ^ (2), 554651 - 22-8p - 76-01? = 17A + 5 + 83 - 35? - 22-8^ 25. X (2, 3), - 18571 - 125-5? 25, 296 = 18517 - 1-4? + 32df. ix] THE d AND / SEQUENCES 185 Cu (The d' in Cu, Ag, Au refer to the inverse D (1) sets.) 7307-087 --331 + -2p, Qdv, dv<>W. d 2 "' (1), 946246 -Sp- 33-65 = 694 (1363-4 - - -048). d B '" (1), 945796 - 24^> - 33-65^. d' (1), 762390-30^-24-9^=559 (1363-84 --044^)- /'"(I), 1195105-55^ + 12^-48-2^. X'" (1, 2), 135020 - 10011. Y'"(l, 2), -159829 -67^ 70= -(117A 2 +55+21 +67^)70. 3951 -58 --084^ + lldv, d 2 " (2), 312286 -p - 14-07^ = 79 (3952-987 - -175). /" (3)J, 983343 - 21^ - 72^. X" (2, 3), 47471 - 29-2$ 2 = 12A + 50 - 28 2. Y denotes order differences off. $ // FI' (2) is n = 33247, as suggested in tables f" (2) = 1000018 + 30^> - 13-772 =253 (3952-640 - -121 + 186 ANALYSIS OF SPECTRA [OH. Sr 5528-7; 5485-10 - -262? + 9-3^, dv<-Ql. d a '" ( 1 ), 987352 - 5p - 35-78? = 180 (5485-288 - -200?) - 5p. / 3 (2)*, 926337 - U2p - 114? = 169 (5481-28 - -Sp - -68?). Z'"(l, 2), 181178 -110?14 = 33A 2 + 170-101?-307 - 18-67? = 14 (38543-57 - 2-Qp - 1-33?). / 3 '" will be less, but disruption of triplet precludes exact determination. The value of d%" (1) is by the limit 8(co). The asymptotic D() gives no multiple. Ite d 3 (l) has maniissa = 8232Q6. The whole Ba D'" sets are so irregular and abnormal that their data have small evidential value for our present purpose. Ea No reliable data. Zn 3486-29; 3486-01 --121? + dv, dv<-Ql. 15. d 1 /// (2)t, 902053 -27^3 -111-4? = 87 (10368-41 --21p - 1-280?). d' (2), 869794 -0 - 107-7?' =84 (10354-33 -0 - 1-282?'). X'"(2, 3), 8580-161-2?180 =195-74.... 27348 - -424? + 10-81^, dv < -7. , <2, dv<-01. d 9 '" (2)*, 921943-4^ - 110-12| = 31 (29740-09 - -12p -3-55). d'(2), 921421 -4^-113-6^ =31 (29723-23 --12;p -3-55')- f"(2), 980734- -120-7 = 33 (29719-21 -3-66*). X."' ( 2, 3), 10609 - 164-6| 18 = 7J5 + 95 A" not yet determined. * If determined from Z) 33 , mantissa = 921997. Ill Al 1752-07 - -054 + I5dv, dv < -01. d t (2), 631414 - 4p - 83-06 =360 ( 1753-92 - -231). d 2 (2), 631304 - 4p - 83-06 =360 (1753-62 - -231). = 361 ( 1748-86 --225). X(2, 3), -205 105 -100-3| 20= -117A + 113 - 106^ 20. Ga 13541-7 --435 + !G-Idv, ?, dv<-05. d 2 (2), 978363 - 12p - 120-5 = 72 (13588-3 -p - 1-67|). In 37687-5 -l-241| + 16-4^^ - 120"'. d" (2), 980380 - 93^ - 121". These differ by 7897 ... =84 (94-009 ...)=84A 2 . S, Se No D sets lower than m =4 have been observed. 4. In examining these data the reader should, for the immediate purpose of testing the approximate truth of law II, pay no attention to the data under X, nor to those elements with small A. In the remainder he will find convincing evidence that this law is very closely obeyed in the majority of elements. The evidence might have been exhibited perhaps in a more striking manner by giving the results of dividing the mantissa by the A to obtain the required 188 ANALYSIS OF SPECTRA [OH. multiple. Thus in Au this multiple is 8-9994 or in Sr is 180-006. But the numbers so obtained would be of no further use. The closeness can, however, be easily gauged by estimating the change produced by altering the multiple given by unity. The exceptions to the rule are chiefly seen in the alkalies in which the lowest order is m = 2. All the evidence at our disposal especially the long F series in Cs goes to show that these are really the lowest orders. In Cs, which has satellites, its d l (2) mantissa only differs by about two ouns from being a complete multiple of A. Those of d (2) in K and Rb clearly do not conform to the rule. If the non-conformity is due to the absence of satellites to which the law directly applies their satellite separations should be 30 in Rb and 11 in K. We have already* alluded to the indications in Rb of attempts, now and then successful, at producing satellites with separations 6-9 or 27 or 29-4. Also in K, the p (2) d (m) and s (1) d (m) indicate small separations in two d lt d 2 sequences. In any case it is suggestive that the only definite instances of non- approximate conformity to the rule occur where no satellite sequence has been observed. The anomalous behaviour existing in Cs D deprives its data of value here also. The approximate multiple of A shown by its d 1 may therefore possibly be only a coincidence. The data for the old allocations of the lowest D orders in In and Tl are added. These show the impossibility of these sets conforming. It is explained by the existence of sets of order m = I in which the law is obeyed. The existence of these orders in this sub-group and in that of Cu brings to light a regularity which may be stated as follows. The two sub-groups of elements in each group of the periodic table are distinguished from one another by the fact that in one the melting point rises with increasing weight, and in the other decreases. Those of the former have m = 1 for the first order d sequence whilst the latter have m = 2. Thus in the A, Cu, Ca, Ga (In, Tl) sub-groups, the lowest order is m = 1 whilst in the Na, Mg (Zn and Cd), Al (Sc ...), it is m = 2. 0, S, Se . . . belong to the ascending sub-group of group VI. Here the lowest order observed is m = 4 in S and 2 in 0. We should expect there- fore another order m = I in 0. It would be in the ultra-red above Paschen's longest. The inverse D sets in Cu, Ag, Au have been included because d l in Cu shows the multiple of A. Those in Ag and Au however do not. As yet the relation of these to the D system is not known beyond the fact that they exhibit the Zeeman pattern proper for them. One important fact emerges quite definitely, viz. that in the triplets the law refers to the A 2 as calculated from the true S and not to that deduced directly from i> 2 It has been seen that the triplet modification corresponds to a trans- ference from AJ to A 2 . The possibility of such transfer involving one or more ouns in addition to that calculated direct has been referred to when dealing with the cause of this effect in Chapter VI. This possibility must be kept in mind. For instance a transfer of one oun in Eu makes the true A 2 = 17975-2 and d s (2) = 51 x 17976-25. A 1? A 2 are now 61p, 2118, and better than those on p. 128, * Chapter III, sect. 13. ix] THE d AND / SEQUENCES 189 The material for the/ sequences is not so reliable as for the d, partly because the lowest orders of many lie in the ultra-red and partly on account of the dis- ruptive phenomenon in the lowest orders. So far as it goes it shows that the/ sequence also conforms to law II. 5. A closer discussion of the data is better taken with that of the effect of the error in N, to which we now proceed. The evidence adduced in Chapter IV indicates the probability that the p, s sequences have N of the same, or nearly the same value, that the d have a somewhat smaller value and that, while the / may have the same as that of d, it may possibly be close to Rydberg's N. Suppose the true value of N is N (1 4- ) 2 , where N is Rydberg's value, and the true A is A', A denoting the value found using the old N. Further let denote the value for the d and ' for the s, from which A is determined. Then since A is calculated as the difference of two mantissae of the same order A' = A (1 + D. In dealing with the mantissa //, of order m, the true mantissa will be m + /z ( 1 + ). In testing law II then it is necessary to apply the condition ml, + M (1 + f) = M (A') = (1 + D M (A), where m is 1 or 2. This may be written, since squares and products of , ' are negligible, m + /* (1 + - f ') = ^ (A). We may then work with the old values, if we suppose the old mantissae increased by w + /^ where 1 = - '. In testing law I, that the order differences are multiples of the oun, the true order difference is .+ X (1 + ). The condition to apply is that, using the old values of the oun and of X, the latter is to be increased by + X^ . In the preceding table the X are expressed in the form A8 + r. Hence, r being small, ASj. + + ^ 1 A8 1 + r= multiple of 8 X or + 1 Z + r = y8 1 , where y is a small integer and the true order difference is (A + y)B l . These conditions introduce two new unknown numbers and so render it easier by their proper manipulation to secure an exact agreement of the two laws. If it is possible to obtain this by small values of , ' which are closely the same for all cases, or for the same sequences in the same periodic groups, we not only get good evidence for the exact truth of the laws, but also some reliable information as to the true values of N. If on the contrary the values of , ' vary considerably from case to case, no inference is justifiable, beyond the fact, already established, that the laws are very approximately correct as correct for instance as are the gas laws when applied to actual gases. If Bohr's value of N be the true value, is of the order of magnitude -000250, or, dropping the decimal point, 250. This is comparable with the ouns of all but a few of the elements, so that the test of law I is difficult to apply without some indication of the value from law II. Here the A is so large that no adjustment 190 ANALYSIS OF SPECTRA [OH. is possible by altering the multiple. In applying the two conditions above it must be remembered that if the decimal point be suppressed in , it must be retained in X or /x, in the terms Z or /*.. In discussing the data we shall first deal with the d sequences in the order of doublets, enhanced doublets, triplets, and then consider the less reliable data for the/. Doublets. The alkalies are excluded. Cu. ^ (1), 132 (A - 1-002 + -070 - -2p) ... + -964^ = 132 - 9-25 + 2Qp - -51^ + -67? dj (1), 68 (A - 1-924 + -lllf - -2jp) ... I + -496^ = 129 - 7-55 + I3p + 1-5^ X, + -014^ = 10-8 + 85-3 + 36-5y 2-5. The line observation errors are negligible. If the rf/ (1) allocation corre- sponds to reality and the agreement is so close as to point to this conclusion we can eliminate the x and find { = 126 - 5-9 + Op 4. In Cu, is very small, comparable with !. Hence if the d^ agreement is not a mere coincidence, is determined as = 126 5, with x very small or , ' practically equal. With these, the last condition is satisfied by y = 3 and g^g 2-5 _ Q The last is easily met with < -1, and the order difference is 2 A 1 J8. It should be noted that in d 2 (I) d^ (1) the orders being the same, does not enter and the difference is an exact 64A. We must, however, remember that d^ do not obey the law in Ag, Au, so that provisionally we shall neglect it in Cu. Ag. d 2 (1), 34 (A - 2-45 + 2-27 - -2p) - WO Pl + -944^ = 79-3 - 73 + 1p + 100^ + -032^ - 44 + 85-6 - 100^ + 105-2^ + -004^ = 50 + 167f 10 + 105-2y. Au. d 2 (1), 9 (A - 8-5 + M4 - 27^v) - 9-6^ + 1-025^ 76-5 - 10-26| + 243dv + 9-6^, f < 1-7, dv< -3. - -058^ - - 22 + 85-6^ - 13dv + 351-6y 16. Al. Too small to be useful. Ga. Too uncertain and also probably has lowest order m = 1. In. d 2 (1), 24 (A - 4-7 - -07 - 11-ldv) - 4-2^ + -904i - 112-7 + l-68f + 417-6^ + 4-2^ - -089^ = - 3-6 + 73| - 37 dv 55 + 119-2?/. ix] THE d AND / SEQUENCES 1S1 Tl. There is evidence for D (1), but very uncertain data for the value. It may be well to test the d 2 (2) as 7A - 27|S - 231-5 (Sj = 377). This gives 2 + -897^ = 231-5 + 81 + 100-4^ - 27p. or + -448^ = 115-7 + 40-5f + 50-2^ - 13-5jt>. This agrees with the others. Then X (2, 3) gives - -001^ 211 + 159 120 + 376-S?/. These data show clearly that law II can be satisfied with the same values of , f t in all the elements tested. The closest value is from Cu with + -964^ = 132 28. For this Ag requires an observation error of about one-half the possible, say 100^ - 73f = 53. In Au the v should be about half its possible error larger. This change in dv brings the spectroscopic weight to 197-185 and so closer to the chemical 197-20. In In, dv should be about -05 as against a possible -3, and in Tl there are only very small fractions of uncertainties. Thus law II is satisfied with + -964^ = 132 2 + 26jo, wheiep = 1 means observation errors of -001 A.U. on one interf erentially measured line and -001 on a second. The discussion of law I requires the allotment of y in each element. With the unknown and x this cannot be done in Cu without some knowledge of the magnitudes of , f j_ . In Ag we have to deal with the unfortunate observation error 100^. If, however, we regard laws I and II as both holding, we can eliminate the p l by adding the two conditions, when 2 + -976f! = 123-3 + 12-6 + lp + 105-2y or + -488^ = 61-6 + 6-3 + 3-5^9 + 52%, f < -3. Remembering that f x is probably negative and therefore > 132, y= I will not satisfy the conditions. But y = 2 gives 4- -488^ . 166-8 + 6-3 + 3-5p. With y = 2 and 100^ - 73 = 53, the X condition gives -h -032^ - 201 + 12f = 201 4. Deducting this from the last gives 45^ = - 34 - 6^ 3-5 = - 34 5 f!= -75 11. Thus f j_ is of order of magnitude 80 and therefore of order 200. With this information the y in Cu can be definitely settled. The -014^ is negligible. Then y - 5 gives = 193 10, y = 6 - 229 10. The latter cannot be made to agree. When y = 5 + -0144 - 193-3 -f 85-3 2-5. . 192 ANALYSIS OF SPECTRA [OH. Au. y = 1 with - -058^ = 327 + 85-6 16, dv = -2, satisfied within .the possible variations of f , 1-7. In. With rfv=-05, y = 1 gives - -089^ = 114 + 73 55. y = 2 - 233 + 73 55. The former only satisfies the conditions with the extreme possible errors, the latter with very small proportional errors. Hence y = 2 and - -089^ = 233 + 73 55. Tl. y = 0. - -001 k = 211 - 159 120. Collecting the results, the conditions are Law II. Law I. Cu. ^+ 964f 1 = 132 + 26#l-9-25 f+ -014& = 193-3 + 85 2 Ag. f+ 944f 1 = 129-73 + 50ft f + -032& =204 + 85-6* -50ft Au. f + 1-025^ = 124-5- 10-26? + 81d/ 9 f - -058ft = 301 +85-6 In. f + 904f 1 = 134 + l-68-4-2p4 f- -089^=233 + 731 55 Tl. + '448ft = 115-7 +40-51 +50-2dv -13^) f --001^=211 - 159^120. These show about 200 and f x about 80. By combining them and weighting each with their possible errors it is possible to obtain closer probable values. For this purpose put = 200 -f z, x = 80 -1- z l . Then they become, omitting Tl as too indefinite, z + '96^ = 9 23 z + -014Z! = - 6 10 z+ -94^ =4 72 z + -032^ - 6-5 75 z + 1-025ZJ = 6-5 24 z - -058^ = 96 160 z + -90^ = 6 12 z - -089*! = 26 200. In the first set z is so small that its coefficients can be taken the same for all. The respective possible errors are in the ratio 2, 6, 2, 1. The least square value is then found to be 6*5, or, say, z + -952! = 6-5. In the second set the possible errors are too large with the exception of the first. With this the most probable values from the two equations are z = - 6-1 z 1 = 13-2,' whence =194, x = -67, r - 261, corresponding to N = 109717 for d sequences, N - 109732 for p", s" sequences. This is in remarkable agreement with the direct values found from He D', D" and He P f , S', S" respectively and from Na P. The discussion shows that when more accurate observations are attained, the method is capable of giving values of N with accuracy. We are now in a position to discuss the data for Al, in which the lowest ix] THE d AND / SEQUENCES 193 observed order is m= 2. As Al belongs to the group of descending melting points this must be regarded as its first D line. The data give d 2 (2), 361 (A - 3-21 - -171f - 15*0 - p, dv < -01, whence 2 + -631^ = 1159 + 63-9 + 5415^ + 4p or + -315^ = 579 -f 32f + 2707dv + 2p. With the above values of and x 406 + 32 + 27Wdv + 2p = 0. With dv= - -01 this requires f = - 11-8. This is quite possible and, as a fact, makes the D mantissae converge asymptotically much better than that adopted in the table of formulae, but D (oo ) would not be S ( )*. If we take the other supposition given under Al, viz. 360 (A + 1-55 ...) + -315^ = - 280 + 32 + 2707*> + 2p or - 455 + 32f + 2707dy + 2p - 0. This requires of the order +12 and would make the march of the D mantissae much worse. We conclude the multiple is 361. This element has too small a A to be capable of affording evidence for or against the law. But the law being established, its multiple is 361. The data from the enhanced doublets are not sufficiently reliable for use in establishing a general law. There are none for Eu or Hg. In Zn the uncertainty in v alone renders it valueless. Mg has too small a A and in all the elements the limits are only determined within large possible errors. It will be useful, however, to put the results on record, and to see if it is possible to satisfy them with the same values of , f ' as serve for the other doublets although other values for this type should not be unexpected. Ca. d 2 (2), 79 (A + 1-40 - -091f - 11 dv) - p, dv < -03 2 + -312 1 = - 110-6 + 7-2f+1343efr + 2> or +-156^= - 55-3 + 3-6f + 671di> + Jp and + -047^ = - 50 + 28f + 14-5y 2. Sr. ^(2), 27 (A -15-73 --236f- 19-9*0 -12;?, dv < -01 + -217^ - 212-3 + 3-18f + 269 812-02 (1) 19928-46 | 78( , 67 ( ^ 20718 . 13 308.30 j (2) 21026-33 1352-16 >1280.6> ((2)21271-57 =(25^1 \(2) 21289-68 = (-2d 1 )D ll In both cases the satellite separations are in the normal ratio 5:3. In the second case the Z> u appears disrupted into two equal and opposite 28 X displaced lines. This effect appears as persisting from the similar disruptions in S 3 f referred to above. The triplet separations in (2) are those of S l9 S 2 , S 3 . It is unexpected X] THE MONATOMIC GASES 205 that those in (1) should also depend on the same, and not v z 340, that of S 3 . The common abnormality of group in the triplet separations is also here seen. The fact that a triplet is seen for D 2 where in analogy with D series in other groups a doublet should be expected is a frequent occurrence in this group. In certain cases weak triplets are even present with D n . In X also two D sets are found, but here with only one S s recognised, i.e. one A 2 . The extreme satellites depend on it alone and have mantissae equal to (1) 79 A 2 , (2) 70A 2 . For the order m = 1 they are (1) 79A, [19623-05] 1777-90 (2) 21400-95 809-53 (2) 22210-48 366-67 369-04 (1) 19989-72 1780-27 (Cm) 21769-99 591-92 (1) 20581-64 (2) 70Aa [16013-45] 1777-90 (1) 17791-35 816-44 (8) 18607-79* 1711-94 171194 [17725-39] 1777-90 (3) 19503-29 2580-21 (1) 20305-60 * is F l (2), ? overshadowing 7) 33 . In these the satellite ratios are 1-61, 1-62 and thus close to the usual value 1-66. The second set cannot, however, be considered so well established as the first. The whole region around these D sets is complicated by the presence of displaced triplets. A good example is the following triplet close to the Z) 3 of the first set (1) 19602-66 1774-45 (3w) 21377-11 821-04 (2) 22198-15 2039 [19623-05] Here the oun displacement in the sequent shifts 5' 14. The first line is, therefore, #13 (!) ( - 8)- xt ma 7 be noted tnat tne mean of 821-04 and 809-53 is 815-28, normal v 2 being 815-05. The Red Spectra. 5. Little progress has been made in analysing these spectra until quite recently in Ne by Paschen and by the arrangement of sets of series in A by Nissen. Of Kr, X nothing is known beyond the existence of certain constant differences. In the former Runge had noticed amongst his measures constant separations of 944-9. To these Paulson* has added a few other instances as well as of another of 4731-5. In X also he has adduced cases of triplet separations of 3683-7, 759-5 and doublets of about 116, but many others also exist. Baly in his original measures of Kr and X found a large number of lines in the red spectrum apparently common to both Kr and X. Argon. The spectrum of A is notable as being that in which Rydberg first recognised the existence of sets of constant separations capable of arrangement in parallel lines and columns his type II. They all lie towards the shorter wave lengths. Amongst them Kayser has indicated three triplets v = 339, 152. No * Beit-rage zur Kenntniss der Linienspektren. Lund (1914). 206 ANALYSIS OF SPECTRA [CH. further analysis of these has yet been made. Nissen* has allocated a number of lines into definite series which, while clearly related to one another, involve none of theRydberg sets. They lie mostly towards the longer wave end of the spectrum. According to his allocation they consist of (a) a doublet series of the S type with separation 774 and limits p (2) of 20872, 21647, (6) a doublet series of the D type with the same limits and showing satellites of abnormally large separa- tions, (c) a congery of eighteen parallel series p t (2) s (m) amongst the limits of which those of the two S and D belong to i = 8, 11. There can be no doubt as to these lines forming portions of a related system, but a closer inspection brings to light certain difficulties as to the correctness of the allocations. In the S series only four orders m = 1, 3, 4, 5 are given, so that by themselves it is not possible to make a reliable test that they form a series, since the order m = I never falls in with any of the usual formulae. If, however, the limits be taken to be the same as the p 8 , p n of category (c), the formulae constants can be cal- culated from m = 3, 4 and tested on m = 5. The result for S is that with these limits the sequence is of the d or/ type, i.e. with a positive, and the C for m = 5 is dX = -66. This is larger than the permissible observation error. Further the line allocated to m = 1 has a mantissa 344939 compared with 326974 for m = 3. It is thus quite definite that the mantissae decrease with increasing order and that the sequence must be of the d or/ type. Either then the sequence is of the d or / type with a considerable C for m = 5, or the first line does not belong to the series. With D or F series the large C error in m = 5 often occurs and is not decisive. If, on the contrary, the first line be omitted, and the constants calculated from m = 3, 4, 5 the resulting formulae have limits three or four units less than p 8 or p u , but now with a sequence of the s type and the m = 1 line definitely excluded. No further lines exist, however, by which to test it. The D series with the p 8 , p n limits give a formula which reproduces m = 5 with the small C, dX = -04, but the a is negative. It is true this is not unknown with D series, in fact it is common in the blue spectra of these gases. But the satellite separation is much larger than those of any D which are known, especially for an element of such a small atomic weight, and the intensities of the supposed D u lines are less than those of the Z) 12 . The satellite separations as shown in m = 3 ... 6 would correspond to one of about 1080 for m = 2 with a D n line at about n = 8307 and D 12 about 7226. The appearance of the lines certainly suggests a D set, but the Z) u , Z> 12 may be either independent series of the P type or combinations p 8 TT (m), p 8 7r 2 (m), p u 7r x (m). The congery of eighteen parallel series, amongst which occur the limits p 8 , p^ of the preceding series, are denoted by him as s n (m) from n= 1 to 18. All possess the order m = 1, with negative wave number. The orders m = 2 are in the unobserved ultra-red. The orders m = 3 are observed if certain blue spectrum lines are selected for all from s s to 18 , those preceding s 8 lying in the ultra-red. The orders m = 4 are seen up to s n . Otherwise the series are very fragmentary. The most complete, n = 5, 9, 11, 17, are represented by five orders, * P.Z.8. 21, 25 (1920). For data see tables. x] THE MONATOMIC GASES 207 each with m = 1, 3, 4 and respectively 7, 10 6, 9 7, 8 6, 8. As illustrating the fragmentary character may be adduced s 2 with m = 1, 4, 10; s 4 with 1, 4, 7; s 7 with 1, 4; s 12 with 1, 3, 10. Moreover, the corresponding lines of different series differ in relative intensity. All these peculiarities point to the presence of the linkage effect and possibly disruption of normal lines with formation of others. It is suggestive that many of the observed separations recall some of those of the blue spectrum. It will be seen on referring to the table of data that Pc> ~P2= 718-89 which is e - -82 ; p 6 - p = 176-27 - Vl - 3-23 =v l -x (say) ; So again p 8 - p 1 = 76-13 - v 2 + -53 ; p<>-p 8 = 555-09 - 2 (e - v) + 1-01 ; p w p 9 = 115-5, which is the separation of F lt F 2 in the blue triplets. If so, it would be a d link of which as yet we have little knowledge beyond the fact that such exist. p n p lQ = 104-28 = ^ v 2 + *3. If all these are links, then p n p 8 the observed separation in the S, D would be due to the series of links 2 (e v) + cr of F + 1^ v 2 and not to a. true separation, i.e. one based on displacement in the limits of the series. If this latter separation is 774-91, the required displacement is exactly 6988. The observed means are 774-87 from p ll9 p 8 ', 774-52 from S', 774-82 from D. As the oun produces a shift of only 28 in these m = 2 limits the evidence is not decisive. It would seem probable though not certain that this separation corresponds to a true doublet and that the 115-5 does not enter as a F^F^ link. Finally Pi*. ~ Pis = 266-71 = v v + 3-3 = vv 1 + x', p l6 p l5 = 72-50 =i> 2 3 = v 2 x. It will be noted how frequently the difference 3 occurs. It must be accounted for by displacement concurrent with linkage. In fact the displacement in p u producing 3 in v v is exactly annulled in the p l6 p l5 by 3. The whole congery appear divided into four groups separated by considerable gaps. Thus s 1 which is problematical is 1378 behind s 2 ; the other groups would be s 2 ... s 6 , s 7 ... s n , s 12 ... s 17 , s 18 . These are separated by 790, 1295, 2742. The links above indicated would then connect the different series in each group. If this suggestion is established it would show that the series discovered by Nissen really belong to the "blue" system and stand in close connection with the considerable number of independent F systems and independent S and D systems which we have seen to exist in the other gases of high atomic weight. This would also explain why so many of the lines included by Nissen are taken from the blue spectrum, as also why these series have no relations with any of the Rydberg type II lines, which undoubtedly belong to the "red" spectrum. These series are also quite distinct in their properties from those discovered by Meissner and Paschen in Ne. The Zeeman effect in A has been studied by Hartmann* and others. In the red spectrum 6964, 5651, 5607, 5559, 5496, 5187 all have a Zeeman pattern = 0/1/1. Of these 5607, 5559 are amongst Nissen's lines. In the blue spectrum * Ann. d PJnjs. 38, 43 (1912). 208 ANALYSIS OF SPECTRA [CH. five lines were found affected by the field, 4880 (0/6/5) ; 4806 (0/8/5) ; 4736 (0/3/2) ; 4609 (0/9/8?) ; 4545 (0/11/9?). The A lines are almost irresponsive to the electric field. With the very high fields of 100000 and 170000 volts/cm. Takamine and Kokubu* could only find a few, slightly displaced to red, amongst the type II lines. 6. Neon. The early measures! of the spectrum by Liveing and Dewar, Baly, and Watson, are now, to a considerable extent, replaced by certain inter- ferential measures^ of Priest, Meggers, and Meissner and very accurate deter- minations by Meggers, Burns and Merrill, and by Paschen. These latter give very complete and accurate measures for the spectrum stretching from A 9840 to 2550. The spectrum is notable for the large number of lines in the red region, and for the number of strong and apparently real monochromatic lines. The first regularities observed were certain constant separations due to Watson of about 1429, 417, 1070, 359, the last two being components of the first. When the strong lines giving these separations are taken, the exactness of the equality of the different measures obtained from them is most remarkable. Using the interferentially measured lines by Priest, Meissner, and Meggers, the following values are found in i.u. for the means 1429-4292 8 -0065 -0048 . 417-4533 7 -0120 -0064 Here the second column gives the number of cases used, the third the maximum deviation of a single reading from the mean and the last the root-mean square of all the deviations. The next step was due to Rossi || with the allocation of two doublet series each with the same separation and the same limits and indications of close satellites. But the great achievement in this element is the allocation of the whole of 840 measured lines'with the exception of about 50-^or, if the 35 at each end be omitted, 770 with the exception of 23 to definite series. The first steps towards this were the series of Rossi and sets determined by Nissen^f and Meissner**. Induced by these, Paschenff undertook a new measurement of the spectrum with increased accuracy, and with greater resolving power. The result was the full establishment of Meissner 's series and their completion and exten- sion. In the discussion of his results, by failing to recognise the existence of the linkage effect he was led astray in one particular which, however, he rectified in a later paper JJ. The general results may be stated as follows. * Mem. Coll Sc. Kyoto, 3, No. 6 (1919). | Liveing and Dewar, Proc. Roy. Soc. A, 67, 467 (1900); Baly, Phil. Trans. A, 202, 183 (1903); Watson, Proc. Roy. Soc. A, 81, 181 (1908). J Priest, Bull. Bur. Stand. 8, 2; Meggers, ib. 12, 198 (1915); Meissner, Ann. d. Phys. 51, 115 (1916); Paschen, Ann. d. Phys. 60, 405 (1919). Meggers, Burns and Merrill communicated to the author and used in [v]. Camb. Phil. Soc. 16, 130 (1911); Astro. J. 33, 399 (1911). || Phil. Mag. 26, 981 (1913). If Letter to Paschen, Dec. 13 (1917) referred to by Paschen. ** Ann. d. Phys. 58, 333 (1919). tt Loc. cit. JJ Ann. d, Phys. 63, 201 (1920). x] THE MONATOMIC GASES 209 (1) There are a number of series with nine constant separations depending on ten limits. These are taken as of the S type. In other words the series are Pi (2) Sj (m) with ten different p and four s, i.e. i runs from 1 to 10 and j from 2* to 5. (2) There are a number of series with decreasing separations depending on four limits. These are taken as of the P type. In other words the series are represented by 8 t (1) p t (m). (3) There are a number of series of the D type depending on the same Pi (2) limits and twelve different d sequences d k (m) including four denominated (4) According to his allocation no F series depending on d k (2) for limits are known. They would lie in the far ultra-red, with limits between d^ and d 6 12228, 12419 or s about 11500. The lower orders of the sequence can therefore only be recognised in summation lines. In this connection may be noted two doublets unallotted by Paschen whose wave numbers are (1) 10671-70 12337-99 (3) 14004-29 26-21 2620 (0) 10697-91 12364-20 (3) 14030-49 The accurately equal separations show that they are related to one another. Regarded as difference and summation lines of the same order the mean limits are as given. As the value of the sequent d (2) is 12337-32, there can be little doubt but that these belong to lines d (2) /(m), although there is nothing to show by themselves that the sequence is of the/ type. The sequent is given by half the difference = 1666-3 = #/(8-12) 2 . Other related summation lines of lower order are found amongst lines observed by Watson and Meggers. As a consequence of these connections any particular sequence occurs in a number of independent series, and the values of the different orders can be independently found in terms of one only of the whole set. That taken was the mean of the determinations of s 5 (1), which he took as 39887-610 -05. The different sequent values should therefore be indeterminate only to the error in this limit. When these sets of values for any particular sequence, as determined from the different series in which this sequence enters, are compared, the agree- ment is remarkable. Consequently if we could assume that no displacements occur in the different series, the means for each sequence ought to be more or less freed from merely observational errors, and the wave numbers reliable within only a few units in the third decimal place. But we cannot be certain of the absence of displacement in an element of the low atomic weight of Ne where the oun, 3-6, produces such an extremely small shift. There are in fact evidences that such displacements occur, but they are certainly small. Paschen's mean values of these sequences are reproduced in a tabular form in the Appendix. As a rule the value of any sequent determined from a given line only deviates * A set which he originally regarded as s and called s t was afterwards seen to be of the d type. It will be best to keep to his original notation until at least their respective relations are better known. H. A. s. 14 210 ANALYSIS OF SPECTRA [CH. from the mean in the table by a few units in the second decimal place, except for orders greater than m = 9. If the formula for a sequence be calculated in the usual way from the sequence itself instead of from a series, the limit term ought to come out as zero. When, however, Paschen applied this method to his sequences he found that in a large proportion this was not the case, and he at first attempted to find a new formula which would reproduce the sequence with zero limit. But his formula included exponentials of a complicated kind and gave bad agreement with observation. In his second paper, however, he rejected these and recognised that the limits found by using one of the ordinary formulae were real. This was not a new kind of fact, as he supposed, but was clearly due to the presence of links, although perhaps their persistence throughout a whole series is not frequent. Analogies have been seen for instance in the blue spectra of Kr and X. A comparison of the mantissae of the first five p sequences seems to indicate that they are linked collaterals of the last five. Another important point is that series representative of p s, s p and p d do not occur for all i, j, k, but only for a selection. These are given in tabular form below, and in the tables with the number of representatives in each series. Paschen's formulae are of the Ritz form n = N/{m 2 + /z + yn} 2 in which the direct determination of n must be very laborious. The constants of the formula of simpler type in a/m are given in the tables, together with their C, dn, values and the corresponding values given by Paschen's formulae. In comparing these it should be noticed that Paschen seems to have determined his constants to get a good general agreement including the first line, whilst those here given have been determined directly from the second and third lines in p and s or the first two in d, and from the limit as found from the high orders. This means that the C for m = 1 in the s sequence is considerably wrong as is always the case in s. But the results by this method are more generally useful, give C = for the two low order lines, and are more easily obtained. For the actual comparison of the high orders the exact type of formula is almost immaterial, the C depending chiefly on the limit used. Both forms give considerable deviations f or m = 5 or 6. They are real deviations from regularity and should afford valuable data in any critical discussion of the relationships of these series, such as has yet to be made. The link-effect is shown in the p f or i = 1, 2, 3, 4, 5 in s 2 , s 3 , and in the d sequences s/ ... s^'" . The actual values of the links are not, however, all easily settled. In s 2 , s 3 and the four s x they are close to 781. Paschen gives 7804 and 7834 for p^, p 5 , 763 for p 2 , 730 for p l9 40 for p 3 , and 10 for p lQ . This is on the assumption that the link is the same for every term of a sequence. The obser- vational evidence is, however, distinctly against this assumption in p , p s and it would seem that several link values are involved. Indeed for the first orders Pi (2) and s 2 (1) much larger links, or the sum of two or more would seem called for. The 10 for p w may be doubtful. 7. The facts that the allocation gives ten distinct ^sequences, that in A eighteen have been found, and in He a set of doublet series, have suggested to x] THE MONATOMIC GASES 211 Nissen that the number of independent series in an element of this group will be found to be given by the atomic number of the element, those for He, Ne, A being respectively 2, 10, 18. This generalisation would not, however, seem to be justified by our present knowledge. The red He are singlets and the blue He are doublets depending on d, f sequences, with no correlation with the A red. We have seen there is evidence pointing to the existence in Nissen's red A of three groups, each group being link connected. The fact that there are no represen- tatives of P systems in A whilst they are strongly developed in Ne may possibly be explained by the fact that the A spectrum has not yet been fully explored. It is also to be noted that in A the whole number of eighteen p (2) limits are associated with a single s (in) sequence and that only in three cases do two other independent s sequences occur, viz. two with p 8 and one repeated with p u . In Ne, on the contrary, the arrangement is quite different. If the limit separations in the spectrum be arranged in a list in horizontal lines and the order separations in vertical columns, we shall get a scheme of precisely the same appearance as those givenbyR-ydbergin A, with the column numbers alternating irregularly be- tween small and large amounts. We should conclude that the Ne spectrum is the analogue of the Rydberg portion of the red spectrum of A, with which Nissen's have been shown to have nothing to do. Further, if the Ne sets be compared, a remarkable regularity in association will be noted, which may be stated as follows : To every series p f (2) Sj (m) occurs the corresponding series Sj (1) p t (m) and vice versa. This rule holds without exception, as may be seen by the following arrange- ment of all the series excerpted from the Ne tables in the Appendix. The numbers enclosed in [ ] refer to ihej of the Sj sequences which occur in each case. i 'S series P series 2 p 2 - s [2, 3, 4, 5] (m) s [2, 3, 4, 5] -p 2 (m) 3 p 3 -*[2,4](m) 5 [2,4]-p 3 (m) 4 p, -s [2, 4, 5] (m) s [2, 4, 5] -p t (m) 5 p b -s [2, 3, 4, 5] (m) s [2, 3, 4, 5] - p 5 (m) 6 p 6 -s [2, 4, 5] (m) s [2, 4, 5] -p 9 (m) 7 p, - s [2, 3, 4, 5] (m) s [2, 3, 4, 5] - p, (m) 8 p 8 -s [2, 4, 5] (m) s [2, 4, 5] -p 8 (m) 9 P 9 -s\5](m) s[5]-p 9 (m) 10 p w - s [2, 3, 4, 5] m s [2, 3, 4, 5] - p w (m) The corresponding statement for A runs Pi s (m) for all the 18 values of i, with, in addition, p 8 s [2, 3] m, Pu - S 2 ( m )- and no series with s limits. In Ne the s 29 s 4 and the s 3 , s 5 are linked sequences. It will be noted that the s 2 , s 4 always occur together in any group, whilst s 3 never occurs without its linked s 5 . In four cases, however, s 5 occurs without s 3 . The d sequents all show themselves amenable to the usual formulae. It may be noted that the separations of d^, d 2 , d 3 and of s^, s/', S/", respectively 64-80, 39-40 and 15-72, 9-76, are both in the usual triplet satellite ratio of 5 : 3. 142 212 ANALYSIS OF SPECTRA [CH. 8. Paschen has compared the Zeeman patterns of some of the lines observed by Lohmann (see Chapter V, sect. 4). As these relations are important, a comparison with the whole of Lohmann's data is here given. It will be noted that all the lines involved are of a type allocated by Paschen to first order P lines i.e. are of the type Sj (1) p { (2). The first column gives the line type; thus j. i means s 3 (I) f p i (2); the second the wave length, and the third the eeman pattern in the form adopted in Chapter V. j. i X Zeeman pattern j. i \ Zeeman pattern 2.1 5852 0/1/1 4.6 6304 0.1/4.5.6/4 2.2 6599 2/7.9/7 4.7 6383 1/1.2/7 2. 4 6678 0. 1/4. 5. 6/4 4. 8 6506 0. 1/-25 +2. 3. 4/3* 2.5 6717 0/1/1 5.2 5882 0. 1/-5 +8. 9. 10/6* 3.2 6163 0/9/7 5.4 5944 1.2/5.6.7.8/5 3.5 6266 0/1/1 5.5 5975 0. 1/2. 3. 4/2=S 1 /// 3. 7 6533 0/2/3 5. 6 6143 3. 6/11. 14. 17. 20/12 J 4. 1 5401 0/7/5 5. 7 6217 0. 5/4. 9. 14/6 4.2 6030 1/-1+3. 4/7* 5.8 6335 1. 2/2. 3. 4. 5/? 4. 3 6074 0/3/2 5. 9 6402 0. 1. 2/6. 7. 8. 9. 10/6 4.4 6096 0.2/11.13.15/111 * These were allocated by Runge to high sub-multiples, 6030 to a/14 and 5882, 6506 to a/12, viz. as 2/7. 9/14; 0. 2/17. 19. 21/12; 0. 4/9. 13. 17/12. But Lohmann's intervals are accurately all a/7 in the first, a/6 in the second and a/3 in the third, with, however, the first s-component in each definitely not aliquot parts of a. This is, however, allowed for on the Ritz theory and the notation in the list means that the values are all displaced by the fraction of a indicated. f Runge's allocation. All the separations are -86 which is no simple aliquot part of a = 4-69, but close to 2a/ll. J So Runge, but while Lohmann's separations are equal to 1-25, except the first p (1-17), this is no simple aliquot part of a. 3a/12 or a/4 is 1-17. The twelve components enter at 16800 gauss. The change possibly has not been completed. The shifts are all exact multiples of 1-69, but 1-69 has no simple relation to a. a/3 is 1-59; 3a/8isl-75;4a/ll=l-70. Paschen gives 5401 as three halves the normal triplet, but Lohmann's measures are not this. The latter gives for the s-component 6-50 and not 7-0. Also he states that 5975 is the S^" type which is clearly true and that 6506, 6402, 6335 are of the D^", D u " f , D 12 " types. The latter statement is difficult to reconcile with the patterns shown above. D 22 does not show an undisplaced ^-component, the normal pattern being probably 0/1/1. D u has 0/7/6 of which it is possible 6402 may show an amplification. Z) 12 has probably 4/7/6 whilst 6335 is the exception to Runge's rule noted above. 9. Nyquist* has studied the Stark effect on Ne lines with some completeness. He gives a considerable number of lines made visible by the electric field (Koch lines), a few of which, however, are found as weak lines in Paschen's list. They seem chiefly to belong to the s and d series. Also his results are noticeable as containing a long list of lines which are split into more than one component and displaced to the red, a large number appearing as unpolarised. In several of these, weak companions also appear with strong fields. All the lines in this list, with the possible exception of two or three, depend on d sequences, and a con- siderable proportion of the double shifts are possibly due to the existence of close lines. * Phys. Rev, 20, 226 (1917). x] THE MONATOMIC GASES 213 10. The radiation and ionisation potentials of Ne have been discussed in their relation to general theory in Chapter V, sect. 26. The second paper by Horton and Davies is of special importance in connection with the series alloca- tions of Paschen. They observed the spectrum of the glow as the potential was increased from 10 to 30 or 40 volts. No glow appeared until the voltage rose to 20. Above this certain lines appeared and when the voltage rose 2 volts or more above 20, others suddenly made their appearance. The brightest of these two sets were those given in the following tables I and II. Table III gives the additional lines observed at about 40 volts. In Table I the Zeeman patterns are also added. In the second column the figures in [ ] refer to the i,j of the sequences indicated at the top of the column. I 6402 [5. 9] 0. 1. 2/6. 7. 8. 9. 10/6 6143 [5. 6] 3. 6/11. 14. 17. 20/12 6096 [4.4] 0.2/11.13.15/11 6074 [4. 3] 0/3/2 5944 [5. 4] 1. 2/5. 6. 7. 8/5 5852 [2. 1] 0/1/1 5401 [4. 1] 0/7/5 II Pi (2)- 0(m) 5764 p -d/(3) 5145 5341 p 10 -rf s (3) 5116 5331 Plo -d 3 (3) 5080 5189 p 9 -5 5 (4) 5038 III Sf(l)-p t (2) 6717 [2.5] 5820 p s -rf 4 (3) 6678 [2.4] 5748 p 9 -d/(3) 6599 [2.2] 5690 p 10 -*5(3) 6533 [3.7] 5657 p 7 -V'"( 3 ) 6506 [4.8] 5563 p 6 -a/" (3) 6383 [4.7] 5298 p 4 -a, (4) 6304 [4.6] 5222 p 8 -a 4 (4) 6266 [3.5] 5204 p s -d/(4) 6217 [5.7] 4710 p w -d 6 (4) 6163 [3.2] 5976 a 6 (l)-p 6 (2) 6030 [4. 2] It will be noted that Table I contains none but P lines, whilst Table II has all D lines with the single exception of 5189 of the S type. Even at 40 volts no more than four of the S type were seen. In fact the omissions are almost as significant as those appearing. About twenty of the strongest lines in the region of observation fail to appear, the most striking absentees being the P lines 5882 and 6334 of intensities 20 and 10 in Paschen's list and s 5 (1) p 2 (2), S 5 (1) ~~ Ps (2) in hi s allocation. It may be noted that 6074 has a Zeeman pattern of the s r p 2 '" type and 5852 of the s f p', but Paschen's allocations definitely rule them out from being those lines. We know that these singlet systems show lines corresponding to both s' (1) (m) and s' (2) (f> (m). It is therefore just possible that the observed red Ne spectrum refers to the latter but the radiation and ionisation potentials to the former.. CHAPTER XI MISCELLANEOUS Groups IV, V. 1. In the descending melting point sub-groups of IV and V, viz. [Ge], Sn, Pb and As, Sb, Bi, regularities of type II have been found by Kayser and Runge*. In group IV, Sn and Pb exhibit each three parallel sets with separations 5185-3, 1735-5, ratio 2-99, in Sn and 10807-3, 2831-0, ratio 3-18, in Pb. They are weakened in the spark, show strong reversals, and the intensities in each set do not diminish regularly with increasing wave number. The arrangement would seem to indicate triplet or linked series and that a set contains representatives of more than one sequence. 2. Lohuizenf has attempted an allocation of series in Sn and Sb. He has employed formulae of the form indicated as impossible on p. 36, but this will not affect his allocations. A short discussion of his results will here be given. It must be read in close connection with the data given in the tables. In Sn his series depend on two sequences with several limits, the first sequence of a d or /type and the second of a p or s. As, however, their nature is not definitely settled by other relations the two sets are here labelled A, B respectively. In 'the A he suggests six parallel series, of which three are connected with Kayser and Runge's three sets. The latter are referred to as A I, A II, A III, the others being labelled Aa, Ab, Ac. The second group B I, B II, B III have the Kayser and Runge separations, but a different sequence from the A. In the A\ ... a first calculation of the formula gives a large a, yet it shows without doubt that the lines fit into a series of the d or/ type. When a is large for a D series it is better to take a formula with a/(m + /u,). The formula calculated on this basis (see formulae table) is in exceedingly good agreement with observa- tion, the - C, dX, errors for m = 2 ... 6 being, 0, 0, 0, 02, 015, but for m = 7, calculating A I by deducting v l from A II gives dX = 2. Further, the line given as A II (7) is a true A III (5). It must therefore be rejected as A II (7). The separations of II and a are close to 430-7 except a (4) which gives 446, and also belongs to Kayser and Runge's type II. It must be excluded. Also c (2) belongs to Kayser and Runge's I, and b (4), c (4) are repeated from A II (6) and Aa (6) and give wrong separations from A III. All these exceptions are marked ? in the table. The question arises as to the nature of the separations of the six sets. Are they true series separations depending on displacements of a single sequent or are they links? The separations are 5185-32, 1735-55 for I, II, III; 430-65 for a - II; 2579-96 for b - a; 419-12, 415-90, 431-0 for c - b, an irregularity * Wied. Ann. 52, 93 (1894). t Z. S. wiss. Phot. 11, 397 (1912). CH. xi] MISCELLANEOUS 215 which again throws doubt on the c set. It may be noted how close these separa- tions are to integral ratios 13, 4, 1, 6, as if built up of units 430. This is consonant with either supposition as to their origin. We may test the supposition of dis- placement by regarding the I, II, III as a triplet series. Calculation then shows A! = 81986 - 2-57f + 14-6^ = 160J (511-632 ... ) A 2 = 24676 - -72 + 13-86rfv a = 48 (514-083 ... ) Aj -|- A 2 - 106662 ... - 208 (512-182 - -0157 + -067^). Also 8 = 512-182 with f < 10, dv < -3 gives w = 118-984 -02, compared with the chemical value 119-0. By itself this is merely a numerical determination and has no evidential value for displacement. But if the series is a D triplet with m = 2 f or the first order, as should be expected from the rule outlined in Chap. IX for a sub-group of descending melting points as here, then the D 13 should show a mantissa a multiple of A 2 . The actual mantissa is 469265 - 68-78 = 19 (24698-16 - 3-62). It is therefore a close multiple. If the true A 2 is 488, the exact condition ^quires 2f + -469^ = - 1083 + 54 - QOdv or + -235^ = - 541 + 27 - Wdv, a condition which recalls the result obtained for triplets in Chap. IX. If the sets belong to D triplets we should expect to find Z) 12 and Z) n sets. Now a glance at the Kayser and Runge lines in the table shows that doublets alternate with triplets. For instance (4^)35961-91 5185-27 (6^)41147-18 shows the right order of intensity and is 67-52 ahead of Z) 13 (3). The calculated mantissa difference for this is 12259 + ISOdn - ISlf and 248 = 12292. Exact 248 requires dX = -014 as between two lines and is a usual satellite multiple. But there is no sign of a line suitable for D n (3). The above considerations must at present be regarded as merely suggestive, but encourage further investigation in these series. The second type of Lohuizen's allocations, those here labelled B, show the same separations as the Al ... III. They must therefore have the same limits. Nevertheless the formula for B I calculated direct gives a limit of 43789-22 with a considerable a so that the exact limit depends within several units on the nature of the formula used. The formula for B I gives 00, dX values for m = 5, 6, 7 of -8, - 1, -34, but -02 for B II (5). The line given for BI (5) is also allotted to B II (3) where it gives a correct^ whilst it is 5195-94 here. The line clearly overshadows the true B I (5) and this may be the cause why the Zeeman pattern is quite different from the others 5/6/5, and is apparently modified by two superposed patterns observed together, viz. 0/6/7 for B I and 0/3/2 for B II. The formula reproduces the lines so well that the deviation for m = 6 must be anomalous. The limit found is 1543-90 less than that for the A I which gives the correct separation. Hence the series must form a linked system with 216 ANALYSIS OF SPECTRA [OH. a normal P or S set. Either 1543-90 must be a single link or a collocation. The a link formed on $ 2 ( oo ) by A 2 has a value 1570-95, or if the links are calculated on S-L ( oo ) by A 2 , the c link is 1545-6. The last agreement is close, but A 2 links formed on S l ( oo ) are not as yet known in other cases. The deviation in B II (6) might then be due to a different link. 3. After this more detailed discussion of Sn it will be sufficient to describe briefly Lohuizen's allocations for Sb. They are based on the Kayser and Runge separations 2068-65, 6541-53, and again the types A, B are given as triplets. It will be noted that the order of magnitude is the inverse of that of ordinary triplets, and indeed in this group V we should expect doublets as the prevailing type. Moreover 2068, even if a true displacement separation, would seem to enter also as a link. For instance, after B II (6) there occurs a line with a re- peated 2067. The magnitudes of the separations are such as might be expected from successive A, 3 A on a true limit and suggest links 2068-7 = a, 2068 + 6541 = 8610 = e. The formulae given in the table are based on a/m. That for A gives - C, dX = 0, 0, 0, -03 and for B, 0, 0, 0, -1-7, -26, the devia- tion for B I (5) indicating that the line is wrongly allocated or has a different link. As in the case of Sn the A, B limits do not agree except that the calculated values for A I and B II differ by only 398 whilst A I and B I should be the same, thus again suggesting that the 2068 enters as a link. Lohuizen suggests a third set of three lines, reproduced in the tables, but they would seem doubtful. A much more thorough discussion of these spectra is required before their definite constitution is settled, and Lohuizen's first attempt should be followed up. The special congeries in II (a). 4. In Chap. Ill, sect. 28, attention has been drawn to the presence in the spectra of group II (a) of several corresponding congeries of lines in each depending on combinations of d" r (1) andjo" ' (1) with unknown sequents. Their constitution will here be more closely considered in connection with the fuller knowledge of spectral relationships now obtained. Two types of these congeries were recognised of the form d X, and p Y 9 involving the three d, the three p, and three each of X and Y. Consequently in each type two sets of separations occur, viz. OL , cr 2 , with two new, say, x lt x 2 ; and v 1 , v 2 with, say, y^ , y 2 . In the first type again two different forms of grouping appeared which were provisionally labelled as A, B, whilst the second was labelled L. The lines with their arrangements and separations are given in Table III after the general data relating to II (a), to which the reader should refer. An individual line will be referred to by subscripts as in satellite series. Thus d X 2 will be referred to as A 12 oip 2 Y 3 as 1/23 . In all three elements, Ca, Sr, Ba, the wave lengths have been determined in I.A. in general to the third place of decimals. We shall probably be justified in taking the maximum possible observational errors in these as -01. A. (in Ca certainly < -003) or, say, in W.N. a few units only in the second decimal, with considerably greater accuracy when separations of related lines are in question. This is justified by the close agreement found by different observers for the xi] MISCELLANEOUS 217 measures of the same separations in a given congery. For instance comparing the measures of Schmitz and of Werner in the first A congery in Ba we find ff 1 0/3/2 0/4/3 0/4/3 ? 0. 2/5/3 (1 > 0/1/1 0/4/3 ? 0/5/3 0/4/3 0/2/3 0/5/3 (2) 1 0/4/3 ? Notes. (I) for A Z3 , the only observation is uncertain for Ba, which gives 0. 7/21/12, probably indicating 0. 2/5/3. (2) for A 32 , Sr gives 0. 4/7. 11 - /6, probably indicating additional p components and uncompleted split of the normal s. (3) The Zeeman patterns for B in Ca have not been noted. Those given above are from Sr. Ba gives normal triplets for all except 0/1/2 for j5 33 , B 32 . 5. Type A. We have already seen (p. 68) that in A the x separations for the different elements are roughly proportional to the squares of the atomic weights, whilst the ratio xjx^ is close to 3/2 in each element. The complete set of cr separations is only given by the X 2 sequent. Consequently the denominator of X 2 is first determined from A 12 = d X 2 , and those of X l , X 3 then found from X = X 2 x l9 X 3 = X 2 + x 2 . In Ca the cr separations 21-7, 13-9, agree with those given by the F series but differ from those of the D satellites by an oun displacement in F 2 ( oo ) over d 2 (1). The sum c^ -f cr 2 = 35-68 agrees within limits with the value from D whereas the sum of the F is less, viz. 35-18 for the first order and 35-32 for the next clearly a F satellite effect*. In Sr, Ba, the cr are the same within errors as in the D and F. Hence the limit term for A 12 is definitely d or F ( oo ) without any displacement, although such appear in some related sets in Ba, and the x separations must have their source in the X sequents, provided no linkages are present. The values of d for the three elements are respectively 28933-14, 27609-77 and 32433-00. The denominators of the X calculated with these are given below. The respective values of 8 and true A 2 are also given for reference. Ca Sr Ba A 2 1363-40 - -059^ 5485-09 - -262 11978-20 --608^ 5 58-017 277-726 684-468 X,. 3-151218 -142-6 3-421407-182-6^ 2-536326-74-4^ X 2 3-145527 - 141-9 3-389397-177-5^ 2-503624 - 71 -5 X 3 3-141740 -141-37 3-368717 - 174-3 2-479687 - 69-5 * The -50 difference is due to S, giving -51, as between / 3 and/j. 218 ANALYSIS OF SPECTRA [OH. On account of the simpler constitution of the spectra of Ca and Sr, their discussion will be taken first. Their mantissae differences, with the nearest oun multiples, are Ca 5691 -?? 3787 --51 9478-l-28 98^5=5685-7 65^5 = 3785-6 9471-3 Sr 32010-5-08^ 20680-3-23^ 52690-8-31^ 1155 = 32007-9 74 J5 = 20690-7 52698-6 This close agreement with oun multiples within possible ranges of and x shows that we are here concerned with pure difference lines and that all the X belong to one type. What this type may be is not so easy to decide. The triplet Zeeman pattern would suggest some reference to the singlet sequences. On the other hand the triplet displacements with such excessive oun multiples show analogy with the instances of large A 2 multiple displacements which the F series exhibit in all the elements, both of groups and II. This last suggestion of connection with / or d sequences is worth testing. In Ca the denominator of / (2) is 2-935381 - 115-3 with possibly close satellites and / 3 (2) = 2-935323, The mantissae difference of this and X l is 215895 - 27-3 = 158 (1366-235 - -17f) = 158 (A 2 - 2-83 - -llf ). The A 2 is so small that the large multiple involved does not allow a definite conclusion that with the conditions the difference is 158A 2 . But if so, the sequent X is/ (2) (158A 2 ). In Sr, as well as in Ba, we do not know the value of / 3 (2) on account of the disruption in the first F triplet. But if it follows the rule and the mantissa is M (A 2 ) and X 1 is a displacement by another M (A 2 ), its mantissa for m = 2 which is 1421407 must also be a M (A 2 ). Now 1421407 - 182-6 = 259 (5488-056 - -70f ) - 259 (A 2 -I- 2-97 - -44f ). The condition for the multiple relation is then 2 -f 1421^ = - 770 -f- 114f or + -710^ - - 385 + 57f. This recalls the conditions occurring for D triplets in Chap. IX. There is some justification, even if it is not conclusive, for putting In Sr we find incipient traces of the elaborate systems of displaced and linked lines exhibited in Ba. In connection with the A congery are found several lines shifted about 1-47. Thus ^33, A 22 have near them the lines AA = (1) 5521-303, (In) 5503-72 separated by 1-47 in each case, and A u has (n) 5481-23, (In) 5480-41 separated by 1-30, 1-43, whilst A 2l is a close doublet, dn = -06. They clearly form portions of a related and displaced set, although the source of the dis- placement is not easily assigned. The oun displacement on the limit d shifts by 1-923, whilst on the three sequents the shifts are -398, -391, -380. These cannot reproduce the observed shifts within the error limits adopted in sect. 4 except 1-30 + 1-43 = 2-73, where seven ouns on X give 2-78. Four ouns on X 2 , X 3 give 1-56, 1-52 and cannot represent the observed 1-47. It is possible the ob- served separations may be those of the four ouns combined with the other cause* which produces the shift in the close doublet A 2l oi dn = -06. These new lines would then be A^ (8), ^ 22 (8), and A^ ( 38 X and + 48 X ) modified accordingly. * E.g. observed line a close multiple line of which one is to be taken. xi] MISCELLANEOUS 219 It remains to test whether the X conform to A 2 displacements on d. In Sr the d (2) denominators are 3-174307, 3-170952, 3-168767. Of the nine possible combinations, only d 2 , X 3 and d 3 , X 1 show approximate possibilities. They give for mantissae differences d 2 , X 3 197765 - 32-2f - 36 (5493-32 - -9f) = 36 (A 2 + 8-15 ... ) da, Z x 252640 - 37 - 46 (5492-17 - -8f) - 46 (A 2 + 7 . . . ). For agreement these require, being differences of the same order, 198^ = - 293 + 32 -252^ = - 322 + 37 which are quite incompatible with any value of x obtained in Chap. IX. Thus a connection of the X sequents with the d would seem to be definitely excluded. They may be possibly displacements from/, or independent sequences of the / type depending like them on A 2 . Passing now to the case of Ba we find in the red a very large number of lines showing by their separations relations to the F series depending on the anomalous D (1) set with which we are now so familiar, and which appears as the only strong D (I) set. In the tables a second A congery is given from lines in the extreme red measured by Meggers, as well as another weaker set apparently related to a more normal D (I). Taking the strong representative, and using the d l (I) limit, which is out of step with those of Ca, Sr, the resulting X is seen to depend on the order m = 2 in place of 3, but the mantissa is in analogous order of magnitude with them. The mantissa differences for the x l9 x 2 are 32702 - 2-84| 23937 - 2-03 56639 - 4-87 47| 5 =32690-8 - l-42 355 =23961-9 - 1-05? 56652-7 - 2-48 is indeterminate to a few units only. The agreement with oun multiples is well within error limits in Ba, but it may be noted that the multiples are much less than in Ca or Sr. This can scarcely be due to the fact that the orders are different. Again we cannot test against / 3 (2) for the same reason as in Sr. But X 9 = 40 (11992-17 - l-74) = 40 (A 2 + 10-14 - M3f) X 2 = 42 (11991-04 - 1-70) = 42 (A 2 + 9-0 - Mf) X 1 = 45 (11918-3). Here X l is excluded as a multiple of A 2 . Either X 2 or X 3 may follow the multiple constitution. They both enter because the two happen to differ by nearly 2 A 2 . The complete conditions for the two would be 2+'-480f 1 = -405 + 46 2 -f -504^ = - 398 or + -240^ - - 202 + 23 - + -252^ = - 199 + 22-5 also recalling the conditions of Chap. IX. Ba also shows sets of lines apparently collateral to this set. There are, for instance, A 119 (2) 6514-552; (2) 6488-583; displaced - 36-67, 24-75. ^ 22J (2) 6531-895; (2) 6514-552 - 10-13, 30-61. .4 33 , (3v) 6654-120; (1) 6580-99; (I) 6564-49 - 33-89, 33-65, 38-19. 220 ANALYSIS OF SPECTRA [CH. The lines in R.A. are due almost entirely to one observer, Hoeller, as is frequently the case with disrupted lines. Here the oun shifts on X lt X 2 , X 3 are 2-334, 2-394, 2-431. In X 19 48 shifts 37-332 and 98! 24-41. Hence 6514 is not a collateral of A n whilst the other may just be A u (+ 98 X ). But 6514 appears also with A 22 . In X 2 , 8 gives 9-58 and 138 X 31-12. Neither agrees with the observed but their sum, 40-70, and the observed, 40-74, do a similar effect to that in Sr A u . They are therefore possibly A 22 ( - 8 and + 138!) thus modified. In X 3 , 38 gives 32-54 so that neither of the first two under A^ fits in, but their mutual separation is 67-54 and 258 X gives 67-80. The third is 71-84 ahead and 298 X gives 71-66 so that it is A 33 (298j). In addition (3) 6707-823 is A 12 ( - 138J ; (1) 6323-46 is A 21 (158J. The second A set suggested is in a region very full of v and cr separations and apparently of links. For the present purpose of thro wing light on the nature of the A categories, the data for this set are too uncertain to call for further discussion. The general conclusion to which the discussion in these elements leads is that the sequence in the A category is of the / type. The cause of the curious quasi-satellite arrangement is not explained, but the satellite displacements are large and in a ratio quite close to 3/2, corresponding to the ratio 5/3 in d satellites. There are indications also that two orders at least occur. 6. Type B. In the A type the arrangement of the lines is definitely settled by the previously known a separations. In the B there is nothing, beyond the occurrence in each element of the strong .633 line, to show that it belongs to the set, and no indication at first sight of its relative position in the set. Nevertheless if it is placed in any other position, e.g. as following the B n , the x separations show no correlation in the different elements. As shown in the tables, with this single line treated as B&, the ratios of the x separations and the ratios of the x to the square of the atomic weight are : Ca Sr Ba xjx, 2-59 3-179, 2-532 4-07 ajj/io* -003 -004, -013 -013 thus showing a curious inverse correspondence in the two Sr representatives. The X denominators are (the Sr set with x = 33*88) : Ca Sr Ba JC, 3-318543 3-572762 2-612205 X, 3-317987 3-565739 2-591933 X, 3-317762 3-563539 2-587022 The inantissae differences are : Ca 556, 9|8= 551-2; 225, 45= 232-0; 781, 13|5 = 783-2 Sr 7023, 25 5 = 6943-1; 2200, -8 5 = 2221-7; 9223, 33 5= 9165 Ba 20272, 29$* = 20192-1; 4911, 75 = 4962-5; 25183, 36|5= 25154-6 If in Ca, Holtz's measures are used, the differences become 558,227 with the sum an exact oun multiple. The agreement with oun multiples is far from good in all the elements and in this respect distinguishes the B category from A, L. The second (a^ = 104) set in Sr with larger separations would, if the two belong to the same X sequence, refer to a lower order, but it has a larger wave number. Treated with the same d limits the denominators are found to be xi] MISCELLANEOUS 221 i 3-028779, 3-015597, 3-010429 with differences 13182 = 438-10, 5168=1618+30. The data of Meggers, who has unfortunately not measured below 15709, give the small separation as 41-33, which makes the last difference 5153 = 16J8 + 15 with the sum = 59J8 + 5, and they come easily as multiples within errors. But the mantissae will not march with the first as belonging to the same sequence, and moreover the oun multiples are about double. It is probably linked to a normal set. Indeed the lines (In) 6295, (2) 6272, (2n) 6248 with wave numbers 15879-59, 15939-34, 15999-37 are respectively 6369. a' or 33 .a', 5 21 .o', and B 3l .a f , where a' is the a link formed by A 2 on p 2 and is 185-02. In Sr the e link is 1592-39. If the set is linked by 3e = 4777-2 to a normal set. the latter would have denominators 2-560186, 2-552503, 2-549084 with mantissae differences 27 J8 + 8, 12JS +18 and mantissae, as well as the oun multiples, in step with those of order m = 3, increasing with the order (a negative). The new lines, if existing, would be in a region between the shortest ultra-red by Randall and the longest by Meggers. In Ba the order is m 2, as in the A. set. The mantissae, however, march with those of Ca, Sr, but the oun displacements quite definitely do not exist. Possibly the observed set is linked to a normal. The material at disposal for forming an opinion on the nature or origin of the B sequence is defective. It does show, however, that it cannot belong to any of the known sequences. The oun multiples indicated between the three X, however, approximate to those shown by d satellites, in contradistinction to those of the A, and as will be seen later, of the L, which have very large values (see end of sect. 7). 7. Type L. Here also appears a single line which is shown by its separation from the others to belong to the Z 23 position. In Sr it is absent in the first set and in Ba it is represented by two strong lines of the same character which suggest collaterals from a normal single line. With this arrangement the ratios y-Jyz are 1-84, 1-92 in Ca. In Sr the first y 2 is wanting, but the second set show the ratio 1-91. In Ba the ratio of y 1 to the separations for the two collaterals are 1-75 and 2-24, thus supporting the view that they have opposite, and about equal, displacements from a normal. No second set is given in Ba, but in this element there are a large number of linked membra disjecta. The common ratio of 1-9 shows that the allocation to Z 23 is correct. Moreover in Ca the same ratio for the two sets suggests that those with the smaller separations depend on the order next above the first. The ratios of the y of the first sets to the squares of the atomic weights are Ca, -054; Sr, -036; Ba, -042. These are of the same order of magnitude. It will be noted that both the y^y^ and y^w 2 are much more in step in the different elements than is the case in the B. The exact agreement of the v lt v 2 separations with those of the S'" shows that they depend on precisely the same p^" sequents, viz. 33988-23, 31031-51, 28514-80. With these the Y denominators of the first sets in Ca, Sr are supposing no linkage : Ca Sr 7j 3-193787 3-270291 7 2 3-180980 3-227369 7 3-174072 ? 222 ANALYSTS OF SPECTKA [OH. The mantissae differences are, in Ca, 12807 (220fS - 12807-2), (1198 = 6904-0). The first is thus an exact oun multiple. The second is calculated from Crew and McCauley's x 2 = 47-23. Holtz's measures here seem preferable as he gives both v l the same value. His x 2 is -038 less with consequent mantissa difference = 6902-6 and is thus a close multiple within possible errors. The y^ + y 2 are now 19709 and 339fS = 19711-2. In Sr the first difference is 42922 with 154|S = 42908-7. The oun value would make y l = 274-51 and nearer the second observed value 274-57. The oun multiple is thus sustained within possible errors. These results support the supposition that we are here dealing with pure difference lines. In other words the sequences producing the y separations are those deduced directly from p^" as the other sequent. Passing now to the second sets in the two elements, the diminished separations have values to be expected as belonging to a higher order (m = 4). But the sequents calculated from the p 1 are far too small. Thus the values of the Y 2 are 766 in Ca and 1334 in Sr, corresponding to denominators 11-96 and 9-06 and so clearly not to be accepted. The conclusion is that they are not pure difference lines but are linked* in some way to normal representatives, which may either exist or be completely disrupted. No lines are as a fact found near positions which such representatives should have. It may be instructive, however, to test the supposition that the linkage is composed wholly of e links, depending on A x on p l . With such it is possible to determine uniquely the number of such links, if the resulting sequents belong to the order m = 4. These e linksf are 424-50 in Ca and 1592-39 in Sr. It is necessary to take 13e = 5518 in Ca and 3e = 4777-17 in Sr, treating the observed lines as being positively linked to the normal. The 13e in Ca is certainly a high multiple, but the Ag spectrum also shows many instances of high multiples. If then the normal lines are linked in this way the wave numbers of L 12 should be 33221-64 - 5518-50 - 27703-14 in Ca and 29697-35 - 4777-17 = 24920-18 in Sr. These give for the denominators of the Y sequents Ca Sr Y l 4-186050 4-283467 Y z 4-177400 4-236374 Y 3 4-172927 4-212236 with mantissae differences Ca 8650, 1495 = 8659-0; 4473, 775= 4467-2; 13123, 2265 = 13126-2. Sr 47093, 169|5 = 47069-4; 24138, 875 = 24162-2; 71231, 256^5 = 71231-6. The y l + y 2 show in both cases close agreement with oun multiples, but a small triplet modification, whilst the y lt y 2 multiples are now in step with those for m = 3. They so far add some weight to the supposed linkage. But it must be regarded at present merely as an illustration. It is against the actual supposed * Unless there is some other as yet unknown effect. f These are only indeterminate in so far as the "modified" A x directly calculated, or the "true" A! as calculated from its oun multiple are used. This question has not yet been investigated for triplets, since in the rare gases, in which alone the triplet links have been fully discussed, the "triplet modification" practically does not exist, i.e. the two A x are the same. If the "true" A A are used, the values of the links are a few units larger than the above values. xi] MISCELLANEOUS 223 linkages that the mantissae increase with the order in Sr and decrease in Ca, but the substitution or addition of a u or v for one of the e might make them of the same type. In Ba the problem is complicated by the presence of portions of disrupted sets, so that it has not been found possible to settle definitely what the normal L set should be. Moreover, we cannot proceed with such certainty as in the other two elements as the A 2 11978-2 is subject to an uncertainty of one or two units, and with the considerable multiples of A 2 involved in the displace- ments this uncertainty may prevent definite conclusions. Moreover, uncertain- ties due to on the limit are magnified. The set given in the tables appears to be the only complete and strong one, and the lines all possess the same Zeeman pattern normal for this category. It is natural to take them as the normal set for this element. Nevertheless the denominators of the Y l , Y 2 are found to be 4-138409, 3-901298. These are altogether out of step with the m = 3 sets of Ca, Sr, nor is their difference an oun multiple. They are nearer the values of, but still not in step with, those of order m = 4. Also the mantissae differences ex- pressed as ouns, about 346 JS, are far in excess of the corresponding 149JS, and 169J8 of Ca and Sr. Since the actual separations, expressed in terms of the square of the atomic weight as given above, are of the same order of magnitude, these oun displacements should also be so. The inference is that the limit used is not correct. Now the v separations of the set are accurately the same as those of the S series and consequently depend on exactly the same limit. We must conclude that the set are not of the pure difference type but include linkages or some other as yet unknown effect. In other words, the normal set is replaced by a linked one leaving either none, or only remnants, of the original. That this is so is suggested also by the existence of the two lines on opposite sides of the expected L 23 with all the appearances of being collaterals. We should note that if the observed is such a related system, it must be regarded as linked to the whole normal set, that is, each line is connected to its corresponding one by the same linkage. This is indicated by the fact that the v separations remain intact, and although the supposition that the Y l , Y 2 , Y 3 lines may have different links, the same for each, is not excluded, such a special accommodation is scarcely probable. It follows that the observed y = 793-26 is the normal value due to displacement between Y l and Y 2 , and that y 2 = 458-49 and 329-59 correspond to direct displacements on the normal L% 3 . As a fact the spectrum on examina- tion shows unmistakable signs of such linked, as well as displaced, incomplete systems. It will be sufficient here to consider one of them. The e link in Ba is 3600-07. At almost exactly this distance behind the observed set occurs a distorted set whose wave numbers are abs. (In) 18496-53 878-22 (2^)18264-13 314-46 (1+) 18578-59 796-16 (4^)19374-75 364-06 (Inn) 18942-65 The 18496 is 3605-34 or e + 5-3 behind 22101-87, the observed L u . The xnm displacement on the S l limit shifts by 4-95 and would almost account for the 224 ANALYSIS OF SPECTRA [OH. extra 5-3, but such an explanation is excluded here, since the v l of the two Z u , L 2 i are both the same. The more probable explanation is that e depends on the "true" A x which gives e = 3604-82. If 18496 be treated as the normal L n and the real separations as the 793-26, 452, 329 of the observed, the denominators of the Y are y l 3-308768 7 2 3-185071 123697 180f = 123717-7 13- 120441 -138O 64630 945= 64682-4 3 (3-137605-140-8^ 47466 69J5= 47399-4 If the second reading for y l 793-32 be taken, the first difference is 123707 and agrees with an oun multiple within errors. Moreover the multiple is now comparable with those of Ca, Sr, viz. 220|, 154|-, 180|. The other two, however, are not multiples nor is their difference. The first result sustains the hypothesis that 18496 is normal and that the Y 19 Y 2 sequents are as given. The second shows that the two Y 3 are neither single displacements on Y 2 , nor from one another. We must therefore expect double displacements with different* dis- placements for p 2 in each. The oun displacement on the p limits shifts them respectively by 4-983, 5-207, 5-241, on Y 19 Y 2 by 1-0357, 1-1617 and on the two collateral L 23 by 1-224, 1-235. Here the p 2 limit is in question. If this is displaced 28j for the first L^ and 8 X for the second, their mantissae are respectively diminished by 2 x 5-207 x 138-01 = 1437 and increased by 5-207 x 140-81 = 733. The mantissae differences from that of Y 2 are now 66067 = 96|8 +16 and 46733 = 68J8 + 18 with a mutual difference of 19334 = 28JS - 2. These are exact multiples within our limits since 16 corresponds to dX = -02 between two lines')*. There is nothing, however, to show what the normal Y 3 should be. The observed y 2 separations are, however, now 452-49 + 10-41 = 462-90 and 329-59 5-21 = 324-38. Judging from the Ca, Sr we should expect a normal y 2 about 793/1-91 or 415. The two collaterals would then be and (Si) 33 (143 + a^). e, where Z 23 is the normal, a? is a small integer and normal Y 3 = Y 2 ( 82J8 + zSj). Returning now to the supposed disrupted set, L n , L 2l have been taken as normal on account of their exact v . There is no representative of L 12 and the others show abnormal separations. The 18578 is 796-16 instead of 793-26 behind L 12 . One oun on the limit and two on the sequent shift 5-207 2-323 = 2-88 and produce the separation 793-26 + 2-88 = 796-14, or the observed. This line is therefore (8 X ) L 22 (28^. The line 18942 is 364-06 ahead of this. If the displacements on the limits were the same 8 X , the separation should be 370-56 -03 = 370-53. An extra oun on the limit and one less on the sequent shifts 5-241 + 1-161 = 6-40, and produces a separation 370-53 - 6-40 = 364-13 which agrees with the 364-06. The line is therefore (28^ Z 23 (8j). The denominators of 18264, 18578 calculated from S 1 (oo ) - 28514-8 differ by 45315 6-20f . But if the limits in both take the 8 X displacement it is necessary * Else the mutual mantissa difference would be an oun multiple. f If the error occurs on the L 22 alone, Y 2 is 16 less and all the differences are exact including now the Y^ - 7 2 with 123713. xi] MISCELLANEOUS 225 to put = 5-207 and the mantissa difference is now 45347, whilst 66 JS = 45346-5. It is thus (8J L 22 (28! - 66J8) = (8J L 22 (- 65f S), or, using the normal value of F 3 expressed as above, the line is (8-^ 23 (16JS + x8 ). Additional fragments of the normal set are also indicated by the existence of near displaced lines. Thus the next lines to 18942 have wave numbers (Inn) 18935-50 separated by - 7-15 and (4n) 18980-74 by 38-09. They belong to the Y 2 sequent where the oun shift is 1-1617. Thus 6S X gives 6-97 and 338 X gives 38-33, or the mutual shift of 45-24 is due to 39S X or 45-30, much closer and again suggesting the unknown modification (? close multiple lines) found in Sr A, and RaA. So also a line (Inn) 18457-51 at- .39-02 from L u where 38 x 1-0357 = 39-36, may be L n ( 388^. All that can be said at present of the preceding arrange- ment of 18496 as the true L u is that it forms a consistent scheme, in step with the normal sets in Ca, Sr, and is consonant with what is known as to link and collateral relations. 8. The discussion of the data shows clearly that in the L category we are dealing with a real sequence. The fact that only 'two orders have been found suggests that these, as well as A, B, are really combinations of the already known persistent types, but no relation to any of the triplet or singlet sequences is apparent, the mantissae showing no approximation to any of them. It is re- markable, however, that they seem to be close to the enhanced doublet mantissae of s" (m). This is shown especially in the Y 3 of Ca. The connection is shown by the following numbers for Ca, Sr : Ca s" Sr s" F 3 , 3-174072 3-174392 7 lf 3-270291 3-267068 Tj, 4-186050 4-186882 Y lt 4-283467 4-286616 In Ba, s" (3) has 3-387476 44-3 with f a possible large value but the mantissa must be correct to at least -38, and s" (4) = 4-409. With this we have no estab- lished Y to compare. There is only the value 4-138 calculated from the observed set as a pure difference line which has been seen to be very doubtful, or the 3-3087 determined from an unestablished, if probable, hypothesis. The numerical agreement is striking, but it is impossible to accept an actual connection, for the two systems, triplet p and doublet s, arise from independent sources the atom and the atom with one electron absent. Moreover, here Rydberg's constant is N whilst in the s" it is 42V. The analogy is, however, so close that we are justified in suspecting that the Y sequence depends on some configuration in the atom which is closely similar to that which, in the positive atomion, gives the enhanced doublets. This would also explain the source of the B sequence as arising from the corresponding configuration giving the d" sequence. That these roughly run parallel may be seen from the following comparison : *i <*T Ca 3-318 2-313, 3-360 Sr 3-572 3-517 Ba 2-612 3-569 H. A. s. 15 226 ANALYSIS OF SPECTRA [OH. The first S, D lines in Group III. 9. We conclude with some remarks on the question of the first lines in the S, D series in Al, In, Tl. The matter is of special importance in the case of the D lines, since the hitherto accepted first lines, depending on m = 2, form practi- cally the only outstanding exception to the law that the denominators of the extreme satellites are very close to multiples of A. Any S (1) lines must lie far in the ultra-violet with negative wave numbers, that is, they must be the first lines of a new P series parallel to that already recognised. In fact the latter will be P (2. m) and the new P (I. m). It is not possible, however, to deduce any close estimate of their position as the formulae of the s-sequence are in general not suitable for extrapolation and especially where, as here, they are based on the assumption //, = 1 + fraction. The run of the mantissae shows* that Al P (1) should be in the neighbourhood of 1750 and TIP (I) of 2000. In recent years a considerable amount of material from the far ultra-violet has been placed at disposal by several investigatorsf. It shows evidence of considerable displacement and linkage effects which, in the absence of any close a priori indications, render a definite allocation a matter of some difficulty. An application of the theory of linkages, however, enables us to obtain independent support for the allocations suggested in the tables. The u, v links depend on the first s-sequent, and can be calculated when this is known. The suggested lines give the corresponding 5(1) and it is found that the u, v links calculated from them occur in considerable numbers and in association with the e and other p links. At least this is the case in In, Tl. In Al the links are small and the linkage effect is not prominent, but in this element displacement, especially in the ^-sequence, is marked. 10. Al. If Handke's measures be employed, we find strong lines at AA 1722-0, 1725-3 K.A., nn = 58072-0, 57960-9, giving a separation 111-1, within observation errors of v = 112-04. Treated as the S (1) set they give s (1) = 106238-16. Its denominator is 1-016067, which runs plausibly with the 2-187, 3-219 for m = 2, 3. The u, v links found from it are practically equal and about 366. Unfortunately we cannot test it as the S, D lines in the visible and violet regions do not show a single linkage. But in connection with these two lines a curious phenomenon occurs. Lyman measures what at first sight would appear to be the same lines, but his results differ from those of Handke by amounts greater than their observation errors. At the same time he finds lines which show a remarkable regularity, indicating that the whole are definitely related. Their wave numbers followf, with separations from succeeding lines : - (8)56574, 61 (-375)S 2 . 3e - (8)56635,60 ( -675) # t . 3e = ( -5) S 2 . 3e (-105) # 8 -(10)57971-0,123 -(10)56695,62 (-315)^. 3e Si - (9)58099-0, 64 - (8)56757,61 (55) ^.36 (385) tfj - (9)58163, 34 3 (e -166) - (8)56818 (415)^.36 (585) S x - (1)58197 2e - (1)57297 (585)^.26 * [H. p. 55]. f Handke, Diss. Halle (1907). Lyman, Spectroscopy of the Ultra-violet, which also contains Handke's results. Saunders, Astro. J. 43, 240 (1916). Bloch, C.R. 171, 909 (1920). McLennan, Young, and Ireton, Proc. Eoy. Soc. 98 A, 95 (1920). J The wave lengths are 1725-0, 1721-2, 1719-3, 1718-3 and 1767-6, 1765-7, 1763-8, 1761-9, 1760-0. xi] MISCELLANEOUS 227 The separations on the right (61 ) are all equal, due to the same wave length difference of 1-9 A. In Al the e link is 449-99, while the S displacement on Pi(l) produces a shift of 1-693, practically the same for p 2 (1), and on s (1) one of 5-61. A = 668. It is clear at once that the separations do not depend on dis- placements in s (1). The line 58099 is the representative of Handke's 58072-0, which we have taken as /S^ (1). It is algebraically smaller by 27-0. Now 168 on p (1) shifts it by 16 x 1-693 = 27-08 so that 58099 is - (168) S l (I) or P x (1) (168). The separations in the set are met by the following displacements: 768 - 128-67, 388 = 64-33, 208 = 33-86, 368 = 60-95. The linkage 3 (e - 1-66) indicates that at each addition of e a displacement of 8 takes place in the p l . If 58099 be denoted as S l (I), the lines are as represented by the formulae entered above. If Handke's reading be taken as the true S l , 168 must be added to the designations in these formulae. The important point for the present purpose is that the separations forming a related system are all numerically met by displacements on a p l sequent, and consequently that this p 1 sequent enters in the constitution of the lines as it should, if they are connected to S (1) lines. The prevalence of displacement in the p (1) sequence is also shown in certain sets which are membra disjecta of the combinations p (1) p l (2), Pi (1) - Pi (*). 11. In. Amongst the observed ultra-violet lines of In occur two doublets with wave numbers 46372-3 2212-3 44160-0 57187-00 2253-42 54933-58 The first set give the normals, the second an enlarged v as in the case of Lyman's measures for Al$ (1). Treated as S (1), the values of s (I) are respectively 90862-57 = N/(l-098654) 2 and 101641-76 - 2V/(1-036376) 2 . Either denominator might run with those of the next two orders 2-218, 3-252. The choice, however, is settled in favour of the second set by the link test. The u, v links calculated from it are u = 6570-64, v = 8321-37. The e link is 9222-61. These are found in considerable numbers. A few instances will suffice. (a) D 2 (4), X (SB) 2389-64 (8) 2983-01 (2) 3710-45 (8) 5644 n, 41834-88 8321-24 33513-64 6570-21 26943-43 9230 17713 (ft) ^(2), X (10i2) 4511-44 (1)3186-92 2462-5 n, 22159-78 e-13-0 31369-40 e + 5-2 40597-1* u+4-1 24794-7; X= 4032-0 (c) S t (3), 71 = 34088-40 v+4-2 42414*; \ = (QB) 2932-71, 2357-0 S 2 (3), n = 36300-80 u-6-3 42865*; X = (QB) 2753-97, 2332-2 (d) ^(4), w = 38423-12 v + 18-1 46762-6*; \ = (QB) 2601-84, 2137-8 * These lines are by Hartley and Adeney with possible errors dn = 2 or 3. The 8 displacement on p l (1) shifts 27-003 and on p 2 (1), 29-045. The separation of the two lines is v + 30-8, which is equivalent to a 8 on p 2 (dX = -04 between two lines and well within error limits). The second line 54933 is therefore - ( - 8) S 2 (1) and the first - S l (1). In (a), 9230 is e + 7-4. As the linkage depends on D 2 (4) the first sequent here is p 2 (1) where the oun, or 8/4, produces 7-26. The u t v links are exact. The set is therefore D 2 (4), v. D 2 (4), u. v. D 2 -(4), e. u. v. (8 X ) D 2 (4). 228 ANALYSIS OF SPECTKA [CH. In (6), two ouns on p l produce 13-50. The oun on s (2) produces 2-397. The set are then ^ (2) ^ S (2). e (8J S (2). 2e M. #! (2) ( - 78J. e = ...94-97 In (c), 8 on 5 (3) shifts 3-044. The sets are S l (3), S x (3) (3). v = ... 12-8 and S 2 (3), > (3) ( - 23). u = ... 65-35. In (d), the set is S (4), ( - 3S X ) ^ (4). t? = ... 64-72. These cases are sufficient to show that the u, v links exist and consequently that the S (I) lines are correctly allocated. 12. Tl. In Tl is found the set nn = 54406-33, 46616-57 which have a separa- tion 7789-76 = v 2-64, or the normal doublet value within the two observation errors, especially when allowance is made for the lines having been measured by different observers Saunders and Eder and Valenta. It is in due order with the sets allocated to Al, In and gives s (1) = 95876-56 = ^/(1-069541) 2 , with a denominator in step with 2-194, 3-229 for the next two orders. There is also a set 45237-95, 37443-63 (similarly by Saunders, Eder and Valenta) with separation 7794-32 =v + 1-92 and again normal within observation errors, but it gives for s (1) a denominator 1-124 with a mantissa closer to that of m = 2 than should be expected. But the question is settled definitely in favour of the first by the presence of u, v links. The values for the two sets are, in Rowland units: u 20180-11 17296-33 v 29473-38 25077-7 whilst e = 37841-34. These links being so large, stretching from one end of the spectrum to the other, it would not be surprising if few or no examples were found. As a fact, however, those of the first set appear in considerable numbers and none have been noted for the other. The following cases may be given in illustration, out of many others. 29471-1 66350-4 =D 12 (4). v X = (l) 1507-1, I.A., Bloch. 37503-04 20180 17323 =u. 8^ (4) X=5771, Huggins. 38663-20 20194 18469 =u. S t (5) or u. (5j) S (5) X=5412, Thalen. 39860-17 20179-27 19680-90 = u. /S x (7) \ = (5) 5079-68, Eder and Valenta. X = < 2 > 1837-4, z.A.Bloch. The first, second, and fourth give exact v, u links. The third is from a line measured by Thalen and has been reduced on the supposition that his scale was based on Angstrom's value of the D line, but the uncertainties are great. A displacement of 8 on p 1 shifts 76-83 or 19-2 per oun, so that if Thalen's measure is not very largely wrong, it would be u. (8J S 1 (5). On d (3) a displacement of S produces a shift of 5-579. In the fifth example neither 9-6 nor 27-9 can be pro- duced by displacements on p l alone. But 53 on d (3) shifts 27-90, or If 8 by 9-77, so that the second line 54425-6 is D 12 (3) (53). u or D n (3) ( - 78J. u, since D 12 (3) = _D n (3) ( 6|-8). The number of exact u links without displacement is noticeable. There are also a large number of cases of v and other links involving simultaneous displacements in the sequences. xi] MISCELLANEOUS 229 The new P (1) line would indicate a radiation potential of 6-71 volts and an ionisation of 11-83 volts. Those given in Chap. V are 1-07 and 7-3. It would raise the suspicion that about -8 volts were required for dissociation of T1 2 , that weak radiation could be excited at slightly higher potentials (> 1-07), that the observed ionisation might really be a strong radiation, viz. 6*71 + -8 = 7-5, and that the true ionisation, say 11-83 + -8 = 12-6, was not reached. We cannot but regard the correspondence of 1-07 with P (2. 2), as being a mere coincidence. 1 3. Incidentally the existence of the v links in In, Tl illustrates an important point in general theory. Take for example Tl. The value of s (I) as given above is N/(l-069541), whilst A 134153. Hence v = ^7(1-069541 - -134153) 2 - #/( 1-069541 ) 2 We have therefore here to deal with a case of an apparent sequent denominator less than unity, and the same occurs in In with a denominator -998689. These are the only instances so far known, but we have no evidence that the (A) s (I) is a real sequent and it is difficult to believe that it can serve as such. 14. The D series in the two sub-groups in each of groups I, II are contrasted by the fact that the first order in one depends on m = I and in the other on m = 2. In group III the Sc sub-group has not yet been investigated, but Al shows indications that spectrally it does not belong closely to the Ga sub-group. As Al D has a first order with m = 2, we should expect to find that in Ga, In, Tl there exist first orders with m = 1. The fact that no F series depending on d (2) two sets 3, 4 in Tl excepted occur in these spectra certainly points to the conclusion that D (2) are not the first lines. Also now that we have learnt to expect that the first d 2 satellite has a mantissa which is extremely close to a multiple of A and that in these elements this is definitely not the case with the d (2) sequents, we are led to suspect the existence of d (I). Of the three elements belonging to this group any D (1) lines must be in the red or near ultra- red regions which have not been very closely examined, nor indeed, the metals being so rare, have their complete spectra, especially the arc, been investigated with the same detail as those of other elements. Nevertheless there are indica- tions, in single lines, that such D (1) lines may exist, as well as corresponding F series. At the same time, as spectral relations become more complicated in the higher groups of elements, new effects may not be unexpected. As an in- stance of this may be noted the presence both in In and Tl of numerous examples of separations of the same order of magnitude as those occurring in the suggested D (I) satellites and at the same time successive separations equal to the half of the foregoing. This effect and that of possible F satellites, the probable instability of the / sequence, and the repetition of the same separations in the spectra caused by links, render any definite conclusion very difficult. These spectra should well repay a more thorough analysis than has yet been attempted. Here it will be sufficient to indicate the evidence in favour of the D (I) allocations suggested in Table III. 230 ANALYSIS OE SPECTRA [OH. In In the longest wave lengths observed by Eder and Valenta and by Clayden and Heycock are (7) 6891-61, (8) 6197-98, (7) 6097-26. They are in a region where any D (1) lines should lie. If they be treated as D n and two Z) 22 lines, with the D 12 further up in the unobserved ultra-red, their wave numbers may be repre- sented as follows : [13917-30] 2212-61 16129-91 589-16 [14183-74] 2212-61 16396-35 322-72 14506-46 the 589 being taken from 14506 as Z) n . ^(00) = 44454-76. Treated as such and allowing observation errors of about -1 A. or dn = -3, the denominators, with their mantissae differences from that of Z> n , are : 1-895123(10) -31-03^ 18549(20) 395 =18605-18 1-903440(10) -31-44^ 10232(20) 21 5 = 10256-7 1-913672(10) -31-95^ The difference 10232 may be an oun multiple within error limits, but the other is definitely not. We find, however, so many examples of the double separations 294 to 281, about half of 589, that this 16129 set would seem to be related to normal D lines. Many instances of limit displacements in D series are known. If in this case the limit, p (1), has been displaced by two ouns, the limit used in calculating the denominator should be 13-50 less, which increases its mantissa by 419 and the mantissa difference is thereby decreased to 18130. Since 388 = 18127-9 the satellite condition is now satisfied very closely and the true satellite separation is 589-1613-50=575-66. We have then a D n (I) = 14506, a satellite set with a = 322-72 and a displaced set with a = 575-66. ^ D & ( - 388) or (28,) D 12 (D ( - 1618) Further, the mantissa of d 2 (1) is 903440 *= 23- 972 A or very close to the multiple 24A. Apparently the F separations are about one-half of 575 or 281 to 294, corresponding to a displacement on d l (1) of a few ouns on either side of 198. The satellite mantissa would then be within an oun or two of 904633 = 24-0035A, and a = 284-75. This would correspond to the multiple 24A with the slight positive addition required by the , ' conditions of Chap. IX. The second d condition that the mantissae of two successive orders should be an oun multiple is also satisfied. It is (see Table V for d (2)) 89683 == 2A + 303 - 3. As compared with In the TID are noticeable for their much smaller oun satellite separations, being 78 in Tl against 258 in In. As the oun in Tl is rather larger than three times that of In, we should expect actual values of a about the same in both. As a fact this is so, and we find successive double separations of about 290. The suggested value is A = (5) 4982-40 (Eder and Valenta) or n = 20065-17 for Z) 22 (1). This requires a weaker line at n = 12272-77 in the ultra- red for D 12 . D(oo ) = 41470-23. The mantissa of the d 2 (l) is 938123 - 6-9929A and therefore close to 7 A. It is also greater than that of d 2 (2) by 49779 = 338 + 33, or an oun multiple within easy values of and observation errors. Thus the two xi] MISCELLANEOUS 231 conditions for d sequences are satisfied but there is nothing to indicate the CT, or the position of D n . Sounding for the 12272 two observed linked lines are found and with them other lines suggesting the satellite separations. They are [12272-77] 294,73-21 41745-98; 37844-8 50117-6 524-29 579-4 42270-27 50697-0 [wave lengths (3) 2394-72, (3) 2365-00 (Eder and Valenta) and (2) 1994-6, (3) 1971-8 (Takamine)]. These are practically exact v, e links, leading to lines associated with separa- tions 524 and 579, of the same order of magnitude as in In, and thus in conson- ance with the considerations given above. The 579-4 corresponds to a mantissa difference of 19523 =138 71. If the latter be made an exact 138 the separation becomes 2-15 larger or equal to 581-5, with d\ = -08 between the two lines and within error limits of 501 17 alone. If dX is wholly on this, the link becomes e + 1-3. Again, the other separation of 524-29 (small errors) is 57-2 less. The oun shift on p l (1) is 19-219, so that 42270-27 is (38 X ) Z> n (1). v. Assuming then that the 581-5 is the true satellite separation. D n (1) = [12854-27]. Again sounding for this there is found a line at n = 33051-84, 20197-5 or u + 17-4 ahead. The shift 17-4 cannot be due to displacements on d (oun shift = 11-35), but may be 19-2 or one oun on the limit p (1) ; so that the two lines linked to it are (38 X ) Z) u (1). v and (8 X ) D n (1). u. The conclusion is that [12272-77] 7792-40 20065-17 581-5 [12854-27] is the required D (1) set. The curious repetition of the same d separation is indicated also in the Dj, (2) set in In. Thus there are found D u (2) D 12 (2) 30702-25 23-45 30678-80 23-89 30654-91. APPENDIX TABLES OF DATA 234 ANALYSIS OF SPECTRA TABLE I Corrections to be added to wave length in air to reduce to vacuum. NOTE. The columns Ms. Ps. ; K. R. ; K. R. contain the corrections as determined respectively by Meggers and Peters and by Kayser and Runge on the international scale and by K. and R. on Rowland's scale. X Ms. Ps. K.R. K. R. Diff. X Ms. Ps. K.R. K.R. Diff. ' 10000 2-7391 2-744 8000 2-1972 2-201 2-164 0272 0270 9900 2-7119 2-717 7900 2-1702 2-174 2-138 0271 0271 9800 2-0848 2-090 7800 2-1431 2-147 2-111 0271 0270 9700 2-6577 2-063 7700 2-1161 2-120 2-085 0271 0270 9000 2-6300 2-636 7600 2-0891 2-093 2-058 0271 0271 9500 2-0035 2-608 7500 2-0620 2-066 2-030 0272 0270 9400 2-5763 2-581 7400 2-0350 2-039 2-005 0271 0270 9300 2-5492 2-554 7300 2-0080 2-012 1-978 0271 0270 9200 2-5221 2-527 7200 1-9811 1-985 1-951 0271 0270 9100 2-4950 2-499 7100 1-9541 1-958 1-925 0271 0270 9000 2-4679 2-472 7000 1-9271 1-931 1-898 0271 0270 8900 2-4408 2-445 6900 1-9001 1-904 1-872 0271 0269 8800 2-4137 2-418 6800 1-8732 1-877 1-846 0270 0270 8700 2-3867 2-391 6700 1-8462 1-850 1-819 0271 0270 8000 2-3596 2-364 6600 1-8193 1-823 1-793 0271 0269 8500 2-3325 2-337 6500 1-7924 1-796 1-766 0271 0269 8400 2-3054 2-310 6400 1-7655 1-769 1-740 0270 0269 8300 2-2784 2-283 6300 1-7386 1-742 1-713 0271 0269 8200 2-2513 2-256 6200 1-7117 1-715 1-686 0270 0269 8100 2-2243 2-228 6100 1-6848 1-688 1-660 0271 0268 8000 2-1972 2-201 2-164 6000 1-6580 1-661 1-634 0270 0269 APPENDIX 235 TABLE 1 (contd.) Corrections to be added to wave length in air to reduce to vacuum. NOTE. The columns Ms. Ps. ; K. R.; K. R. contain the corrections as determined respectively by Meggers and Peters and by Kayser and Runge on the international scale and by K. and R. on Rowland's scale. X Ms. Ps. K. R. K.R. Diff. X Ms. Ps. K.R. K. R. Diff. 6000 1-6580 1-661 1-634 4000 1-1268 1-128 1-109 0269 0260 5900 1-6311 1-634 1-607 3900 1-1008 1-102 1-084 0268 0259 5800 1-6043 1-607 1-581 3800 1-0749 1-076 1-058 0268 0259 5700 1-5775 1-580 1-554 3700 1-0490 1-050 1-032 0267 0257 5600 1-5508 1-554 1-527 3600 1-0233 1-024 1-007 0268 0256 5500 1-5240 1-527 1-501 3500 0-9977 0-999 0-982 0267 0255 5400 1-4973 1-500 1-475 3400 0-9722 0-973 0-956 0267 0253 5300 1-4706 1-473 1-448 3300 0-9469 0-948 0-932 0267 0252 5200 1-4439 1-447 1-422 3200 0-9217 0-922 0-907 0266 0249 5100 1-4173 1-420 1-396 3100 0-8968 0-897 0-882 0267 0247 5000 1-3906 1-393 1-370 3000 0-8721 0-872 0-857 0266 0245 4900 1-3640 1-366 1-343 2900 0-8476 0-847 0-833 0265 0241 4800 1-3375 1-340 1-318 2800 0-8235 0-823 0-809 0265 0238 4700 1-3110 1-313 1-291 2700 0-7997 0-799 0-786 -0265 0233 4600 1-2845 1-287 " 1-266 2600 0-7764 0-775 0-762 0264 0229 4500 1-2581 1-260 1-239 2500 0-7535 0-752 0-739 0264 0222 4400 1-2317 1-234 1-212 2400 0-7313 0-729 0-717 0263 0216 4300 1-2054 1-207 1-186 2300 0-7097 0-707 0-695 0262 0206 4200 1-1792 1-181 1-160 2200 0-6891 0-686 0-675 0262 0196 4100 1-1530 1-155 1-136 2100 0-6695 0-665 0-654 0262 0183 4000 1-1268 1-128 1-109 2000 0-6512 0-646 0-635 0260 236 ANALYSIS OF SPECTRA TABLE II Values of the function 109721-6/(w + ft) 2 f r &J1 values of m from m = 1 to 9 and of fj, from p = 0-00 to 1-00, with their differences from m to m+ 1. M 1 ATI 2 Aw 3 An 4 Aw 5 M 0-00 109721-6 822912 27430-4 152391 12191-3 53337 6857-6 24687 4388-9 0-00 01 107559-7 80401-6 27158-1 15047-7 12110-4 5287-0 6823-4 24520 4371-4 01 02 105461-0 78571-1 26889-9 148595 12030-4 52409 6789-5 24355 4354-0 02 03 103423-1 76797-5 26625-6 14674-5 11951-1 51952 6755-9 24192 4336-7 03 04 101443-8 750786 26365-2 144926 11872-6 51501 6722-5 24030 4319-5 04 05 99520-7 73412-0 26108-7 14313-8 11794-9 5105-6 6689-3 23869 4302-4 05 06 97651-8 71796-0 25855-8 141379 11717-9 5061 5 6656-4 2371-0 4285-4 06 07 95835-1 70228-1 25607-0 139653 11641-7 50180 6623-7 23552 4268-5 07 08 94068-6 68707-7 25360-9 13794-7 11566-2 4974-9 6591-3 23396 4251-7 08 09 92350-5 67231-7 25118-8 136273 11491-5 49324 6559-1 2324-1 4235-0 09 10 90679-0 657988 24880-2 134628 11417-4 48902 6527-2 23088 4218-4 10 11 89052-5 644076 24644-9 133008 11344-1 4848-7 6495-4 22935 4201-9 11 12 87469-4 63056-4 24413-0 13141-5 11271-5 48076 6463-9 2278-4 4185-5 12 13 85928-1 61743-8 24184-3 12984-7 11199-6 47669 6432-7 22635 4169-2 13 14 84427-2 60468-4 23958-8 128304 11128-4 47268 6401-6 22486 4153-0 14 15 82965-3 592289 23736-4 126785 11057-9 4678-1 '6370-8 22339 4136-9 15 16 81541-0 580239 23517-1 125291 10988-0 4647-8 6340-2 2219-3 4120-9 16 17 80153-1 568522 23300-9 123821 10918-8 46089 6309-9 22049 4105-0 17 18 78800-4 557128 23087-6 122374 10850-2 45705 6279-7 21906 4089-1 18 19 77481-5 546042 22877-3 120950 10782-3 45325 6249-8 21764 4073-4 19 20 76195-6 535259 22669-7 119547 10715-0 44950 6*20-0 21622 4057-8 20 21 74941-3 524762 22465-1 118168 10648-3 4457-8 6190-5 21483 4042-2 21 22 73717-8 51454-7 22263-1 116808 10582-3 4421 1 6161-2 21345 4026-7 22 23 72524-0 504601 22063-9 115470 10516-9 4384-8 6132-1 21208 4011-3 23 24 71359-0 49491-7 21867-3 11415-2 10452-1 43489 6103-2 21072 3996-0 24 25 70221-8 485484 21673-4 112856 10387-8 43132 6074-6 20938 3980-8 25 26 69111-6 476296 21482-0 11157-8 10324-2 4278-1 6046-1 20804 3965-7 26 27 68027-5 46734-3 21293-2 110320 10261-2 42434 6017-8 20671 3950-7 27 28 66968-8 45862-0 21106-8 109081 10198-7 42090 5989-7 20540 3935-7 28 29 65934-5 45011 6 20922-9 10786-1 10136-8 41750 5961-8 20409 3920-9 29 30 64924-0 44182-7 20741-3 106659 10075-4 4141-3 5934-1 20280 3906-1 30 31 63936-6 43374-5 20562-1 10547-4 10014-7 41081 5906-6 20152 3891-4 31 32 62971-5 425862 20385-3 104309 9954-4 40751 5879-3 20026 3876-7 32 33 62028-2 41817-5 20210-7 10316-0 9894-7 40425 5852-2 19900 3862-2 33 34 61105-8 410675 20038-3 102027 9835-6 40104 5825-2 19774 3847-8 34 35 60203-9 40335-8 19868-1 100912 9776-9 39784 5798-5 1965-1 3833-4 35 36 59321-8 39621-7 19700-1 9981 3 9718-8 3946-9 5771-9 19528 3819-1 36 37 58459-0 38924-8 19534-2 9873-0 9661-2 39157 5745-5 19406 3804-9 37 38 57614-8 38244-4 19370-4 97663 9604-1 3884-8 5719-3 19285 3790-8 38 39 56788-8 37580-2 19208-6 9661-0 9547-6 3854-3 5693-3 19166 3776-7 39 40 55980-4 36931-5 19048-9 9557-4 9491-5 3824-1 5667-4 19047 3762-7 40 41 55189-2 36298-1 18891-1 9455-2 9435-9 37941 5641-8 18930 3748-8 41 42 54414-6 35679-3 18735-3 93546 9380-7 3764-4 5616-3 1881-3 3735-0 42 43 53656-2 350747 18581-5 92553 9326-2 3735-3 5590-9 18696 3721-3 43 44 52913-6 344841 18429-5 9157-5 9272-0 37062 5565-8 18582 3707-6 44 45 52186-3 33907-0 18279-3 90609 9218-4 3677-6 5540-8 1846-8 3694-0 45 46 51473-8 33342-8 18131-0 8965-8 9165-2 36492 5516-0 1835-5 3680-5 46 47 50775-9 32791-4 17984-5 8872-1 9112-4 3621-1 5491-3 1824-2 3667-1 47 48 50092-0 322522 17839-8 8779-7 9060-1 3593-3 5466-8 1813-1 3653-7 48 49 49421-2 31724-5 17696-7 8688-4 9008-3 3565-8 5442-5 1802-1 3640-4 49 50 48765-2 31209-7 17555-5 8598-6 8956-9 3538-5 5418-4 1791-2 3627-2 50 APPENDIX 237 TABLE II (contd.) Values of the function 109721-6/(w + /x) 2 for all values of m from m = 1 to 9 and of [L from /JL = 0-00 to 1-00, with their differences from m to m + 1. M 5 Aw 6 Aw 7 Aw 8 Aw 9 V- 0-00 4388-9 1341-1 3047-8 808-6 2239-2 524-8 1714-4 359-8 1354-6 0-00 -01 4371-4 1333-7 3037-7 804-9 2232-8 5227 1710-1 358-5 1351-6 01 02 4354-0 1326-4 3027-6 801-1 2226-5 520-6 1705-9 357-3 1348-6 02 03 4336-7 1319-1 3017-6 797-5 2220-1 518-5 1701-6 356-0 1345-6 03 04 4319-5 13119 3007-6 793-8 2213-8 516-4 1697-4 354-8 1342-6 04 05 4302-4 13047 2997-7 790-1 2207-6 514-4 1693-2 3535 1339-7 05 06 4285-4 12976 2987-8 786-5 2201-3 512-3 1689-0 352-3 1336-7 06 07 4268-5 1290-6 2977-9 782-8 2195-1 510-3 1684-8 351-0 1333-8 07 08 4251-7 1283-6 2968-1 779-2 2188-9 508-3 1680-6 349-8 1330-8 08 09 4235-0 12766 2958-4 775-7 2182-7 5062 1676-5 348-6 1327-9 09 10 4218-4 1269-7 2948-7 7721 2176-6 504-3 1672-3 347-3 1325-0 10 11 4201-9 1262-8 2939-1 768-6 2170-5 502-3 1668-2 346-1 1322-1 11 12 4185-5 1256-0 2929-5 765-1 2164-4 500-3 1664-1 344-9 1319-2 12 13 4169-2 12493 2919-9 761-6 2158-3 498-3 1660-0 343-7 1316-3 13 14 4153-0 12426 2910-4 758-1 2152-3 496-4 1655-9 342-5 1313-4 14 15 4136-9 12359 2901-0 754-8 2146-2 494-3 1651-9 341-4 1310-5 15 16 4120-9 12293 2891-6 751 3 2140-3 492-5 1647-8 340-1 1307-7 16 17 4105-0 . 1222-8 2882-2 747-9 2134-3 4905 1643-8 339-0 1304-8 17 18 4089-1 12162 2872-9 744-5 2128-4 488-6 1639-8 337-8 1302-0 18 19 4073-4 1209-8 2863-6 741-2 2122-4 486-6 1635-8 3366 1299-2 19 20 4057-8 1203-4 2854-4 737-9 2116-5 484-7 1631-8 335-5 1296-3 20 21 4042-2 1197-0 2845-2 734-5 2110-7 482-9 1627-8 334-3 1293-5 21 22 4026-7 1190-7 2836-0 731-2 2104-8 480-9 1623-9 333-2 1290-7 22 23 4011-3 1184-4 2826-9 727-9 2099-0 479-1 1619-9 332-0 1287-9 23 24 3996-0 1178-1 2817-9 724-7 2093-2 477-2 1616-0 330-9 1285-1 24 25 3980-8 1171-9 2808-9 721-4 2087-5 475-4 1612-1 329-7 1282-4 25 26 3965-7 1165-8 2799-9 718-2 2081-7 473-5 1608-2 328-6 1279-6 26 27 3950-7 1159-7 2791-0 715-0 2076-0 471-7 1604-3 327-5 1276-8 27 28 3935-7 1153-6 2782-1 711-8 2070-3 469-9 1600-4 326-3 1274-1 28 29 3920-9 1147-6 2773-3 708-7 2064-6 468-0 1596-6 325-3 1271-3 29 30 3906-1 1141-6 2764-5 705-5 2059-0 466-3 1592-7 324-1 1268-6 30 31 3891-4 1135-7 2755-7 7024 2053-3 464-4 1588-9 323-0 1265-9 31 32 3876-7 1129-7 2747-0 699-3 2047-7 462-6 1585-1 321-9 1263-2 32 33 3862-2 1123-9 2738-3 6962 2042-1 460-8 1581-3 320-8 1260-5 33 34 3847-8 1118-1 2729-7 693-1 2036-6 459-1 1577-5 319-7 1257-8 34 35 3833-4 1112-3 2721-1 690-1 2031-0 457-3 1573-7 318-6 1255-1 35 36 3819-1 1106-5 2712-6 687-1 2025-5 455-6 1569-9 317-5 1252-4 36 37 3804-9 1100-9 2704-0 684-0 2020-0 4538 1566-2 316-5 1249-7 37 38 3790-8 1095-2 2695-6 681-0 2014-6 4522 1562-4 315-3 1247-1 38 39 3776-7 1089-6 2687-1 678-0 2009-1 450-4 1558-7 314-3 1244-4 39 40 3762-7 1083-9 2678-8 675-1 2003-7 448-7 1555-0 313-2 1241-8 40 41 3748-8 1078-4 2670-4 672-1 1998-3 447-0 1551-3 312-2 1239-1 41 42 3735-0 1072-9 2662-1 669-2 1992-9 445-3 1547-6 311-1 1236-5 42 43 3721-3 1067-5 2653-8 666-3 1987-5 443-5 1544-0 310-1 1233-9 43 44 3707-6 1062-0 2645-6 663-4 1982-2 441-9 1540-3 309-0 1231-3 44 45 3694-0 1056-6 2637-4 660-5 1976-9 440-2 1536-7 308-0 1228-7 45 46 3680-5 1051-3 2629-2 657-6 1971-6 438-6 1533-0 306-9 1226-1 46 47 3667-1 1046-0 2621-1 654-8 1966-3 436-9 1529-4 305-9 1223-5 47 48 3653-7 1040-7 2613-0 651-9 1961-1 435-3 1525-8 304-9 1220-9 48 49 3640-4 1035-4 2605-0 649-2 1955-8 433-6 1522-2 3039 1218-3 49 50 3627-2 1030-2 2597-0 646-4 1950-6 432-0 1518-6 302-8 1215-8 50 238 ANALYSIS OF SPECTRA TABLE II (contd.) Values of the function 109721-6/(w + /x) 2 for all values of m from m = I to 9 and of ju, from JJL = OOO to 1*00, with their differences from m to m + 1. M 1 An 2 An 3 An 4 An 5 M 0-50 48765-2 312097 17555-5 8598-6 8956-9 3538-5 5418-4 1791-2 3627-2 0-50 51 48121-4 307055 17415-9 8510-0 8905-9 3511-5 5394-4 17804 3614-0 51 52 47490-3 302124 17277-9 8422-5 8855-4 3484-9 5370-5 17696 3600-9 52 53 46871-6 297300 17141-6 83363 8805-3 3458-5 5346-8 1758-9 3587-9 53 54 46264-8 292579 17006-9 8251-3 8755-6 3432-3 5323-3 1748-3 3575-0 54 55 45669-8 287960 16873-8 8167-5 8706-3 3406-4 5299-9 1737-8 3562-1 55 56 45086-1 28343-9 16742-2 8084-7 8657-5 3380-8 5276-7 1727-4 3549-3 56 57 44513-6 279014 16612-2 8003-1 8609-1 3355-5 5253-6 1717-0 3536-6 57 58 43951-9 27468-3 16483-6 79226 8561-0 33303 5230-7 1706-8 3523-9 58 59 43400-8 270442 16356-6 78432 8513-4 33054 5208-0 1696-7 3511-3 59 60 42860-0 266290 16231-0 7764-8 8466-2 32809 5185-3 16865 3498-8 60 61 42329-2 262223 16106-9 7687-6 8419-3 3256-4 5162-9 16766 3486-3 61 62 41808-3 25824-1 15984-2 7611-3 8372-9 32324 5140-5 16666 3473-9 62 63 41296-9 25434-1 15862-8 7536-0 8326-8 32084 5118-4 16568 3461-6 63 64 40794-8 250519 15742-9 7461-8 8281-1 3184-8 5096-3 16470 3449-3 64 65 40301-8 24677-5 15624-3 7388-5 8235-8 3161-4 5074-4 16373 3437-1 65 66 39817-7 24310-7 15507-0 73161 8190-9 3138-2 5052-7 1627-7 3425-0 66 67 39342-3 239512 15391-1 7244-8 8146-3 3115-3 5031-0 16181 3412-9 67 68 38875-3 23598-8 15276-5 7174-4 8102-1 3092-5 5009-6 1608-7 3400-9 68 69 38416-6 232535 15163-1 71049 8058-2 3070-0 4988-2 1599-2 3389-0 69 70 37966-0 229150 15051-0 70363 8014-7 30477 4967-0 1589-9 3377-1 70 71 37523-2 225831 14940-1 6968-5 7971-6 3025-6 4946-0 15807 3365-3 71 72 37088-2 222577 14830-5 6901 7 7928-8 3003-8 4925-0 1571-5 3353-5 72 73 36660-6 219386 14722-0 6835-7 7886-3 2982-1 4904-2 1562-4 3341-8 73 74 36240-5 216258 14614-7 6770-5 7844-2 29607 4883-5 1553-3 3330-2 74 75 35827-5 213189 14508-6 67062 7802-4 29394 4863-0 15444 3318-6 75 76 35421-5 21017-8 14403-7 66427 7761-0 2918-4 4842-6 1535-5 3307-1 76 77 35022-4 207225 14299-9 6580-0 7719-9 2897-6 4822-3 1526-5 3295-8 77 78 34630-0 20432-8 14197-2 6518-1 7679-1 2876-9 4802-2 1517-9 3284-3 78 79 34244-1 20148-5 14095-6 6457-0 7638-6 2856-5 4782-1 15092 3272-9 79 80 33864-7 19869-6 13995-1 63967 7598-4 2836-2 4762-2 1500-6 3261-6 80 81 33491-5 19595-8 13895-7 63371 7558-6 2816-2 4742-4 14920 3250-4 81 82 33124-5 19327-2 13797-3 6278-2 7519-1 27963 4722-8 1483-5 3239-3 82 83 32763-5 190635 13700-0 62201 7479-9 2776-7 4703-2 1475-0 3228-2 83 84 32408-3 188046 13603-7 61627 7441-0 2757-2 4683-8 1466-7 3217-1 84 85 32058-9 18550-5 13508-4 61060 7402-4 27379 4664-5 14584 3206-1 85 86 31715-1 18301-0 13414-1 60500 7364-1 27187 4645-4 14502 3195-2 86 87 31376-8 18056-1 13320-7 5994-6 7326-1 2699-8 4626-3 1442-0 3184-3 87 88 31043-9 178155 13228-4 59401 7288-3 2680-9 4607-4 1433-9 3173-5 88 89 30716-3 17579-3 13137-0 5886-1 7250-9 26623 4588-6 14259 3162-7 89 90 30393-8 173472 13046-6 5832-8 7213-8 2644-0 4569-8 1417-8 3152-0 90 91 30076-4 171193 12957-1 5780-1 7176-9 26257 4551-2 1409-8 3141-4 91 92 29763-9 16895-4 12868-5 5728-1 7140-4 2607-6 4532-8 1402-0 3130-8 92 93 29456-3 16675-5 12780-8 5676-7 7104-1 2589-7 4514-4 1394-2 3120-2 93 94 29153-4 16459-4 12694-0 56259 7068-1 2572-0 4496-1 1386-4 3109-7 94 95 28855-1 162470 12608-1 5575-8 7032-3 2554-3 4478-0 1378-7 3099-3 95 96 28561-4 16038-4 12523-0 55262 6996-8 2536-9 4459-9 1371-0 3088-9 96 97 28272-2 15833-4 12438-8 5477-2 6961-6 3519-6 4442-0 13635 3078-5 97 98 27987-3 15631 8 12355-5 5428-8 6926-7 25025 4424-2 13560 3068-2 98 99 27706-8 15433-8 12273-0 5381-0 6892-0 2485-5 4406-5 1348-5 3058-0 99 1-00 27430-4 15239-1 12191-3 5333-7 6857-6 2468-7 4388-9 1341-1 3047-8 1-00 APPENDIX 239 TABLE II (contd.) Values of the function 109721-6/(m +-/x) 2 for all values of m from m = 1 to 9 and of fji from /* = 0-00 to 1-00, with their differences from m to m + 1. M 5 Aw 6 An 7 Aw 8 Aw 9 M 0-50 3627-2 10302 2597-0 646-4 1950-6 432-0 1518-6 302-8 1215-8 0-50 51 3614-0 1025-0 2589-0 643-6 1945-4 4303 1515-1 301-9 1213-2 51 52 3600-9 1019-8 2581-1 640-9 194CU2 428-7 1511-5 300-9 1210-6 52 63 3587-9 1014-7 2573-2 638-1 1935-1 427-1 1508-0 2999 1208-1 53 54 3575-0 10097 2565-3 6353 1930-0 4256 1504-4 298-8 1205-6 54 55 3562-1 10046 2557-5 632-6 1924-9 4240 1500-9 2978 1203-1 55 56 3549-3 999-6 2549-7 629-9 1919-8 4224 1497-4 2969 1200-5 56 57 3536-6 994-7 2541-9 6272 1914-7 420-8 1493-9 2959 1198-0 57 58 3523-9 989-7 2534-2 6245 1909-7 4192 1490-5 295-0 1195-5 58 59 3511-3 984-8 2526-5 621-9 1904-6 417-6 1487-0 294-0 1193-0 59 60 3498-8 979-9 2518-9 6193 1899-6 416-1 1483-5 292-9 1190-6 60 61 3486-3 975-1 2511-2 616-9 1894-6 414-5 1480-1 292-0 1188-1 61 62 3473-9 970-2 2503-7 614-0 1889-7 413-0 1476-7 291-1 1185-6 62 63 3461-6 965-5 2496-1 611-4 1884-7 411-5 1473-2 290-1 1183-1 63 64 3449-3 9607 2488-6 608-8 1879-8 4100 1469-8 289-1 1180-7 64 65 3437-1 956-0 2481-1 606-2 1874-9 408-5 1466-4 288-1 1178-3 65 66 3425-0 951 3 2473-7 603-7 1870-0 407-0 1463-0 287-2 1175-8 66 67 3412-9 946-6 2466-3 6012 1865-1 4054 1459-7 286-3 1173-4 67 68 3400-9 9420 2458-9 598-7 1860-2 403-9 1456-3 285-3 1171-0 68 69 3389-0 9375 2451-5 596-1 1855-4 4024 1453-0 284-5 1168-5 69 70 3377-1 932-9 2444-2 593-6 1850-6 401 1449-6 2835 1166-1 70 71 3365-3 928-3 2437-0 591-2 1845-8 3995 1446-3 2826 1163-7 71 72 3353-5 923-8 2429-7 588-7 1841-0 398-0 1443-0 281-7 1161-3 72 73 3341-8 919-3 2422-5 586-2 1836-3 3966 1439-7 280-7 1159-0 73 74 3330-2 9149 2415-3 583-8 1831-5 3951 1436-4 2798 1156-6 74 75 3318-6 910-4 2408-2 581-4 1826-8 393-7 1433-1 2789 1154-2 75 76 3307-1 906-1 2401-0 578-9 1822-1 3923 1429-8 278-0 1151-8 76 77 3295-8 901 9 2393-9 576-5 1817-4 390-8 1426-6 277-1 1149-5 77 78 3284-3 8974 2386-9 574-2 1812-7 389-4 1423-3 2762 1147-1 78 79 3272-9 893-0 2379-9 571-8 1808-1 388-0 1420-1 2753 1144-8 79 80 3261-6 888-7 2372-9 569-5 1803-4 3865 1416-9 274-4 1142-5 80 81 3250-4 884-5 2365-9 567-1 1798-8 3852 1413-6 2735 1140-1 81 82 3239-3 880-3 2359-0 564-8 1794-2 383-8 1410-4 2726 1137-8 82 83 3228-2 876-1 2352-1 5624 1789-7 382-5 1407-2 271-7 1135-5 83 -84 3217-1 871-9 2345-2 560-1 1785-1 381 1404-1 2709 1133-2 84 85 3206-1 867-7 2338-4 557-9 1780-5 379-6 1400-9 2700 1130-9 85 86 3195-2 863-7 2331-5 555-5 1776-0 378-3 1397-7 269-1 1128-6 86 87 3184-3 8595 2324-8 553-3 1771-5 376-9 1394-6 268-3 1126-3 87 88 3173-5 855-5 2318-0 551 1767-0 3756 1391-4 267-4 1124-0 88 89 3162-7 851-4 2311-3 548-8 1762-5 374-2 1388-3 266-5 1121-8 89 90 3152-0 847-4 2304-6 5465 1758-1 372-9 1385-2 2657 1119-5 90 91 3141-4 843-5 2297-9 544-3 1753-6 371-5 1382-1 264-9 1117-2 91 92 3130-8 8395 2291-3 542-1 1749-2 3702 1379-0 264-0 1115-0 92 93 3120-2 835-5 2284-7 539-9 1744-8 368-9 1375-9 263-2 1112-7 93 94 3109-7 831-6 2278-1 537-7 1740-4 3676 1372-8 262-3 1110-5 94 95 3099-3 827-7 2271-6 535-6 1736-0 366-2 1369-8 2615 1108-3 95 96 3088-9 823-9 2265-0 533-3 1731-7 3650 1366-7 2607 1106-0 96 97 3078-5 8200 2258-5 531-2 1727-3 3636 1363-7 259-9 1103-8 97 98 3068-2 816-1 2252-1 529-1 1723-0 3624 1360-6 2590 1101-6 98 99 3058-0 812-4 2245-6 526-9 1718-7 361-1 1357-6 2582 1099-4 99, 1-00 3047-8 808-6 2239-2 524-8 1714-4 359-8 1354-6 2574 1097-2 1-00 240 ANALYSIS OF SPECTRA TABLE III Wave lengths and Wave numbers of Series Measures in i.u. are printed in roman figures; in R.U. in italic. The wave lengths are given as observed. Each periodic group is preceded by a numbered list of authorities on whom individual measures are based. At the bottom of a list of series lines, the authorities are referred to by the corresponding numbers in brackets. Thus 1, (7); 2 ... 8, (3); ... means that the lines of order m = 1 are due to reference 7, those from 2 to 8 are due to reference 3. Where individual lines of an order are due to different observers, the lines are distinguished as la, 16, etc. In cases where in a column, C, dX are given, the calculated values are those from the formulae in Table IV. In cases where summation series occur, they are printed to the right of the difference series, in a reverse order, so that the corresponding W.N. shall come next to their mean, i.e. the common limit. Where only a few summation lines occur, they are given separately at the bottom of the list. Note. In the text difference and summation series are represented by ordinary and clarendon capitals respectively. The author feels that the distinction might have received still greater emphasis. In Table III therefore block letters have been used for summation series; thus the two principal series are distinguished by P, P instead of by P, P as in the text. Hydrogen and Helium REFERENCES 1. LYMAN. Spectroscopy of the Ultra-violet. 11. STARK. Ann. d. Phys. 56, 577 (1918) 2. CURTIS. Proc. Roy. Soc. 90, 605 (1914). 12. KOCH. Ann. d. Phys. 48, 98 (1915). 3. DYSON. Proc. Roy. Soc. 68, 33 (1901) and 13. LIEBERT. Ann. d. Phys. 56, 589 (1918). Trans. Roy. Soc. 206, 403 (1906). 14. NYQUIST. Phys. Rev. 10, 226 (1917) 4. MITCHELL. Astro. J. 38, 407 (1913). 15. MERTON. Proc. Roy. Soc. 98, 258 (1921). 5. MEISSNER and PASCHEN. Ann. d. Phys. 50, 16. FOWLER. Monthly Not. Roy. Astro. Soc. 901(1916). - 73,62(1912). 6. WOOD. Proc. Roy. Soc. 97, 460 (1920). 17. PICKERING. Astro. J. 4, 233 (1896) and 7. RUNGE and PASCHEN. Astro. J. 3, 4 (1896). 5, 92 (1897). 8. PASCHEN. Ann. d. Phys. 27, 552 (1908). - 18. EVANS. Phil. Mag. 29, 284 (1915) 9. PASCHEN. Ann. d. Phys. 29, 660 (1909). 19. PASCHEN. Ann. d. Phys. 50, 901 (1916). 10. SCHNIEDERJOST. Z, 8. wiss. Phot. 2, 265 20. PLASKETT. Nat. 108, 209 (1921). APPENDIX Hydrogen 241 m X n m X n 1 -1216 -82236 20 3679-50 27170-02 2 f 21 3676-54 27191-91 3 6562-793 1 15232-70 22 3673-90 27211-43 4 4861-326 1 20564-04 23 3671-46 27229-53 5 4340-467 23031-78 24 3669-58 27243-46 6 4101-738 24372-24 25 3667-89 27256-03 7 3970-075 25180-49 26 3666-21 27268-51 8 3889-051 25705-10 27 3664-78 27279-15 9 3798-06 26321-90 28 3663-58 27288-08 10 3770-79 26512-26 29 3662-35 27297-24 11 3750-32 26656-97 30 3661-39 27304-40 12 3734-52 26769-75 31 3660-47 27311-27 13 3722-05 26859-43 32 3659-57 27317-99 14 3712-12 26931-27 33 15 3704-00 26990-31 34 3658-80 27323-74 16 3697-29 27039-29 35 3658-19 27328-29 17 3691-70 27080-24 36 3657-40 27334-19 18 3687-00 27114-76 37 3656-80 27338-68 19 3682-92 27144-80 1 in vac. (1); 3 ... 8 (2); 9 ... 30 (3); 31 ... 37 (4). 1 Zeeman patterns are triplets with larger spreads than normal (Paschen and Back). Meissner and Paschen (5), H a , 6562-849, 2-725; H0, 4861-326; H v , 4340-465; Hg, 4101-735. Wood (6), m = 13 ... 21. 3722-12, 3712-22, 3703-92, 3697-35, 3691-72, 3686-99, 3682-96, 3679-46, 3676-44. Combinations p3-p4, 18571-3; p3-p5, 12817-6. Helium Lines marked * have been measured by interferometer methods and are collected in a special table. HeP' m / X n d\ m / X n d\ I 2 3 4 5 20 6 4 3 9 20582-21 *5015-732 l *3964-875 1 *3613-785 3447-734 4857-299 19931-81 25214-48 27664-09 28996-41 096 -03 005 002 020 8 9 10 11 19 <1 <1 <1 <1 3258-336 3231-327 3211-626 3196-81 30681-83 30938-28 31128-06 31272-32 -028 -025 -020 000 6 7 1 <1 3354-667 3296-900 29800-82 30322-96 000 028 13 <1 3176-61 31471-27 27 1(9); 2. ..13 (7). 1 Zeeman pattern =0/1/1. m 7 X n d\ m / X n d\ 2 3 *7281-81 13729-13 2-95 8 3878-330 25777-12 010 3 2 *5047-816 19805-12 002 9 3838-240 26046-36 000 4 1 *4437-718 l 22527-89 001 10 3809-22 26244-78 -022 5 1 4169-131 23979-18 000 11 3787-64*'! 26394-31 08 6 4024-136 24843-16 005 12 3770-72 26512-74 -207 7 3936-064 25399-04 -060 2 ... 12(7). Zeeman pattern 0/1/1. 2 CoveHsS'(ll). 242 ANALYSIS OF SPECTRA He 7)' m 7 X n d\ m I X n d\ 2 6 *6678-37 1 14969-65 545 8 3871-954 25819-57 009 3 4 +4922-096 1 20310-98 000 9 , 3833-710 26077-13 007 4 3 *4388-100 l 22782-63 000 10 , 3805-900 26267-68 000 6 2 *4143-919 24125-07 000 11 , 3785-031 26412-50 012 6 1 4009-417 24934-37 005 12 3768-95 26525-20 016 7 3926-678 25459-75 -024 13 3756-24 26614-95 -020 2... 13(7). 1 Zeeman pat tern = 0/1 /I. HeP" m 7 X n d\ m 7 X n d\ 1 200d 10830- 5 1 1 9230-76 80 7 1 2723-275 36709-83 -012 2 10 *3888-785 z 25707-82 046 8 <1 2696-230 37078-04 013 3 8 *3187-830 2 31360-41 -018 9 <1 2677-2 37341-58 -024 4 6 *2945-220 z 33943-59 016 10 <1 2663-3 37536-45 -080 5 4 2829-173 35335-82 -004 11 . 2653-10 37682-86 -002 6 2 2763-900 36170-28 002 12 2644-94 37797-01 -014 1(9); 2. ..10(7); 11,12(10). 1 P gives d\ = 1-2, dn = 1-02. He 8" Zeeman pattern =0/1/1, m 7 X n d\ m 7 X n d\ 2 1 7066-00 14148-44 7 1 3652-269 27372-59 5 *7065-48 14149-48 2-84 1 3652-121 27373-70 - -000 3 1 4713-475 21209-95 8 1 3599-610 27773-03 3 *4713-252 l 21210-94 -026 1 3599-472 27774-08 020 4 1 4121-143 24258-37 9 <1 3563-125 28057-39 007 3 *4120-973 24259-39 007 10 <1 3536-963 28264-92 014 5 1 3867-766 25847-93 11 <1 3517-48 28421-47 030 2 3867-613 25848-96 -004 12 <1 3502-47 28543-27 - -051 6 1 3733-142 26779-62 13 <1 3490-77 28638-93 - -055 1 3733-004 26780-61 -002 14 <1 3481-6 28714-37 107 2. ..14 (7). 1 Zeeman pattern =0/1/1, He D" m 7 X n d\ m 7 X n d\ 2 1 5876-209 17013-14 8 1 3587-570 27866-22 10 *5875-870 1 17014-13 005 2 3587-426 27867-34 006 3 1 4471-858 22355-93 9 1 3554-725 28123-66 6 *4471-646 l 22356-97 006 1 3554-594 28124-73 028 4 1 4026-512 24828-51 10 <1 3530-646 28315-49 002 5 +4026-342 1 24829-56 003 11 <1 3512-65 28460-56 -017 5 1 3819-899 26171-42 12 <1 3498-78 28573-37 021 4 * 3819-7 '51 26172-44 - -005 13 <1 3487-87 28662-74 -007 6 1 3705-287 26980-94 14 <1 3479-10 28735-00 -017 3 *3705-151 26981-92 002 15 <1 3471-93 28794-33 -049 7 1 3634-523 27506-24 16 <1 3466-04 28843-27 -047 2 3634-393 27507-23 005 17 <1 3461-41 28881-93 24 18 <1 3456-91 28919-53 -10 2 ... 18(7). 1 Zeeman pattern =0/1/1. APPENDIX 243 Wave lengths in I.A. by interference methods; n reduced from Merrill's measures. Jf 1 *(a) R(b)* E* n JIP n 8' (2) 7281-349 13729-94 >'(4) 4387-928 22783-41 S" (2) 7065-188 189 197 207 14150-01 #'(5) 4143-759 24125-89 D'(2) 6678-149 145 148 151 14970-08 S' (4) 4120-812 24260-25 D" (2) 5875-618 616 623 639 17014-78 D" (4) 4026-189 24830-40 8' (3) 5047-736 , , . 19804-97 P'(3) 3964-727 25215-29 P'(2) 5015-675 5 680 678 683 19931-95 P" (2) 3888-646 25708-62 IX (3) 4921-929 925 928 934 20311-57 D" (5) 3819-606 26173-31 S' (3) 4713-143 (171) 142 154 20211-35 D" (6) 3705-003 26982-88 D" (3) 4471-477 (-478) 480 493 22357-72 P'(4) 3613-641 27665-07 '(4) 4437-549 . . 22528-66 P" (3) 3187-743 31361-13 P" (4) 2945-104 33944-77 1 P. W. Merrill, Astro. J. 46, 357 (1917). 2 Lord Rayleigh, Phil. Mag. (6) 11, 685 (1906). 3 Lord Rayleigh, Phil. Mag. (6) 15, 548 ( 1908) ; measures altered from Michelson's Cd = 6438-4722 to I.A. Cd = 6438-4696. 4 P. Eversheim, Z. 8. wiss. Phot. 8, 148 (1910). Merrill, 5015-679. Combinations He' ("Parhelium") si -dm sl-sm pl-pm Priest, given by m Calc. Obs.(13) Calc. Obs.(13) Calc. Obs.(14) 2 5042-261 1,2 5378-799 i 6631-915 . 1 2 3 3972-141 3974 4063-625 i 4910-926 4910-8 4 3616-942 3618 3650-590 3 4383-452 4384-5 5 3449-406 3450 3466-856 3468 4141-510 4143-4 6 3355-699 3356 p2-d3, 19090-58 (9); d2 -/4, 18694-2 (8); d2 -/5? 12792-8 (8). 1 Not investigated by Liebert or Nyquist. 2 Since observed by Merton (15) at 5043, 6635. 3 Hidden by Hg line. si- He" ("Helium"] -sl-sm pi -pm m Calc. Obs. Calc. Obs. Calc. Obs. 2 3809-206 3809 4275-936 6067-393 6060 3 3164-888 3166 3284-040 4517-581 4518-77 4 2936-127 2936 2985-100 2986 4045-359 4046-02 5 2823-788 2824 2849-861 2851 3829-607 3830-0 6 2760-662 2761 2776-098 2777 3710-983 3711-3 7 2721-185 2722 2731-113 2732 3638-117 3636-9 8 3590-010 3586-7 2 (7); 3 ... 7 (11). 2, 3 not investigated; 4... 7 (11). 2 ... 4 (12); 5 ... 8 (13). p2 -rf3, 17003-28 (9); d2 -/4, 18684-2 (8); d2 -/5, 12784-6 (8). 16 2 244 ANALYSIS OF SPECTRA He (enhanced) m 7 X n m 7 X n 4 10 4685-98 21334-40 8 5 2385-47 41907-92 5 8 3203-30 31208-98 9 2 2306-20 43348-32 6 7 2733-34 36574-67 10 2 2252-88 4437*14 7 6 2511-31 39808-11 4... 10(16). Paschen's components (19) m / Cont. current / Spark m / Cont. current m / Cont. current 4 4686-028 4686-0500 5 3203-223 1 2 2511-249 7 5-905 * 5-9262 7 3-165 3 1-216 2 5-809 7 5-8037 8 3-111 1 1-117 7* 5-703 6 5-7005 i 2-996 8 1 2385-440 1 5-5498 5-5490 4 2-952 2 5-414 3 5-3883 * 5-3978 6 2 2733-345 i 5-326 , 4 5-3072 3 3-307 9 2306-215 1 3-189 Paschen's components (19) Plaskett Pickering m X w 6559-71 6 6560-43 15238-77 5411-54 5410-5 7 5411-67 18473-54 4859-07 , 8 4859-5 20572-6 4541-65 4541-3 9 4541-93 22011-60 4338-77 t 10 4339-97 23035-29 4200-00 4200-3 11 4199-95 4099-96 t 12 4026-0 13 , . 3924-0 15 > 3860-8 17 . 3815-7 19 3783-4 21 (20) (17) (18) 4A7{l/2 2 -l/m 2 } 2 . m X 6 6560-130 7 ((2)5411-551 1 "((0)5411-290 8 j(2)4859-342 {(0)4859-135 (4541-612 (4541-436? j 4338-694 10 (4338-536 14199-857 (4199-68? 1 9 (4100-049 12S 14099-913 = 109720. m 7 X n d\ m 7 X n d\ 3 1640-2 60968-2 -3 6 4 1026-0 97465-9 + 6 4 10 1216-0 82236-8 + 8 7 3 992-0 100800 -3 5 2 1084-9 92174-4 --1 8 1 972-7 102800 + 6 This series is doubtful. The measures are by Lyman, but he has criticised the allocation as he regards the lines m = 5 ... 8 as due to impurities. APPENDIX 245 GROUP I (a). Alkalies REFERENCES 1. LIVEING and DEWAR. Phil. Trans. Roy. Soc. 174 (I), 187 (1883). 2. KAYSER and RUNGE. Wied. Ann. 41, 302 (1890). 3. FABRY and PEROT. C.R. 130, 492 (1900). 4a, 4c BEVAN. Proc. Soy. Soc. 85, 54 and 58 (1911). 46. BEVAN. Phil. Mag. 19, 195 (1910). 5a, 56. PASCHEN. Ann. d. Phys. 27, 537 (1908), and 33, 717 (1910). 6. RAMAGE. Proc. Roy. Soc. 70, 303 (1902). 7. MEGGERS. Bull. Bur. Stand. Wash. No. 312 (1918). 8. SAUNDERS. Astro. J. 20, 188; Phys. Rev. 18, 452 (1904). 9. HAGENBACH. Ann. d. Phys. 9, 729 (1902). 10. STARK. Ann. d. Phys. 48, 210 (1915). 12. WOOD and FORTRAT. Astro. J. 43, 73 (1916). 13. ZICKENDRAHT. Ann. d. Phys. 31, 233 (1910). 14. DATTA. Proc. Roy. Soc. 99, 69 (1921). 15. BERGMANN. Z. S. iviss. Phot. 6, 113 (1908). 17. RANDALL. Ann. d. Phys. 33, 739 (1910). 18. ExNERandHASCHEK. W . L. Tables (1002). 19. MEISSNER. Ann. d. Phys. 50, 713 (1916). 20. MEISSNER and PASCHEN. Ann. d. Phys. 50, 901 (1916). 21. KENT. Astro. J. 40, 337 (1914). 22. SCHILLINGER. Wien. Ber. 118 (Ha), 605, (1909). 23. WOOD and GALT. Astro. J. 33, 72 (1911) (cathode rays). 24. MOLL. Arch. Need. (2) 13, 100 (1908). Lithium LiP m / X d\ n m I \ d\ n 1 IOR 6707-844 1 ' 2 14903-39 15 2321-9 -22 43055-20 2 SR 3232-77* 30924-61 16 f 2319-3 -15 43103-45 3 6R 2741-39 36467-33 17 . 2317-1 -13 43144-36 4 5R 2562-60 -06 39011-45 18 , 2315-2 -14 43179-76 5 4R 2475-13 -15 40390-00 19 . 2313-6 -14 43209-61 6 3R 2425-55 -12 41215-52 20 , 2312-2 -18 43235-76 7 IR 2394-54 -07 41749-30 21 , 2311-1 -11 43256-34 8 2373-9 08 42112-36 22 . 2310-0 -19 43276-93 9 g 2359-4 21 42371-09 23 . B 2309-0 -28 43295-67 10 2348-5 01 42567-68 24 t 2308-3 -15 43308-79 11 . 2340-5 ; 07 42713-14 25 , 2307-5 -24 43323-80 12 ( 2334-3 10 42826-55 26 p 2307-0 -10 43333-19 13 2329-0 -03 42923-98 27 9 2306-5 -03 43342-58 14 2325-2 17 42994-11 1 (3); 2 ... 8 (2); 9, 10 (1); 11 ... 27 (4o). US m / \ d\ n 2 8126-52 12301-60 3 Inr 4971-98 1 20107-24 4 5nr 4273-34 23394-44 5 3nr. 3985-86 07 25081-76 6 Inr 3838-3 2-4 26046-03 2 (7); 3, 4, 5 (6); 6 (2). 1 Kent (21) gives these as double, viz. f-084 (-339 m / X d\ n 2 IQR 6103-51 1 ' 2 16378-96 3 9 4603-07 1 ** 21718-76 4 8n 4132-93 05 24189-60 5 On 3915-59 -01 25531-84 6 5n 3795-18 -12 26341-89 7 3w 3718-9 -2-2 26882-23 8 In 3670-6 -1-3 27235-94 I* 115 1-309 2(7); 3... 6(6); 7,8(2). f ' 070 1-328 - Zeeman pattern =0/1/1. 246 ANALYSIS OF SPECTRA LiF m / X n 3 4 50 20 18697-0 12782-2 5347-007 7821-267 3, 4 (5). Combinations Comb. X n Comb. X n 1 pl-p2 6240-3 16020-52 8 P 2-f 12232-4 8173-224 2 3 pl-p3 pl-p* 4636-14 4146-7 21563-76 24108-90 9 10 d2-p3 /3-/4 19290 40475 5182-6 2470 4 p 1 -p5 3923-2 25482-32 11 ^4-^5! 74360 1344-4 5 p2-s2 26875-3 3719-880 12 (26890-5 3717-783 6 p2~s3 24467 4086-1 13 unallotted \23990-8 4167-140 7 p2-d3 17551-6 5659-950 14 (13566-4 7369-165 I (10); 2 (12); 3, 4 (12); 5, 7, 8, 12, 13, 14 (5); 6, 9, 10, 11 (0). 1 Or /4 -/ 5, or K impurity. Paschen N/& - NfQ\ Sodium NaP m / X d\ n m / X d\ n 2 WE 5889-963 1 16973-34 '21 2420-520 043 41300-92 9R 5895-930 2 16956-16 28 2419-922 033 41311-13 3 SR 3302-34 1 157 30272-87 29 2419-380 028 41320-39 8R 3302-94 2 172 30267-38 30 . 2418-893 022 41328-71 4 6R 28S2-828 3 35042-66 31 2418-454 015 41336-20 2853-031 35040-18 32 2418-062 002 41342-90 5 4R 2680-335 -021 37297-73 33 2417-695 000 41349-18 2680-443 -035 37296-23 34 2417-362 -004 41354-87 6 2R 2593-828 002 38541-58 35 2417-058 -009 41360-07 2593-927 -040 38540-10 36 2416-779 -012 41364-85 7 IR 2543-817 -002 39299-26 37 2416-518 -012 41369-31 2543-875 -022 39298-47 38 , 2416-271 -012 41373-53 8 1R 2512-128 -014 39794-96 39 2416-046 -002 41377-39 2512-210 -075 39793-66 40 2415-838 000 41380-95 9 2490-733 -034 40136-75 41 , 2415-651 -004 41384-15 10 2475-533 -005 40383-17 42 . 2415-474 -005 41387-18 11 2464-397 -020 40565-65 43 2415-305 -002 41390-05 12 2455-915 Oil 40705-74 44 . 2415-147 003 41392-78 13 2449-393 -010 40814-13 45 2415-006 001 41395-21 14 2444-195 002 40900-92 46 . 2414-872 000 41397-50 15 , 2440-046 - -025 40970-46 47 , 2414-746 000 41399-66 16 2436-627 -019 41027-95 48 2414-627 000 41401-69 17 2433-824 -042 41075-21 49 ' f . 2414-518 001 41403-57 18 2431-433 -019 41115-59 50 2414-411 000 41405-40 19 2429-428 -016 41149-53 51 2414-313 000 41407-08 20 2427-705 -003 41178-72 52 2414-218 002 41408-70 21 2426-217 015 41203-97 53 2414-131 002 41410-20 22 2424-937 018 41225-71 54 . *" 2414-050 000 41411-58 23 2423-838 008 41244-42 55 2413-971 000 41412-94 24 2422-856 013 41261-13 56 . 2413-910 - -013 41413-99 25 2421-997 012 41275-75 57 2413-873 -046 41414-63 26 2421-233 012 41288-77 58 . 2413-837 -079 41415-24 1 Zeeman pattern = 1/3. 5/3. 2(3); 3 (2); 4. ..58 (12). 2 Zeeman pattern = 2/4/3. 3 Zeeman pattern =0/1/1, APPENDIX Na/Sf 247 m / \ n d\ m / X n d\ 2 500 11404-2 8766-71 8 4344-8 23009-5 -00 700 11382-4 8783-50 4341-5 23027-1 3 Snr 6160-725 16227-37 9 4290-8 23299-3 ' 9 8nr 6154-214 16244-54 4287-7 23316-1 4 Qn 5153-645 19398-34 10 m 4252-6 23508-5 5n 5149-090 19315-51 4249-5 23525-7 5 4n 4751-891 21038-40 -09 11 t 4223-5 23670-5 t 3rc 4748-016 21055-55 4220-5 23687-4 6 3w 4545-218 21995-00 -06 12 4201-2 23796-1 . 2n 4541-671 22012-18 4198-5 23811-5 7 4423-31 22601-18 -01 4419-94 22618-40 2(5o); 3... 8 (14); 9 NaD 12(13). m 7 \ n d\ m / X n d\ 2 10 8194-82 12199-48 8 4324-5 23117-7 8 8183-30 12216-65 4321-3 23134-8 3 Snr 5688-222 17575-32 9 , 4276-7 23376-0 f Inr 5682-675 17592-49 4273-6 23393-0 4 Qnr 4982-864 20063-20 03 10 4241-8 23568-4 1 5nr 4978-608 20080-35 4239-0 23584-0 5 4 4668-597 21413-73 01 11 4215-8 23713-8 , 3 4664-858 21430-89 4213-0 23729-5 6 2n 4497-724 22227-26 02 12 , 4195-7 23827-3 . 4494-266 22244-36 4192-8 23843-8 7 t 4393-45 22754-78 08 13 g 4180-2 23915-7 , 4390-14 22771-94 4177-2 23932-9 14 4168 23985-7 2(7); 3 ... 7(14); 8... 14(13). The intensities are by Kayser and Runge. m I X n 3 100 18459-5 5415-85 4 30 12677-6 7885-87 3, 4 (5). Combinations Comb. X n Comb. X n 1 /Pi 1 -Pi 2 7418-3 13476 9 pS-s3 54300 1841 1 Iftl-ftS 7410 13491 in (Pi 1 ~/3 5675-92 17613-49 /Pi 1 -Pi 3 5532-7 18069-43 1U lp 2 l-/3 5670-40 17630-66 (P 2 1-P 2 3 5528-2 18084-15 [ftl-/4 4976-1 20090-57 fPi 1 -Pi 4 4918-4 20326-37 - IP 2 l-/4 4973-0 20103-08 IP2 1 -P2 4 4914-0 20344-47 12 Pi ~/5 4660 21453 lAl-ftfl 4633-1 21577-90 10 J Pl l-d3 23391-3 4273-98 \p 2 l -p z 5 4629-4 21595-16 lt> Ip 2 l-rf3 23361-0 4279-52 5 pi - P 6 4472-5 22352-6 f ft 2-d2 90850 1100-5 6 p\ -pi 4372 22866 1^2-^2 90480 1104-9 7 fAS-a 22056-9 4532-550 15 p3-d4 50230 1990 1 lp 2 2-2 22084-2 4526-945 16 /3-/4i 40449 2471-6 fft2-t8 34303 2923-7 17 /4-/6 74430 1343-2 Ip 2 2-s3 34163 2926-9 1, 2, 3, 5, 6 (8); 4, 11. 12 (15); 7, 8, 9, 13 ... 17 (5). -rJ4.-fJ4.-tJX 2 Or AT imnnritv. PasoTipn A/75 2 - 2 Or A" impurity. Paschen N/5* - iV/6 2 . 248 ANALYSIS OF SPECTRA Summation lines The column next n gives the mean with the corresponding difference line. NaSj tf(oo) NaS m I \ n 24400 + I X n 24400 + 3 6 ( - A) 3056-46 (32725-5) 75-9 4 3054-09 32733-7 88-6 5 2 3582 27909-6 73-4 6 3 ( - A) 3711-30 (26954-4) 75-0 8 Iv (- A) 3857-6? (25940-0) 75-1 10 1 ( - A) 3933-3 (25441-1) 74-8 11 1 3955-0 25284-4 77-9 1 3953-2 25296-0 91-7 12 1 3972-3 25174-3 92-9 The true limits are 24474-85 and 24492-03. 3, 6 (22); 5 (23); 8, 10, 11, 12 (13). Displacements by about v are quite common in this arc (13). S (2) would be beyond observed in violet. 7) (oo) NaD 2 1 i m I X n 24400 + I X n 24400 + 9 In 3910-0 25575-4 75-7 In 3908-7 25584-0 88-5 10 1 3940-1 25380-0 74-2 2 3934-5 -v (25399-0) 91-5 11 1 3962-1 25239-1 76-4 1 3956-3 - v (25258-9) 94-2 1 12 2 3981-1 25118-7 73-0 3 3978-4 25135-7 89-8 13 1 3995-2 25030-0 72-9 2 3992-2 25048-8 90-8 14 1 4005-4 2 24966-3 76-0 1 4003-1 24980-6 These are all in the vacuum arc by Zickendraht (13). For m <9 the lines lie beyond his observa- tions. In the spark lines by Schillinger (22) there are possible D! (4) =(ln) 3462-73 + v, n=28888-03, limit = 24474-32. D 1 (5) = (5)3631-46, n=27529-5 t limit, = 24469 -83. 1 There are two lines here appearing equally and oppositely displaced, viz. this and (1) 3957-4. Their mean gives n- 25255-46 and limit = 24492-5. 2 Also close to this are (2)4006-7, n = 24958-2 and (1)4003-8, n = 24976-3. These show the normal separation and are shifted about \v, that is, are the displaced set (395 2 ) D (14). Potassium KP m ' X n d\ m ' X n d\ 2 IQR 7664-94 13042-84 11 2928-0 34143-21 12 IQR 7699-01 12985-06 12 2916-6 34276-67 20 3 8R 4044- 140 1 24720-18 13 2907-6 34382-76 13 GR 4047-201 2 24701-49 14 2900-4 34468-10 00 4 8R 3446-722 3 29004-79 15 2894-6 34537-16 -10 GR 3447-701 3 28996-56 16 2889-7 34595-72 -32 5 GR 3217-01 31075-82 17 . 2885-9 34641-28 -25 4-R 3217-50 31071-09 18 2882-9 34677-32 00 6 4R 3102-15 32226-56 09 19 2880-3 34708-63 15 2R 3102-37 32224-26 06 20 2877-9 34737-56 09 7 4R 3034-94 32940-23 -11 21 2875-8 34762-94 02 8 2R 2992-33 33409-28 -10 22 2874-1 34783-50 09 9 1R 2963-36 33735-80 -18 23 2872-5 34802-88 00 10 IR 2942-8 33971-43 -20 24 2871-1 34819-84 -09 25 2870-0 34833-19 03 1 2 (7); 3 ... 5 (14); 6 ... 10 (2); 11 ... 25 (46). 1 Zeeman pattern = 1/3. 5/3. 2 Zeeman pattern = 2/4/3. 3 Kayser and Runge give for these, reduced to I.A., 3446-38 and 47-38 with maximum errors -03. They agree much more closely with the calculated. APPENDIX 249 m / X n m / X n 2 90 100 12523-0 12434-3 7983-22 8040-17 2 500 500 11771-73 11689-76 8492-63 8552-17 3 8 7 6938-93 6911-30 14407-48 14465-08 3 WRn 6966-3 1 ? 14350-89 4 6R 5R 5801-96 5782-60 17230-77 17288-48 4 lEn QRn 5832-31 5812-71 17141-13 17198-91 5 4JS 4 5339-670 5323-228 18722-56 18780-40 5 5Rn IRn 5359-521 5342-974 18653-20 18711-00 6 3.B 2R 5099-180 5084-212 19605-54 19663-28 6 3Rn 3Rn 5112-204 5097-144 19555-61 19613-38 7 IB IB 4956-043 4941-964 20171-61 20229-34 7 IRn IRn 4965-038 4950-816 20135-23 20193-08 8 1 1 4863-61 4849-88 20555-16 20613-33 8 4869-70 4856-03 20529-46 20587-23 9 1 1 4800-16 4786-89 20826-82 20884-58 9 4805-19 4791-08 20805-03 20866-33 10 4754-5 4741-6 21026-7 21084-0 10 4759-31 4745-58 21005-58 21066-38 2 (5);-3, 4 (7); 5 ... 10 (14). 2 (60); 3 (8); 4 ... 10 (14). 1 Ritz gives 6964-4. KF m / X n nt / X n 2 10 74260*'! 1346-3-! 5 9590 10424 3 100m; 15165-8 6592-00 6 8908 11223 4 WQnv 11028-0 9065-42 7 8500 11761 2, 3, 4 (5); 5, 6, 7 (15). 5 ... 7 large observed errors. Paschen suggests N (1/5 2 - 1/6 2 ). Combinations Comb. 7 X n Comb. ' X n Pl 3-s2 20 27065-6 3693-73 p z 3 - d 3 30 37075-6 2696-39 p 2 3 s 2 8 27215-0 3673-44 P-, 4 d 3 20 62030 1611-6 Pi 3 - s 3 15 36614-3 2730-44 p 2 4 - d 3 15 62360 1603-1 p 2 3 - s 3 10 36372-7 2748-58 p l 4 - d 4 5 85100 1174-8 ^4-s3 8 64310 1554-4 4 d 4 4 84520 1182-9 8 64610 1547-3 r t 4642-172 21535-63 j 30 31401-8 3183-6S * 2 - a 2 1 -I 4641-585 21538-36 Pl 6 -d 2 ^ 50 31388-1 3185-07 2 10 74260 1346-3 p. 2 3 - rf 2 40 31596-8 3164-03 rf 3 rf4 20 40144-2 2490-36 ( 10 37370-7 2675-18 Pi > -, 40 37354-3 2676-35 Doubtful: p2- P 3, 8500, 117611; p2-p4, 6246-5, 160052; p2-p5, 5516, 181242. 1 These suggest the presence of satellites. The s2 -d2 is by Datta(14) and should give accurate separation values here o- = 2-73 requiring mantissa difference 290, which is exactly 5J5. The 7> x 3 - d 2 is by Paschen (5 6) with a = l-39 -8. His possible errors must be larger. ^3 - d 3 also by Paschen gives 251 m / X d\ n m / X d\ n 2 100 15290-3 6538-34 1 5260-51 34 19004-38 150 14754-0 6776-00 5195-76 19241-20 3 7759-58 1 12883-32 8 5150-8 29 19409-19 7757 -80 1 12886-27 5088-6 19646-41 7619-12 13120-82 9 5075-7 -25 19696-33 4 4w 6298-50 1-80 15871-88 5015 19934-7 4w 6206-48 16107-20 10 5021-8 06 19907-75 5 4w 5724-41 1-1 17464-28 4963 20143-57 3nr 5648-18 17700-00 11 4982 1-8 20066-77 6 2w 5431-83 60 18405-00 4926 20294-88 2w 5362-94 18641-35 12 4953 -2-8 20184-29 4892 66 20435-93 2 (17); 3, 4 (7); 5, 6 (2); 7 (6); 8, 9a <8); 96, 10, 11, 12 (18). 1 Meissner ...9-63, ...7-86. m / X d\ n m / X dX n 2 40 46960 2129-0 4 160 10081-9 9917-20 50 46370 2156-1 5 t 8872 --03 11268-37 3 270 13443-7 7436-43 6 8271 -2-5 12087-17 2(56); 3,4(17); 5, 6(15). Combinations Comb. I X n ^3-s2 8 27319-8 3659-36 pi 3 - s 2 8 27909-8 3582-01 p<> 3 s 3 15 38511-4 2595-91 Pi 4 - s 3 10 64360 1553-3 P 2 4 - 5 3 8 65670 1522-3 fe4-2 5 12924-1 7735-49 5 12986-6 7698-17 p 1 3 - d 2 35 22533-0 4436-74 p 2 3-d2 12 22936-7 4358-65 pll-dll 10 52313-4 j Wll-1 1 ??, 4 d 3 2 5 46190-1 2164-38 5 1 - d 2 , 5165-35 19354-50 s2 f 2 3 15 74280 1345-9 s 2 -/ 2 10 72690 1375-3 /! 3 - JV/5 30 39898-5 2505-69 / 2 3 - N/5* 15 39827-4 2510-16 1 Calculated 1908-00, 1910-91; observed sometimes double. 2 pz-d 2 3 calculates to 2133-34. Paschen allots this to 2129. This has here been adopted as F (2). The error would seem too large for the combination. 3 ? K impurity. Paschen - N/5* - N/G*. 4 Or / 2 3 -/4 = 2509-9. Summation All P outside observation. D i (4) ('">) 3861-40, 25890-17; mean with D l 20881-0. O, (4) (2) 3828-1, 26115-4; mean with Z) 2 21111-30. Spark lines (18). 252 ANALYSIS OF SPECTRA Caesium CsP i m I X n d\ m / X n d\ 2 IOR 8521-12 11731-77 10 32871 30414 SR 8943-46 11177-92 11 3270-4 30568-7 -14 12 3256-6 30698-3 -15 3 8R 4555-46 21945-64 13 3245-9 30799-4 _ .j GR 4593-30 21764-87 14 . 3237-8 30876-5 3 15 3230-6 30945-4 4 (iR 3876-31 25790-52 00 16 3224-6 31002-9 _ .3 R 3888-75 25708-05 07 17 . 3220-3 31044-3 18 3216-4 31081-9 1 5 R 3611-70 27680-07 17 19 , 3212-9 31116-8 2R 3617-49 27635-77 21 20 3210-1 31152>6 21 3207-7 31166-2 (i 1 3477-25 28750-33 42 22 3205-6 31186-6 1 7 1 3398-40 29417-38 41 23 , 3204-0 31202-2 27 8 1 3348-72 29853-77 1-0 24 , 3202-4 31217-8 4 9 3314 30167 9 25 3200-7 31234-4 1 1 (7); 2... 9 (6); 10... 25 (4o). CsS m / X n d\ m 7 X n d\ 2 14696-4 6802-33 5 4 6034-43 16567-07 00 13590-7 7355-76 2 5839-33 17120-58 3 . 7944-11 12584-06 6 1 5746-37 17397-53 -09 7609-13 13138-06 1 5568-9 17951-96 4 8 6587-16 15176-86 03 7 1 5574-4 17934-25 13 8 6355-19 15730-82 1 5407-5 18487-80 2(17); 3,4 (7); 5,6,7 (6). CsZ) m / X n d\ m / X n d\ 2 20 36127-7 2767-22 6 5847-86 17095-60 70 34892-5 2865-18 1 5844-7 17103-63 -49 60 30099-9 3321-37 1 5663-8 17649-88 3 16 9208-40 10856-31 7 5635-44 17740-00 -20 26 9172-23 10899-12 5466-1 18289-6 56 8761-35 11410-25 8 5503-1 18166-6 -15 4 56 6983-37 14315-32 5341-15 18717-44 106 6973-17 14336-25 106 6723-18 14869-33 9 , 5414-4 18464-2 47 5256-96 19017-23 5 16 6217-27 16079-25 86 6212-87 16090-66 -46 10 5351 18683 3 76 6010-33 16632-88 5199 19229 11 5304 18848 2 (56); 3, 4, 5, 66c (7); 6a, 7 ... 10 (6). APPENDIX C&F 253 m / X n d\ m 7 X n d\ 2 23500V 42551 8 6475 15440 5 6434 15538 3 10124-0 9874-62 10025-5 9971-88 9 . 6366-4 15703-2 -8 6327-0 15801-0 4 Snr 8079-46 2 12373-25 8nr 8016-28 2 12470-75 10 , 6289-4 15895-4 -9 6251-3 15992-3 5 6wr 7280-80 13730-52 6nr 7229-28 13828-37 11 ' 6232-4 16040-8 -7 6 4w 6871-10 14549-23 6 4 8053-62 3 12413-38 ' 47?, 6825-91 14647-26 7990-94 12510-72 7 6630-5 15077-2 2 5 7270-94 3 13749-58 6588 15175 7219-94 13846-72 3 (17); 4, 5, 6 (19); 7, 8 (8); 9... 11(10). 1 This is given by Moll (24), a very rough measure. There is just the possibility of its repre- senting F (2). 2 Meggers (7) gives both as double, d\ = -l, equivalent to F (4) (6). 3 Related lines by Meissner (19), say F' (4) = F (4) (35 J5) and F' (5) = (35) F (5 sets related to F (4, 5) referred to on p. 56 in R. A. If the defect from the full F separation is 3 Related lines by Meissner (19), say F' (4) = F (4) (35 J5) and F' (5) = (35) F (5) (685). The two s related to F (4, 5) referred to taken as due to satellites, they are ( - 195j) Fi (4), d\ = - -15, ( - 95j) F^ (4) (35j), d\ = - -03. ( - 195 t ) F z (4) ( - 35^, d\ = - -06, Satellites due to 35 r ( - 95 X ) F 2 (4) ( - 35,), d\ = - -01. Satellites due to 65 r Combinations Comb. 7 X n Comb. 7 X n , ^2-52 80 29318-3 3409-93 4 Pl 2-d,2 ^ i i p 2 2-s2 40 30962-9 3228-81 p 2 2 - d z 2 13761-4 7264-75 2 4 42202-3 2368-90 5 / 3 /' 4 30 39398-5 2537-5 p 2 s 3 10 39180-1 2551-58 6 10 74250* 1346-4 3 P! 3 - s 3 15 68070 1468-6 p 2 3 - s 3 13 71930 1390-2 Same region as S 2 (2). 2 Paschen suggests 2V/5 2 - P x (5) D x (4) (28) D x (4) F! (3) Summation lines (1) 2700-7, 37016-74 mean with P v 31043-63 (1)2846-1,35125-7 P 1 31042-88 4001-6, 24983-0 - 6-3d\ D l 19659-6 -3d\ 4001-6. (25004-3) 7)! 19670-3 4214-1, 23721-6 F, J 6798-1 254 ANALYSIS OF SPECTRA GROUP I (6) REFERENCES 1. KAYSER and RUNGE. Wied. Ann. 46, 225 (1892). 2. HANDKE. Inaug. Diss. Berlin (1909). 3. MEGGERS. Bull. Bur. Stand. Wash. No. 312 (1918) 4. HASBACH. Z. S.wiss.Pliot. 13,399(1914). 5. ARETZ. Z. S. wiss. Phot. 9, 256 (1911). 6. CREW and TATNALL. Phil. Mag. 38, 379 (1894). 7. RANDALL. Ann. d. Phys. 33, 741 (1910). 8. STARK and HARDTKE. Ann. d. Phys. 38, 712 (1919). 9. DE RUBIES. Ann. Soc. Espanola d. Fis. y Quim. 15, 215 (1917). 10. CATALAN. Ann. Soc. Espanola d. Fis. y Quim. 15, 222 (1917). 11. MEISSNER. Ann. d. Phys. 50, 727 (1916). 12. KASPER. Z. S. wiss. Phot. 10, 53 (1911). 13. FABRY and PEROT. C.R. 130, 492 (1900). 14. LEHMANN. Ann. d. Phys. 39, 75 (1912). 15. PASCHEN. Ann. d. Phys. 33, 733 (1910). 16. EDER and VALENTA. Denkschr. Wien. Akad. 63, 189 (1896). Copper a = 245-54; 6=248-44; c =251-39; d = 254-39; e = 999-77; u = 680-68; v = 692-02. CuP m 7 X n d\ m 7 A n d\ 1 107? 3247-65* 30782-77 3 1 1817-3 55026-7 17 3274-06* 30534-54 4 4 1732-4* 57723-4 -37 5 4 (59140-9) 00 2 1 2037-28 49069-64 6 5 (59995-38) -30 1 2068-45. u (49010-87) 1,2(1); 3. ..6 (2). 1 Zeeman pattern = 1/3. 5/3. 2 Zeeman pattern = 2/4/3. 3 is P 2 (4). Pj (4) calculated from p l 1 -p 1 4 is n = 57 7 14-51, d\ = -l. 4 Mean of u. 1761-6 and 1710-6. u; nn = 59142-24, ...39-70. 5 From combination p 1 l-p 1 6 = 29212-61 or \=(2n) 3422-22. CuS CuS m 7 X d\ n 31500 + 31700 + n X 7 2 10 8092-74 12352-95 23-502-5 50694-0 1971-99 1 10 7933-20 12601-37 (66-76) (50932) e. 1925 3 SR 4530-843 1 22064-07 (23-08) (40982-09) ( -85)2441-625 672 SR 4480-376 2 22312-58 (72-03 -5) 41231-48 2424-62 6 4 2n 3861-755 2 25886-80 28-27 1-3 37 169-7 5 3 2689-58 s 10 In 3825-050 15 26135-20 73-03 1-6 37410-87 2672-24 2n 5 2n 3598-01 -05 27784-34* In 3566-14 02 28032-65 6 In 3463-5 -29 28863-51 20-87 34178-24 5 2924-90 lin 7 2n 3384-815 -34 29534-28 24-76 33515-04 2982-77 In 8 3 3335-235 38 29973-32 23-43 33073-54 3022-608 3 2 (3); 3 ... 8 (4); in S, 2a, 46 (1); 3a, 6, 7, 8 (4); 36, 4a by E. H.; 26 by M'Lennan. 1 Zeeman pattern = 1/3. 5/3. 2 Zeeman pattern = 2/4/3. 3 This is ( -6Sj) Sj (4) giving separation 248-53 and mean limit = 31524-09. 4 Also u. 3512-19 = ...83-56 and 3688-60. u= ...83-67. Calc. == ...83-86. 5 S x (6) is split into two (63^ 8^6), viz. (In) 2924-90 and (2n) 2923-714. Mean ...85-19 and mean limit = 31524-25. CuD APPENDIX (00) 255 CuD m / X d\ n 31500 + 31700 + n X / 1 59916-12 1669-0 1 2 6 IQR 5220-083 1 5218-202 1 6 19150-81 19157-72 (22-95) (23-77) (43895-10) (43889-83) M. 2242-599 (5J5) 2276-244 4 4 8# 5153-251 1 19399-18 (72-17\ \72-35J (44145-17\ \44145-53J (5J5) 2263-09 w. 2230-071 6 6J? 3 In WE 4063-296 4062-694 6 24602-82 24606-46 24-17 1 38442-47 2600-53? 10 4 WR 3w 4022-667 3687-5 -27 24851-25 27110-1 (72-09) (38692-94) 2630-002. w 2 2n 3654-3 27356-34 (72-53) (36188-74) ( - 3 5) 2763-705 1 5 4w 4 3512-122 3483-760 -26 28463-77 28695-49 22-21 34580-65 2890-85 2n 6 1 Iw 3414-77 10 29275-22 (22-42) (33769-62) (34023-19) 3021-56. w 2998-384. w 3 2 7 2w 3354-475 27 29801-44 (23-70) (33246-96) 3070-86. v Iw 8 1 3392-Ol.v 2 15 30164-09 (23-08) (32882-70) %. 2978-293 2n D; 2 ... 8 (4). D; 1 (2); 2, 4, 5, 6 (4); 7 (1); 8 (4). 3 is a spark by Eder and Valenta and too strong. 1 The Zeeman patterns are anomalous and uncertain, numerically about 5/10/6; 0/6A/12; 0/5/6 instead of 2/4/3; 0/3/2; 0/1/1. 2 Also (2) 3391-09. u=30163-46. CnF CnF m / X n 28300 + 28400 + I n X I 3 55800-46 7709.7 o 2 1 6199-195 16126-12 82-82 In 2n 2n 40639-53 40622-16 40655-36 J. t *7& J. o 2659-4 s 2460-98 2458-97 3 2 2n 4649-31 s 4642-78 21502-65 21532-88 4 4n 4177-87 1 23929-06 , In 32739-77 1 3053-52 5 In 3947-09 25328-06 6 In 2 3821-01 26163-83 7 In 2n 3748-50 s 3745-53 26669-94 26691-08 8 2n 2n 3699-19 3695-42 27025-42 27052-98 9 In 3664-21 27283-41 10 2n 2n 3636-01 3632-65 27494-96 27520-39 F; 2 (5); 3 ... 6, 8, 10 (1); J\ (7) is spark (Eder and Valenta); 76, 9 (6). F; 1 (2); 2, 4 (1). 1 (12JS) F n (4) and (125) F n (4). - C'lose to S 2 (4). 256 ANALYSIS OF SPECTRA Combinations d(2)-f(m) d(2) d(2)+f(m) 1 9 2n 2n -6621-623 - 6629-730 ("ultra-red] - 15097-37 - 15078-90 12358-15 12385-39 1 5n 39813-67 39849-68 2510-95 s 2508-68 s 3 6 18229-5 5485-61 10 18194-6 5496-13 1(5); 3 (7). 1, spark (16). m ' X n m ' X n 9, 5 2n 3524-31 28366-38 3 2n 2n 5410-97 4123-38 18475-93 24245-24 6 2n 2 3422-22 3393-09 29212-61 29463-41 4 2n 2n 3712-05 3676-99 26931-74 27188-69 m / X n 31500 + 31700 + I n X 1 , [4078] . 1 58969-2 1695-8 2 1 2 5188-96 5120-00 s 19266-38 19525-91 3 2v Iv 4056-8 4015-8 24643-17 24894-76 71-38 In 38648-00 2586-70 s 4 - 3686-10* 3652-3 27121-48 27372-36 23-48 71-98 2n 1 35925-47 36171-60 2782-73 2763-60 s 5 6n 3512-19 28464-24 22-39 -8 2n 34580-54 2890-97 6 2n 9n 3413-41 3384-8S 2 29287-98 29534-86 23-9 QR 33759-83 2961-25 2a (E. H.); 26 (spark, E V.) ; 3(1); 4 (8); 5, 6(1) 1 By Stark. Koch line. 1 (2); 3, 46 (spark, E. V.); 4a, 5, 6(1). 2 This also agrees with S t (7) and e. P z (1). Inverse D = D' 5782- 158 1 5732-36 5700-249 2 17289-22 17439-40 17537-66 (4) (4) (4) 1 Zeeman pattern same as in Cu Z> 2 = 0/5/6. 2 Zeeman pattern seems to be the combined Cu Z> u and Z) 12 and is 5/6^ . 10/6. d/l-djl (2n) 4866-38, 20543-50 } d^ 1-dtl (2) 4859-12, 20574-25-! d 2 1 =N/(l + 132A) 2 d z 'l-d z l (In) 4842-2, 20645-3 ) d z ' l-d z l (2n) 4794-23, 20852-66 d z !=#/(!+ 133A) 2 APPENDIX Cu (d'= sequent of diffuse triplet) 257 d'+f m 2 4 7 X n Mean I 4 n X 6 2R 2724-04 2715-67 36699-53 36812-61 49064-6 -15d\ 2369-97 42181-99 55947-19 1787-4 2238-52 44658-81 5 Unobserved region 6 7 2 2 I 2136-05 1 2134-51 s (46817-8) (48345-5) 2112-19* 1 The second line is a spark line by Eder and Valenta. These are numerically (75j) d 2 ' -f and ( - 75^ d z ' -f, giving jy (6) =48617. 2 Also (75,)rf 2 '-/ > . Cu ( ? a second P series, Q) Q #(*>) Q m 7 X n 59100 + I n X 1 ?lw nn 3656-901 3624-351 27337-94 27583-46 Unobse rved region 2 4R QR 2181-80 2178-97 45819-64 45879-14 3 Unobserved region 4 ?3 ?8 ( - 95) 1834-9 (115) 1826-1 (54619-7) (54621-8) (74-45l-7) I (63727-1) 1594-2. e 5 7 1783-7 56063-2 76-50 1-7 .1 62289-8 1605-4 6 3 6 (75) 1760-0 (-18)1754-5 (56907-2) (74-36 1-7) 4 61451-5 1627-3 7 8 1741-0 57438-2 73-50 1-7 9 60908-7 1641-8 8 1 1729-7 57813-5 74-92M 7 60536-3 1651-9 9 8 1721-9 58075-4 (73-16l-7) 5 3 (60270-9) (-38)1660-2 l (45) 1657-8 1,2(1); 4 ... 9(2). 1 These displacements are exact. Since the author's allocation L. and E. Bloch (C. R. 171) have observed 1658-4, n = 60299-1 = ( - 15) Q. X n q l l-g l 2 (4n) 5463-55 18298-11 q 2 l -q z 2 (3w) 5408-55 18484-20 g l I -q l 4 (2n) 3695-42 27052-98 ? 2 1 - 7 2 4 (In) 3664-21 27283-41 H.A.S. 17 258 ANALYSIS OF SPECTRA Silver a = 880-77; b =920-44; c = 962-54; d = 1007-26; e = 377 1-0; = 2458-64; v = 2616-61. AgP m I X d\ n 1 10 3280-80 30471-73 10 3383-00 29551-26 2 1 4 2066-2 48382-8 Irc 2075-9 48156-8 3 5 1849-4 35 54071-6 4 1853-4 53954-9 1(1); 2 (16); 3 (2). 1 Catalan (10) suggests for these, two lines by Rubies (9), 2061-61, 2070-11 with nn = 48491-03, 48291-00. Regarded as P (2) these give as p l 1 -p t 2, p z 1 -p 2 2, p 2 1 -p l 2 the inverse Z) 22 , D n , D lz with a small shift. m 7 X d\ n m / X d\ n 2 8273-59 12083-33 5 In 3710-1 -21 26946-95 7687-87 - 13003-93 3 3587-40 27867-42 3 m 4668-512 1 21414-12 6 2 3568-46* -02 28015-45 QR 4476 -093 2 22334-67 7 In 3487-68* -01 28664-31 4 QR 3981-618 25108-34 2R 3840-817 26028-77 8 In 3436-01 3 24 29095-35 2 (3); 3, 4 (12); 5a (1); 56, 6, 7, 8 (10). 1 Zeeman pattern = 1/3. 5/3. 2 Zeeman pattern = 2/4/3. 3 These are all S (6, 7, 8) ( - 605). The d\ refer to displaced values. They were suggested by Catalan (10). AgS m / \ n mean limit 3 2 1 2507-39 2450-49 39870-34 40796-01 30641-87 -7 3 1564-97 -7 4 In e. 2502-3 t (36180-42) (37105-17) (30643-9 1-3) (31 566-5 1-3) 3 (E. H.); 4(16). f Doubly linked, e. (I) 2445-64 = ...05-89, (I) 2999-13. = ... 04-44: mean = ...05-17. AgT) D(oo) AgD m 7 \ d\ n 30600 + 31500 + n X I 1 (59643-4) 7375-4(145,) I 59569-9 1678-7 2 60561-9 t 2 8 547 1-55 1 1 18271-29 10/2 5465-489 1 6 18291-56 42-53 -5 42994-11 2325-20 6 1072 5209-081 ! 19191-94 63-24 -5 43935-19 2275-39 2 3 8R 4212-011 23734-97 (42-97-7) (37551-63) 2664-6 (-235) In 672 4055-532 24650-75 61-22 1 38471-01 2598-6 1 4 2% 3810-9 -01 26233-11 38-32 1 35044-4 2852-7 1 M 3682-303 27149-21 (65-35) (35982-39) 2982-16. u 1 s 1?? 3624-4 1 27582-9 4w 3507-5 28502-3 68-9 1 34635-51 2886-44 5 6 5w 3520-5 02 28397-1 (39-4) (32881-7) J 4 3409-9 29326-7 63-59 33801-5 2957-6 1 7 3w 3456-4 09 28923-7 2n 3349-8 29840-0 8 In 3413-8 1 29284-6 A 1 (2); 2a, 3, 4 (12); 2&, c (13); 5 (12); 6, 7, 8 (10); D are Eder and Valenta or Exner and PTaschek. 1 The Zeeman patterns are anomalous as in Cu, numerically about 5/10/6; 0/7/6; 0/5/6. f Bloch 1651-5, n- 60551-1; McLennan 1650-8, n = 60576-7; mean taken. As they stand they are S sequent displacements on 7) 22 . $ e. (2) 2727-5 is n = 32882-0; (I) 3286-08. n is n = 32881-43; mean taken. AgF AgF m 7 \ n 28900 + n \ I 1 - (57921-6) 57846-9 1846-7. e l 1728-7 2 1 4 2 - 41539-9 41607-72 2406-6 2402-68 1 3 3 4 \n 1 4552-41 4537-1 21960-36 22034-01 (22-30 -4) (96-9 ?) (35884-25) (35959-8) 33316-34 3113-10. e* e. 2516-2 3000-67* 1 1 Iw j u. 3694-85 (24598-52) F, 3a (16); 3fo in a gap, but given as appearing in band spectrum by Dumeld and Rossi. F, 1(2); 2, 3,4(16). 1 Also 1808-0. v = 57926-34; and 1755-7. c = ... 19-84, both with equally probable 1-4. 2 Also linked by c, to 1757-9. 3 Also 11. 2607-0 = 35888-4, c. 2516-2=35959-8, a parallel inequality w-4, e + 4. 4 Also v. 2786-60-33316-96. Inverse D = D' 4r 5545-635 18027-22 - 7) 2 2r 5333-359 18744-71 -A (12) (12) \r 5276-384 18947-11 -7) 12 ' (12) 260 ANALYSIS OF SPECTRA Combinations -A 2 -P* 3 / X n In 5575-21 s 17913-41 (16) 2 4096-70 s 24403-16 (16) t 18382-0 5438-65 (7) , 18307-9 5460-66 (7) 12251-0 7965-33 (7) t 39951-4 2502-37 (15) 39889-6 2506-25 (15) i 2684-97 s 37233-69 (16) 3 2343-5 s 42658-48 (16) 1 2223-15 s 44967-46 (16) 1 2149-38 s 46510-7 (16) j shifted to red by electric field. 2-d4 -d 4 Gold a = 3195-20; 6=3815-56; c=4607-59; rf = 5634-93; e = 17253-28; ?/^11340-95; = 14934-95. AuP m / X d\ n m X d\ n 1 1072 2428-061 41172-94 5 (1480-5)1 02 67541-5 1(XR 2676-05 37357-62 (1483-12)1 67425-2 2 5 1725-5 57954-2 6 (1462-63)1 04 68364-22 4 1756-0 56947-6 (1464-09)1 68301-68 3 (1572-5)1 01 63587-79 7 (1451-28)1 04 68904-88 (1582-48ft 63191-9 8 (1443-5)1 -01 69275-59 4 (1511-16)1 -04 66149-96 (1516-16)1 65953-1 1 Zeeman pattern =2/4/3. $ From (2) 1900-9. v. AuS 1(1); 2 (2). f Deduced from p 1 - p m combinations given below. S (w ) Au S m / X n 29400 + 33200 + I n X t 2 4 6 7509-8 5837-64 1 13309-98 17125-54 71-77l I 45633-56 2190-7 3 4 5 10 4811-81 4065-22 20776-50 24592-07 (84-95) (41977-83) * In 3573-941 27972-50 83-27 5 38595-88 2590-19 5 2r I 3856-60 3361-38 25922-38 29741-28 6 1 2r ( - 5 X ) 3714-96 ( - dj) 3253-86 (26921-42) (30736-94) 2a ( 14) ; 26, 36 ( 1) ; 3a (Exner and Haschek) ; 4, 5a, 6 (Eder and Valenta) ; 56 (Exner and Haschek) 1 Zeeman pattern = 2/4/3. * (47i) 2382-50 ( - 105^= 41977-40 f This belongs to a displaced S (4). (In) 2380-5 (105^ = .. .78-21 APPENDIX 261 Au7J> AuD m 7 \ d\ n 29400 + 33200 + n \ d\ 7 1 2 (36550-5) (33502-2) (15264-1) (2735-94) (2984-82) (6551-30) [17043-41] 69-85 69-13 87-65 (69-73) [56203-77] 55953-45 60024-01 (41896-27) [1779-2] 1787-2 1666-0 ?387-82 ( 105j) 05 25 4 1 4 3 6 5837-64 1 4792-79* 17125-54 20858-97 [22496-97] (69-36) 85-90 69-59 (41815-82) 45712-83 36442-22 2391-7 (-55^ 2186-9 2743-27 05 -06 In 2 1 4 5 4 2n I 1 4437-44 3799-44 (25 t ) 3990-0 3470-47 -02 22529-32 26312-33 (25034-17) 28806-40 [26384-50] 69-00 83-85 87-15 36408-65 40255-38 37767-91 2745-80 2483-4 2646-98 s 1 2n I 6 7 2 2 1 2 2w 2 3787-37 3310-34 3675-11 3674-0 3223-03 (-Sj) 3604-94 -40 18 00 26396-23 30199-89 27202-44 27210-66 31017-94 (27742-70) (85-22) (69-56) (69-89) (68-76) (36370-60) (31736-68) (31729-12) 31194-82 2748-9 ( - 25) (5) 3145-77 (5) 3146-52 3204-75 In 1 3 4?t 8 9 2r 1% 2n 1 3557-13 3131-75 ( - 35J 3528-25 3106-70 2 -01 -1 28104-65 31921-95 (28366-99) 32179-38 66-58 82-93 (68-86) 83-58 30828-51 34643-91 30570-84 34387-78 3242-83 2885-68 3270-17 2907-18 2 2 1 3 2n 5 2, 3a(l); 36 ...9(16). 1 Zeeman pattern = 2/4/3, is also S s (2). 1 (2); all others (16). 2 Zeeman pattern =0/1/1. = 1. 7> 12 = e. (2) 19988-97; D 12 is calculated from 7> 12 ; also is (5 X ) 38962-81. e. D n =v. (5r) 17920-37; D^ = e. (2n) 23805-56. = 2. D 12 , mean of (4) 41866-75 ( - 105j) and (2) 41928-72 (118J; D n is (In) 41798-68 ( -55 X ). m = 4. The whole set seems dispersed. Thus Z) n shows displaced lines all of intensity 1 by suc- cessive 5 X on the limit, viz. (5 X ) 25045-39 = ...34-63; (2dJ 25055-69 = ...34-17; (45 t ) 25077-80 = ...34-66, agreeing very closely with the calculated. The 7> 12 gives a satellite separation whose source is 85. There seems also a parallel set: (3/i) 3971-80, 25170-53 (1)3437-32, 28984-23 . . .72-88 I (Ir) 2959-90, 33775-23 . . .86-99 I (1) 2659-53, 37589-75 m = 5. D 22 is shown by two displacements: (5) 56374-88 (35) =...70-52 and (In) 36367-70 ( - 25) = ...70-60. But the first is 7) u (4). u. m = Q. The displaced D 12 , D n would seem justified by their order of intensities and same dis- placement = 5. w = 7. 3604-94 is exactly the calculated (3 1 ) D x (7). But this line is also the combination line Pil -Pi 7. The values coincide. Whether the observed is either or both, there is nothing to decide. m = 8. The calculated 7> n gives a better v with 7) 22 , and a closer mean limit. 262 ANALYSIS OF SPECTRA F(<*) AuF m / \ n 26400 + 26700 + I n X } In v. 5487-87 -(3532-51) 3 v. 5413-42 -(3282-00) (31-02 + 1-61) I 56744-0 1762-3 2 1 (2dJ v. 3492-991 (13667-41)? (84-68) 4 2 39292-11 39542-25 2544-29 2528-2 3 3 In (5) 5747-76' (25 X ) 5087-87 (19384-04) (19629-94) (85-25) (32-73) 6 (33586-45) 33835-33 ' (5J 2975-73 2954-64 4* 6n 4549-64 21973-73 (82-17) 5 (30990-61) 3228-0 (-85)* 5 In 3 4279-24 (25j) 3752-90 23362-19 (26619-36) . (82-17) (32-64) 1 1 (29602-15) 29845-93 (5) 3373-02 3349-60 6t In 4128-80 24213-43 84-62 In 28755-79 3476-58 7 2 3 4041-07 4001-60 24739-07 24983-08 83-06 (29-80) 3 In 28227-06 (28476-51) 3541-71 ( - S) 3515-19 8 In Ir 3984-18 3945-19 25092-34 25340-32 82-83 (33-18) 7 3 27873-33 (28126-04) 3586-66 (-8J 3555-58 All spark lines by (16). This is one of several F types, for even orders 2, 4, 6 not seen. * There is a displaced set F (4) (85): (3n)4543-86, 22001-67, (2n)4492-49, 22253-23 f There is a displaced set about F (6) (165): (2n) 4126-31, 24228-04 (2)4084-31, 24477-17, ...30-70, I (2); 3a(l); others (16). It depends on F 2 =N/(l +9A) 2 , f(l)=N/(l + 8A) a ; ...85-93, 5, 30970-20, 3228-0 1, 28984-23, 3437-32 note Inverse D = D f 6278-37 15923-38 -Z> 22 ' 4 4 5230-47 2 5064-75 19113-51 - 19738-92 - (D (1) (1) Combinations m 1 Comb. ' X n Comb. I X n ft+ftl i 1696-5 58944-9 -36d\ 2 Pi-Pi 2 ^ Pi+p z 2 4 4 7 5957-24 2371-69 2315-94 16781-73 42151-41 43165-97 3 v - :| 2n 3869-75 3811-60 25834-32 26228-41 4 ft -ft* 3 4002-57 24977-02 p*-p*4 2 3496-08 28595-45 5 p 2 -p 2 5 1 3324-9 30067-6 6 Pi-^6 1 3676-62 27191-28 p z -p 2 (j 4n 3230-73 30944-04 7 Pi-Pil 2 3604-94 27731-94 8 ft-M 2 3557-13 28104-65 * 1 (2); 2. ..8 (16). 1 (4n) 4523-20 22102-18 l (2) 4576-15 21846-41 APPENDIX 263 GROUP II (a) 10. 11. 12. 14. 15. 16. REFERENCES KAYSER and RUNGE. Wied. Ann. 43, 385 17. (1891). 18. NACKEN. Z. S. wiss. Pivot. 12, 54 (1913). 19. FOWLER and REYNOLDS. Proc. Roy. Soc. 20. 89, 137 (1913). 21. FOWLER. Proc. Roy. Soc. 71, 419 (1903). 22. FOWLER. Phil Trans. 214, 225 (1914). PEROT. C.R. 172, 578 (1921). 23. PASCHEN. Ann. d. Phys. 29, 625 (1909). 24. LORENSER. Diss. Tubingen (1912). 25. MEGGERS. Butt. Bur. Stand. Wash. No. 312 26. (1918). 27. EDER. Denks. Wien. AJcad. 74, 45 (1903). 28. SAUNDERS. Phys. Rev. 20, 117 (1905). 30. LYMAN, also (13) HANDKE. Spectroscopy in extreme violet. 31. SAUNDERS. Astro. J. 43, 234 (1916). HERMANN. Ann. d. Phys. 16, 684 (1905). 32. CREW and MCCAULEY. Astro. J. 39, 33 (1914). HOLTZ. Z. S. wiss. Phot. 12, 101 (1913). SAUNDERS. Astro. J. 52, 265 (1920). MEISSNER. Ann. d. Phys. 50, 713 (1916). HAMPE. Z. S. wiss. Phot. 13, 348 (1914). SAUNDERS. Astro. J. 32, 153 (1910). RANDALL. Astro. J. 34, 1 (1911) and Ann. d. Phys. 33, 745 (1910). LEHMANN. Ann. d. Phys. 8, 649 (1902). FOWLER. Astro. J. 21, 84 (1905). SAUNDERS. Astro. J. 21, 195 (1905). WERNER. Ann. d. Phys. 44, 294 (1914). SCHMITZ. Z. S. wiss. Phot. 11, 209 (1912). SAUNDERS. Astro. J. 51, 23 (1920). RUNGE and PRECHT. Ann. d. Phys. 14, 419 (1904). EXNER and HASCHEK. Wien. Ber. 120 (Ila), 967 (1911). EDER and VALENTA. Denks. Wien. Akad. 67 (1898). Magnesium MgP'" m / A n m / \ n 1 8R 5167-303 - 19347-07 4 2nr 6318-55 15822-11 WR 5172-673 - 19326-97 In 6319-08 15820-80 IOR 5183-800 - 19286-24 5 In 5784-9 17281-6 2 60 15028- 3 l 6652-34 3 36r 7658-43 13053-93 1 (2); 2 (7); 3 ... 5 (8). For 3 Meggers (9) gives 7657-5. 1 With this goes for P (2), (2), 2915-471, (2), n =34288-64; mean limit = 20470-49 -7. m / \ n d\ m / \ n d\ 2 IQR 5183-614 1 19286-20 5' GR 2782-9S9 2 35922-03 WR 5172-690 1 19326-94 8R 2779-853 35962-55 8R 5167-340 1 19346-94 GR 2778-289 35982-78 3 10 3336-688 29961-25 6 In 2698-16 37051-32 018 10 3332-163 30001-93 In 2695-21 37091-88 8 3329-934 30022-01 In 2693-75 37111-98 4 6 2942-01(5 33980-40 7 Inn 2649-08 37737-75 022 5 2938-487 34021-22 Inn 2646-24 37778-25 4 2936-754 34044-04 Inn 2645-09 37794-67 5 GR 2781-431 2 35942-15 13 8 2617-57 38193-46 -014 GR 2778-289 35982-78 2614-74 38234-81 GR 2776-704 36003-33 9 2596-01 38510-66 -026 2593-28 38551-19 1 (6); 3 ... 8 (2); 9, 10 (3). Perot (6) gives interferential measures for 2 of -614, -690, -340 which give i^, v 2 mean of the others. 1 Normal Zeeman pattern. 2 m = 5 gives abnormal v lt v 2 ; m=5' is a parallel set to S (5) and is (A 2 ) S (5). 264 ANALYSIS OF SPECTRA Mg D" f m / \ n d\ m / X n d\ 2 IOR IQK 8R 3838-283 1 3832-306 2 3S29-364 3 26045-95 26086-57 26106-61 8 2606-73 2603-98 2602-59 38352-34 38392-83 38414-32 01 3 10 8 8 3096-914 3093-011 3091-093 32280-87 32321-61 32341-66 9 2588-37 2585-63 2584-32 38624-10 38665-21 38684-91 01 4 5 4w 2851-67 2848-38 2846-75 35056-93 35097-40 35117-49 10 2575-02 2572-34 2570-96 38824-64 38865-07 38885-29 -02 5 4raw 4nm 2w 2736-60 2733-55 2732-04 36530-92 36571-67 36591-49 06 11 2565-00 2562-30 2560-96 38976-25 39017-32 39037-73 -02 2 i 3 ; 6 7 2im 2/m Inn 2672-56 2669-65 2668-20 2632-98 2630-14 2628-73 37406-22 37446-98 37467-63 37969-95 38010-94 38031-31 10 005 12 13 2557-29 2554-79 2551-22 2548-56 39093-72 39133-35 39186-71 39227-60 -02 -03 6 (2); 7 ... 13 (3). But D^ (4) is from (3) since (2) does not separate from the strong JP' (1). Zeeman pattern =0. 1/1. 2. 3/2. 2 Zeeman pattern = 1. 2/0. 1. 3/2. Seeman pattern = 0. 2/0. 2. 4/2. Mg F"' 3 (60) 14874-6 6721-05 4 (30) 10812-9 9245-73 3, 4 (7). Combinations Comb. / X n Comb. I X n 1 2 3 4 5 ft 1 -ft 2 ft 1 -ft 2 P 9 l-p l 2 Pi 1-ft 2 ft 1 -ft 2 2 2 2 1 2 3854-26 3848-24 3845-12 3854-68 3848-93 25938-11 25978-68 25999-76 25935-30 25974-03 6 7 8 9 10 11 12 pl2-d4 35 10 20 10 1 1 15768-3 15759-1 10969-85 10963-2 3050-75 3046-80 2833 6340-15 6343-85 9113-53 9119-05 32769-5 1 32811-9 1 35288 6 I ... 5 (8); 6 ... 9 (7); 10, 11 (10); 12 (11). p-p (m) allocated by Lorenser; p -d (m) by Paschen; p -f(m) by Hicks. The last as usual shifted by electric field to violet. Mg"P(l. m) Mg" P (2. m) m / 10# 10JB X n d\ m / X n d\ I 2795-523 2802-698 35760-97 35669-44 3 3 4 3615-64 3613-80 27649-78 27663-86 2 (1239-90) (1240-37) 80651-3 80620-8 10 3 (1025-96) (1026-11) 97469-1 97455-05 -01 I (2); 2, 3 calculated from observed combination lines. 3(5). APPENDIX 265 Mg" D m ' X n d\ m ' X n ' m / X n m / X n 1 (55461 J 1 -(1803-07) 4 2 4685-264 21337-56 2 1 7326-099 13646-07 5 4412-30 22657-59 3 3 5188-846 2 19266-75 2... 4 (16); 5(18). is P' (I) - 21849-23. ~ Zooman pattern ^ 270 ANALYSIS OF SPECTRA m / X n m / X n 3 5 4878-132 1 20493-93 7 1 3889-141 25705-36 4 5 4355-099 22955-15 8 3833-96 26075-35 5 1 4108-544 24332-68 9 3795-62 26338-74 6 1 3972-578 25165-46 10 3767-42 26535-83 3 ... 7 (16); 8, 9, 10 (18). l Zeeman pattern = 0/1 /I. This is Saunders' SL 3. These singlets are as finally allocated by Saunders (18). Combinations ,v ( 1) - d (m) = 23652-30 + D' (m) 1 4575-43 21849-51 2 2680-36 37297-43 3 2329-33 42917-71 4 2221-91 44991-94 p'l-p'2 In 7645-25 " 13076-48 a' (1) -*' (ra)= 23652-30+$' (m) 3 2392-22 41789-42 4 2257-40 44285-02 5 2177-8 45903-5 p' 1 -p' 3 2/1-2/4 d'l-s'3 in a band about 5546 4929-25 20302-02 - No reference to observation given. 19935-2 6572-783 3761-72 15210-05 26576-09 Pi" 1 - a' 3 These combinations, s' -p 2 '" excepted, are due to Saunders (18). Strontium BtB"' m 7 X n d\ m 7 X n d\ 1 In 7070-102 1 14140-17 4 2 3628-62 27551-93 7 6878-347 2 14534-37 1 3577-45 27945-99 6 6791-046 3 14721-21 2 3553-7 28132-78 2 4w 4438-044 1 22526-13 5 2w 3504-27 28528-47 -05 4 4361-710 2 22920-35 3456-52 28922-56 -03 3 4326-444 3 23107-19 1 3434-95 29105-31 3 4 3865-59 25862-94 4 3807-51 26257-45 3 3780-58 26444-48 1, 2(20); 3,4, 5(1); 4c (21). 1 Zeeman pattern anomalous and same for m = l, 2, is apparently near 0/3/2 or two com ponents in normal 0. 1/2. 3/2 suppressed. 2 Zeeman pattern anomalous for both = 1/3 + /2. ? the two normal s not separated. 3 Zeeman pattern normal for both =0/4/2. APPENDIX SrD'" 271 m / X n m / \ n ] 4 3/172, 3705-90 3 26976-34 J S 30110-7 3321-19 v2r* 3653-91 27360-17 1 6 29225-9 3421-74 3rc 3653-26 27364-03 i 6 27356-2 3655-60 to 3629-12 27547-06 o 26915-4 3715-47 6 26024-5 3842-66 5 4ww 3548-1 28176-07 4w 3499-61 28566-46 2 ( 3 4971-649 1 20108-46 Oil 3477-2 28750-56 1 4 4967-92S 2 20123-51 (QRn 4962-244 3 20146-56 6 3457-54 28914-03 ) 6 4876-062 4 20502-64 In 3411-62 29304-33 j Qn 4S72-485 5 20517-68 In 3390-09 29490-43 Cm 4832-075 20689-27 7 In 3400-39 29401-11 3 ( 4033-19 24787-29 1 3 4032-387 24792-22 ( 4v 4030-386 3 24804-53 J 3 3970-049 25181-50 1 3 3969-270 6 25186-43 4 3940-806 25368-37 . 1 (22); 2 .. 1 Zeeman pattern =0/5/2? 3 Normal Zeeman pattern = 0/7/6. 5 Zeeman pattern possibly 0/1/1 normal. 6(20); 66 ...7(1). 2 Zeeman pattern = 4/8 +/6 instead of 4/7/6. 4 Zeeman pattern = 0/8 + /6 ? 6 Zeeman pattern = 0/8 + /6. m 7 X n d\ m / X n d\ 2 1 4 6754-21 14802-06 4 4r 4337-704 23047-21 4 6708-10 14903-86 3r 4319-090 23146-53 4 6643-545 15048-05 B 2w 4308-13 23205-42 5 6617-268 15107-80 5 4087-67 24457-87 3 4071-01 24557-93 12 4892-666 20433-05 4061-21 24617-18 |6 4892-009 2 20435-81 13 4869-194 20531-55 6 , 3950-96 25304-16 -17 )4 486S-739 3 20533-47 3935-33 25404-64 Aril 4855-078 4 20591-24 3926-27 25463-25 7 3867-3 25851-47 -31 2 (23); 2 ... 4 (20); 5, 6 (24); 7 (25). 1 Those are membra disjecta, viz. F l (2), F z (2), F 2 (2) (3A 2 ), F 3 (2) (3A 2 ). 2 Zeeman pattern =0/5/4. 3 Zeeman pattern = 0/7/6. Zeeman pattern =0/4/3. TO ' X n m 7 X TO 1 1072 m 4077-714 1 4215-515 1 -24516-64 -23715-23 3 2 1 2471-71 2423-67 40446-56 41247-49 o 4 4 4305-459 l 4161-812 1 23219-81 24021-24 4 ITO On 2053-3 2020-5 48688-5 49478-6 1. 2(20); 3. 4(31). All Zeeman patterns normal. 272 ANALYSIS OF SPECTRA Sr" D m I X n m / X n 2 iioo 10038-8 -9961-68 4 jl 2324-60 43006-63 \ 200 10328-3 - 9682-45 11 2322-52 43045-14 200 10915-0 -9162-01 2 2282-14 43806-74 3 14 3474-901 ! 28769-58 5 On 1995-7 50093-6 |6 3464-470 2 28856-20 On 1965-2 50870-8 5 3380-721 3 29571-02 6 1847-0 54143-6 1820-0 54946-8 2 (22); 3, 46 (20); 4, 5 (21); 6 (12). 1 Zeeman pattern = 3/4/3. 2 Zeeman pattern = 0/3 - /2. 3 Zeeman pattern = 0/1 + /I , m 7 X n d\ m 7 X n d\ 2 In 4051- n 24678-65 4 9 1778-8 56218-9 8 1769-8 56504-9 3 372 2166-11 46154-46 2 2152-82 46437-81 5 5 1620-7 61704-0 007 4 1613-3 61987-0 2, 3 (21); 4, 5 (12). Sr P' (I. m) ... 20149-6 ... d' (1) -p' (m). m 7 X n m 7 X n I 1072 4607-340 1 21698-43 2 2 2931-856 34098-14 2 < 6 7167-24 13948-53 3 2 2569-502 38906-42 3 5 5329-816 18757-16 4 2 2428-113 41171-79 4 2n 4755-467 21022-56 5 ITto 2354-40 42462-33 5 2n 4480-540 22312-49 6 In 2307-5 43325-2 6 Wr 4313-23 23177-98 7 In 2275-5 43934-4 7 In 4202-95 23787-15 8 In 2253-5 44363-1 9 \n 2237-4 44682-2 10 In 2226-0 44911-0 1 ... 4 (20); 5 ... 10 (21). 2 (9); 3 ... 6 (20); 7 (21). 1 Zeeman pattern =0/1/1. These are Saunders' original SLl, SL2. SrF' m 7 X n m 7 X n 2 8n 6408-465 1 15600-06 5 U 4406-11 22689-40 3 4 5156-068 2 19389-23 6 Inr 4253-7 23503-1 4 4n 4678-304 3 21369-30 1 Zeeman pattern = 0/6/5. 2. ..5 (20); 6(21). 2 Zeeman pattern =0/7/5. 3 Zeeman pattern =0/1 /I. Combinations p* "2 (6) 6892-62 14504-28 allocated by Lorenser (8). APPENDIX Barium BaP'" 273 m / \ n m 7 X n 2 40 15 20712-0 21477-2 4826-9 4655-0 3 ^i 10189-1 10272-9 10326-4 9811-8 9731-7 9682-4 2 (22); 3 Randall given by Saunders (28). 1 The set are doubtful. Mantissae much too small and second difference > A 2 . m 7 X n d\ m 7 X n d\ 2 1 10 8559-90 11679-17 5 Inn 397S-362 3 25147-84 5-0 1 7961-20 12557-47 In 3841 -15 4 26026-6 Onv 3787-23 26397-1 3 4r 4902-898 20390-42 6 3828-93 26110-3 -76 6r 4700-446 21268-63 3704-23? 26988-5 5r 4619-978 21639-07 4 3r 4239-576 23580-63 Inn 4087-371 2 24458-71 2 4026-57 24828-97 2 (9); 3, 4a6, 5a (27); 4c, 5bc, 6 (28). 1 The S (2) set have been also given as 7905-770, 7392-423, 7195-246 or n = 12645-63, 13523-77, 13894-38. But these are the linked S (2). d. In Ba, d = 963-14. 2 is also 7) u 4. 3 is possibly (65 t ) S r * Original measure 3841 -72 -2, see p. 138. BaD" m 7 X n m 7 X n 1 (20 ^30 (50 $30 J50 30 22313-4 23255-3 25515-7 27751-1 29223-9 30933-8 -4480-56 -4299-08 -3918-23 -3602-61 -3421-05 -3231-3 4 5 (Inn J2r \lnn \lnn 4087-371 3 4084-802 3947-475 3945-173 3890-57 24458-71 24474-09 25325-50 25340-28 25696-0 2 * * * (1072 (IQE \ 8R Ir 5818-906 5800-299 5777-695 1 553S-534 2 5519-115 2 5426-616 17180-60 17235-71 17303-14 18060-10 18113-82 18429-36 6 j 3898-58 3894-34 3771-93 3769-48 3719-92 25643-3 25671-0 26504-1 26521-5 26874-7 3 ( . 3789-72 26379-89 t J5, (Iv Uv \ A-. 4493-641 4488-973 4332-919 22247-44 22270-57 23072-65 i 3788-18 3667-93 3667-60 26390-6 27255-7 27258-1 (4v 4v 4roZo-UU4 4264-386 Z6LZo-oi 23443-45 7 ! 3721-17 3720-85 3603-40 26865-7 26886-0 27743-7 1 (22); 2, 3, 4 (27); 4c, 5, 6, 7 (28). 1 Zeeman pattern =0/7/6. 2 Zeeman pattern = 0/1/1, intensity too large, probably P' (1). 3 is also S z (4); better take 7) 12 =7) 22 - v. * ? normal set. ? a D' set; probably 7) 3 (2) is \n, 5416-344, r? =18457-51. t Probably 7> 23 (3) is 3, 4325-152, /? =23114-09. H. A. S. 18 274 ANALYSIS OF SPECTRA For displacements in list see note at bottom. ra / X n d\ m 7 X n d\ 2 (Inn 5279-619 18935-50 00 8 i 3222-28 1 31025-1 J4w 5267-033 18980-78 00 i 3221-63 31031-4 15 3n 5175-619 19315-99 3183-96 31398-6 I 3 5303-576 18849-96 i 3183-16 31406-4 \lnn 5253-807 19028-52 3165-60 31580-6 3 (1 3998-05 25006-08 9 i 3193-97 31300-2 U 399S-663 2 25020-07 00 i 3193-91 31300-8 -03 (872 399S-395 3 25034-28 00 3155-67 31680-1 J 3 3937-876 25387-24 I 3155-34? 31683-4 J7r 3935-715 4 25401-16 3137-70 31861-4 6r 3909-922 5 25568-74 10 ( 3173-72 1 31499-7 4 ( ! 3596-33 27798-3 \ 3173-69 31500-0 -02 3r 3593-282 27821-80 3135-72 31881-5 3 3588-132 27861-73 009 3117-94 32063-4 3 3586-562 27874-25 Uw 3547-767 28178-72 11 3158-54 31651-1 -04 J6r 3544-713 28203-00 3121-02 32031-6 6r 3525-025 28360-51 12 , 3146-90 31768-3 -05 5 f 3421-48 29218-9 3109-63 32148-9 3421-01 29222-9 - -25 llr 3420-405 29227-94 -11 13 3137-80 31860-6 -02 ( 3377-39 29600-3 \ 3376-98 29603-9 14 t 3130-6 31934 00 3356-80 29781-9 g f \ 3323-06 30084-3 \4r 3322-80 30086-7 40 j 3281-77 30462-8 \ 3281-50 30465-3 3262-30 30644-6 7 ( 3262-24 1 30645-2 \ 3261-96 30647-8 17 3222-44 31023-6 } 3222-19 1 31026-0 3203-70 31205-0 39826-77; mean limit -32430-1 8 36989-84 =32428-91 2 ... 4 (27) except F 13 4 (28); 5 ... 13 (28). Saunders gives no indications of line character. Allocated by Saunders except the usual fragmentary F (2). They do not appear all normal, but as collaterals. The readings of (27), (28) differ by more than their probable errors. 1 Not clearly resolved. 2 Zeeman pattern = 0/4/3 ? 3 Zeeman pattern = 0/6/5 ? 4 Zeeman pattern = 0/1 /I ? 5 Zeeman pattern = 0/4/5. F n (3) 1 2510-26* ? F u (4) 6r 2702-646 Displacements in above list : w = 2. The set are F 12 (2), F u (2), ^ 22 (2), (185) F 23 (2), (185) F 3 (2). w = 3. The first is (5 X ) F n (3). F u (3) gives with F u (3) above mean limit = 32433-21. m = 4. The set are F 13 (4) (4A 2 ) ; ( - 35 X ) F 12 (4) (2A 2 ) ? ; F n (4) (4A 2 ) and 27874 is ( - 25 t ) F u (4) (2A 2 ). m>5. The F^ are calculated from/ 2 , i.e. the F t have not split into F 1Z and F n . Combinations (by Saunders) lv 4673-621 21390-71 3v 4591-825 21771-74 fM> 4628-330 21600-03 3w 4589-762 21781-53 3?> 4605-012 21709-40 Measures by (27). APPENDIX BaS" 275 m 7 X n m / X n 2 107? 4554-038 1 -21952-39 5 2 2286-21 43728-74 107? 4934-099 2 -20261-48 2201-07 45420-06 3 8 4899-971 * 20402-59 6 2082-8 48098-91 8 4S24-946 2 22093-53 4 3 2771-354 36072-82 4 2647-280 37763-40 2, 3, 4(27); 5, 6(21). Zeeman pattern = 1/3. 5/3. 2 Zeeman pattern = 2/4/3. BaD' m * \ n m 7 X n 2 \ 8 J107? 87? 5853-699 * 6141-760 2 6496-902 3 - 17078-48 - 16277-48 - 15387-69 4 5 2641-390 2634-795 2528-52 37847-61 37942-34 39538-48 2* ^60 |80 60 10034-8 10650-5 12084-0 - 9963-2 -9387-1 - 8273-4 5 1 2235-50 2232-79 2154-02 44720-59 44774-85 46412-04 3 1 87? 8r 4166-017 1 4130-683 2 3891 -788 2 23996-99 24202-26 25687-87 6 1 2055-0 48648-15 2, 3, 4 (27); 4r, 5, 6 (21); 2* (30). 1 Zeeman pattern = 3/2. 4. 6/3. 2 Zeeman pattern = 0/3 -/2. 3 Zeeman pattern 0/1/1. * m " *-- ^ /nx ----- ---. Ba z^eeman patrern = u/rf - /a, * Two sets for D (2) giving rise to two F. m / X n m 7 X n 2 3 2 2n In 5614-141 5437-393 2500-27 17807-90 18386-06 39985-20 2 3 l-i !5 10233-8 9608-83 9455-94 2347-577 9769-27 10404-23 10572-46 42584-11 4 67? 2335-247 42808-93 5 67? 2304-216 43385-38 li 6 3 1694-3 1677-9 59021-4 59598-3 4 5 1 1 2 1786-61 1592-9 1572-9 59023-3 62780-6 63578-8 2(27); 3(21); 6(12). 2a(22); 26, c (9); 3(27); 4, 5(12). Ba P'\ ... 11395-2 ... {rf/ -/ (m) m 7 X ft m 7 X 71 1 107? 5535-534 1 18060-10 1 40 15000-4 6664-9 2 87? 3071-615* 32546-75 .) 8r 4726-45S 3 21151-60 3 6r 2702-646 36989-84 3 2 3906-20 25593-97 4 6r 2596-678 38499-27 4 3>- 3688-473 27103-79 5 , 2543-2 39308 6 2500-2 39985 7 2473-1 40423 ... 4 (27); 5 ... 7 (21); 6, 7 not positively identified. I (22); 2 ( 1 Zeeman pattern 0/1/1 is a ? A,;/" (2). 3 Zeeman pattern " Zeeman pattern 0/1 -i-/l. 1 (22); 2(27); 3(1); 4 (27) 1 8 2 276 ANALYSIS OF SPECTRA BaT)' m / X n m / X n 2 40 15000-4 - 6664-9 5 4ra 5267-033 18980-74 3 70 9831-7 10171-5 6 3w 4877-650 20495-96 4 2w 6233-586 16037-69 7 Irc 4663-80 21436-56 2, 3(22); 4,- 5, 6(27); 7(21). BaT? 1 ' 2, (77?) 5826-294, 17158-82; 3, 4080-93, 24497-4; 4, 3789-74, 26397-7 2 (27); 3, 4 given by Saunders (28) without reference. Singlet combinations s'l-/'2 87? 3501-107 28554-25 (27) Zeeman pattern =0/1/1. ,5' l-f 3 Gv 2785-264 35892-69 (27) s'l-/'4 2646-50 37774-8 (28) s'l-s'2 4w 3900-54 25631-2 (1) ? (153J Z>, 8 "' (4). ,s'2-2/3 2 8799-70 11360-91 (9) s'2-p'4: 2 7766-80 12871-78 (9) '(2) p'l-s'2 40 7.S207-3 7569-85 (22) p' 1 -/' 1 100 9527-3 10493-6 (22) Triplet singlet combinations a' 1 - ,"' 1 6 20 7911-36 3244-20 11304-2 4284-90 1 3599-429 3413-84 12636-57 30815-4 8844-1 23331-2 27774-28 29284-3 (9) King per (28) (22) (28) (27) (28) '*-*'" 2 i*'"\~- p ''l d z '" l-p' 4 1 The strong line (8) 4283-111 (27) has the proper Zeeman pattern = 0/1/1. The last six allocations are by Saunders (28). Radium RaT)" Lines have been suggested in [11. p. 64] for these two series but they are extremely dubious, and are here omitted. It is, however, clear that v l is close to 2050 and probably v 2 to 882. RaS" RaTT' m 7 X n m 7 X n 2 100 3814-578 1 -26207-94 2 \ 5 4903-2 - 20389-27 50 4682-359 l - 21350-94 MO 5660-84 2 -17660-51 4 6439-1 - 15525-9 3 15 5813-85 1 17195-63 10 4533-327 1 22052-79 3 ^20 4436-489 22534-16 )50 4340-830 23030-71 4 1 + 2976-17 33590-75 50 3649-748 27391-50 4 t f 5 2736-20 36547-04 2, 3(30); 4(31). 1 Zeeman patterns normal, 1/3. 5/3; 2/4/3. 2, 3(30); 4(31). 2 Zeeman pattern =0/3/2. APPENDIX 277 m / X n 2 7 4305-0 23222-38 3 3941-3 25365-32 2 (30). The A. B, L congeries of II (a). Wave-lengths A. Ca 5, 5601-283 0/3/2 9, 5588-746 0/4/3 5, 5602-829 0/9/5 8, 5594-464 0/1/1 6, 5581-973 0/4/3 8, 5598-484 ? 5, 5590-109 V Sr 5, 5534-796 0/3/2 7, 5480-840 0/17/12 5, 5540-033 5, 5504-166 0/7/6 6, 5450-834 0/17/12 6, 5521-752 0/2/3? 5, 5486-121 0. 4/7. 11 -/6 Ba 1, 8018-21 In, 7865-51 by () 7, 7877-93 8, 7780-49 2, 7636-88 by (9). 2, 7766-80 7, 7672-12 10, 6693-855 0/3/2 9, 6498-769 0/3/2? 9, 6675-286 0. 7/21/12 10, 6527-324 0/1+ /I 8, 6341-693 0/3/2 9, 6595-341 0/7/12 9, 6450-863 0/3/2? All (26). ? Depending on second D (1). Ir, 5381-25 Inn, 5253-807 In, 5404-920 2, 5309-20 Inn, 5265-566 B. Ca 5, 5270-272 5, 5265-559 3, 5264-237 3, 5264-237 3, 5261-701 1, 5260-375 Sr 6, 5256-897 0/4/3 6, 5238-548 0/1/1 5, 5229-266 0/4/3 5, 5225-110 0/3/5 5, 5222-200 0/4/3 2, 5212-968 6, 6386-507 0/7/5 6, 6388-245 4, 6345-760 5, 6380-740 0/3/2 4, 6363-932 0, 6321-768 5, 6369-959 Ba 8/2, 6110-808 0/1+ A 8/2, TJ063-149 0/1/1 7, 5971-715 0/1/1 1R, 6019-505 0/1/2 IE, 5997-102 0/1/2 6, 5907-656 L. Ca 9, 4318-648 0/3/2 !. 4302-525 0/3/2 7, 4307-738 0/3.2 8,4298-989 0/3/2 9, 4283-008 0/3/2 9, 4289-363 O:M.> 4, 3009-212 5, 3006-864 4, 3000-865 4, 2999-651 4, 2997-309 4, 2994-953 Sr (i, 4876-323 0/3 - I'l 6/2, 4811-867 0/3 -/2 4, 4784-323 0/3/2 6, 4722-i ) 7i ) 0/3 - /2 5, 4741-917 v / v / 0/3/2 / / r>, 3366-339 6/2, 3351-258 4, 3330-011 5w, 3322-237 0/3/2 4, 3307-548 5, 3301-739 278 ANALYSIS OF SPECTRA Ba L. IE, 4691-630 0/3/2 6K, 4573-881* 0/3/2 8, 4505-936 0/3/2 6^,4599-751* 0/3 -/2 7,4431-914 0/3/2 * Allied. 8, 4523-237 8,4350-375 0/3 + /2 Wave numbers A. B. Ca 17848-10 40-04 17888-14 21-76 2171 17843-17 2669 17869-86 3999 17909-85 13-85 13-92 17857-02 26-76 17883-78 Sr 18062-50 177-81 18240-31 100-51 100-41 18045-43 11758 18163-01 177-71 18340-72 59-74 59-74 18105-17 117-58 18222-75 Ba 12468-18 242-44 12710-62 38095 380-13 12690-21 158-92 12849-13 241-62 13090-75 181-57 181-49 12871-78 158-84 13030-62 14935-09 448-33 15383-42 381-05 381-03 14976-64 339-50 15316-14 448-31 15764-45 181-54 181-52 15158-18 339-48 15497-66 Depending on second D(l). 18578-59 499-93 19028-52 258-14 . 18406-53 240-20 18836-73 149-30 18949-03 Ca 18969-08 21-75 18986-06 4-77 18990-83 13-92 13-93 18998-04 1-94 18999-98 4-78 19004-76 Sr 19017-34 100-49 19083-95 33-88 19117-83 59-74 59-76 19133-03 10-66 19143-69 3390 19177-59 15653-69 100-50 15649-43 10476 15754-19 59-78 5980 15667-83 41-38 15709-21 10478 15813-99 15694-35 Ba 16359-93 381-04 16488-52 252-45 16740-97 151-58 181-53 16608-07 62-03 16670-10 252-40 16922-50 APPENDIX 279 23207-52 33314-05 4723 13-48 30021-33 7024 21857-16*) 21734-26* 329-59 452-49 Ca 23148-90 105-85 23254-75 52-20 23306-95 33221-64 10589 33327-53 52-28 33379-81 Sr 20501-54 39422 20895-76 186-87 21082-63 29697-35 394-22 30091-57 18680 30278-37 Ba 21308-61 878-14 22186-75 37054 22557-29 86-75 86-78 2595 26-04 274-62 274-57 133-64 133-63 23235-65 10588 23341-53 33247-59 10598 33353-57 20776-16 394-17 21170-33 29830-99 394-21 30225-20 793-26 22101-87 87820 793-32 22980-07 In the above the Zeeman patterns are based on measures by Runge and Paschen, Moore and Miller. It is not easy to settle the numerical patterns by the two latter and those given must be taken as indicatory. GROUP II (6) REFERENCES 1. KAYSEU and RUNGE. Ann. /*. 7, 909 (1902). STARK. Ann. d. Phys. 16, 490 (1905). BLOCK. J. d. Phys.' 2, 229 (1921). SAUNDERS. Astro. J. 43, 239 (1916). 280 ANALYSIS OF SPECTRA Zinc Zn 8"' m I 1 / X n d\ m / \ n d\ 2 2 2 1817-1 1829-9 1836-6 -55032-7 - 54647-8 -54448-4 5 6r 6r 2r 2567-99 2542-53 2530-34 38929-59 39319-30 39508-65 01 2 Ill 4810-535 2 4722- 164 2 4680-138 2 20781-23 21170-13 21360-23 6 4ft 2r 1? 2493-67 2469-72 2457-72 40089-63 40478-45 40676-03 01 3 10# 10# 8r 3072-19 3035-93 3018-50 32540-76 32929-51 33119-60 7 1 In In 2449-76 2427-05 2415-54 40808-15 41190-06 41386-26 -15 4 Sr 8r Qr 2712-60 2684-29 2670-67 36854-25 37242-98 37432-85 -04 1 (3); 2oe(ll); 26 (2); 3 ... 7(1). 1 The separations arc normal within observation limits. It must be either S (1) or a related iplet. 2 Normal Zeeman patterns = 0. 1/2. 3/2; 1/3. 4/2; 0/2/1. Zn U" m / X n m / X n 2 3 (4 ( SR (IQR ( SR \ SR SR ( 3346-04 3345-62 3345-13 3303-03 3302-67 3282-42 29877-68 29881-42 29885-80 30266-70 30270-00 30456-69 4 5 SR SR QR Qnn Qn 4f 2608-65 2582-57 2570-00 2516-00 2491-67 2479-85 38322-84 38709-72 38899-15 39733-94 40121-80 40313-15 \1R (8R ( QR 1 SR 6R 2801-17 2801-00 2771-05 2770-94 2756-53 35689-05 35691-20 36076-95 36078-42 36267-09 7 4 4 In In 2463-47 2439-94 2430-74 2407-98 40581-11 40972-52 41127-55 41516-17 2 ... 7 (1). D x (3) from Handbuch. D n (2) (2)1790-2; n = 55857-84: mean ^(oo )= 42871-8 1-5 D 22 (3) (2) 1982-21; n = 50447-06 : ., =42873-85^1 Measures by (23), (24). Zn P'" m / X n m / X n 1 1012 WR IQR 4810-535 4722-164 4680-138 - 20780-54 - 21169-43 - 21359-51 4 10 8 6 5772-218 5775-645 5777-240 17319-65 17309-36 17304-60 2 10 8 4 13054-89 13151-50 13197-79 7657-906 7601-649 7574-989 5 8 6 4 5308-714 5310-311 5311-039 18831-82 18826-15 18823-57 3 8 6 4 6928-582 6938-733 6943-474 14429-05 14407-96 14398-12 6 4 2 5068-711 5069-667 5070-16 19723-48 19719-75 19717-8 2... 6(4). APPENDIX 281 (i) (5) (5) Spark, Exner and Haschek Spark, Lockyer Zn F" f 3, (100) 16498-6, 6059-50; (50) 16490-3, 6062-55; (20) 16483-7, 6064-90; 4, (4) 11631-7, 8594-8 3 (4); 4 (6). PI (2) P 2 (2) P. (2) PI (4) PI (5) 2w 1 2 Iw 2736-96 2732-15 2729-30 3720-7 3943-7 n= 36526-34 n = 36590-64 n = 36628-82 n = 26869-2 n= 25349-9 mean P (oo ) = mean P x = 22092- 12 1-4 22096- 14 ? 22100-9 ? 22094-43 1 22090-86 3 Combinations P! 1 -/3 In 3515-26 28439-46 ftl-/4 "In 2575-15 38821-23 ?3 4157-62 2781-33 24045-7 35943-69 ft I-/ 4 51-^2 4 2562-70 10979-4 39009-92 9105-48 2v 2751-47 36333-50 p l 2 - dt 3 23 13784-8 7252-42 2n 2736-96 36526-34 p 2 d 3 15 13792-4 7248-43 2n 2601-03 38435-08 ZnD" m 7 X n m / X n 1 8 2025-57 1 - 49354-69 1 t 1 1741-1 -57435-0 7 2062-08 1 - 48479-44 MO 1743-6 - 57352-6 7 1768-0 56561-1 *> 8 2558-03 1 39081-11 4 2502-11 1 39954-45 2 t 2102-35 47551-12 i 3 2100-06* 47602-95 3 1505-8 66407-7 6 2064-32 48426-85 1485-0 67310-7 l(7);2(l);3(9a). 1 Normal Zeeman patterns = 1/3. 5/3; 2/4/3. ZnJ" m ; X H 3 10 10 4924-16 4911-808 20302-47 20353-54 1\" (3) I (3); 2 (7). Zceman pattern =0/2/3? Combinations 4 7m*-7 53W5-5 (3) 1 1895-1 52767-7 (3) 5 J5^-6' 53630-5 (3) 1 1856-3 53868-8 (9a) 3 976-9 10236-0 (9a) 3(4). m / X n c/X m / X n rfX 1 4 2138-67 - 46743-6 4 2n 4298-54 23257-32 -08 2 22 11055-37 9042-950 5 3966 25207 3 3 5 5181-984 19291-64 6 3799 26315 -2 1(10); 2 (4); 3 (11); 4(1); 5, 6(12). S'(2) 1 2040-99 43982-87 (7) giving limit -29012-9. ZnD' m / X n d\ w / X n d\ 2 10 6362-345 15712-61 4 4114 24301 2 3 8r 4630-06 21592-07 5 3880 25766 2 2 (2); 3(1); 4, 5 (12). 1 Zeeman pattern =0/1/1. 282 ANALYSIS OF SPECTRA Zn P' (1. m)} ... 55786 ... {Zn P' (2. m) m / X n m / X n d\ I 4R 2138-69 46743-6 1 22 11055-4 - 9042-950 2 10 1589-76 62902-57 2 25 14039-5 7120-85 3 8 1457-56 68607-80 3 6 7799-615 12817-69 4 4 1404-19 71215-44 4 5 6479-495 15429-12 5 2 1376-87 72728-49 5 3 5937-930 16836-32 -4 6 1 5654-485 17680-30 -3 7 1 5486-190 18222-60 -08 1(10); 2... 5 (8). 1,^(4); 3 ... Combinations ' l-pt"'l 2 3075-99 1 32500-56 (I) *'' 1 ~'Pz" 2 1 1632-11 61270-38 w P*" 1 ' 2 2 4293-02 23287-22 (1) d' 2 /'" 3 50 15682-1 6374-99 (4) p'2-d,'"2 6238-196 16025-97 (13) 2/2 -da'" 2 3 6239-462 16022-71 (13) 1 Zeeman pattern = 0/3/2. Cadmium Cd 8'" m / X n d\ m / X n d\ 2 10-tf 10R WR 5085-8240 * 4799-91 1 2 4678-37* 19656-40 20827-24 21369-11 00 5 Qr 4r 2r 2712-65 2629-15 2592-14 36853-59 38023-96 38566-85 02 3 8r 2r 6r 3252-63* 3133-29 3081-03 30735-66 31906-27 32447-40 -02 6 2r 4r In 2632-29 & 2553-61 2518-78 37978-61 39148-74 39688-78 00 4 (ir Or 4r 2868-35 2775-09 2733-97 34853-28 36024-47 36566-28 01 7 In In In 2584-88 5 2507-93 2474-15 38673-85 39861-76 40405-99 00 8 2n In 2552-26 2478-44 39168-15 40334-74 ( - 65j) 8 - - -03 2ai(14); 2c, 3 ... 5, 606 (1); 6c, 7a, 8(5). 1 Zeeman pattern =0. 1/2. 3. 4/2. 2 Zeeman pattern =0. 1/3, 4/2. 3 Zeeman pattern =0/2/1. * Exner and Haschek give normal order of intensity 20. 20. 10. 5 Kayser's S t 6 and Huppers' 8 1 7 are ( - 65 t ) 8^ CdD'" m / X n m / \ n 2 f 4 3614-58 27658-69 4 (2R 2764-29 36165-20 \ SR 3613-04 27669-79 IQR 2763-99 36169-11 (lOR 3610-66 27688-02 Sd 2677-65 37335-30 \ 8R 3467-76 28828-99 6J? 2639-63 37873-05 \WR IQR 3466-33 3403-74 28840-86 29371-16 5 4r 2n 2660-45 2580-33 37576-60 38743-32 3 (I 2982-01 33524-88 2n 2544-84 39283-62 \R (8R (4R 2981-46 2980-75 2881-34 33531-06 33539-04 34696-09 6 2n In 2601-99 1 2525-57 38420-89 39583-42 \ SR 2880-88 34701-62 7 2n 2566-10 38956-82 8R 2837-01 35238-19 8 In 2540-08 39355-91 2. ..6(1); 7, 8(5). 1 is also FZ" (5). APPENDIX Cd P'" 283 in / X n m / 8 6 4 X n 1(XK 1(XR IOR 5085-824 4799-911 3678-37 - 19656-40 -20827-24 -21369-11 4 6099-392 6111-729 6116-395 16390-62 16357-54 16345-06 2 150 90 63d 13979-22 14327-99 14474-62 7151-551 6977-466 6906-787 5 6 4 2 5598-989 5604-903 5607-068 17855-49 17836-66 17829-76 3 8 4 7346-100 7382-485 7396-581 13610-83 13541-88 13516-10 6 1 5339-711 18722-52 Possible P summation lines: 1, 3497-097, 28587-12 as (25 X ) P 3 (3) gives 28591-52 1, 3889-8, 25701-13 as (25) P x (4) gives 25717-93 These give as mean limits 21053-81 and 21054-27. 3, (100) 16482-2, 6065-51; (50) 16433-8, 6083-37; (30) 16401-5, 6095-35; 4, (13) 11630-8, 8595-57. 3, 4 (4). . Combinations 3729-21 26807-85 3595-64 27803-73 3005-53 33262-48 2903-24 34434-43 Pz l-p 2 2 Ir P 1 l-p 1 3 Ir pi I -pi 3 Ir 2908-85 34368-04 ^2-^3 35 14853-9 6730-42 P 2 2~d 1 3 14474-62 p 3 2-d 1 '3 14327-99 p 3 2-d 3 3 14354-45 Cd 8" (D (I) (1) (D (1) (4) 6906-787 (4) 6977-466 (4) 6964-607 (4) 8 3535-8203 28274-07 I 3395-570s 29441-86 4v 2961-64 33755-39 ft} 2*3 1 4y 2v 2 2 2r 2632-29 (7) (7) (1) 34926-56 (1) 35467-65 (1) 36264-86 37430-89 37978-61* * Coincides with #/" (5). Cd D" (1) (1) (1) m / X n m / X n I 8/i 2144-44 1 -46617-81 I (2 1900-70 -52593-07 SR 2265-042 1 -44135-88 M 1921-55 -52022-50 10 2748-68 1 36370-51 3 1994-78 - 50112-98 10 2573-15 1 38851-66 2 I 7 2321 -246 1 43067-35 3 1571-40 63637-52 1 10 5rc 2312-88 2194-71 43223-09 45550-14 1,2 (7); 3 (8). Normal Xecman patterns - 2/3. 5/3 and 2/4/3. One F" 1(9); 2 (7). 1 Zeeman pattern = abnormal 2/4/3. m / \ n m 7 \ n 3 10 5379-3 18584-70 5 3 2618-97 38171-73 10 5338-6 18726-38 1 2602-0 38420-75 4 In 3178-594 31451-54 6 In 2374-9 42094-45 Inn 3163-236 31604-22 3. ..6 (7). Combinations 1965-4 1995-1 1873-8 1901-1 2209-8 50864-7 50107-7 53350-4 52581-8 45239 (7) (7) (7) (7) 284 ANALYSIS OF SPECTRA Cd S' Cd D' m 7 X n d\ m / X n d\ 1 IQR 2288-10 1 - 43691-2 2 10 643S-4696 2 15526-84 2 200 10395-17 9617-262 3 2 4662-69 21440-96 3 10 5154-85 19393-90 4 . 2141 24142 3 4 4 4306-98 23211-70 5 , 3905 25601 2-8 5 2 3981-92 25106-51 -30 6 3819 26177 52 7 3723 26853 -25 1,3, 4, 5(1); 2 (4); 6, 7(12). 1 Zeeman pattern =0/1/1. S' mean limit 2 2611 38289 28841-45 4 (15) 4 4r 3068-933 32575-34 28840-93 (7) 5 5n 3173-679 31500-24 28837-77 3. (7) 6 3 3241-785 30838-49 28845-69 3 (7) 2(14a); 3 (1); 4, 5 (12). 2 The red cadmium primary standard. Zeeman pat tern =0/1/1. D' 2980-75 ! 33539-04 63118-976 32052-69 3 mean limit 28849-7 3 (7) 28840-53 (7) .2 (7) GO 1 2980 is I> n '" (3). Cd JF" 15713-60 6362-25 (4); *" (4) 45 11268-36 8872-01 (4) P'(2.m) P'(l.m) m / X n d\ m / X n 1 200 10395-17 -9617-262 1 10.ft 2288-79* 43691-2 2 110 15154-8 6596-81 2 10 1669-29 59905-71 3 5 8202 1 1218885 1-80 3 8 1526-85 65494-31 4 3 6778-332 14748-91 4 6 1469-39 68055-45 5 2 6198-394 16128-85 -25 5 3 1440-18 69435-76 6 1 5895-9 16956-34 -18 6 1 1423-23 70262-71 7 1 5717 17490 3 8 5598-275 17857-75 -14 1, 2, 3 (4); 4, 5, 6,8(13); 7(10). 1 Paschen states bad observation. 1(1); 2... 6 (8). 2 Zeeman pattern = 0/1/1. P(2. 4) 6 4217-ls 23706-43 (7) mean = 19227 -69 1-5 or o> =28844-98. Combinations 2r 3649-74 4r 3500-09 6 6325-404 3 6330-154 8 4674-35 2 4675-23 5 4114-7 s 60 75773-5 ! 25 11268-36 1 3 7132-218 27391-56 (1) 28562-69 (I) 15804-98 (13) 15793-14 (13) 27665-6 UOo) 27655-2 (10a) 242S6-6 (7) 6362-25 (4) SS72-07 (4) 14017-10 (13) s'" 2 - p' ^4 3 6031-631 16574-75 (13) s'" 2 - y; 1 5568 17951 (13) 5'" 2 - J9'6 ? 5324 z 18777 (13) P'l- s'"3 2 5297-905 18870-27 (13) Pt' 5' 1 107? 3261-17 3 30655-20 (1) P.'" 1 -'2 10 4413-23 3 22652-93 (1) P*" -*'3 2nn 3082-80* P*" 1 5' 4 2 2756-69 36264-86 (1) /!-< f'"2 2 1942-9 51453-56 (7) Or F' (3), F' (4). 2 Given by (10) without reference. 3 Zeeman pattern =0/3/2. APPENDIX 285 Europium Eu S"' (All measures in Eu by Exner and Haschek.) w / X n m / X n 2* 3 5377-13 18592-20 4 3 2909-10 34365-08 1 + 4709-95 21225-83 4 2701-99 36998-94 1 + 4495-24 22239-76 (-i)S 5 2 2744-36 36427-75 3* 3 3322-42 30090-02 1 2559-30 39061-73 4 \4 3055-07 2964-35 32723-15 33724-53 6 7 1 2 2659-50 2608-47 37590-17 38325-24 8 1 2577-25 38789-61 * Or, 2 (1) 5381-46, 18577-25; (3) 4713-77, 21208-64; (1) 4500-48 s, 22213-73. 3 (2) 3322-01, 30093-73. Eu D f " m / X n m I X n 2 fl 3638-22 27478-37 3 12 3006-39 33252-96 1 3629-94 27541-00 il 3001-48 33307-36 (1 3616-30 27644-85 3 2782-02 35934-64 II 3320-03 30111-68 2 + 2710-09 36888-38 12 3313-46 30171-45 4 abs. abs. 5 3212-89 31115-81 5 1 2682-72 37264-77 EuP" P(oo) Eu P' m 7 X n d\ 21700 + n X I I 3 5377-13 - 18592-20 } 1 + 4709-95 - 21225-83 } outside observed ultra-violet 1 + (8^)4495-20 -22229-40 J '2 unobserved [6157-33] (59-98) (37362-64) ( - 5j) 2676-15 ( - 5j) 3 Spark ultra -red [5653-40] [5466-28] (59-82) 59-88 ? (37866-25) 38053-49 (2Sj) 2627-11 2 Spark 3 . [13537-04] 59-13 29981-23 3334-48 6 region [13334-64] 58-30 30181-98 3312-29 1 Spark [13267-96] 59-92 30251-87 3304-65 1 4 4 5993-09 16681-34 59-38 26837-42 3725-10 30 8 6018-39 16611-22 60-61 26910-00 3715-05 2 3 6029-20 16581-44 60-33 26939-22 3711-02 2 r> 10 5453-17 18322-95 9 59-47 25186-00 3969-36 2 25237-42 3961-27 1 + 4 5472-50 18268-20 63-10 25258-01 3958-04 1 6 1 24237-55 4124-69 1 1 5193-89 19248-13 58-13 24268-13 4119-49 1 24281-98 4117-14 1 7 3 23629-68 4230-80 1 ?23636-97 4229-49 1 3 + 5033-71 19860-62 58-86 23657-10 4225-89 1 g 2 4924-89 20299-46 . 2 4928-19 20285-87 9 1 + 4861-05 20566-01 4 60-23 22954-46 4355-25 4 1 + 4863-23 20556-80 59-88 22962-96 4353-64 1 4865-09 20548-98 59-24 22969-50 4352-40 1 + 10 22 (58-55) 22724-22 4399-48 1 3 4809-47 20786-61 59-26 22731-92 4397-89 1 + 1 + 4808-83 20789-36 122738-31 4396-65 1 11 1 + 4771-90 20950-27 30 59-08 22567-81 4429-87 1 -;- 3 4770-98 20954-30 12 22441-00 4454-90 1 + 286 ANALYSIS OF SPECTRA Eu F"' m / A n m / X n 1 (1 + 2408-44 41508-22 3 1 5085-80 19657-23 2 2412-17 41444-07 lH- 2419-38 41320-61 4 ( 1 + 5818-94 17180-56 ll 2402-46 41611-53 1 + 5820-2 17176-85 h + 2406-25 41546-01 (10 5831-21 17144-42 i + 2398-97 41672-04 J3 5783-91 17284-62 J1 + 5792-97 17257-59 2 (i + 3961-27 25237-42 is Po'" (f>) 5 5735-40 17340-13 4 3965-06 25213-31 (50 3972-16 25168-25 5 4 6336-01 15778-51 ji 3945-82 25336-21 13 3949-72 25311-20 1 3936-12 25398-70 (2 + ) 6250-71 -(5)6300-00 Pn (1) - -(2)6267-18 -(3)6291-55* -(3)6291-55 15993-83 15868-70 15951-81 J5890-02 15890-02 * Regarded as covered by Combinations = l. 2. 3 Pn (I) -/(m) m ' X n V m ' X n /<<$ 2 5 4039-36 24749-53 3 3 2991-46 33419-00 6932-54 503-51 1 2773-01 36051-50 3 3719-30 26879-23 187-54 4 3 2782-02 35934-64 4416-90 1 3609-66 27695-69 3 6 3111-55 32129-24 201-98 3 2892-65 34560-47 67-1 3 2816-30 35497-37 4 $3 2833-36 35283-58 il 2833-20 5-57 llso under m=3: P 3 l -p^a 3 3130-83 31931-34 -p 3 3 1+ 3137-94 31867-94 -1^3 1 2876-16 34758-55 -ptZ 1 2887-01 34627-96 -p z 3 I 2810-81 35566-68 1 3592-72 27826-24 12525-46 4 3589-39 27852-24 12499-56 N.B. /! 2 = 12460-46 Eu D' m / X n m / X n 1 4 2375-56 - 42082-94 o [1+ 2688-57 37183-71 t 4 2720-71 - 36744-44 >3 2666-93 37485-23 t 9 2350-65 42528-78 2 5 2814-03 35526-12 * 4 2446-11 40869-04 or 3 2811-86 35553-39 3 2444-51 40895-95 f or 2 2391-29 41805-84 2 2374-20 42106-86 APPENDIX 287 m / X n m / X n 3 00 00 tS 6075-80 6049-77 5967-30 16454-26 16525-05 16753-45 5 6 3 2 2816-24 2792-62 35498-25 35798-29 4 (14- i 3460-45 3457-19 3424-75 28889-87 28917-11 29191-02 7 2 2 2 2522-26 2391-29 2374-20 39635-35 41805-84 42106-86 OT(S)F n ' (oo ) EuS' m / X n d\ 28800 + \ n X / 1 2 1 3076-20 -32498-36 [9742-37] 3 4 if&0$ 19473-90 (30-18) (38186-46) ( - 75J 2620-93 1 + 4 5 4298- S 8 23255-43 (30-04) (34404-64) ( - 25i) 2906-80 1 5 S 4 3978-60 25127-52 30-2 32533-0 3072-9- ft l + br f, 1 3817-14 s 26190-35 02 30-32 3 J 470-3 3176-7 ft 1 + 7 2 3722-77 26854-22 04 (29-96) (30805-71) (dj 3244-S& * 'l 8 I.V 3663-10 3662-6 27291-75 27295-41 5 -01 {30-62\ \30-2l) 30369-49 30365-01 (oS^ 3288-5 ft (75i) 3287-65 s l+d\ 1+ i 9 1 + (25 t ) 307.9-07' (27604-47) -14 (30-55) 30056-66 3326-11 s 2 10 1 3,5.92-72 27826-24 11 (30-04) (29833-43) ( - 5 t ) 3357-70 1 Jl 2 (-25^ 3572-75 (27994-17) -03 (30-04) (29665-91) (+5i) 3369-22 3 12 1 + 3555-53 28123-47 03 (30-18) (29573-98) (65j) 3380-41 2 13 I ( - 35j) 3544-28 (28225-14) -03 (30-18) (29435-23) ( - 55^ 3400-0 l + br 14 2 3531-96 2830-1-96 10 30-60 29356-25 3405-57 l + br 15 1 3523-63 28371-85 - -04 (29-83) (29287-81) ( - 5j) 3414-25 1 + Hi 1 (33 t ) 3574-05 (28425-79) -02 (30-37) (29234-96) (Sj) 3418-98 I 17 1 3577-33 2.V/77-2/ -07 (30-38) (29189-55) (55!) 3421-40 I 18 1 ( -35 X ) 3509-00 (28508-64) -01 (30-14) (29151-64) (25j) 3427-93 1 + 19 1 3502-66 28541-66 -10 (30-60) (29119-53) ( - 35j) 3435-34 2 Mean S' (oo ) : 1 Also 1 +, (35 t ) 2904-20 gives w = 34404-51. 3 Also 1 . ( - 25 t ) 3246-54 9 gives n ^30805-00. -28830-236. - Also I +, (25j) 3071-735 gives w ^32533-37. X 5457 J1S2 2972- 2677 77 -18337-76 40 $3683-23 SS ,v 37 41 5-9 1 288 ANALYSIS OF SPECTRA P'(2. m) P'(oo) P'(2. m) m 7 X n 19000 + n X I 3 . [11953-36] 26229-30 3811-47 4 4 3 6864-81 14563-10 91-33 96-38 23619-56 23629-66 4232-61 4230-80 s 1 1 5 2 6267-18 15951-81 89-88 95-81 22227-95 39-81 4497-60 s 4495-20 1 + 1 + 6 1 5954-54 16789-34 90-05 95-16 (21390-76) 21400-99 4671-40 l+d -2/3 1+ (-5j) 4601-38 21732-79 p'2-p'G 1+3762-50 2657 *-p'4 4 4107-01 24341-85 p'2-p'l 1 3687-90 2710 -p'5 f> 3884-91 25733-47 EuTT D'(GO) Eu D' m 2 7 X n d\ 28800 + n \ I 20 6645-44 15043-81 35-24 (42626-68) (-58^2346-95 1 + ?? 3 50 4662-10 21443-67 36-74 36229-81 ( - 28j) 2760-30 2 4 100 4129-90 24206-98 35-81 33464-64 (98J 2982-40 3 5 1 (S t ) 3894-86 25661-57 05 35-96 32010-35 (25j) 3124-30 1 + 6 2 3769-46 26521-61 -21 36-96 31152-32 (GSj) 3212-95 2 7 1 + 1 3692-25 (8)3689-12 27076-21 27074-55 -3 -07 36-45 36-59 30596-70 30598-63 ( - 25) 3272-91 (8J 3266-54 2 2 8 1 (-28^3644-10 27446-30 - -25 36-37 30226-45 3307-43 1 9 2 1 + 3606-96 (-28^3608-40 27717-18 27717-72 --1 36-75 36-09 29956-33 29954-46 (-28J 3338-61 (-28^3338-85 2 2 10 1 + (25J 3580-06 27912-31 05 36-09 29759-87 (-Z8J3361-34 1 Mean 28836-249. Mercury Hg/sr* w 7 X n d\ m 7 X n d\ 2 107? 5460-742 1 18307-44 0, 7 2 2625-238 38080-44 01 WR 435S-343 2 22938-06 1 2340-601 42710-97 6.K 4046-557 3 24705-41 3 6r 3341 -479 1 29918-39 8 1 2593-41 38548-13 -02 6r 2893-606 2 34548-85 In 2314-7 43190-56 8r 2752-802 3 36316-06 4 2224-73 44936-69 4 8r 292S-386 4 34173-61 9 2571-85 38872-47 -04 8r 2576-32S 5 38803-36 In 2292-1 43616-2 6r 2464-086 40570-71 10 2556-36 39107-95 -12 5 6r 2759-780 36224-06 03 2284-2 43767-2 6r 4r 2446-917 2345-490 40855-36 42621-91 n - 2545-09 2275-5 39281-07 43934-5 00 6 Iw 2674-987 37372-27 04 19 2 2380-061 42002-90 A 2 - 2 2284-2 43767-24 13 ; 2529-47 39523-72 -27 14 2524-48 39601-98 03 au* \^) *B* OM< V- 10 /' ut; A""* x rt/ V- 1 * 7 /' av f { 1 Zeeman pattern =0. 1/2. 3. 4/2. 2 3 Zeeman pat tern =0/2/1. 4 Zeeman pattern itJ\LIU,), OI,{1J, VW, J.UU>, iiU, J.O, It (\J). Zeeman pattern = 1/3. 4/2. =0/2 + /2. 5 Zeeman pattern = ?/3/2. APPENDIX 289 A possible '"(1): (1 1662-6 -60146 \l 1800-7 -55534 1 1 1861-0 - 53734 It is, however, a spark set by Lyman (3a) and does not pccur in Wolff's arc (8). Hg D'" and p"\, z , 3 - d' (m), latter are denoted by *. m / X n m / X n 2 5 1 *2700-92 37013-47 [3 3663-274 1 27290-23 iln 2699-503 37032-89 U 3662-881 2 27293-16 J4 2698-885 37041-37 I 6 3654-S32 3 27353-26 *2400-570 41644-12 U 3650- 144 4 27388-40 i 2 2399-812 41657-27 2 *3144-550 31791-87 |3 2399-435 41663-82 ( 4 3131 -845 5 31920-84 3 2302-165 43424-04 4 3131-562 6 31923-72 U 3125-617 7 31984-45 6 4w 2639-929 37868-57 5 2967-2T6 8 33691-13 3r* 2352-647 42492-34 1 2258-871 44256-23 3 3 *3027-494 33021-04 |2 3025-617 33041-53 7 3 2603-15 38403-54 \* 3023-485 10 33064-82 2w 2323-302 43029-00 ( 5 3021-502 11 33086-52 4 *2655-142 12 37651-59 8 2578-34 38774-51 J 4 2653-703 13 37672-01 9 2561-15 39036-13 is 2652-069 14 37695-23 10 2548-51 39229-68 6 *2536-520 39412-28 11 2R 2540-39? 39353-87 3 2534-800 39439-02 12 , 2531-74 39490-14 13 2525-90 39580-90 4 1 *2806-844 35616-78 14 2521-27 39653-55 ri 2805-422 35634-80 15 2517-57 39711-81 2 2804-521 35646-24 16 2514-48 39760-61 U 2803-530 35658-83 3 *2483-871 40247-63 J 3 2482-763 40265-58 J4 2482-072 40276-78 2 *2380-061 42002-94 4 2378-392 42032-40 2 ... 7 (18); 8 ... 10, 12 ... 16 (10); 11 (1). Zeeman patterns: 1 3. 6/4. 7. 10. 13/7. 4 1/4/3. 7 0. 2/4. 6. 8/5. 10 2. 3/??/2. 13 6/4. 9/6. Hg P"' 2 0. 2/1. 3. 5/2. 5 0. 4/7. 10/7. 8 0/1/2. 11 May be 1/4/3. 14 0/1/1. 3 1. 2/2. 3. 4. 5/3. 6 2. ? 4/1. 3. ? 4/2. 9 1/1/1.' 12 ? 0/5/7. Hg P"' m / X n 21800 + n X / I 10# 5460-742 - 18307-44 (31-0) (61968-2) ? 1611-9(5) 1 10# 4358-343 - 22938-06 (32-1) (66600-2) 1497-3 (2J5) 1 R 4046-557 - 24705-41 (32-3)- (688674) 1467-4 ( - 2|S) 2 2 2-6 12071-32 8282-213 . , 4 13208 7569-2 17 13674-32 7311-313 H. A. S. 290 ANALYSIS OF SPECTRA Hg P'" Continued P"' (oo ) Hg P'" Continued m / X n 21800 + n X / 3 10 1 3 6907-776 7044 7092-456 1 14472-99 14192-91 14096-15 (31-92) 30-35 31-26 1 29189 2 j 29191-35 29468-27 29566-86 ( - 5j) 3425-8 (5 X ) 3423-751 3392-397 3381 -085 l 1 4 2 4 4nr 1 In 1 5803-774 5838-988 5854-5 5868-28 17226-06 17122-16 17076-8 17036-72 34-53 33-8 32-6 /32-54\ V31-94/ 26442-20 26545-4 26588-40 26628-33 26627-00 3780-637 3766-2 3759-910 ( - 35^ 3757-200 (2i) 3752-410 1 1 2 2 1 5 4%r 5354-240 18671-91 33-2 24994-5 3999-9 1 3nr 5384-904 18566-00 (32-40) 125099-36 \ 25199-48 ( - 58J 3988-522 (45j) 3978-790 1 1 6 3w 5120-830 19523-40 34-06 24144-73 24188-99 4140-384 4132-812 2 1 2 5138-258 19457-18 7 3wr 1 2 4980-995 4988-036 4991-7 20071-91 20041-73 20028-4 30-63 29-80 30-48 23590-36 23617-87 23632-53 4237-489 4232-755 4230-126 3 1 4 8 2nr 2n 1 4890-450 4895-8 4897-1 20442-89 20420-8 20415-3 31-11 30-8 32-7 23219-34 23240-96 23250-1 4305-404 4301-7 4300-0 1 2n 1 9 2 4827-3 20710-5 \- 1 4832-4 20688-7 ' - 10 1 4782-3 20905-4 33-1 22760-81 22795-64 4392-138 4385-575 4 3 11 1 1 4748-3 4751-173 21055-1 21040-86 31-4 22607-7 22615-8 4422-2 4420-6 2 2 12 1 4723-0 21167-8 (33-3) 22498-7 (-25,) 4446-4 3 13 1 4702-0 21262-4 (32-2) 22402-0 ( - 5j) 4464-2 3 14 1 4685-5 21337-2 (31-7) 22326-12 ( - 28j) 4480-496 1 15 1 4672-9 21394-7 30-4 22266-07 4489-732 1 16 1 4662-6 21442-2 30-0 (30-95) 22217-9 22219-6 4499-8 (5 X ) 4498-0 1 17 1 4653-6 21483-7 30-3 22176-93 4507-778 1 18 . . . ,H)gj| 22138-33 4515-789 1 21 /,: 22057-93 4532-099 1 1 (see 8); 2 (10); 3 ... 17 (13) except 4c, 86 from rich line spectrum by Eder and Valenta, and 7&, 116, do. (18). The ar- rangement for m = 2 is very doubtful, i Probably P 3 (3) ( - 5) and P 3 (3) ( - 5). 1 (9); 3 ... 21 (18) except 5, 8bc, 11, 12, 13, 16 by (7) and 46 by (22). APPENDIX 291 Hg F'" Hg F' m / X n F(cc) n X / 2 ' 25092-73 (25125-37 (25127-81 25180-0 3983-963 3978-790 3978-417 3970-3 3 |l 3 3 J4 a 4-6 17195 17110-05 17073-07 16919-84 5814 5842-995 ) 5855-651 \ 5908-682 12741 12775-7 12836-2 19668-0 19703-0 19763-7 5083-0 5073-6 1. 5058-4 2 2 1 4 2-4 12021-28 8316-408 12744-46 17172-51 5821-678 3 2-6 11887-71 8409-855 12838-26 17266-66 5789-521 2 3, 4 (10). 1 ~/3 3011-17 2642-70 2524-80 HgS" 33200-19 (I) 37829-06 (1) 39595-49 (1) 2d, 3oc (7); 2, 36, 46 (18); 4a (13). Combinations 4 lw 2799-826 35704-82 (18) 40331-13 (18) (1) ft 1 ~/4 ftl-/4 ft I-/* 2478-657 2374-10 HgD The separation is 9831. The large number of doublets with this separation shows that con- siderable disruption has taken place and no satisfactory allocation of normal series lines has yet been made. Hg S' = p'- s'm and ? - s'm m 7 X n d\ m 7 X n d\ 1 20 9 1849-57 1798-7 - 54066-6 - 55595 4 6 1 4108-170 4383-189 24335-00 22807-28 2 71 10140-58 12021 9858-793 8316-408 5 4 1 3801-780 4037-240 26296-15 24761-61 05 3 5 3 4916-180 1 5316-870 20335-41 18802-93 6 i 3863-927 [27404-78] 25872-23 7 i 2 (28091-4) 18 S', 1(8); 2(10); 3,4,5(13). (Parallel set) 1 (3a); 2 (10); 3 (13); 4, 5, 6 (18); 7 (22). 1 Zeeman pattern =0/1/1. 2 Two oppositely displaced lines: (1)3558-2; n = 28096-2. (2) 3559-4; w = 28086-7. Mean taken. HgZX, p'-d'm P' ~ d a '"m p'-d 2 '"m m 7 X n m 7 X n 2 10 5790-659 17263-85 6 2 3592-908 27824-85 4 5789-875 17266-83 1 3591-63 27834-76 10 5769-598 17326-86 1 3591-10 27838-87 3 6 4347-617 1 22994-78 7 2 3524-42 28365-56 2 1343-793 23015-11 6 4339-323 23038-71 1 3523-15 28376-03 4 8 3906-590 25590-69 8 1 3479-13 28735-22 2 3903-793 25609-05 1 3478-00 28744-35 6 3902-087 25620-20 9 1 3447-36 28909-79 5 2 3704-288 26988-22 1 3702-509 27001-19 1 3701-593 27007-90 2ac(2); 26, 3 ... 9 (13). Zeeraan pattern =0/1 /I. 192 292 ANALYSIS OF SPECTRA , HgP'(2. m)=s'2-p'm and 5'" 2-^' w a'(2) Hg P' (2. ra)=s'" m 7 X n 20200 + n X I 2 71 2-6 10140-58 12071-32 -9858-793 - 8281-408 48812-9 1 50305-6 1 2048-01 1987-31 5 4 3 12 13671-90 7366-244 . 4 ii 5 7295 6716-680 6072-839 13704-30 2 14884-27 16462-28 55-33 1 54-55 26806-38 22024-78 3729-399 3901-349 3 1 5 8 5 6234-556 5676-075 16035-40 17613-00 53-99 24472-59 4085-057 1 6 4w 3rw 5803-774 5316-870 17225-46 18803-00 50-13 (Sj) 53-25 23274-81 4295-3 2n 7 3m> 2nv 5549-500 5102-600 18014-93 19592-50 49-46 (dj 52-61 22484 4446-4 3 8 1 1 5393-698 4970-305 18535-14 20114-00 46-51 (25 a ) 52-83 21957-9 4552-886 2 9 2 1 5290-3 4883-3 18897-52 20473-80 53-80 21610-09 4626-2 2n 10 2 1 5219-1 4822-5 19155-25 20730-54 54-74 21354-29 4681-6 2n 11 1 5166-0 19351-6 49-80 (Sj) 52-95 21148-00 4727-260 1 12 1 5129 19491-30 (53-3) (21015-4) 2 13 Iw 5101-51 19596-70 53-5 2 20910-4 4781-0 1 2, 3 (10); 4 ... 12 (13); 13 (la). 2 (21); 4, 5, 8, 11(18); 6 (la); 7, 9, 10 (7); 13 (22). 1 Wolff (8) gives in arc 1988-07, n- 50300-0. The separation is possibly correct within observation errors, but if allocation is correct they are displaced. 2 There are two lines by Stark (22), viz. : (1) 4762-7 as (25) P and (1) 4753-4 as ( -5^) P give for P 21015-4, ...5-5. HgP'(l. m) p z '"(2)-s'(m) m 7 X n m 7 X n 2 20 1849-57 54066-6 1 6 2536-520 1 -39411-13 3 4 1402-72 71290-06 2 6 4077-842 1 24515-16 4 5 1269-7 78758 3 3 2856-973 1 34990-85 4 1 2563-90 38990-31 2, 3(8); 4(3a). All Zeeman patterns =0/3/2. Combinations (1 2-6 p' 2 - s'" m \ 2 3 (3 1 12071-32 5025-818 4140-182 ?jr(4)=d'2-/4 11887-7 8281-937 (10) 19891-82 (13) 24147-00 (13) 8409-8+ (10) For p (1) - df (m), see * in D'" list. For p^ I - d'" z> 3 m, see in D' list. APPENDIX 293 GROUP III REFERENCES 1. KAYSER and RUNGE. Ann. d. Phys. 48, 126 (1893). 2. GRUNTER. Z. S. wiss. Phot. 13, 1 (1913). 3. HANDKE. Lyman's Spectroscopy of extreme ultra-violet. 3a. LYMAN. Spectroscopy of extreme ultra-violet. 4. PASCHEN. Ann. d. Phys. 33, 733 (1910). 5. MANNING. Astro. J. 37, 288 (1913). 6. EXNER and HASCHEK. Tabellender Funken- spektra. Wien (1902). 6a. Tabellen der Bogenspektra. Wien (1904). 7. MEISSNER. Ann. d. Phys. 50, 713 (1916). 8. RAMAGE. Proc. Roy. Soc. 70, 1 (1902). 9. HARTLEY and ADENEY. Phil. Trans. 175, 63 (1884). 10. EDER and VALENTA. Wien. Ber. 118 (Ho), 571 (1909). 10a. - Wien. Ber. 119 (Ila), 519 (1910). 11. PASCHEN and MEISSNER. Ann. d. Phys. 43, 1223 (1914). 12. CORNU. C.R. 100, 1181 (1892). 13. SAUNDERS. Astro. J. 43, 240 (1916). 14. PASCHEN. Ann. d. Phys. 29, 626 (1909). 15. FOWLER. Phil. Trans. 209, 47 (1909). Aluminium Al/Sf m ' \ n d\ m ' X n d\ 1 9 10 1722-0 1725-3 -58073-9 -57962-8 4 3 3 2378-408 2372-084 42032-14 42144-18 2 10.R IQR 3961 -540 1 3944-032 1 25235-59 25347-61 5 2 2 2263-731 2257-999 44161-20 44273-33 00 3 WR IQR 2660-393 2652-484 37577-29 37689-34 6 2R 1 2204-627 2 2199-569 45345-01 45449-27 01 1(3); 2... 6(2). 1 Normal Zeeman patterns = 1/3, 5/3; 2/4/3. 2 2 (6) and Z> 2 (6) coincident. All the 8 and D lines are given by Stark as A1+. Combinations p 1 2-s2 8 21166-3 4723-22 (4) p 3 2-s2 5 21098-2 4738-46 (4) ^2-^(3) 30 16752-2 5967-76 (4) AID m / X n m '/ X n 2 \ QR 3092-843 32323-36 6 2R 2210-046 45233-88 \IOR 3092-716 32324-69 2R 2204-627 ! 45345-01 WR 3082-159 32435-39 7 IR 2174-028 45983-16 3 ( 3R 2575-411 38817-15 IR 2168-805 46093-91 }WR 2575-113 38821-64 IOR 2567-997 38929-23 8 1 2150-59 46484-27 1 2145-39 46596-93 4 \ 2R 2373-360 42121-53 \8R 2373-132 42125-57 9 1 2134-70 46830-26 SR 2367-064 42233-55 1 2129-44 46945-91 5 ( 2R 2269-212 44054-55 10 1 2123-44 47080-33 \4R 2269-093 44056-86 1 2118-58 47188-30 4R 2263-453 44166-62 2. ..9 (2); 10(1). S l (6) and D z (6) coincident. All the S and D lines are given by Stark as A1+. 294 ANALYSIS OF SPECTRA A1P m / X n m / X n 1 1072 1072 3961-540 3944-032 - 25235-59 - 25347-61 4 i In 5557-08 5557-95 17990-08 17987-25 2 400 200 13125-36 13151-65 7617-04 7601-82 5 2 I 5107-5 \5105-57 19573-7 19581-08 3 3 3 6696-064 6698-734 14930-02 14924-07 1, 3, 4 (2); 2, 56 (14); 5a (5). P (1) by Stark are A1+ P 1 l-p 1 5 P 2 l-p 2 5 Combinations 2 2312-56 43229-03 (1) Ir 2231-27 44803-86 (1) Ir 2225-77 44914-54 (1) ? Those for m = 2, 3, 4 appear in displaced groups 2321-2312 for (4), 3066-3050 for (3). Combinations 4r 2426-22 41204-14 (1) 2r 2419-64 41316-16 (1) m 7 X n d\ 3 300 77255-5 8882-48 4 4 8774-56 11393-45 5 5 7836-85 12756-73 -13 3 (4); 4, 5 (7). 39108-6, n = 2556-3 may be a related or displaced ^ (2). Gallium Gatf GaT) m / X n m / X n 2 3072 4172-22 23961-44 2 \ 572 2944-29 33954-35 3072 4033-18 24787-45 )1072 2943-77 33960-35 3 1 2780-28 35957-25 1072 2874-35 34780-43 2718 36781 3 2R 2500-27 39983-85 4 . 1 2481-1 40292-85 2R 2450-18 40801-17 2 (60) ; 3a, 4 (6) ; 36 (8). 2 (6a) ; 3 (8). The series relationships of Ga are very uncertain. The spectrum observed contains few lines. Paschen (11) has suggested for P (4) XX, 6397-10, 6413-98 and P (5) 5354-0, 5360-0. Indium In S m / X n d\ m 7 X n d\ I 1 1 1748-65 1820-38 - 57185-10 -54931-75 4 6 472 172 2399-33 2278-3 41665-80 43879-08 13 2 1072 872 4511-44 4101-87 22159-78 24372-41 7 172 172 2357-7 2241-6 42401-44 44597-47 -12 3 4 672 672 672 2932-71 2753-97 2601-84 34088-40 36300-80 38423-12 o 8 9 172 2332-2 s 2218-3 42865-10 45065-75 03 5 672 472 2460-14 2468-09 40636-03 40505-18 04 10 172 2200-0 45426-87 1-8 672 2340-30 42716-79 2191-2 45622-1 35 1 (13); 2 ... 7, 86, 96 (1); 80, 106 (9). APPENDIX InD 295 m / \ n m 7 \ n 1* i . 6 1ft 2379-74 42008-86 IT 7 6891-61 6097-26 14506-46 16396-35 7 17* 2260-6 44222-5 2 I 67* \WR 3258-66 3256-17 30678-80 30702-25 8 172 2230-9 44811-3 3 WR ( QR 3039-46 2714-05 32891-17 36834-59 9 IR 2211-2 45210-6 \IOR SR 2710-38 2560-25 36884-44 39047-25 10 IR 2197-5 45492-4 4 I 4A! 8/2 SR 2523-08 2521-45 9 389 -64 39622-48 39648-08 41834-88 11 IR 2187-5 45700-3 5 ( IR IR IR 2430-8 2429-76 2306-8 41126-5 41144-13 43337-1 IR 2180-0 45857-5 1(10); 2. ..11(1). See Chap. XI, sect. 14. InP m / X n d\ m / X n d\ 1 107? 1072 4511-44 4101-87 - 22159-78 -24372-41 4 5709-75 5728-27 17508-48 17451-88 9 2 12857 13359 7775-7 7483-6 5 5254-14 5262-38 19026-71 18996-91 9 3 6847-77 6900-37 14599-26 14487-50 6 5017-5 5023-0 19924-0 19902-3 04 7 4878-8 20490-4 1 Combinations ?',3 P'\ Pi * 2 tin 2r 2n 2720-10 2572-71 2565-59 36752-68 38858-20 38966-00 su Thallium . TIP 2v, 2666-33, 37493-77 suggested by Paschen, but no proof. m / X n m 7 X n 1 10# 5350-65 - 18684-22 6 2 4891-3 20438-9 WR 3775-87 - 26476-59 2 4906-5 20375-6 2 1000 11513-22 8683-33 7 1 4760-8 20999-1 700 13013-8 7682-085 1 4768-7 20964-3 3 8 6649-99 15263-05 8 3 4678-3 1 21369-4 6 6713-92 14890-39 9 2 4617-4 21651-3 4 4 2 5528-118 5584-195 18084-39 17902-80 10 11 1 4574-8 4548-1 21852-9 21981-2 5 2 5109-65 19565-45 1 5137-01 19461-27 Pi 1 -Pi 3 In 4r 1(1); 2. ..11 (14). 1 It is the mean of PjP 2 by calculation, d\ = -3. 3653-10 27366-5 (i\a) Pi^-p^ lr 2978-05 2945-15 33944-44 (1) p 2 l-p 2 3 lr 2416-78 33569-44 (1) 41365-05 (1) 296 ANALYSIS OF SPECTRA TIS m / \ n d\ m 7 \ n d\ 1 1 1837-96 - 54406-33 7 2R 2538-27 39385-26 00 1 2144-50 -46616-57 2119-2 47172-9 2 WR 5350-65 1 18684-22 8 IR 2508-03 39860-17 02 10jR 3775-87 1 26476-59 2098-5 47638-3 3 1(XR 3229-88 30952-18 9 IR 2487-57 40187-92 12 8R 2580-23 38744-81 2083-2 47988-1 4 SR 2826-27 35372-20 10 IR 2472-65 40430-50 -18 QR 2316-01 43164-66 2072-4 48238-1 5 2nn 2665-67 37503-04 -1-21 11 IR 2462-01 40605-19 -02 4R 2207-13 45293-96 12 IR 2453-87 40739-83 03 6 4R IR 2585-68 2152-08 38663-20 46452-42 -02 13 IR 2447-59 40811-33 12 14 IR 2442-24 40933-95 -19 la (13); 16 (10); 2 ... 14 (1); but S 2 (7, 8, 9, 10) by (12). 1 Normal Zeeman patterns = 1/3. 5/3; 2/4/3. Combinations Si (2. 2) 40 27889-6 3584-60 (14) 8 t (2. 2) 30 21803-0 4585-3 (14) ^(2.3) 15 12491-8 8003-07 (14) ^(3.2) 15 -38131-0 2621-84 (4) 2 (3. 2) 10 - 33393-2 2993-82 (4) x (3. 3) 10 70230 1423-5 (4) &. (3. 3) 10 55500 1798-6 (4) m) m / \ n m / \ n 1* [12272-77] 7 4-R 2517-50 39710-27 [12854-37] 2105-1 47489-0 5 4982-49 20065-17 8 2R 2494-00 40084-34 2 ( 8R 3529-58 28324-04 2088-8 47859-5 \WR IOR 3519-39 2767-97 28406-02 36117-12 9 IR 2477-58 2077-3 40350-07 48124-3 3 ( QR IIQR 8R 2921-63 2918-43 2379-66 34217-63 34255-13 42010-27 10 IR 2465-54 2069-2 40547-07 48312-7 4 ( 4R \ 8R 2710-77 2709-33 36879-27 36898-88 11 IR 2456-53 2062-3 40695-73 48474-3 QR 2237-91 44670-96 12 IR 2449-57 40811-33 5 ( 4JR 2609-86 38305-08 2057-3 48592-3 j 6^ 2609-08 38316-52 13 IR 2444-00 40904-48 4R 2168-68 46096-76 2053-9 48672-7 6 (2R 2553-07 39157-03 14 IR 2439-58 40978-57 \QR 2552-62 39163-93 2050-9 48759-1 IR 2129-39 46947-25 15 2048-7 48811-4 All by (1) except D z (1 ... 15) by (12), and 1 by (10). * See Chap. XI, sect. 14. APPENDIX 297 Tl D (2. m) m / X n m / X n 2 2 60 10292-3 9713-36 5 51057-9 1958-04 3 1 6420-66 15570-50 3 ( 25 14597-8 6848-52 8 14592-6 6850-96 4 2 5489-00 18213-28 1 100 14515-5 6887-34 U50 12736-4 7849-42 5 1 5093-46 19627-66 1 20 12728-2 7854-47 4 \ 80 10496-4 9524-54 50 10492-5 9528-08 30 9512-8 10509-3 5 20 9136-5 10942-1 10 8376-5 11934-9 2 (4); 3, 4, 5 (14). Tl F (2. m) m / x n 3 180 150 16340-3 16123-0 6118-19 6200-67 4 80 50 11594-5 11482-2 8622-47 8706-78 2... 5(14). 39266-5 2547-32 (4) Tl^(3. 4)?? 4 20 35950 2781 (4) 10 35680 2803 (4) 3,4(14). p 1A l-fm m 3 / X n 4v 2v 2895-52 2362-16 34526-21 42321-40 4 2nn 2700-3 37022-23 3,4(1). Scandium ScP m / X n m / X n d\ 1 3 5146-43 - 18457-31 4 5 5717-51 17485-35 5323-94 - 18777-96 5721-20 17474-08 2 5 5 5258-49 19011-70 6 2 5021-67 19908-26 7 1 4880-90 20482-40 - -55 3 3 6819-80 14659-21 8 2 4791-69 20863-72 85 2 6829-83 14635-55 9 2 4728-95 21140-54 26 10 4682-16 21351-78 -1-8 1 (15); 3(10); 4... 10(15). Combinations P 1 l-p l 3 4 3019-48 33108-9 (6a) Pil-/ 8 3 1 3021-14 33090-6 (6) ^1-^4 Ib 2782-6 35927-3 (6a) 298 ANALYSIS OF SPECTRA Sc S Parallel to Sc 8 m / X n m / X n I 3 5146-43 18457-31 1 6 6413-54 15587-78 5323-94 18777-96 3 6284-66 15907-43 2 2 15 3645-46 27423-71 2 3273-76 30537-33 10 3603-1 s 27746-10 3 2 3139-98 31838-3.1 1 3108-70 32158-68 1(15); 2, 3(6, Go). GROUPS VI, VII. REFERENCES 1. RUNGE and PASCHEN. Wied. Ann. 61, 641 5. (1897); Astro. J. 8, 70 (1898). 6. 2. MEISSNER. Ann. d. Phys. 50, 713 (1916). 7. 3. PASCHEN. Ann. d. Phys. 27, 561 (1908). 4. PASCHEN and BACK. Ann. d. Phys. 39, 897 (1912). Oxygen OS"' KILBY. Astro. J. 30, 243 (1909). FBITSCH. Ann. d. Phys. 16, 793 (1905). EXNEB and HASCHEK. Tabellen der Funken- u. Bogenspektra. Wien (1902 and 1904). m / X n d\ m / X n d\ 1 10 7771-97 -12862-79 S 5 5020-31 19913-63 -03 8 7774-20 - 12859-09 4 5019-52 19916-78 6 7775-42 - 12857-07 3 5018-96 19918-99 2 1-7 11300 8847-28 6 4 4803-18 1 20813-84 + 10 2 11294 d 8852-00 3 4802-38 20817-30 3 9 6456-287 15484-58 2 4801-98 20819-04 7 6454-756 15488-25 7 3 4673-88 21389-63 06 6 6453-900 15490-31 3 4672-93 d 21393-97 4 8 5437-041 18387-34 8 3 4590-07 21780-17 -02 6 5435-968 18390-97 2 4589-16 21784-49 5 5435-371 18392-99 1(2); 2. ..8(1). 1 The calculated value makes v l correct. OZ>'" m / X n d\ m / X n d\ 2 7 9264-28 10791-32 6 5 4773-94 20941-31 00 3 10 8 6158-415 6156-993 16233-52 16237-28 4 3 4773-07 4772-72 20945-12 20946-66 7 6156-198 16239-38 7 3 4655-54 21473-88 01 4 10 7 5330-835 5329-774 18753-65 18757-39 3 4 4654-74 4654-41 21477-57 21479-09 6 5329-162 18759-54 8 3 4577-84 21838-35 00 5 6 4968-94 20119-50 2 4576-97 d 21842-50 5 4968-04 20123-14 9 4523-70 22099-71 20 4 4967-58 20125-01 4522-95 d 22103-37 2(3); 3... 9(1). APPENDIX 299 OP'" OP" m / X n m / X n 2 10 7771-97 12862-79 2 8446-36 11835-78 8 7774-20 12859-09 8446-76 11835-22 6 7775-42 12857-07 3 10 436S-466 2 22885-23 3 1 10 3947-480 25325-59 7 3947-661 25324-43 4 7 3692-586 27073-74 4 3947-759 25323-81 2 (2); 3, 4(1). 2 Zeeman pattern = 0/1 /I. 2 (2); 3(1). (4) give for ra = 3, -438, -626, -731. 1 For Zeeman pattern of group see (4). Analogous to triplets in S, Se. 1 6264-78 15957-92 . 3 5410-97 3 6261-68 15965-81 4 5408-80 1 '6256-81 15978-24 3 5405-08 Note. These two sets have same separations in the ratio 3 : 5. O 8" O D" 18475-92 18483-34 18496-08 m / X n d\ m / X n d\ 1 8446-36 - 11835-78 2 4 11287-0 8857-48 8446-76 -11835-22 3 2 7002-48 14276-78 2 1-5 13163-7 7594-68 4 6 5958-7 5 d 16777-48 3 2 7254-32 13781-15 2-33 5 5 5512-92 d 18134-27 09 4 7 6046-564 16533-81 2 6046-336 16534-44 6 4 5275-25 18951-28 08 5 6 5555-16 d 17996-36 7 3 5130-70 19485-20 -95 6 5 5299-17 18865-72 + 09 8 2 5037-34 19846-31 -17 7 5 5146-23 19426-38 -43 9 1 4973-05 20102-89 -27 8 2 5047-88 19804-89 05 9 1 4979-73 20075-93 -12 1 (2); 2... 9(1). 2.. .9(1). Sulphur SJP"' m / X n m / X n X At 2 3 9212-71 10851-23 3 10 4694-357 21296-32 2 9228-17 10833-05 8 4695-690 21290-27 2 9237-71 10821-87 6 4696-488 21286-66 2 (2); 3(1). Analogous to triplets in O, Se. 6, 5279-19, 18937-13; 5, 5278-81, 18938-50; 3, 5278-31, 18940-29. 300 ANALYSIS OF SPECTRA SS" m / X n d\ m / X n d\ 1 3 9212-71 -10851-23 6 5 5614-48 17806-23 2 9228-17 - 10833-05 4 5608-87 17824-04 2 9237-71 - 10821-87 3 5605-52 17834-70 4 4 6415-68 15582-57 7 3 5449-99 18343-64 28 3 6408-32 15600-47 2 5444-58 18361-87 2 6403-70 15611-73 5 2 5890-08 16973-07 2 5883-74 16991-36 1 5879-79 17002-78 1(2); 4.. .7(1). S7T" m / X n m 7 X n 4 7 6 5 6757-40 6749-06 6743-92 14794-58 14812-87 14824-16 7 5 4 3 5507-20 5501-78 5498-38 18153-09 18170-98 18182-22 5 7 6 5 6052-97 6046-23 6042-17 16516-32 16534-73 16545-85 8 4 3 2 5381-19 5375-98 5372-82 18578-17 18596-18 18607-12 6 8 7 6 5706-44 5700-58 5697-02 17519-28 17537-29 17548-26 9 4 4 2 5295-86 5290-89 5287-88 18877-50 18895-24 18906-00 4... 9(1). Selenium Se P"' m 7 X n 3 10 4731-04 21131-19 9 4739-28 21094-47 8 4742-52 21080-06 Analogous to triplets in O, S. 10 5374-27 18602-09 10 5370-04 18616-73 8 5365-59 18632-20 3(1). SeS" m 7 X n m 7 X n 4 6 6746-65 14818-15 6 2 5878-88 17005-42 6 6699-78 14921-81 2 5843-10 17109-55 5 6679-72 14966-63 1 5827-90 17154-16 5 3 6177-87 16182-41 7 3 5700-32 17538-10 2 6138-51 16286-17 3 5666-95 17641-35 2 6121-95 16330-23 3 5652-62 17686-09 4... 7(1). APPENDIX Se D"' 301 m / X n m / X n 4 5 7062-14 14156-19 7 i 7 5753-52 17375-92 J3 7014-25 14252-83 ! 5752-31 17379-58 <3 7010-84 14259-76 j i 5718-5 17482-33 4 6990-96 d 14300-30 7 5718-28 17483-01 3 5705-18 17523-17 5 J6 6325-81 15803-95 M 5703-86 17527-22 1 6325-4 15804-98 f 3 6284-51 15907-83 8 5 5618-05 17794-92 h 6284-19 15908-64 U 6283-54 15910-29 9 4 5528-64 18082-69 J3 6269-28 15946-47 3 5497-06 18186-58 M 6266-36 15953-90 10 3 5464-82 18293-88 6 J5 5962-08 16768-11 jl 5961-7 16769-18 5925-31 16872-17 i 4 5925-13 16872-69 3 5909-49 16917-33 i 2 5907-10 16924-17 4... 10(1). Manganese Mn 8'" m I X n d\ m 7 X n d\ 2 10 4823-521 20725-97 00 5 1 2670-346 37440-06 09 10 4783-454 20899-59 1 2657-952 37613-30 10 4754-046 21028-86 1 2648-917 37741-55 3 6 3178-495 31452-37 00 6 2 2594-170 38537-97 4 5 3161-053 31625-91 1 2582-52 38711-77 5 3148-188 31755-13 7 2 2548-40 39230-07 00 4 3 2817-278 35485-02 - -05 I 1 2537-45 39399-31 4 2803-716 35656-64 j 1 2536-91 39407-69 2 2 2793-350 35788-96 I 1 2529-78 39528-09 |l 2528-76 39536-14 2 2, 3, 4(5); 6a(6); 66,7 (7). 1 Collateral (5dJ S l possibly ^ (6) covered by the strong line 2593-906, n = 38540-40. 2 Collaterals, both lines equally displaced from the normal lines. Mn D"' m / X n m / X n 2 ( 4 3570-061 28002-76 4 5 2726-22 36671-42 I 4 3569-796 28004-84 5 2713-434 36844-16 u 3569-485 28007-27 5 2703-987 36972-90 ( 5 3548-187 28175-40 5 3548-025 28176-67 5 4 2624-158 38097-57 w 3547-790 28178-54 4 2612-939 38261-15 J6n 3532-002 28304-51 2 2604-44 s 38386-05 ffin 3531-839 28305-81 6 ji 2567-529 38937-82 1 3 5 2940-512 33997-76 }2 2566-348 38955-73 l 6 2925-597 34171-08 6 2914-618 34299-97 7 (2d 2531-94 39485-17 i* 2530-797 39502-93 2, 3 (5); 3, 46c, Soft, 6, 76 (6); 4a, 5c, 7a (7). 1 Collaterals equally and oppositely displaced. 302 ANALYSIS OF SPECTRA RARE GASES REFERENCES 1. KAYSER. Astro. J. 4, 1 (1896). 2. EDER and VALENTA. Denks. Wien. Akad. 64,216(1896). 3. PASCHEN. Ann. d. Phys. 27, 537 (1908). 4. RUNGE. Astro. J. 9, 281 (1899). 5. BALY. Phil. Trans. 202, 183 (1904). 6. LEWIS. Astro. J. 43, 67 (1915). 7. RUTHERFORD and ROYDS. Phil. Mag. 16, 313 (1908). 8. WATSON. Proc. Roy. Soc. 83, 50 (1910). 9. CAMERON and RAMSAY. Proc. Roy. Soc. 81,210(1908). 10. MEISSNER. Ann. d. Phys. 51, 115 (1916). 11. RUNGE and PASCHEN. Astro. /. 8,97(1898). 12. NISSEN. P. Z. 8. 21, 25 (1920). 13. PASCHEN, Ann. d. Phys. 60, 405 (1920). BLUE SPECTRA Argon 719-71; u= 439-47; v = 442-67 AS m 7 X n m / X n d\ I 5 2344-4 - 42642-10 3 1 2484-1 40244-05 3 2354-3 - 42462-67 2 2473-1 40423-15 1 2358-5 -42387-07 2 e. 2425-4* (40498-37) 2 5 3765-463 26549-76 4 1 u. 2191-4 (45179-5) -02 2 3739-88 26731-40 1 e. 2190-6. v (45358-6) 00 9 3720-4501 26806- 14 1 2257-9e. it (45434-6) -01 5 v. 2077-2 (47684-0) -12 6 1 2e. 2092-1. r (48780-8) 16 1 2e. 2103-6 (48962-1) 09 1 2e. u. 2120-0 (49034-2) -10 1,3.. .6 (2); 2(1). 1 A strong line covering S s . 2 n= 40493-54 is (55j AD m 7 X n m 7 X n d\ 1 J 1 4203-609 23782-51 3 \ 1 2230-1 44827-37 12 4183-106 23899-08 J3 2229-7 44835-41 -06 6 4172-05 23962-43 2221-4 45002-88 2 (3 2540-1 39357-06 3 2536-0 39420-68 (5 2534-8 39439-33 4 2528-6 39536-01 1(1); 2, 3(2). APPENDIX 303 m I X n 27800 + n \ I 1 4 4 13505-6 13719-9 - 7404-33 -7288-68 2 1 1 1 7435-77 7372-28 7353-42 13444-52 13560-64 13595-43 (31-42) (42218-33) (42334-22) (95) 2367-1 (55) 2361-9 1 1 3 \20073-40] (31-14) (35588-89) ( -55) 2809-7 I 4 2 4 10 (55),4949-53 4943-17 4348-222 (20190-25) 20224-41 22991-57 (30-13) (35703-2 2) (32668-69 ) 2 (32875-0) (-55)2800-7 (55) 3048-552 I 32819-19 3046-130 9 5 5 4 4076-854 (185) 4053-111 24521-94 (24637-25) 29-60 31137-27 (31253-84) 3210-678 (15^)3196-109 1 1? 2 3 1 3931-382 ( - 65J 3914-931 3907-896 25429-28 (25545-82) 25582-12 32-12 30234-96 30351-81 3306-499 3293-768 1 4 7 1 3 3952-892. e ( - 2S) 3826-976 (26010-73) (26127-07) (33-29) 29655-76 3371-077 3 8 4 2 5 3786-536 ( - 25) 3770-719 3765-463 1 26402-01 (26516-05) 26549-76 (30-99) (29259-97) (29378-79) 3502-841. e 3488-316. e 2 1 9 1 3747-135 26679-62 34-96 28990-30 (29109-30) 3448-46 3521-431 e 2 1 10 1 5 3725-665 3718-403 26833-37 26885-78 34-10 29140-81 28782-42 3430-650 3473-368 1 .1 28930-65 3455-572 1 1 (3); 2 (4); 3 (2); 4 ... 10 (1). 2, 3 (2); 4 ... 10 (1). 1 is tfj (2) covering F' (5). 2 Calculated from F'(4). Krypton e= 3183-34; u = 1884-03; v = 1942-44 KrS (Two sets for 3 ) m / X n d\ m / X n d\ I 2 10 10 3 1 10 9 2353-95 2398-38 2416-31 2418-13 3778-23 3669-16 -42468-98 - 41682-46 -41373-26 -41341-95 26460-07 27246-6? 4 5 1 1 2 2 2 2216-72 2179-3 2 2164-6 2162-7 2259-83. e 45097-86 45872-2 46183-6 46224-17 (47421-14) 12 -08 3 4 3 1 2 3623-74 2489-51 2442-68 1 e'. 2353-95 27588-11 40156-61 40926-41 (41252-81) G 3 G 6 I 1 6 2299-02. e. n 2291-26. e. n 2362-18. 2e 2159-5. e 2302-88. 2e (48551-12) (48698-34) (48688-12) (49476-18) (49777-72) 12 22 8 2300-35. 2e (49825-2) 1, 3c, 4... 6(6); 2, Safe (5). 1 is 2 (3)( -95). 2 is also F 8 (2). 3 A displaced S 19 8 a , &,'. 304 ANALYSIS OF SPECTRA KrZ> m / X n m 7 X n 1* '1 5229-67 19116-44 8 /V 2 (1 2574-87 38825-45 * 1 5016-58 19928-46 7 J 2 2559-20 39063-26{ 2, 4836-75 20669-36 6 I 2 2556-01 391 12-00 \ f 5 A* 1 2544-79 39284-39 I f 2n 4796-48 20842-89 -*^13 4 \ [2 2554-351 39137-41 ' I 4789-89 20871-60 3 1 2535-97 39420-99 <1 4788-93 20875-78 2 (2 2525-07 39591-26 t * * 6 2 2 2 1 4765-90 4699-82 4695-82 5022-57 5022-01 20976-63 21271-57) 21289-68 \ 19904-69) 19906-91 \ 1 D u 8 JV 3 (2 3 2 4 2251-13 2250-22 2211-88 2362-18. e 44408-53 44426-67 45196-52 (45504-59) 1 4826-21 20714-49 4 |1 2382-99. e. v (47077-37) * 3w 4825-37 20718-13\ |2 2211-88. u (47080-55) 5 4659-04 21457-76 6 2339-15. e. r (47863-57) t 2 4638-53 21552-65 5 D M 2 2322-40. e. v (48171-72) t * 1 5 2 2 4621-58 4615-46 4614-67 4945-75 21631-67 21660-35 21664-06 20213-86 4 3 2 8 /V 5 1 2 6 2304-78. e. v 2263-71. e. v 2245-34. e. u (48500-71) (49287-59) (49590-57) 41 2 4757-63 21026-33 7 6 2 2260-72. e. v (49345-98) 3w 4592-94 21766-58 6 (49349-39) t 2 4573-52 21858-98 8 Aw 1 2318-26. e. w (50133-95) 4 4556-77 21939-35 4 (50443-84) 1 2628-19 38037-85 8 7 1 2232-90. e. r (49896-96) 7 6 In 2596-83 38497-23 5 1 2594-49 38531-94 3 >5 2592-57 38560-46 1 1,2 (5); 3. ..7 (6). * Depending on type 197 A 2 '. See p. 204. f Depending on type 189A,. Note. The numbers 1 ... 8 refer to the type d, with r 1 ... 8. Kr F r Kr F r For more complete data as to Kr F see [v. p. 370]. m * / X n F(>) I n \ 2 1 1 5771-60 17321-51 30674-77 2 44028-04 2270-59* 2 1 5753-19 17376-92 + 102-10 1 44176-83 2262-94 4 . , 2 44161-81 2263-71 5 3w e. 4525-37 (17534-79) + 211-58 8 (44237-72) 2301-69. c 6 1 5672-94 17622-73 + 301-78 3 44330-38 3255-10 7 2 5446-51 18355-36 + 1043-00 1 i 45080-18 2217-59 8 3 5208-50 19194-16 + 1858-40 ,1 45872-18 2179-3 3 1 In 4280-77 23353-84 30677-27 2 38000-71 2630-76 8 4 3965-02 25213-56 1 2 4252-87 23507-07} [30674-76] [37842-45] 3 1 37946-48 2634-52 4 1 4228-98 23639-82 6 f 4 38148-86 2620-54 7 1 38890-99 2570-54 8 Iw 3941-03 25367-061 + 1859-81 1 39702-07 2518-02 4 1 3 3836-64 26057-20 2 In 3821-93 26157-54 4 3 3817-23 26189-73 1 2w 3835-10 26067-66\ 30677-16 6 35286-68 2833-11 4 1 35416-16 2822-75 5 1 2 6 35493-85 2816-58 6 2n 3791-22 26369-36 f 7 In 36330-48 2751-71 8 I 3580-11 27924-30} + 1857-92 1 37145-86 2691-31 1 The displaced set F (10A 2 ' +5). 2 The set F' = F +4x; see [v. p. 370]. 3 ? (35,) F. APPENDIX 305 Kr F r Continued Kr F r Continued m r / X n *(*) I n X 5 I [27497-70] [30678-23] 4 33857-67 2952-69 8 7 3405-28 29357-89 5 1 34071-90 2934-13 6 1 [28357-47] [30675-60] [32993-80] 5 2n 33127-50 3017-78 6 1 3487-61 28664-88 + 305-47 1 33297-26 3002-39 8 4 3308-28 30218-69 7 1 2 u. 3246-74 (28907-8) (30674-71) 1 (32441-62) e. 2806-21 2 7w 3446-66 29005-44 5 3 u. 3224-99 (29115-5) 7 3 u. 3139-71 (29957-4) 8 1 [29286-33] 5 3 3389-06 29498-44 9 1 [29552-20] 6 2 3348-28 29857-70 10 1 [29728-00] 6 In 3328-34 30036-53 2... 10(5). The values in [ ] are calculated from the formula. Xenon e=7314-l; u =4133-18; v =4428-00 XS m I X n d\ m / X n d\ 1 10 4 12371-57] 2476-02 2526-97 - [42153-39] -40375-49 -39561-50 8 2 1 2n 2658-37. e ( - dj. v 2538-16. e. v 2468-54. e. u (49350-39) (51129-08) (51945-08) 00 02 00 2 4 5 1 3854-44 3607-17 3503-99 25936-90 27714-80 28530-91 9 2850-41. 2e 2713-50. 2e (49700-78) (51470-15) -05 24 16 3 4 1 <1 2527-10 2418-47 2869-71. e 39559-46 41336-15 (42150-88) 10 2616-79. e ( - 8J. v(-8 l ) 2701-99. 2e 2432-87. e ( - 8J. u ( - 5 t ) (49949-59) (51727-14) (52542-75) 16 00 13 4 In 4 1 2689-82. e 2871-85. e. u 2829-35. e. v (44480-53) (46257-97) (47075-65) 02 02 -08 11 I 2 1 2584-04. e. u 2470-30. e. n 2943-07. 2e. u (50134-99) (51916-24) (52729-81) -02 -28 -08 5 1 2828-01. e. u 2944-78. 2e (46797-58) (48576-91) 08 01 12 2 1 3 3202-17. 2e. v 2479-98. e. v 2614-13. 2e (50276-15) (52053-14) (52870-73) -02 01 -07 Q 2 2452-76 e (48072-37) 02 13 In I 2623-31. e. v 2549-05. e. u (49850-70) (50666-04) 00 00 2 <1 2663-43. 2e 2921-74. 2e. v (52162-72) (52977-72) 03 04 1 <1 4 1 2921-74. e.e(- 5J 2777-10. e. e (5j) 2715-91. e.e(-S l ) (48846-68) (50624-48) (51439-70) 00 00 00 1 ... 13(5). For other links see fv. p. 353]. H. A. S. 20 306 ANALYSIS OF SPECTRA XD (After m = 2, no satellite sets given) m / X n d\ m / X n d\ 1 7 3 2641-25. e. u (49297-14) 29 i 5001-20 19989-72 1 4857-37 20581-64 i 2 4671-41 21400-95 8 <1 2853-28. 2e (49665-59) -08 6w 4592-22 21769-99 2 4501-14 22210-48 9 <1 <1 2832-59) 2 2832-19\' 2 (49923-88) 00 2 / 1 2621-88 38129-37 ( 1 2617-06 38199-58 10 <1 3188-80. 2e. u (50112-27) 11 1 1 2615-83 38217-68 4 3017-58. 2e. u (51892-69) do 2605-69 38366-36 5 2945-41. 2e. u (52704-44) r i 2505-05 39907-58 11 1 2805-24. 2e (5,) (50260-84) 03 J 3 2672-35. 2e (52037-53) 13 3501-86. e. u (39995-54) 1 2615-54. 2e (52850-12) 1 2455-19 40717-94 12 2 2796-73. 2e (50373-89) 05 3 1 2723-09. c (44026-48) 00 4w 2597-14. e (45806-77) i 2607-68. 2e (52965-29) 13 1 2789-64. 2e (50464-72) -03 4 < 1 * (46577-38) 3 2708-65. e. u (48355-28) 14 3 3175-80. 2e. r (50535-41) 13 * (49171-45) 15 2 2779-78. 2c(-5,) (50596-56) -05 5 <1 3000-12. 2e (47950-73) -18 1 2648-79. 2e (52370-32) 4 2847-81. 2e (49732-87) 4 2783-49. 2c (50543-95) C <1 2928-20. 2e (48769-16) 09 2 2782-86. 2e (50552-08) 1 3066-69. 2e, ?/(-25 1 ) (51364-07) Mean n {(2) 35126-05, (2) 35136-05} 2e and {(1)37720-0,5, (1) 37728-30} 2e. D (1) above depends on 79A 2 . The following D 1 set depend on 70A 2 , m 7 \ n 1 1 4923-40 20305-60 j 1 5619-18 17791-35 1(3) ' 5125-94 19503-29 8 5372-62 18607 All measures by (5). APPENDIX Table of the 1864 F and F lines For fuller tables of other F and F series see [v. p. 414]. XT? TT F .A. r 307 m / \ n limits I n \ 1 6 3 1 2e. 5667-85 2e. 5125-94 2e. 4916-71 (3010-35) (4875-09) (5705-02) (30725-77) (32590-35) (33420-35) 1 1 (58441-20) [60305-70] (61135-70) (-8j) 2739-91. 3e ( - Sj) 2550-70. 3e 2 8 6 <1 5372-62 4883-68 4693-50 18607-79 20470-75 21300-21 (30726-05) (32589-09) 4 <1 (42844-26) (44707-43) 3214-30. e. v 3032-63. e. v 3 10 8 1 4180-20 3877-95 3757-03 23915-72 25779-64 26609-33 30725-15 (32589-28) 33418-35 2 2 1 37534-58 39398-94 40227-37 2663-43 (8j) 2537-04 2485-13 4 5 1 4 3791-82 u. 3089-07 ( - 5j) 3440-91 26365-19 (28229-80) (29059-47) 1 (30724-58) (32589-96) (33420-07) 1 1 1 (35083-97) (36950-13) (37781-67) (d) 2851-10 (d) 2707-15 (18j) 2648-79 5 5 1 1 3609-60 3381-81 3807-42. u 27696-15 29561-66 (30390-38) 30725-48 32589-38 (33419-32) 1 <1 In 33754-81 35617-10 (36448-27) 2961-69 2806-83 ( - dj 2743-24 6 1 <1 <1 (25 t ) 3506-74 ( - 8J 3293-17 (-28^3206-21 (28498-61) (30362-28) (31190-57) (30725-29) (32589-86) (33417-27) I )3 1 32951-97 34815-79 34817-73 35642-62 3033-86 2871-43 2871-27 2804-82 7 g 1 5 5 3445-01 3236-97 3151-98 29019-32 30884-31 31717-13 30724-37 32588-57 33418-13 [30725-60] 2 1 2n 1 32429-42 34292-84 35119-14 32074-21 3082-74 2915-22 2846-63 3116-88 i 1 3199-87 3119-34 ( - 6A 2 ) 31242-39 (32070-17) 32590-19 (33418-91) 2 2 33937-99 (34767-65) 2945-71 2873-65 (-6A 2 ) 9 1 In 5 2 3374-11 (28j) 3173-15 I (-28J3175-38 2 \ 3092-57 29629-10 (31494-43) 32326-37 30724-64 (32589-98) 33418-72 2 3 4 31820-18 (33685-54) 34511-08 3141-77 ( - 28J 2968-74 2896-79 10 1 3 4 ( - 8) 3354-51 ( - Sj) 3155-66 (28J 3073-62 (29822-05) (31685-5S) (32514-41) (30725-20) (32589-74) (33418-29) 2 4 5n 31628-35 33493-89 34324-16 3160-82 2984-77 2912-56 11 3 2 3 4413-23. e (-28^3141-77 (-28j) 3061-71 (29967-00) (31830-04) (32662-50) (30725-18) (32590-25) (33420-21) 5 2 <1 31483-37 33349-45 34176-93 3175-38 3 2997-69 2925-11 12 G 2* 1 (25j) 3322-30 ( - 25 t ) 3130-48 ( - 2dj) 3049-04 (30081-19) (31945-78) (32776-69) (30725-25) (32589-48) (33419-31) 1 3 1 31369-31 (33233-19) 34062-04 3186-93 ( - 25J 3009-16 2934-98 13 1 1 3 ( - 2dj) 3315-00 3121-15 3042-22 (30168-38) 32030-34 32861-34 (30725-48) 32589-18 33419-61 3 1 4 (31283-39) 33148-03 33977-89 (-28^3196-68 3015-91 2942-25 14 15 4 <1 3306-04 (8J31J3-fi9 30239-16 (32101-73) (30725-21) (32589-87) <1 5 4 (31211-26) 33078-01 (31153-25) (25 X ) 3201-94 (-38^3023-88 ( - 5j) 3209-54 2n (5j) 3107-91 (32161-43) 2 (3J 3029-91 (33089-27) (33418-33) i (33847-39) ( - 5J 2954-08 1 The mean of ( - 5 t ) 3440-9 J, (25J 3438-88, (35J 3438-28 or nn = 29059-54, -73, -15. 2 is also Fj (11). 3 is also (25 t ) F 2 (9). 308 ANALYSIS OF SPECTRA X F Continued X F Continued m I X n limits I n X 16 I <1 3294-09 3103-38 30348-83 32213-80 30725-49 32589-56 4 <1 5 31102-16 32965-33 (33793-89) 3214-80 3032-63 (8j) 2957-771 17 <1 3 ( - 5J 3290-44? 3100-04? (30387-46) 32248-49 (30724-89) <1 (31062-53) (3^) 3219-97 1 33754-81 2961-69 18 1 1 <1 <1 3286-17 ( - 5j) 3097-03 (-28J 3019-96 1 (28J 30 17-89 \ 30421-95 (32285-26) (33114-94) (30725-06) (32588-13) (33418-02) 1 1 3 3 (31028-18) (32891-00) (33720-10) (8j) 3221-45 (8) 3037-47 ((-8)2965-13 j (5) 2964-35 19 <1 In 1 (-28^)3283-75 3093-55 3015-91 (30454-31) 32316-13 33148-03 (30725-42) 32588-93 33420-61 2 3 3 30996-51 32861-34 33693-18 3225-26 3042-22 2967-11 20 1 5 2 ( - 28J 3281-36 3091-22 ( -28^3014-77 (30476-47) 32340-48 33171-17 (30524-60) 32589-36 33419-07 4 2 1 30976-73 32838-25 33666-98 3227-32 3044-36 2969-42 21 3 1 <1 <1 (5j) 3277-41 3089-07 (-8J 3012-45) (8^3011-44^ (30498-27) 32362-98 (33191-66) (30724-07) 32589-61 (33418-10) 1 3 2 30949-88 32816-25 33644-54 3230-12 3046-40 2971-40 All measures by (5). Radium emanation e = 23678-4; u = 11191-8; v = 13680-0 Ra. Em. 8 m / X n d\ m / X n d\ 1 2 3 4 2 3 4383-47. v 4958-0. v 3930-9 3952-7. v [41864-3] - (36493-6) - (33844-1) 25432-35 (38972-12) 02 4 5 6 7 8 4 3 i 4950-2. e (8J 4435-25. e 4280-5. u. v * (43874-02) (46183-25) (48227-00) (48728-4) -01 07 00 -1 1,2,3,5... 8(7); 4(8). * Meanw of j^j f^^j^. v X 4187-97, 4193-1. Ra. Em. D. Two D sets m / X n m 7 X n 1 ( 2 5363-0 18641-4 I (1 5715-0 17493-05 1 5038-3 19842-4 \0 5372-0 18609-94 16 4604-46 21712-09 U 4891-3 20438-8 Jl 4160-57 24028-52 j i 4371-70 22868-07 }2 3965-0 25213-7 1 10 4166-59 23993-82 1 3748-6 1 26669-23 2 4039-5 24748-6 2 (3 7057. e (37844-4) 2 10 4203-39. u (37463-75) 6749. e (38491-4) (5 6309. e? 2 (39524-4) )3 5119-5. e (43206-2) (4 4950-2. e (43874-1) 2 4503-89. e (45875-3) All measures by (7) except D l (2), D 22 (2), and the second Z> 12 (1), D 13 (I), by (8). 1 is also F! (5). z is also F^ (2). Both sets have the same limit, 50403, and the two _D n lines are displaced 23 in their sequences. Ra. Em. F APPENDIX J-(oo) 309 Ra. Em. F m / \ n 29900 + / n \ 2 3 (55^ F WJF 5 3 6 3 3 9 1 1 6309 4652-5 4114-71 4501 7057. v 5887-0. v ( - 35j) 3981-83 v. 4806-5. e u 4732-v e 15846 21488 24296-31 22211 (27846-6) (30662-6) (25149-02) (30796) (33612) (8) 66 (7) (9) (7) (7) (8) (9) (8) (8) (8) (8) (9) (7) 62-5 (9) (9) (7) (8) 3 8 3 2 3 3 (44086-7 + 2dv) (49731-3) (52531-3) (37654-29) (43305-2) (46100-2) (34776-0) (40431-2) 5977-4. 2v (35^ 3650-0. 2u 3971-82. 2v 4170-08. v 6270. 2v 5335. 2v 4239. u (-2d 1 )5977-4.el 5 6 1 1 2 1 3 3748-6 4732-2. u 4174-5. u 3626-6 4541. u I 5119-5. v\ 26669-23 (32317-8) (35139) (27566-3) (33207-6) (7) 64-1 (7) (8) (8) (9) (9) (7) 64-2 (7) (9) m (7) (9) 1 2 2 4 33259-05 (33908-26) (41730-2) 32362-14 (38004-8) (40831-6) 3005-84 ( - 8J 3965-0. v ( - 25j) 5546-6. e 3089-15 v. 5944-9. e. u 5419-2 u References to measures inserted opposite each line. RED SPECTRA Argon Nissen's s-sequence [Chap. X, sect. 8]. (These are calculated from means of series on supposition that in $ 17 (1), n - 13093-792 and limit = 24644-53.) m 1 3 4 n m n m n 37738-32 7980-16 4950-35 5 6 7 3367-01 2436-78 1 1845-69 -5 8 9 10 1446-35 1 1162-74-6 955-51 1-7 The observed lines (references after each). The s refer to series, not sequences. s. 1 (6)4579-527* -21831-03 (1) ^(13)9123-69' 10957-98 (3) s. 2 I (5)4888-21 - 20452-46 (2) 4(3) 8103-691 12336-664 (10) 10 (2) 6121-93 16330-85 (2) s, 1 (6) 5559-02 - 17984-58 (2) 4 (5) 6753-15 14804-49 (2) 5 (3) 6101-33 16385-95 (2) *, I (3)5582-20 - 17909-91 (2) 4 (2) 6719-33 14878-91 (11) 7 (3) 5559-93* 17981-39 (2) s 5 I (8)5607-44* - 17829-28 (2) 4 (2) 6682-7 1 * 14960-4 (11) 5 (8) 6043-48 16542-82 (11) 7 (1)5534-73 18063-40 (2) 10 (1) 5275-3 18952-0 (1) 6 > 6 1 (1)5637-68 - 17733-54 (2) 4 (1) 6640-5 15055-5* (11) 9 (4) 5306-04 18841-94 (2) s, 1 (1)5900-70 -16943-08 (11) 4 (1)6309-36 15845-70 (U) s' 1 (3)5927-34 -16866-96 (11) 4 (2) 6278-80 15922-81 (11) 7 (2) 5254-79 19025-66 (2) s, I (3)6129-02 -16311-93 (11) 3 (1) 743S-77 5 13445-31 (4) 4 (1) 6067-18 16477-39 (11) 6 (1)5265-05* 18988-61 (2) 9 (6) 4933-49** 20264-75 (2) s w 1 (5)6172-7** -16196-4 (11) 3 (1) 7372-28* 13561-09 (4) 4 (4) 6025-40 16592-44 (11) 7 (1)5076-25 19694-84 (2) a u 1 (6) 6212-73 -16092-15 (11) 3 (1) 7316-15 13665-14 (4) 4 (5)5987-61 16697-17 (11) 7 (3)5049-18 19800-45 (2) 8 (2) 4949-53 20199-06 (2) ,9 12 1 (1)6756-58 -14796-90 (11) 3 (2) 6682-7* 14960-4 (11) 10 (2)4547-SS* 21983-05 (2) * 13 1 (2)6937-99 -14409-97 (11) 3 (1) 6513-87 15348-19 (11) 4 (4) 5440-28 18377-42 (2) *i 4 1 ( 5 ) 7067-54 -14143-82 (11) 3 (1) 6402-21 15615-95 (U) *is 1 (3) 7273-13 -13745-82 (11) 3 (3) 6243-45* 16012-98 (11) 8 (2) 4434-037* 22547-35 (1) s l6 1 (1) 7377-S0 - 13673-32 (4) 3 (1) 6215-6* 16084-7 (1) 17 1 (3)7635-107 -13093-792(10) 3 (4) 5999-29 16664-66 (11) 4 (1) 5076-25** 19694-84 (2) 6 (1)4501-66 22208-65 (2) 8 (4) 4309-31* 23199-04 9 (2) * w 1 (1)9658-90 - 10350-79 (3) 3 (4) 5151-74 19407-25 (2) * From the blue spectrum. i . (4) =s 6 (3). 2 (1) gives 3-406, n= . . .65-09. This is the only line of Nissen's series which has been found shifted by the electric field to the red (Takamine). 4 * io (7) =8l7 (4). s Also given as Si (2) and p 9 - S (3). It is given as p t - S (4), and as 2 (3). 8 Zeeman pattern =0/1/1. 3 In red (1) gives ..72-9, (2) ..73-32. ^'" (2). 6 It is F z '" (2). 7 Also 9 is a Stark's A++. 310 ANALYSIS OF SPECTRA The limits and the separations of the above as given by Nisseii, modified by the deduction of 1-07 from Nissen's limits in accordance with the formula in a/nt, are: 1 2 15907-00 1378-63 17285-62 467-95 19752-57 4 5 74-67 19828-24 80-63 19908-87 95-64 6 20004-51 790-49 20795-00 8 . : 9 10 76-13 20871-13 555-09 21426-22 115-50 21541-72 104-3 11 12 21646-00 1295-25 22941-35 13 14 15 386-89 23328-14 266-71 23594-85 397-48 23392-33 72-50 16 17 18 24064-83 579-53 24644-36 2742-33 27386-69 AS AD m / X n m / X n 1 3 2512-3* -39793-9 2 (1 7435-77* 13445-37 6 2562-3* - 39017-4 |.l 7207-20 13871-78 * 7030-54 14220-32 3 13 9123-69 1 10957-98 3 J 5 6170-39 16202-57 5 8522-83 l 11730-50 4 6090-97 16413-84 6 5888-79 16977-44 4 36 6660-92 15009-36 4 J4 5659-47 17665-38 1 6334-24 15783-45 2 5621-28 17785-40 6 5421-68 18440-05 5 1 5880-41 17001-55 5 1 5394-20 18534-00 1 5624-06 17776-51 2 5177-81 19308-57 1, 56 (2); 3 (3); 4, 5a (11). 2ab (4); 2c, 3 (11); 4, 5 (2). *Blue spectrum. 1 The separation is too small. X = 8517-9? n = 11736-59 gives a separation about as much too large. Also 9123 has been allocated to s 1 (4) and p 1 -8(4). 2 Also given as s fr (3) and p 9 - S (3). It is JF 1 /" (2). Combinations si -82 1 5691-94 17536 (2) Sl-p 5 2 I 2453-0* 40755-6 (2) Sl-p 1 2 I 2233-6* 44757-2 (2) * Blue spectrum. Paschen's data of the s-sequences m f a a 4 1 38040-731 39110-808 39470-160 39887-610 3 7272-964 7323-132 8016-679 8101-291 4 4201-806 4223-467 4962-103 5004-811 5 2605-422 2616-576 3372-371 3396-713 6 1667-672 1675-101 2439-967 2456-121 7 1072-452 1077-331 1848-546 1858-065 8 670-006 674-195 1447-593 1454-136 9 386-17 1 389-45 1 1164-914 1169-614 10 . . 957-058 960-902 11 800-659 803-40 1 Lines (0) 4442-243, n = 22504-83; (-5) 4442-89, n = 22501 -55 observed later in his second paper. APPENDIX 311 "*& O CO CO O OS -H QO < I CO ^ f-< CD >* -H IO QO O *Oi I (N COi-^OiCOSCDcost-- *l OS GO GO CO ^1 CO OS O COGO SS CO ^H l> 10 Th O t> l> ^ O O CO ^H ^l IO CO >~^ CO GO ~' O CO O O Tt< ^H Kt) IO OS COCO I-H ^ co o c co ^^ co O 1C CO O QO "-H O CO O CO CO (N - O i * GO tO GO 1 O CD t- OS O^ ~^ ^~* - 1 *-* 1 ????? b r-H GSI OS O _0 t** "^ t^* C^ LO'-^coe^Ttiosoco $; ^K 5 OS (M > CSI OS OS l> ^ GSI os O QO Gi 10 co 'M CO 00 O o r~ co co o GO t~ Tt< (M (N O OS^-lcbrHOOS^rh^l t ^ CO "^ GO CD >O CO' ICDCDOS COCOi-HlOt>' I t-GOt-OCOTjHp^iCSIo4 O O t> GO rHGOCbpHsOCOTM^COOS qSGp-^rHCpCplOCpCOGSl i>ocbobcsiO'^ds'*6s CD CO C^ O O QO CO ^H IO CO CO I> GOGO-HIO" i ^5 GO l> l> CO (M S CO O OS t> CD 4 Pi ?>7 P ^9 ^10 * * * * * S 2 38040-73 10 4 7 5 5 3 5 5 5 39110-81 4 7 4 5 5 4 39470-16 6 5 7 6 ? 8 8 6 6 % 39887-61 5 6 7 9 9 7 8 5 TYPE II . \ REFERENCES 1. KAYSEB and RUNGE. Wied. Ann. 52, 93 4. PURVIS. Proc. Camb. Phil. Soc. 13, 82 (1894). (1905). 2. EXNER and HASCHEK. Tabellen der Funken- 5. VAN DER HARST. Academisch Proefschrift. spektra (1902). Amsterdam (1919). 2a. Tabellen der Bogenspektra ( 1904). 6. SCHIPPERS, from ~Ka,yseT'sHandbuch, Bd. vi. 3. LOHUIZEN. Z. 8. wiss. Phot. 11, 397 (1912). The measures are by Kayser and Rungc (1). Pb I II III 3R 4168-21 23984-49 10807-44 4# 2873-40 34791-93 2831-19 2 2657-16 37623-12 3R 4019-77 24870-17 07-16 5R 2802-09 35677-33 3R 3740-10 26729-83 07-15 4 2663-26 37536-98 31-03 4R 2476-48 40368-00 3JB 3671-65 27228-08 07-32 2E 2628-36 38035-40 30-80 R 2446-28 40866-20 5E 3572-88 27980-80 07-30 4R 2577-35 38788-10 30-70 R 2402-04 41618-80 4 3262-47 30642-98 07-46 4R 2411-80 41450-44 32-23 1 2257-53 44282-67 APPENDIX 313 I 4 3240-31 30852-58 4 3220-68 31040-57 2 3119-09 32051-49 2n 2980-29 33544-21 Pb Continued II 372 2399-69 06-97 41659-55 3R 2388-89 07-44 41848-01 R 2332-52 07-73 42859-22 3R 2254-02 07-39 44351-60 Sn III QR 2247-00 30-57 44490-12 5R 2237-52 30-75 44678-76 2 2.ZS7-,93 30-84 45690-06 I II III 41i 3801-16 26300-42 0/6/7 5185-53 5R 3175-12 0/3/2 31485-95 1735-54 QR 3009-24 33221-49 0/3/2 411 3330-71 30015-16 6/9/7 85-20 QR 2840-06 0/3/2 35200-36 35-59 QR 2706-61 36935-95 0/3/2 4R 2850-72 35068-77 0/6/7 85-15 5R 2483-50 5/6/3 40253-92 35-89 3R 2380-82 41989-81 3 A' 2813-66 35530-67 85-44 3 2455-30 40716-11 35-20 QR 2354-94 42451-31 3JS 2785-14 35894-39 0/6/5 86-02 2 2433-53 41080-41 36-24 5R 2334-89 42816-65 0/9/5 411 2779-92 35961-91 0/9/7 85-27 6jR 2489-&S 41147-18 4 If 2594-49 38531-94 0/1/1 84-29 4R 2286-79 43716-23 35-63 QR 2199-46 45451-86 5A 2571-67 38873-90 0/4/3 84-40 QR 2269-03 44058-30 3 2524-05 39607-26 85-97 4R 2231-80 44793-23 32-2 5R 2148-7 46525-4 8J2 2495-80 1 40055-44 3/6/5 84-21 QR 2209-78 1 45239-65 18 2408-27 41511-17 79-4 QR 2141-1 46690-6 48-7 4 2063-8 48439-3 3 2358-05 42395-16 88-7 4R 2100-9 47583-9 85 2317-32 43140-27 84-1 4 2068-7 48324-4 .4(4) .4(5) 1 Exner and Haschek (2, 2a) give 2495-81 a, 2209-71 s with separation = 5185-79. The Zeeman patterns are by (4), (5). The 0/6/7, 0/6/5 may possibly be 0/1/1, and 0/9/5 be 0/3/2. Lohuizen's series in Sn in W. N. I 27345-57 1 35894-39 39607-26 41511-17 IT A a 32963-61* 41511-17 2 45239-65*'! 47121-8 1 48224- 1 1 III 42816-65 46525-4 48439-3 b 35542-79 1 44091-90* 47793- 1 1 **! c 35961-91 5 44507-80* 48224- 1 1 1 41080-41 44793-23 46690-6 Q 47793-1 1 - 4 7 48439-3* ? The series I, II, III are from Kayser and Range's lists (1). 1 Additional lines \ = (3) 3655-88; (3fi) 3032-88; (3)2812-70; (4R) 2267-30; (2R) 2246-11: 2121-5; (4R) 2091-7; (5R) 2073-0. 2 belongs to A I. 3 belongs to A Til. 4 Two common. 5 belongs to Kayser and Runge's set I. 6 belongs to Kayser and Runge's set II. The Zeeman patterns are (4), (5) : A I 2, 0/3/5. A 1 3, 0/6/5. A a 2, 0/1/1 ? A III 3, 0/9/5 ? 314 ANALYSIS OF SPECTRA Sn Continued B 1 II III I II 3R 3801-16 26300-42 572 3175-12 31485-95 672 3009-24 33221-49 5 572 2483-50* 40253-92 672 2199-46* 45451-86 472 2850-72 35068-77 572 2483-50 40253-92 372 2380-82 41989-81 6 672 2421-78 1 41279-67 472 2151-22 1 ? 46471-4 472 2594-49 38531-94 472 2286-79 43716-23 672 2199-46 45451-86 7 2n 2386-96 1 41881-62 1 Additional lines to^Kayser and Runge. Exner and Haschek (2, 2a) give 2151-62, n = 46462-35 . with a I-II separation = 5182-68 in place of 5191-7. 2 belongs to B II (3). 3 belongs to B III (4). The Zeeman patterns are (4), (5) : 2 0/6/7 0/3/2 0/3/2 3 0/6/7 5/6/5 4 0/6/7? 5 5/6/5 6 0/1/1? Sb (Lohuizen's series; measures by (6).) A I II III 2 2 3504-451 0/4/3 4R 3267-497 0/6/7 28527-00 3 3R 2718-910 36768-58 4 3 5 6 2481-752 40282-20 2068-66 68-51 68-80 30595-60 6537-30 37132-36 2574-088 0/1/1? 38837-09 2360-50 42351-00 2262-54 44184-44 2212-48 45184-06 B 2 3 3637-830 27481-11 0/3/2 2068-67 3 3383-150 29549-78 0/2/1 I 3 2 2851-115 35063-72 68-64 3 2692-272 37132-36 '4 2 2614-694 38234-02 69-06 3 2480-453 40303-08 ' | 5 3B 2507-783 39863-87 76-26 37, 5 2383-626 41940-13 8 4 2445-531 40878-56 0/1/1 43-51 2 2329-09 42922-07 4 2 472 3232-537 30926-55 (A 0/9/7 7307-47 suggested third set.) 2 2614-694 38234-02 3 3R 2652-608 37687-57 0/4/3 01-75 2 2222-05 1 44989-32 . 2 2478-339 40337-45 0/3/2 01-33 2 2098-47 47638-78 5 2 2395-215 41737-22 1 Linked to B II (6) by 206 5R 2769-939 0/7/8? 6541-48 36091-26 41-59 2289-01 43673-95 3 2137-11? 6474-29 46777-37 2067-25 2222-05 44989-32 TABLE IV Formulae Constants 316 ANALYSIS OF SPECTRA Formulae constants Except where otherwise P() V* a MW) V* a Li 43482-23 951592 + -007409 28580-74 600844 - -007912* 951580 + -007409 28581-08 Na 41449-00 1-148088 - -031215 24475-66 650854 - -021648* 1-147256 -031 126 24492-84 K 35005-06 1-296137 - -061466 21962-39 823547 - -033821* 1-293129 - -061393 22020-07 Rb 33687-85 1-365690 - -073376 20871-76 872623 - -042520* 1-352891 - -073514 21109-34 Cs 31402-18 1-449835 - -088558 19670-41 956066 - -054936* 1-418258 - -089529 20224-30 Cu 62306-25 891742 - -026494 31523-48 431291 - -078858 Ag 61114-33 978206 - -086337 (30642-60 480009 - -098202 \30616-36 481527 - -073372* Au 70642-79 950924 - -021769 29469-85 563932 - -036108 Mg'" 20473-76 879011 - -059990f 39760-00 368500 + 009966$ Ca'" 17764-68 33988-23 1-568338 - -087917 Sr'" 16891-34 31031-51 1-637689 - -093381 Ba'" 16835-63 28514-10 1-796343 - -243898 Ra'" ? ? Mg" 121266-04 1-307827 - -042680 85505-05 937501 - -035448 Ca" 95704-41 70290-0 1-211862 - -074940 Sr" 88838-71 64322-07 1-325712 - -117288 Ba" 58635 1-453920 - -132888? Ra" 83215-94 57030-81 1-341403 - -045673 Mg' 61669-68 936922 092962/ 26618-40 493031 - -071914 Oft' 49304-27 25651-97 Sr' 45929-99 24231-56 Ba' 42029-57 23969-47 Ra' Zn'" 22095-16 42876-42 1-287059 - -059160 Cd'" 21054-39 40710-60 1-349486 - -067133 Eu'" 21759-46 40351-40 1-302343 - -066144 Hg'" 21831-36 40138-13 1-310138 - -068769 Zn" 147272-69 + 97918+Z 735284 - -009356 Cd" 142033-96 95427-00 693511 - -064027 Eu" 91548 + Hg" Zn' 75765-80 898189 + -045531 29020-23 1-372177 - -029106 Cd' 72536-6 949421 - -005584 28845-20 1-424702 - -036411 Eu' 28830-31 470549 - 140465 Hg' 30113-95 1-371085 - -044145 *rjS Al 22928-67 48164-26 1-250206 - -063093 Ga 46318-16 1-292185 - -077314 In 22295-00 44454-76 1-287479 - -069510 Tl 22786-01 41470-23 1-264328 - -070417 Sc 22281-97 828585 -187372 37949-90 1-244902 - -026104 * Terms in a/(m - -5). t With additional term --127704/m 2 . With additional term - -235800/w 2 . APPENDIX 317 Formulae constants noted, N = 109675 R.U. D,(oo) M a /,() A* a Li 28580-74 997546 000984 12202-07 1-014744 - -044832 Na 24475-66 982390 013266 12275-92 997762 + 002004 K 21962-39 685680 335588 13469-76 980740 + -037632 Rb 20871-76 1-644361 121816 14337-25 965264 + -064028 Cs 19673-61 526083 028056 16804-67 963557 + -045275 Cu 31523-48 989542 -022811 28390 Ag 30642-60 993579 - -027504 Au 29469-85 964130 + 033168 Mg'" 39760-00 824196 032088* 13714-05 938018 066121 3?" 33988-23 28933-14 892712 084610 Sr"' 31031-51 27609-77 882231 083818 Ba'" 28514-8 32433-OOf 844603 021570 838349 024492 Ra'" ? ? Mg" 85505-05 946459 044724 49775-66 994654 005919 Ca" 70290-0 81993-30 971775 034704 Sr" 64322-07 74004-52 959616 027864 Ba" 58635? v Ra" 57030-81 74691-32 Mg' 26618-40 317676 885955 15268 Ca' 25651-97 27455-04 Sr' 24231-56 25780-4 Ba' 23969-41 30634-37 Ra' Zn'" 42876-42 12990-62 Cd"' 40710-60 13022-58 Eu'" 40351-40 12706-55 Hg'" 40138-13 12750-98 Zn" 97918 + Cd" 95433-32 Eu" 91548 Hg" -"e Zn' 29019-26 786412 168990 Cd' 28843-62 807684 124266 Eu' 28836-91 915666 -191672 Hg' 30113-95 931883 - -003473 Al 48164-26 15839-57 955353 045504 Ga 46318-16 In 44454-76 Tl 41470-23 Sc * With additional term - -048960/m 2 . t Top is/ x calculated with observed F l (3) as (5 t ) F l (3), lower as/ 2 from observed F (3). Form fjL + a/(m + fj.). 318 ANALYSIS OF SPECTRA Formulae constants Continued Except where otherwise p ( 00) V- a Si (oo) M a 0'" s'" Se'" 36067-12 30936-60 1-216682 1-409100 - -042632 - -072346 23204-33 20085-46 19275-10 778807 939880 932746 - -028752 - -018580 111403 0" Mn"' 33021-80 1-303414 - -028164 21203-98 41250-12 852800 1-379894 - -027022 06804 A Kr X Ra. Em. 94373-15 94120-27 93178-68 51731-05 51651-29 51025-29 50403 095901 093630 096726 101230 - -017878 - -014156 -Oil 826 010966 Note. In several cases D (oo ) has been determined independently of 8 (4 n= _.Q1 + N/[m + -710981 --033847/m} 2 orders 1, 3 ... 11. [ ] -/><)-> -767 -133 -455 --001 -153 -29 -1-63 -066 --195 --518 -764 -100 -411 - -018 -141 *, n - N/ { m + 688700 - -025 1 1 6/w } 2 orders 1 , 3 ... 1 1 . [ ] 00 --049 -330 -060 --570 --Oil - -006 --06 400 --379 -139 - -024 -351 -128 --441 --022 --010 --058 The last five p, p fi ... p in , have the same constant* 4-1 1 and values of ,u, a as follows: /> 6 -200544 - -077347 p 8 -184868 - -090652 p 7 -200464 - -087960 p lQ -101087 The /*'s of the d vary between -976 and -988. For instance 2-989028(5) - 121? 3-986487(44) -289? 4-984555(452) - 565? KD 2-853474(38) -106? 3-795934(224) - 249? 4-769577(74) -495? 5-755967(452) - 869? RbZ) 2-766177(48) -96-5? 3-705269(12) -231 -9? 4-682474(61) -468? CsZ> 2-554651(23)- 76-0? 3-536080(2) -201-5? 4-534410(9) -425? 5-535125(54) -773? CuD 1-965849- 34-63? 2-979095 - 120-53? 3-984072 - 288-30? 964403- 34-56? 978260 - 120-43? 983096 CuF 2-002548 - 36-53? 2-991723 - 153-7? AgT) 1-947241- 33-5? 2-979830 - 120-6? 3-98441 1 - 288-4? AuD 2-035096- 37-87? 2-980714 - 120-7? MglX" 2-828000(3) -103-10? 3-829452(1 2) -256? 4-829158(31) -513? 944746 977386(6) 982832 025340 970506 547238(23) 527484(2) 525540(9) 526324(231) Inverse CuD(l) 1-496751 - 15-24? 495251 001208 Inverse Ag/)(l) 1-490214-14-994? 487161 Inverse An 7) (1) 1-502485 492907 2-968821(2) -29-82? 3-961450 -70-85? 1-946992(8) - 33-65? 3-082012(3) - 133-46? 4-089974(11) - 311-90? 5-078952(26) - 597-2? 6-048590(50) -1008-8? 6-968088(154) - 1542? Ca D'" 946246(16) 081266 089128 077818 046231 960063 Ca D" 2-313145(1) - 14-07? 312286(1) 3-360616(1) - 43-25? 359787(1) 4-369667(9) - 95-05? 369142(12) 5-373872(550) - 176-87? SrD'" 1-993129(7) - 36-09? 989489(8) 3-174307(7) -145-8? 170952(7) 4-196849(10) -337? 192707(10) 5-2006; 6-1976; 7-1970; 8-2019 2-680337(2) - 87-8? 3-584717(2) -210-0? 4-522871(8) -421-8? 5-484275(15) -752-1? 945796(24) 080771 088592 077042 044335 954060 CaT)' 1-998716- 36-40? 3-022490- 125-87? 4-144520- 324-04? 5-041982- 584-43? 6-052134 - 1010-6? 987352(5) Z) 33 168731 7) 33 191051(100) Sr F'" 2-926337(142) -114-2? 3-910169(6) -272-3? 4-903185(16) -536-7? 5-898994 -934-2? 2-943446-116-21?* * from ^3 of the second and disrupted triplet. APPENDIX 321 SrD" 2-434798(12) - 16-45 430218(16) 3-517117(3) - 49-58 512830(3) 4-540854(100) - 106-71 536761( ?) Ba D"' (Limit = 28629, see p. 130) 1-835710(2) - 28-200 825064(6) 3-111879(2) -137-561 102656(2) 4-153177(9) -326-58 145643(9) 2.850595 855388 BaD" SrJ" 1 -901631 -30-6 3-282260 4-132474 4-986102 5-956452 6-939333 820052(3) ( 2-539610(30)- 18-67 (2-419998(0) - 16-15 3-569491(2) - 51-8 4-604516(8) -lll-26 5-6261; 6-6279 * Two independent sets. 528923(18))* 407163(0) J 558899(2) 594011(8) 2-423532 - 16-2 3-592061 4-627844 380439 566116 Zn 2-905899(30) -lll-7 3-907594(109) -272-6^ 4-909041(405) -539-3^ 905373(49) 905004(99) ZnD" 1-680928(15)- 5-4 2-952879(50) -29^ 680482 951348 All the D' of II b are amenable to formulae (Table IV). Cd U" 2-902053(27) -lll-4 900024(40) 3-910633( 150) - 272-6 908458 4-914220 -541-0|; 5-9156; 6-9209; 7-9109 898790(84) 906764 CdD" 1-724896 - 5-85 2-898718(22) -27-76^ 721568 894404 CdF" 3-61 2353 -53-7; 4-597801-110-8^; 5-591413-199-20^; 6-587500 2-937917-115-35^ 3-940870 Eu D' 925985 930723 918859 H. A. S. EuZ>" 2-848621-26-34^ 840711 2-932836(4) -115-0^ 3-943445(14) -279-6| 4-947560(60) -552-3^ Hg ZX" 88 9219 ,91 A 48 A 937378 D t 940586 Z>, 930857 D 3 934263 D a 21 322 ANALYSIS OF SPECTRA AID 2-631414(4) 3-426309(16) 4-261766(31) 6-167465(63) - 83-06? - 183-31 - 352-8| - 629? 6-1 17850(135) -1043-8? 7-0912; 8-0799; 9-0674; 10-0591 GaZ> 1-989636? 2-979086 InD 1-913672 - 31-95? 2-823989(51) -102-67? 3-806244(150) -251 -4? 4-776735 -496-9? 5-755705 631304(4) 425486(16) 260341(31) [988493] 978363 904388?- 31 - 821583 793773 764066 740440 6-6970; 7-6876; 8-6778; 9-6627; 10-651 T1Z> 1-957710 938123 2-897391(27) -110-9? 888344 3-898733(90) -270-16? 888642 4-897983(214) - 535-7? 887512 5-896880 886215 6-895530 885240 7-8946 Constant within errors up to m = 14. OZ>" 2-972495(40) 3-966637(14) 4-964284(18) 5-962953(39) 6-962116(67) - 119-7? - 284-5? - 557-7? - 966-5? - 1538? 7-961880(309) - 2301? 8-961570(951 )-3281 9-9658 +45dn Limit 23204-00 SD'" 4-552686(47) - 430-2^ 5-542926(21) - 776-4 6-536790(38) - 1273^ 7-532654(194) -1944-0? 8-528600(396) -2828? 9-522500(1 141) -3936? Limit 20086 OZ>" 2-980284(93) - 120-7? 3-978613(72) - 287-2? 4-976865(33) - 562-4? 5-975958(68) - 973-9? 6-975400(215) - 1547-3? 7-984900(626) - 2321? 8-983304 - 3305? 9-974023 -4523? Limit 21205-00 Se D"' 4-629262(54) - 452-2? 5-621936(56) - 810? 6-615643(105) -1320? 7-601450(240) -2002? 8-611058(728) -2911? 9-592507(643) -4024? 10-57831(270) -539-6? (365) D (1) (165) D (8) INDEX A congery in II (a), 68; discussion of, 217; tables of, 277-8 Accuracy attainable, 17; inference from differ- ent measures by two observers, 45 ADAMS, W. S., 8 ADENEY, W. E., 279, 293 Alkalies, description of spectra, 51 ; series, 52-6; combinations, 56; summation lines, 59 Aluminium, 75; analogy with Sc sub-group, 75; Doppler effect, 110; the (1), 226, with linked and collaterals, 226; disruption in P (!) -P ( m )' 76 5 series data > 293-4 ANGSTROM, A. J., 3 Angstrom, definition of, 3, 7 Antimony, diagram of shifted sets of lines, 39; series in, 216; line data, 314 ARETZ, M., 254 Argon, type II, 39; Z.P., 207; Stark effect, 105, 208; Doppler effect, 112; potentials, 121; contrast of double spectrum with He, 198; blue spectrum, 199; red spectrum, 205; presence of links in red spectrum, 207; mul- tiple collaterals, 203; series data, blue, 302-3, red, 309 ARONBERG, L., 144 ASTON, F. W., 143, 145 Atomic volumes, in p sequences, 170; mul- tiples of, 175 B congery of II (a), 68; discussion of, 220; tables of, 277-8 BABCOCK, H. D., 9 BACK, E., 94, 97, 298 BAILEY, DORIS, 117 BALMER, J. J., 19 BALY, E. C. C., 208, 302 Barium, triplets, 65; linked 8"' (2) sets, 65; two D'" (1) sets, 66; A, B, L categories, 67, 216; singlets, 70; doublets, 74; displacement in D'" (5), 138; disruption in F (4), 181; series data, 273-6 BELL, L., 4 BENOIT, A., 4, 279 BERGMANN, A., 29, 58, 245 BEVAN, P. V., 245 BLOCK, L. and E., 226, 259, 279 BOHR, N., 49, 114 BOTTCHER, E., 105, 108 Breadth of line, diffraction, 13; temperature, 14; physical conditions, 15 BRINK, F. N., 172, 176 BUISSON, H., 7, 14, 42 BURNS, K., 9, 208 Cadmium, 68; singlets, 71; doublets, 75; collaterals in S, 141; wave length red Cd line, 4; series data, 282-4 Caesium, Meissner's related F doublets, 56; anomalous D separation, 141; series data, 252-3 Calcium, anomalous D'" mantissae, 35; do. P', 70; triplets, 65; A, B, L categories, 67, 216; singlets, 70; doublets, 74; series data, 267-70 CAMERON, A. P., 302 Carriers of series lines, 110, 115 CATALAN, M. A., 31, 254 Character of lines, 12; nomenclature, 17 Chlorine, Doppler effect, 111 CLAYDEN, A. W., 230 Collaterals, definition, 137; disruption into several, 203, 226 Combination, examples of, 37; table III, 240; the p z '" - s' (m), 71 COMPTON, K. T., 117 Continuous spectra, H, 41; the alkalies, 51 Copper, 60; special summation series (Q), 62; ambiguity in limits, 60, 80; collaterals of 8 (2), 139; inverse D sets, 61, 136; D (1) set, 61; M(A), 185; disruption in ^.(4), 181; series data, 254-7 CORNU, A., 21, 293 COTTON, A., 91 CREW, H., 24, 254, 263 CURIE, M., 144 CUETIS, W. E., 41, 51, 240 D lines in sodium, early measures of, 3 d and / sequences, instability, 180; laws of mantissae formation, 182; essential differ- ence from p, s, 182; data of mantissae differ- ences, 184; influence of value of N on exact- ness of laws, 189; double d (1) sets, 180, 204 d, determination of from v, 125 DATTA, S., 55, 245 DAVIES, ANN C., 114, 117, 119, 123, 213 DAVIS, B., 117, 123 DEL CAMPO, A., 31 Denominator, abnormal cases less than unity, 229 Density of Eu, 174; Ra, 175; Sc, 173 DEWAR, J., 19, 21, 208, 245 Difference and summation tones, analogy with, 37 Diffuse series, inverse sets in Cu, Ag, Au, 61; dependence of first order in sub-groups in periodic system of elements, 188; d sequence based on A 2 , mantissae oun multiples, 182; first order in I (6), 61; first order in III (6), 229 Displacement, 137; examples of, Ba 8 (5), 138; KrF, 140; inverse Au A 141; Au F, 181; X JP and A F, 202; hi linkages, 159-61, 202; of double displacement, Cu S, 139; Kr(l, 2, 3), 204; X A 139; X F, 202; normal lines weakened by displacement, Au F, Cu F, E&F", 181; A1S(1), 227 Disruption of low order, F series, 67; into many collaterals, 76, 202, 203, 226 Dissociation potentials, 116 Doppler effect, 109 324 ANALYSIS OF SPECTRA DORN, E., 109 DUFOUR, A., 92, 98 DYSON, F. W., 41, 240 EBERHARD, G., 5 EDBR, J. M., 139, 228, 254, 263, 279, 293, 302 Effect on line measurement, diffraction, 13; asymmetry, 14; temperature, 14 Electric field, effect on p (I) -p (m) in He, 47; in alkalies, 57; effects, 102; new lines, 102; on H, He, 103; Ne, A, 105; series relation- ships, 106; molecular fields and diffuseness, 109 EPSTEIN, P. S., 51 Europium, spectrally belongs to group II (6), 68; singlets, 72; doublets, 75; density of, 174; oun transference in triplet, 188; series data, 285-8 EVANS, E. J., 50, 240 EVERSHED, J., 41 EVERSHEIM, P., 7, 243 EXNER, F., 144, 245, 254, 260, 263, 279, 293, 298, 312 F, disruption in low orders, 67; displacement in, 140; instability in, 181 / sequence, see d and / sequences FABRY, C., 4, 5, 7, 14, 42, 245, 254, 279 FISCHER, A., 109 FOOTE, P. D., 123 Formulae, functional forms, 27, 29, 36; de- termination of constants, 32; dependence on observation errors, 35; tables of N/(m + /j.) 2 , 31, 236; change with N, 84 FORTRAT, R., 52, 245 FOWLER, A., 49, 51, 71, 73, 240, 263, 293 FRANCK, J., 113, 117, 123 FRATJNHOFER, 4 FRICKE, H., 118 FRIEDERSDORFF, K., 109 FRITSCH, C., 298 GALE, H. G., 8 Gallium, 75; Rydberg's deductions of S and D lines, 166; series data, 294 GALT, R. H., 245 GEHRCKE, E., 42, 113 GMELIN, P., 91, 98 Gold, 60; ambiguity in limits, 60; D (1) set, 61, 163; M (A), 188; anomalous separation in inverse D, 141; disruption in J' 1 (4), 181; series data, 260-2 GOLDSTEIN, E., 51 Goos, F., 8 GOUCHER, F. S., 117, 123 Grating, non-normality of concave, 6 GRUNTER, R., 293 HACKSPILL, L., 171, 176 HAGENBACH, A., 58, 245 HAMPE, H., 263 HAMY, M., 279 HANDKE, F., 226, 254, 263, 279, 293 HARDTKE, 0., 254 Harmonic ratios, question of, 18 HARST, VAN DER P. A., 312 HARTLEY, W. N., 19, 279, 293 HARTMANN, J., 6 HARTMANN, W., 60, 207 HASBACH, K., 254 HASCHEK..*., 144, 245, 254, 260, 263, 279, 293, 298, 312 Helium, description of spectra, 44; helium and parhelium, 45; formulae and values of N, 46; type of series in He, 47, 59, 86, 97; relations of D', D", 47; combinations, 48; enhanced series, 49; structure of, 50; band, 51; Stark effect, 103; Doppler effect, 112; potentials, 118; contrast of double spectrum with those of other gases, 198; series data, 241-3 HERMANN, H.. 263 HERTZ, G., 113 HEYCOCK, C. T., 230 HICKS, W. M., 27, 29, 30, 45, 47, 50, 53, 66, 76, 85, 92, 125, 133, 139, 140, 149, 153, 163, 167, 174, 181, 183, 197, 226 HOLTZ, 0., 24, 220, 222, 263 HONIGSCHMID, 143, 144 HOROVITZ, STEPHANIE, 143, 144 HORTON, F., 114, 117, 119, 123, 213 HUFF, W. B., 279 HTJGGINS, W., 41 HUPPERS, W., 279 Hydrogen, description of spectra, 40; notation of lines, 41; doublets, 42; type of series, 43; many lined spectrum, 44; Stark effect, 103; potentials, 116; table of series, 241 HYMAN, H., 143 Indium, 75; the (1), 227; with links and linked lines, 227; the D (1), 229; series data, 294-5 Inequalities, series and parallel, 157 Intensity, distribution in a line, 16; change in collaterals, 140; diminution with concomi- tant linking, 157; or displacement, 181 International Union for solar research, 7 lonisation potential, theory of, 114; table of, 122 IRETON, H. J. C., 226 Isotopes, 143, 145 JOHANSON, A. M., 36 RASPER, F. J., 254 KAYSER, H., 5, 7, 11, 21, 27, 38, 60, 62, 78, 205, 214, 234, 245, 254, 263, 279, 293, 302, 312 KENT, N. A., 52, 245 KILBY, C. M., 298 KING, A. S., 16 KIRSCHBAUM, H., 108, 109 KNIPPING, P., 117, 123 KOCH, J., 16, 102, 240 KOKTJBTJ, N., 103, 106, 108, 208 KONEN, H. M., 58 KRUGER, THE A, 117, 123 Krypton, collaterals of S (1, 2, 3), 139, 204; and of F, 140; blue spectrum, 199; two D (1) sets, 204; series data, 303-5 KUNZER, R., 109 L congery of II (a), 68; discussion of, 221; analogy with the enhanced sequents, 225; tables of, 277-9 LANGMUIR, L, 116 Lanthanum, 75 LAU, E., 42 Lead, radioactive atomic weights, 143; line shifts for isotopes, 144; line data, 312 INDEX 325 LEHMANN, H., 60, 254, 263, 279 LEMBERT, M. E., 144 LEWIS, P. E., 302 LIEBERT, G., 240 Limits, equality of, 80; determined by for- mulae, 32; by convergence, 34; by summa- tion lines, 35 Lines represented by a sum of several sequents, 158 Links, definition, 149; linkage maps, 153; regularities in, 154; apparent modification in, 154-61 Lithium, separations, 52, 55; nature of p se- quence, 58, 97, 107; satellites, 55; series data, 245-6 LIVEING, G. D., 19, 21, 208, 245 LOHMANN, W., 92, 94, 97, 212 LOHUIZEN, T. VAN, 36, 214, 312 LORENSER, E., 70, 263 LORENTZ, H. A., 87 LUNELUND, H., 94 LYMAN, T., 42, 50, 118, 121, 226, 240, 263, 279, 293 MCCAULEY, G. V., 24, 263 MCLENNAN, J. C., 115, 226, 259 Magnesium, 64, 71, 73; analogy with Zn group, 64, 71, 73; series data, 263-6 Magnetic field, 87; theory of normal triplet, 88; proportional to field, 90; specification of pattern, 91; Runge's submultiple law, 92; the Ritz shift, 93; mutual action close companions, 94, 96; anomalous Z.P., 98; Preston's rules, 99; producing new lines, 97; series patterns, 99 MAHOMMAD C. WALT, 91, 94, 97, 101 Manganese, 78; series data, 301 MANNING, A. B., 293 Mantissae, D mantissae, Table V, 320; data of, 184 Measures, successive of D* of Na, 4; red line of Cd, 4 MEGGERS, W. F., 11, 54, 123, 139, 208, 234, 245, 254, 263 MEISSNER, K. W., 42, 54, 56, 139, 208, 240, 245, 254, 263, 293, 298, 302 Mercury, 68; singlets, 72; doublets, 75; Stark effect, 107; Doppler effect, 112; radiation and ionisation potentials, 115; series data, 288-92 MERRILL, P. W., 46, 208, 243 MERTON, T. R., 14, 43, 44, 144, 240 MICHELSON, A., 4, 42, 94, 279 MILLER, W., 98 MILNER, S. R., 279 MITCHELL, S. A., 41, 240 MOGENDORFF, E., 30, 37 MOHLER, F. L., 123 MOLL, W. H., 56, 245 MOORE, B. E., 92, 98, 101 N, dependence on mass, 49, 83; values from He', He", 85; question of uniformity, 82; exact values from p and s sequences, 178; from d and/, 189; value from Na P, 84 NACKEN, A., 263 NAGAOKA, H., 93 Neon, potentials, 119, 213; single spectrum, 198; red spectrum, 208; summation lines, 209; linkage effect, 210; Z.P., 92, 212; Stark effect, 212; series data, red spectrum, 310-2 NICHOLSON, J. W., 14, 31 NISSEN, K. A., 206, 208, 302 Notation of line character, 17; types of series, 25, 30; collaterals, 137; linked lines, 152 NYQTTIST, H., 105, 108, 212, 240 Occurrency curves, 151 OLMSTEAD, P. S., 117 Oun, definition, 126; table of, 127; oun mul- tiples in A, 131; triplet modification, 132; multiples in satellites, 134; relation to atomic number, 147 Oxygen, 77; Z. P., 95; Stark effect, 107; Dop- pler effect, 112; potentials, 122; series data, 298-9 2>-sequence, mantissae relations in p lt p z , 167; triplet modification in, 169; dependence on atomic volume, 171; ratio a//x in alkalies, 175, 179j general formula in alkalies, 175; dependence on JV, 176; essential difference frornd,/, 182 PASCHEN, F., 10, 42, 45, 48, 50, 54, 56, 65, 71, 77, 94, 97, 98, 99, 101, 208, 212, 240, 245, 254, 263, 279, 293, 298, 302 PAULSON, E., 36, 40, 205 PEROT, A., 4, 5, 245, 254, 263, 279 PETERS, C. G., 11, 234 PFUND, A. H., 7 PICKERING, E. C., 49, 240 PLASKETT, H. H., 50, 240 Pole effect, 8, 9 Potassium, question of satellites, 55; series data, 248-50 Potentials, ionisation and radiation, 113; dis- sociation, 116; preliminary, 118 PRECHT, J., 75, 263 PRESTON, J., 99 PRIEST, J. G., 208 Probability of harmonic ratios, 18; of link coincidence, 150 Purity of spectrum, 13 PURVIS, J. E., 312 Radiation potential, theory of, 114; table of, 122 Radium, doublets, 75; density of, 175; series data, 276 Radium emanation, single spectrum, 198; series data, 308-9 RAMAGE, H., 245, 293 RAMSAY, W., 302 RANDALL, H. M., 56, 66, 245, r 254, 263 RAU, H., 50 RAYLEIGH, Lord, 14, 88, 243 REESE, H. M., 91, 98 REICHENHEIM, O., 113 REYNOLDS, W. H., 263 RICHARDS, T. W., 143, 144, 172, 176 RITZ, W., 22, 29, 30, 36, 54, 89, 93 ROGNLEY, O., 123 Rossi, R., 144, 208 ROWLAND, H. A., 4, 5 Rowland's scale, 5; errors in standards, 6; ratio to international scale, 6 ROYDS, T., 302 326 ANALYSIS OF SPECTRA Rubidium, question of satellites, 54; series data, 250-1 RUBIES, S. P. DE, 254 RUNGE, C., 11, 21, 27, 38, 45, 60, 62, 75, 77, 78, 91, 93, 99, 101, 205, 212, 214, 234, 240, 245, 254, 263, 279, 293, 298, 302, 312 RUSSELL, A. S., 144 RUTHERFORD, E., 302 RYDBERG, J. R., 21, 23, 27, 31, 39, 49, 71, L65, 181, 205, 236 Rydberg's rules, 28; tables of N/(m + v) 2 , 31, 236; relations between formulae constants, 166 s sequence, relation to p, 177; general formula in alkalies, 178 S, D limits, equality of, 80 ST JOHN, C. E., 8, 9 Satellites, question of in Rb, 54; in K, 55; in Li, 55; oun multiples, 134 SAUNDERS, F. A., 29, 44, 54, 70, 226, 228, 245, 263. 279, 293 SAVIDGE, H. G., 31 SAWYER, R. A., 279 Scandium, 76; density of, 173; series data, 297-8 SCHILLINGER, R., 245 SCHDPPERS, H., 312 SCHMITZ, K., 263 SCHNIEDERJOST, J., 240 SCHONROCK, O., 14 SCHUSTER, A., 18 Selenium, 77; anomalous D, 78; series data, 300-1 Separations, conspectus of, in Ca D'", S'", D", 24; dependence on atomic weight, 25; ratio of, in triplets and satellites, 63; in A cate- gories of II (a), 68 ; measures more accurate than those of lines, 139, 217; equality of S, D separations, 79, 81; and abnormality in D, 200 Sequence, definition of, .26; formulae, 29, 36 Series, description, 19; multiplicity, 21; the fourth type, 29; comparison of types in periodic table, 40 Silver, 60; ambiguity in limits, 60, 80; inverse D sets, 61, 136; D (1) set, 61; M (A), 185; series data, 258-60 Singlet series in II, 70 SODDY, F., 143 Sodium, nature of p sequence, 53; calculation of formula, 33; series data, 246-8 SOMMERFELD, A., 50 Sounding, definition, 162; in X S, 162; Au, 163; In, 227; Tl, 228, 231 Spectra, similarity of Th and lo, 145; arc and spark, 149; type II, 39, 205, 214; double rctra of He different origin from those of . 198, 211 Standard arc, 7, 10 Standards, Rowland, 5; International, 7-10 STARK, J., 48, 50, 57, 71, 102, 108, 109, 180, 240, 245, 254, 279 Stark effect, see. Electric field STETTENHEIMER, A., 90 STILES, H., 279 STIMSON, H. F., 123 STRAUBEL, R., 279 Strontium triplets, 65; A, B, L congeries, 67, 216; singlets, 70; doublets, 74; displacement in F (2), 140; series data, 270-2 Sulphur, 77; Doppler effect, 112; series data, 299, 300 Summation lines, 27, 201; limits given by, 35; in alkalies, 59; Eu, Hg, 64, 69; Kr F, 140; Au F, 181; in rare gases, 199, 201; in Ne, 209; frequency of displacement, 201; data, Na, 248; K, 250; Rb, 251; Cs, 253; Cu, 254-7; Ag, 259; Au, 260-2; Zn, 281; Cd, 284; Eu, 285, 287, 288; Hg, 289-91; A, 303; Kr, 304; X, 307, 308; Ra.Em, 309 TAKAMINE, T., 103, 106, 108, 208, 231 TATE, J. T., 123 TATNALL, R., 254 Temperature effect, 14 THALEN, R., 21, 228 Thallium, 75; the S (I), 228; with links and linked lines, 228; the D (1), 230; series data, 295-7 Tin, list of type II lines, 39; series in, 214; line data, 313 Transference from A x to A 2 , 132; in Eu, 188 Triplet separations, ratio of, 63; ratio of satellite separations, 63; triplet modification, 169 TUCZEK, F., 105, 108 Type II spectra, 38; Sn, Sb, A, 39 Vacuo, reductions to, 10; Table, 234 VALENTA, E., 139, 228, 254, 263, 279, 293, 302 VOGEL, H. W., 41 WADSWORTH, C., 143, 144 WARAN, H. P., 97 WARE, L. W., 8 WATSON, H. E., 208, 302 Wave numbers, 11 Weakening or absence of normal lines with collaterals and links, 157, 181 WEISS, P., 91 WENDT, G., 109 WERNER, H., 263 WIEDMANN, G., 279 WOLFF, K., 279 WOOD, R. W., 41, 52, 240, 245 Xenon, collateral D sets, 139; blue spectrum, 199; collaterals in F (5), 202; two D (1) sets, 205; series data, 305-8 YOSHIDA, U., 103 YOUNG, J. F. T., 226 YOUNG, T., 3 Yttrium, 75 ZEEMAN, P., 52, 87 Zeeman effect, see Magnetic field ZlCKENDRAHT, H., 245 Zinc, 68; singlets, 71; doublets, 75; series data, 280-2 PRINTED IN ENGLAND BY J. B. PEACE, M.A., AT THE CAMBRIDGE UNIVERSITY PRESS , - - LD ai-lOOw-7/83 UNIVERSITY OF CALIFORNIA LIBRARY