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diff --git a/75914-0.txt b/75914-0.txt new file mode 100644 index 0000000..5703d4f --- /dev/null +++ b/75914-0.txt @@ -0,0 +1,1426 @@ + +*** START OF THE PROJECT GUTENBERG EBOOK 75914 *** + + + + + + Proceedings of the American Academy of Arts and Sciences. + + VOL. 61. NO. 10—JULY, 1926. + + + + + ON THE DISTRIBUTION OF INTENSITY IN STELLAR ABSORPTION LINES + + + BY CECILIA H. PAYNE AND HARLOW SHAPLEY + + + + + ON THE DISTRIBUTION OF INTENSITY IN STELLAR ABSORPTION LINES[1] + +Footnote 1: + + The cost of publication of this research has been met with the help of + a grant from the Rumford Fund. + + BY CECILIA H. PAYNE[2] AND HARLOW SHAPLEY + +Footnote 2: + + National Research Fellow. + + +1. It is unnecessary to emphasize the significance of the form of +absorption lines in the study of problems of atomic structure and the +physical constitution of stellar atmospheres. There has been an +abundance of theoretical work on line contour, but a remarkable scarcity +of quantitative observation. The present preliminary study is aimed to +meet, in part, the need for measurements on the broad and strong lines +in the spectra of stars of various types. + +In general the investigation has been based on objective prism spectra, +analyzed with a photographically recording microphotometer. The ease +with which a photometric scale can be set up on these plates, available +throughout the whole length of the spectrum, and essentially independent +of the variability of plates and development, is a decided factor in +favor of using objective prism spectra. Other advantages include the +efficiency of the objective prism spectrograph and its simple operation. +The possible disadvantage of lack of purity is not important, at least +in the case of the lines discussed in this communication; the extent to +which scattered light affects the true contours of the absorption lines +is considered below. + +That the results from slit spectrographs are in essential agreement with +these slitless spectrograms is shown in Figure 1, where microphotometer +tracings of spectra from the two sources are shown. Through the courtesy +of Professor W. J. Hussey and Professor R. H. Curtiss, of Ann Arbor, +some excellent spectrograms made with the single prism spectroscope at +the Detroit Observatory have been sent to Harvard for this comparison. +The dispersion is practically the same on the Michigan and Harvard +plates. The microphotometer records were made under identical conditions +for the two sets of spectra, though the presence of comparison lines on +the Michigan plates and the narrowness of the spectra made their +analysis more difficult. + +[Illustration: Figure 1.—Microphotometer tracings made from the spectra +of four stars. The names of the stars, and the sources of the analyzed +spectra, are as follows: (1) α Canis Majoris (Sirius), Harvard objective +prism spectrum, (2) α Lyrae (Vega), slit spectrogram, Detroit +Observatory, (3) α Aquilae, slit spectrogram, Detroit Observatory, (4) β +Pegasi, slit spectrogram, Detroit Observatory. The violet ends of the +spectra are to the left.] + +2. The work on the Harvard spectrograms has been carried out by the +method that was described in the preliminary report (H.B. 805, 1924). +The plates were all made with the sixteen-inch refractor, using two +prisms and a special set of apertures. The different apertures provide +relative objective areas of 16, 8, 4, 2, and 1, respectively. The +apertures are rectangular, and the successive reducing strips are placed +perpendicular to the refracting edge of the prism. It is assumed in the +discussion that the amounts of light admitted by the apertures are in +the same ratio as their areas. + +A standard procedure has been adopted in securing the spectrograms. A +series of spectra with the several apertures was obtained upon each +plate. Focus, clock rate, and exposure time were kept constant over any +one series. In general the apertures were used in the order 16, 8, 4, 2, +16. Aperture 1 was omitted in nearly every case, and for a few stars +other apertures were also omitted, or found to be useless owing to +faintness of the image. Omission of apertures is indicated by notes to +Table I. + + TABLE I + LIST OF PLATES USED + ┌────────┬───────────────┬────────┬─────────────────┬─────────────────┐ + │ Plate │ Star │Spectral│ Apertures │ Remarks │ + │ Number │ │ Class │ │ │ + ├────────┼───────────────┼────────┼─────────────────┼─────────────────┤ + │MC 20790│α Lyrae │ A0│1, 16a, 8, 4, 2 │Ap. 2 not used │ + │ 20797│α Bootis │ K0│1, 16a, 8, 4, 2, │Ap. 1 and 2 not │ + │ │ │ │ 16b │ used │ + │ 20800│α Aquilae │ A5│1, 16a, 8, 4, 2, │Ap. 1 and 2 not │ + │ │ │ │ 16b │ used │ + │ 21640│α Cygni │ cA2│16a, 8, 4, 2, 16b│ │ + │ 21645│δ Cassiopeiae │ A5│16a, 8, 4, 2, 16b│ │ + │ 21646│α Cassiopeiae │ K0│16a, 4, 2, 16b │Ap. 16b not used │ + │ 21721│α Aurigae │ G0│16a, 8, 4, 2, 16b│ │ + │ 21722│δ Canis Majoris│ cF8│16a, 8, 4, 2, 16b│Ap. 16b not used │ + │ 21788│β Orionis │ cB8│16a, 8, 4, 2, 16b│Ap. 16b not used │ + │ 21789│ε Orionis │ B0│16a, 8, 4, 2, 16b│Ap. 16b not used │ + │ 21802│α Canis Majoris│ A0│8, 16, 4, 2 │ │ + └────────┴───────────────┴────────┴─────────────────┴─────────────────┘ + +The apertured spectra were examined, and any that showed irregularities +were rejected. In cases of interference by clouds, whether or not the +spectra were visibly impaired, the plates were not measured. Spectra +which appeared from experience to be too strong or too weak for +satisfactory analysis were also rejected. + +3. The present report deals with the spectra of the eleven stars +enumerated in Table I. Successive columns contain the plate number, the +name of the star, its spectral class, the apertures employed, and +remarks. + +In addition to the plates enumerated in Table I, the following focus +plates were obtained. + + ┌─────┬───────────────┬────────────────────────┬──────────────────────┐ + │Plate│ Star │ Apertures │ Remarks │ + ├─────┼───────────────┼────────────────────────┼──────────────────────┤ + │21648│α Canis Majoris│16, 4, 4, 4, 4, 4, 4, 4,│Various focus settings│ + │ │ │ 4, 4, 16 │ │ + │21803│α Canis Majoris│16, 16, 4, 2, 8, 8, 8, │ „ │ + │ │ │ 8, 8, 16 │ │ + └─────┴───────────────┴────────────────────────┴──────────────────────┘ + +4. All the plates have been analyzed by means of the Moll thermoelectric +microphotometer of Harvard Observatory,[3] which furnishes a +photographic record of the plate density. The adjustments of this +instrument were made with several ends in view. The analyzing beam of +light was kept as narrow as possible, so that no integrating effect +should enter into the final result. At the same time it was desired that +the total galvanometer deflection—the quantity on which the measures +depend—should be of reasonable size; otherwise the errors of measurement +would become proportionately too great. Some of the analyzed spectra, +especially those of fainter stars, were so narrow that the slit +admitting the analyzing beam had to be considerably shortened. This cut +down the total light transmitted in the same proportion, and to keep the +deflections of the galvanometer of reasonable size, a wider slit, and +therefore a wider analyzing beam, had to be used. A compromise was +worked out, for each plate, between a narrow analyzing beam and a +reasonable galvanometer deflection. + +Footnote 3: + + This instrument was purchased with the aid of the Rumford Fund of the + American Academy of Arts and Sciences and the Bache Fund of the + National Academy of Sciences. + +Special precautions were taken to secure the greatest uniformity of +conditions possible throughout the analysis of each series of spectra of +any one star. At first it was hoped that the whole series of plates +could be analyzed under exactly uniform conditions. Owing to the +narrowness of some of the spectra, however, it was necessary to +introduce the modifications indicated in the preceding paragraph. Even +if all the spectra had been analyzed under precisely the same +conditions, experience showed that direct intercomparison between +different stars would have been impossible, owing to varying amounts of +fog on different plates. + +The instrumental settings were made and recorded at the beginning of the +analysis of each series of spectra, and when possible were kept +untouched throughout the process. The voltage supplying the analyzing +beam, and the temperature of the room, were recorded at the beginning +and end of each analysis, since both these factors may affect the +galvanometer deflection. + + TABLE II + ┌─────────────┬─────────────┬─────────────┬─────────────┬─────────────┐ + │Plate Number │ Star │ Slit Width │ Slit Length │ Total │ + │ │ │ mm. │ mm. │ Deflection │ + │ │ │ │ │ scale div. │ + ├─────────────┼─────────────┼─────────────┼─────────────┼─────────────┤ + │ MC 20790│ α Lyr │ .25 │ 6.0 │ 77 │ + │ 20797│ α Boo │ .10 │ 7.0 │ 35 │ + │ 20800│ α Aql │ .10 │ 7.0 │ 42 │ + │ 21640│ α Cyg │ .10 │ 5.5 │ 30 │ + │ 21645│ δ Cas │ .10 │ 4.0 │ 35 │ + │ 21646│ α Cas │ .40 │ 3.0 │ 45 │ + │ 21648│ α CMa │ .25 │ 4.0 │ 67 │ + │ 21721│ α Aur │ .25 │ 5.0 │ 62 │ + │ 21722│ δ CMa │ .25 │ 5.0 │ 74 │ + │ 21788│ β Ori │ .25 │ 6.5 │ 91 │ + │ 21789│ ε Ori │ .25 │ 6.0 │ 69 │ + │ 21802│ α CMa │ .25 │ 6.0 │ 90 │ + │ 21803│ α CMa │ .25 │ 6.0 │ 85 │ + └─────────────┴─────────────┴─────────────┴─────────────┴─────────────┘ + +The instrumental settings for the different plates analyzed are +summarized in Table II. Successive columns contain the plate number, the +name of the star, the width in millimeters of the slit producing the +analyzing beam, and the total length of that slit. The effective width +of the slit producing the analyzing beam differs somewhat from the +quantity recorded in the third column. For the three entries .10, .25 +and .40, the corresponding effective slit widths are .101, .262, and +.385 mm., respectively. The corresponding widths in millimeters of the +analyzing beam are 0.010, 0.026, and 0.038, respectively, which are +approximately equivalent to .02, .05, and .08 angstroms at Hδ for the +dispersion used in this series of plates. + +5. _Measurement of microphotometer tracings._—In addition to the line +representing the density of the image at different points along the +spectrum, reference marks were inserted by registering a line for +“darkness,” by interposing an opaque screen in the path of the analyzing +beam, and a line for “clear film,” by passing the beam through the plate +background close to the spectrum, though not close enough to bring it +within range of disturbing photographic effects due to the image. + +The microphotometer tracings on paper prints were measured with respect +to the reference marks. Lines, representing “darkness” and “clear film,” +were ruled from end to end of the tracing, and across the absorption +lines a curve was drawn, completing the curve of the neighboring +continuous background. For early type stars this background curve can be +drawn without ambiguity; but when the spectrum is rich in lines, the +course of the unlined continuous background is largely a matter of +judgment. + +[Illustration: Figure 2.—Diagram of an absorption line, as registered by +the microphotometer, showing the method of measuring the tracings. The +quantities n (“darkness” to “background curve”), _m_ (“background curve” +to “line”), and _l_ (“line” to “clear film”) were measured at intervals +of five scale divisions, indicated by the vertical lines.] + +The quantities measured on the microphotometer tracings are best +described by a diagram. Figure 2 represents a wide absorption line, and +the various distances that were measured in analyzing such a line. The +measures were all made with a half-millimeter réseau scale photographed +upon glass, which was laid directly upon the tracing. + +6. _Method of reduction._—The spectra obtained with various apertures +provide, as was pointed out in Harvard Bulletin 805, several measures of +the intensity at any point of an absorption line. The intensity is +compared, in the present paper, with the intensity that the continuous +background would have at the same point if the line were not present, +which is assumed to be represented by the “background curve” drawn +across the absorption line. + +The method has the advantage of making a determination separately for +each wave length. The difficulties introduced by the varying color +sensitivity of the photographic plate are thus avoided. It has, however, +the disadvantage that the measured quantity depends to some extent upon +the individual judgment of the investigator in drawing the “background +curve”—a matter that is simple for Classes B and A, but may prove +serious for second-type stars. + +The intensity differences, background _minus_ line, were determined for +several points by direct measurement. The distances, _n_ and _m_ + _n_ +for the same wave length in all the spectra of any one series, were +obtained from the microphotometer tracings, and were separately plotted +against the logarithms of the corresponding apertures. Smooth curves +were drawn, joining the plotted points for any one wave length, as in +Figure 3. The drawing of the curves is somewhat simplified by +considering together several for the same star, remembering that the +sections lying between the same abscissae should be roughly parallel. +These various curves represent different sections of the familiar +characteristic curve for photographic blackening, the logarithm of the +aperture being here substituted for the more usual logarithm of the +intensity. Differences of intensity between line and background are then +readily obtained by interpolating values of n on the curve connecting +_m_ + _n_ and aperture, and similarly by interpolating values of _m_ + +_n_ on the curve connecting aperture with measured values of _n_. Each +spectrum thus furnished at least one, and sometimes two, values for the +intensity difference at any point. + +It will be seen from Table IX that for several stars two mean values of +line intensity are given, one being the mean of all the measures, and +the other the “selected mean.” The selected means are obtained by using +only points from the more linear portions of the characteristic curve, +and by rejecting values derived from microphotometer tracings of +exceptional total deflection. + +[Illustration: Figure 3.—Relation between galvanometer deflection +(representing plate density) and aperture (representing light +intensity), from measures of the microphotometer tracings made from the +apertured spectra of α Lyrae, MC 20790. Ordinates are galvanometer +deflections in scale divisions, abscissae are (above) apertures, (below) +logarithms of apertures. Smooth curves are drawn joining the points +corresponding to the same wave length, for the three apertures +represented.] + +The intensity drop from background to line is thus obtained in the form +log. intensity of background _minus_ log. intensity of line. The change +in intensity may readily be converted into stellar magnitudes by +dividing the difference of the logarithms by 0.4. + +7. The results embodied in the present paper differ so materially from +those of some previous workers, that it is of especial interest to +examine the accuracy that may be claimed for each stage of the work, and +the weight that may be assigned to the results, (Cf. Harvard Monograph +No. 1, p. 51). Three stages of the investigation should be considered +separately; the plates, (a and b), the microphotometer records (c), and +the measures (d). + +a. _Accuracy of plates._—A qualitative test of the reliability of the +spectra used is made by examining the reproduction of line detail +throughout the whole series made for one star. Figure 4 shows the +microphotometer tracings for a portion of the spectrum of δ Canis +Majoris, made with apertures 16, 8, and 4. Figure 5 shows a similar +series of tracings made from spectra of α Persei, taken with apertures +16, 8, 4, and 2. It may be seen that the reproduction of line detail is +satisfactorily faithful, although a few spurious details can be +detected. + +[Illustration: Figure 4.—Microphotometer tracings made from a portion of +the Harvard apertured objective prism spectra of δ Canis Majoris, MC +21722. The different apertures used are indicated on the left margin. A +few of the more important lines are marked on the lower edge of the +diagram.] + +[Illustration: Figure 5.—Microphotometer tracings made from a portion of +Harvard apertured objective prism spectra of α Persei. The different +apertures used are indicated on the left margin. A few of the more +important lines are marked on the lower edge of the diagram.] + +The best quantitative test of the reliability of the spectra used in +this work is the consistency of the numerical results obtained from the +different members of a series. From Table IX it may be seen that the +residuals very seldom exceed 0.2 m., while the majority are less than +0.05 m. + +In specific criticism of the use of the objective prism in line +photometry, it has been claimed that the intensity at the line center is +affected, and measurably increased, by stray light, and that such an +effect is inappreciable for slit spectra. The results of the present +work, which deals with lines of various depths, widths, and qualities, +are relevant to a discussion of the question, so far as it concerns +objective prism spectra. + +Presumably the effects of stray light must be greatest in the immediate +neighborhood of the stronger portions of the spectrum, and fall off at +greater distances from the more heavily exposed parts of the plate. +Skylight contributes mainly to plate fog, is uniform over the spectrum +and its vicinity, and is eliminated by the use of the line representing +“clear film” as a reference base in measuring the tracings. + +If the effects of stray light are of importance in the immediate +vicinity of the continuous spectrum, they will presumably affect all +absorption lines to some extent, and will in particular be greatest for +narrow lines. The effects should also be greater for heavily exposed +spectra than for the more lightly exposed spectra of the same star. +Further, the effects of stray light should appear not only within +absorption lines, but also alongside of the spectrum on either edge. + +A comparison of the results for δ Cassiopeiae and α Aquilae, both stars +of Class A5 (see Table X) shows that the observed line depth is not, in +this case at least, a function of line width. The lines of δ Cassiopeiae +are both narrower and deeper (that is, they show greater contrast with +the background) than those of α Aquilae. The same is true of δ Canis +Majoris and Capella; the lines of the former are both narrower and +deeper. + +The results for apertures 16, 8, 4, and 2 have been compared for all the +stars discussed, and the intensity differences between line and +background are not appreciably smaller for the larger apertures, which +would be the case if stray light were an important factor. Indeed, for α +Cygni and β Orionis an opposite effect is shown. + +[Illustration: Figure 6.—Microphotometer tracing taken across the +spectra of Sirius (MC 21647) made with the different apertures indicated +along the upper margin.] + +To examine the distribution of light at the edges of the spectrum, a +microphotometer tracing was made by running MC 21803 (Sirius) through +the instrument in a direction perpendicular to the length of the +spectra. The resulting tracing is reproduced in Figure 6. Effects of +stray light are not to be found, except for the strongest spectrum. +Evidently such effects depend on the heaviness of the exposure, but are +not simply proportional to it; they may indicate mainly the “creep” of +the overexposed image rather than stray incident light. The point of +exposure beyond which stray light begins to be a disturbing factor would +have to be determined separately for each plate. In no case is it likely +to involve any but the strongest spectrum, and spectra that are strong +enough to exhibit the effect are for other reasons not usable. Such +measures, in fact, are omitted in deriving the “selected mean,” and it +would seem that effects of stray light are thus eliminated, while an +upper limit may be assigned to their magnitude by comparing the mean +derived from all the measures with the selected mean in Table IX. Stray +light, although certainly present to some degree, is therefore probably +not an important factor in affecting the results of line photometry with +the present objective prism spectra. + +[Illustration: Figure 7.—Microphotometer tracing taken across the +spectrum of Vega made with the single prism spectrograph of the Detroit +Observatory.] + +Figure 7 represents the result of a similar test made by taking a +microphotometer tracing across an excellent slit spectrogram of Vega +that was made with the spectrograph at Ann Arbor. There are no traceable +effects of stray light outside the edges of the spectrum, but on the +contrary there is a distinct drop in intensity, which may partly be due +to an Eberhard Effect. The objective prism spectrum therefore appears to +have a slight advantage in this regard, judging from a comparison of +Figures 6 and 7. + +b. _Effect of focus._—The effect of poor focus in blurring absorption +lines suggests that this factor may enter into the accuracy of the +results. It is not possible, in a stellar spectrograph, when working +with flat plates, to keep all parts of the spectrum in focus at the same +time. Two plates of Sirius were taken for the purpose of examining the +magnitude of the effect. The apertures used, and the focus settings, +were as follows. + + PLATE MC 21648 + Spectrum 1a 3a 3b 3c 3d 3e 3f 3g 3h 3i 1b + Aperture 16 8 8 8 8 8 8 8 8 8 16 + Setting 17.2 17.2 17.4 17.6 17.8 18.0 17.0 16.8 16.6 17.2 17.2 + + PLATE MC 21803 + Spectrum 1a 1b 2e 3 4 2c 2d 2b 2a + Aperture 16 16 8 4 2 8 8 8 8 + Setting 16.6 16.6 16.6 16.6 16.6 16.2 16.4 16.8 17.0 + +From MC 21648 it is possible to obtain a qualitative estimate of focus +effects; MC 21803, including spectra taken with all four apertures, +furnishes a quantitative estimate of the magnitude of the focus errors. +Microphotometer tracings were made, under uniform conditions, of the +spectra of each of the focus plates, and measures were made at the +centers of the lines only. + +For the plate MC 21648, the observing record book contains the entry: +“Frost in center of prism at close.” Apparently the frosting resulted in +a gradual decrease in the intensity of successive spectra, which is +shown, when the spectra are arranged in the order in which they were +photographed, by a gradual decrease in _n_, a quantity that should +remain constant for the same aperture, since the edges of the spectrum, +the portion where focus would affect the intensity, are not crossed by +the analyzing beam of the microphotometer. The progressive change in _n_ +is shown in Table III. + + TABLE III + Spectrum 3a 3b 3c 3d 3e 3f 3g 3h 3i + _n_ at Hβ 13 (12) 13 15 16 16 17 18 17 + Hγ 8 8 8 11 9 10 11 10 11 + Hδ 11 9 10 12 12 14 12 13 15 + Hε 16 14 17 15 18 19 19 19 20 + K 19 17 19 18 20 22 21 22 23 + Hζ 27 25 28 29 29 31 31 31 33 + +That the change in _n_ is progressive and not due to change of focus is +shown by arranging the columns in the order of focus setting, 3h, 3g, +3f, 3i, 3a, 3b, 3c, 3d, 3e. No regular change in _n_ is then evident. + +The total deflection of the galvanometer is satisfactorily constant for +all the microphotometer records of the spectra on MC 21648, excepting +3i, which is rejected for a large voltage drop (0.2 volts), producing a +reduction of four scale units in total deflection. Spectrum 3i is +omitted from further discussion. The quantity _l_ must be corrected for +change in _n_, and this may be done by adding to _l_ a quantity equal to +the increase in _n_, since the observed change in _n_, which should be +constant, corresponds to a shift of the whole spectrum, tending to +decrease _l_. The change in _l_, the distance from “clear film” to line +center, as measured on the microphotometer tracings, with changing +focus, is shown in Table IV. Values of _l_ are corrected. + + TABLE IV + Spectrum 3h 3g 3f 3a 3b 3c 3d 3e + Focus 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0 + _l_ at Hβ 33 36 40 47 49 49 48 43 + Hγ 37 38 39 47 47 50 46 47 + Hδ 32 35 31 40 41 45 43 40 + Hε 24 26 27 33 33 35 37 31 + K 42 44 42 50 50 52 54 47 + Hζ 12 14 13 19 18 22 24 20 + +The line depth is the greatest, and the focus presumably the best, where +_l_ is smallest. It appears that spectrum 3h is at best focus. + +Table V contains the values of _m_ for different focus settings, in the +same form as Tables III and IV. The quantity _m_ requires no correction +for change of _n_. For all the spectra on this plate the K line appears +double. The last line of Table V contains the distance, in scale +divisions, between the two maxima of the K line on the microphotometer +tracing. One scale division corresponds approximately to one Angstrom. + + TABLE V + Spectrum 3h 3g 3f 3a 3b 3c 3d 3e + Setting 16.6 16.8 17.0 17.2 17.4 17.6 17.8 18.0 + _m_ at Hβ 16 16 14 13 13 12 9 11 + Hγ 19 18 18 16 15 14 12 13 + Hδ 22 20 20 19 18 17 15 16 + Hε 24 22 20 21 22 21 21 19 + K 3 3 2 2 2 2 2 2 + Hζ 24 23 23 24 25 23 29 28 + Width of K 4 4 5 5 7 6.5 9 9 + +The data of Table V, and the changing width of the K line (thus shown to +be an effect of focus) indicate 3h as being the best focussed of the +nine spectra. This can also be seen visually from the plate. + +The focus plate MC 21803 was similarly analyzed and measured. No +progressive weakening of the spectra is shown by this plate, and the +measures are therefore uncorrected. For the same plate Table VI shows +the change of _l_ with focus setting, in the same form as Table IV. + + TABLE VI + Spectrum 2c 2d 2e 2b 2a + Setting 16.2 16.4 16.6 16.8 17.0 + _l_ at Hβ 51 52 51 54 53 + 4481 77 78 79 79 81 + Hγ 54 55 56 55 56 + Hδ 47 48 51 50 50 + Hε 39 39 42 43 41 + K 62 64 65 65 64 + Hζ 22 26 28 28 26 + Hη 8 10 12 12 8 + Hθ 4 5 4 6 2 + +Table VII is in the same form as Table V, and represents the change of +_m_ with changing focus. Evidently Spectrum 2c is at best focus. + + TABLE VII + Spectrum 2c 2d 2e 2b 2a + Setting 16.2 16.4 16.6 16.8 17.0 + _m_ at Hβ 22 22 21 20 19 + 4481 3 3 2 2 2 + Hγ 24 24 23 23 25 + Hδ 28 27 26 27 26 + Hε 31 31 30 28 30 + K 6 5 5 4 4 + Hζ 36 33 34 33 34 + Hη 32 31 30 30 31 + Hθ 20 19 20 19 19 + +By the use of the four apertured spectra that occur on MC 21803 it is +possible to evaluate the differences of intensity, produced by the +change of focus, directly in stellar magnitudes. The method used in +deriving the intensities is the one employed in compiling Table IX. The +intensities at the centers of the lines of the various spectra are +summarized in Table VIII. It appears that Spectrum 2c is at best focus +for lines at either end of the spectrum, and that the curve of best +focus moves towards 2b for intermediate lines. The effect is what would +have been anticipated on general grounds. The magnitude of the effect is +satisfactorily small, as may be seen by comparing the differences in +Table VIII with the residuals in Table IX. Errors arising from bad +focus, while they are of appreciable size, do not exceed the errors due +to other causes. If the spectra to be analyzed appear upon visual +examination to be in good focus, they will probably not give results +impaired by serious focus error. + +[Illustration: Figure 8.—Microphotometer tracings made from Harvard +objective prism spectra of Sirius, MC 21648, to illustrate the effects +of focus. Analyses are shown of the five lines indicated on the left +margin, for the focus settings given above. The best focus is at 16.8; +the short lines below the absorption minima indicate the change in line +depth with changing focus. The doubling of the K line, and the +increasing distance between the components, is a noticeable effect of +focus.] + +Figure 8 shows, for MC 21648, the lines Hβ, Hγ, Hδ, Hε, and K, for four +out of the nine focus settings. The change in line depth, and the +blunting of the intensity curve, are at once apparent. + + TABLE VIII + Spectrum 2c 2d 2e 2b 2a + Setting 16.2 16.4 16.6 16.8 17.0 + Hβ .53 .53 .51 .49 .47 + 4481 .13 .13 .09 .09 .09 + Hγ .60 .59 .60 .60 .63 + Hδ .63 .65 .65 .66 .62 + Hε .62 .62 .66 .62 .65 + K .15 .14 .13 .12 .10 + +c. _Accuracy of microphotometer records._—As was pointed out in Harvard +Bulletin 805, the width of the analyzing beam, which is not in any case +greater than one-tenth of an Angstrom, is such that no smoothing effect +need be considered at the line center. + +In a few cases the same line of the same spectrum was registered twice. +The measures made upon the two tracings were always satisfactorily +accordant. + +[Illustration: Figure 9.—Test of the consistency of spectra taken with +different apertures.] + +Ordinates are distance from “clear film” to “line center” taken from +microphotometer tracings of spectra of α Aquilae, MC 20800. Abscissae +are the ratio (_l_ + _m_ for one aperture)/(_l_ + _m_ for twice the +aperture). The fact that the points lie on a smooth curve indicates that +the results are satisfactorily consistent. + +The consistency of the results given by the tracings of several spectra +of the same star, when photographed with different apertures, may be +examined by means of the plot shown in Figure 9. Ordinates are values of +_l_ + _m_. Abscissas are values of the ratio + + ((_l_ + _m_) for one aperture)/((_l_ + _m_) for twice the aperture). + +It is evident that if the points thus derived fall on a smooth curve, +the results derived from different tracings of the same spectrum will be +mutually consistent. The method of interpolation described in Section 6 +may therefore be used in deriving the differences of intensity between +line and background. + +If the method of Section 6 is to be successfully applied, it is +essential that the total range (“darkness” to “clear film”) shall be +uniform for a single series of tracings. In general the variations in +total range do not exceed three or four scale units, but, for some +spectra, occasional changes of eight or ten units have occurred, +generally owing to changes of voltage or room temperature. + +Under these circumstances, it has been thought best not to attempt to +apply any correction for variations in total range, but to reject from +the “selected mean” readings from spectra that gave very discordant +total ranges. + +d. _Accuracy of measures._ In comparison with the errors of the plates +and of the microphotometer tracings, the errors in the measurement of +the records are of relative unimportance. The chief difficulty, as +mentioned above, is that of drawing from fiducial points the reference +lines representing the continuous background and the “clear film.” The +error thus introduced may occasionally amount to one millimeter, or two +divisions of the scale. + +It is sometimes difficult to decide upon the position of the center of a +line, especially when it is wide, without a sharp maximum. This may lead +to large residuals for measures on the wings, especially for such lines +as Hε and Hζ. + +8. The results of the investigation are given in Table IX, which +contains, in successive columns, the name of the line, the wave length, +expressed to the nearest Angstrom, the mean value of the difference of +intensity, background _minus_ line, expressed in stellar magnitudes, the +residuals, the “selected mean” value of the same intensity difference +(see Section 6) and its residuals. The stars are mentioned at the +beginnings of their respective records, and are arranged in order of +plate number. In the case of stars for which no “selected mean” is +quoted, all the values used for the mean conform to the criterion for +“selected mean.” + + TABLE IX + DIFFERENCES OF INTENSITY, BACKGROUND _minus_ LINE + ┌───────────┬──────┬──────────┬────────────────────┬──────────┬───────────────┐ + │ Plate and │ Wave │ Mean │ Residuals │ Selected │ Residuals │ + │ Star │Length│Intensity │ │ Mean │ │ + │ │ │Difference│ │Difference│ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 20790 │4877 │ .11│1, _4_, 4 │ .11│_4_, 4 │ + │α Lyrae │4872 │ .23│2, _3_, 2 │ .23│_3_, 2 │ + │ │4866 │ .49│_2_, 1, 1 │ .50│ │ + │ │4861 │ .95│_10_, 0, 7, 5 │ .95│ │ + │ │Hβ │ │ │ │ │ + │ │4856 │ .73│2, _3_, 2, _3_ │ .73│_3_, 2 │ + │ │4851 │ .35│_5_, 5, 2, _3_ │ .38│2, _1_ │ + │ │4846 │ .17│_5_, 3, 3, 0 │ .19│1, 1, _2_ │ + │ │4840 │ .07│_2_, 0, 3, _2_ │ .07│0, 3, _2_ │ + │ │4358 │ .11│_6_, _9_, 6, 6, 1 │ .10│_8_, 7 │ + │ │4354 │ .23│_11_, _1_, 9, 4 │ .27│_5_, 5 │ + │ │4349 │ .45│_15_, 0, 15, 2 │ .52│_7_, 8 │ + │ │4345 │ .83│8, _3_, 19, _8_ │ .86│_6_, 16, _11_ │ + │ │4340 │ 1.43│_6_, 19, _6_, _3_, │ 1.62│ │ + │ │Hγ │ │_3_ │ │ │ + │ │4336 │ .92│8, _17_, 5, 3 │ .92│8, _17_, 5, 3 │ + │ │4331 │ .51│_19_, 4, _11_, 14, │ .55│0, _15_, 10, 7 │ + │ │ │ │11 │ │ │ + │ │4327 │ .25│_8_, _5_, _5_, 15, │ .29│_9_, _9_, 11, 8│ + │ │ │ │12, _10_ │ │ │ + │ │4322 │ .14│2, _4_, _4_, 11, 8, │ .17│_7_, _7_, 8, 5 │ + │ │ │ │_7_ │ │ │ + │ │ │ │ │ │ │ + │ │4116 │ .13│_3_, 4, 9, _8_ │ .19│_2_, 3 │ + │ │4112 │ .32│_10_, 3, 8 │ .37│_2_, 3 │ + │ │4109 │ .60│_15_, 2, 12 │ .67│_5_, 5 │ + │ │4105 │ .92│_17_, 18, _17_, 13, │ .92│18, _17_ │ + │ │ │ │5 │ │ │ + │ │4102 │ 1.60│0, 22, _15_, _5_ │ 1.82│ │ + │ │Hδ │ │ │ │ │ + │ │4098 │ 1.11│ │ 1.11│ │ + │ │4095 │ .72│_17_, 8, 8 │ .80│0, 0 │ + │ │4091 │ .33│_1_, 7, _1_, _3_ │ .36│4, _4_ │ + │ │4088 │ .21│_6_, _1_, _4_, 9 │ .22│_2_, _5_, 8 │ + │ │4084 │ .13│_6_, _3_, _3_, 12 │ .15│_5_, _5_, 10 │ + │ │ │ │ │ │ │ + │ │3986 │ .11│_1_, 1 │ .11│_1_, 1 │ + │ │3983 │ .21│_4_, 1, _6_, 9, 6 │ .23│_1_, _8_, 7, 4 │ + │ │3980 │ .45│_10_, 0, _5_, 7, 10 │ .48│_3_, _8_, 4, 7 │ + │ │3976 │ .73│_26_, 7, 14, 4 │ .80│ │ + │ │3973 │ 1.08│_6_, 5, _3_, 2 │ 1.17│ │ + │ │3970 │ 1.68│_8_, 7 │ 1.60│ │ + │ │Hε │ │ │ │ │ + │ │3967 │ 1.17│ │ │ │ + │ │3964 │ .70│_13_, _8_, 20 │ .62│ │ + │ │3960 │ .56│_21_, 4, 14, 4 │ .65│_5_, 5 │ + │ │3957 │ .28│_11_, 2, _3_, 12 │ .32│_2_, 7, 8 │ + │ │3954 │ .13│_3_, _3_, _1_, 7 │ .13│_3_, _3_, _1_, │ + │ │ │ │ │ │7 │ + │ │ │ │ │ │ │ + │ │3936 │ .05│0, 0 │ .05│0, 0 │ + │ │3933 K│ .23│_1_, _3_, _3_, 7 │ .23│1, _3_, _3_, 7 │ + │ │3930 │ .11│1, _4_, _4_, 4, 4 │ .11│1, _4_, _4_, 4,│ + │ │ │ │ │ │4 │ + │ │ │ │ │ │ │ + │ │3899 │ .55│5, 5, 2, 0 │ .50│ │ + │ │3895 │ .76│1, _1_, 1, _1_ │ .77│ │ + │ │3892 │ 1.03│4, _3_ │ 1.07│ │ + │ │3889 │ 1.42│ │ │ │ + │ │Hζ │ │ │ │ │ + │ │3887 │ 1.10│ │ 1.10│ │ + │ │3884 │ .78│_3_, 2, _3_, 2 │ .75│ │ + │ │3880 │ .43│_1_, _1_, _1_, 2 │ .42│ │ + │ │ │ │ │ │ │ + │ │3845 │ .62│ │ │ │ + │ │3842 │ > .75│ │ │ │ + │ │3839 │ > .75│ │ │ │ + │ │3835 │ > .75│ │ │ │ + │ │Hη │ │ │ │ │ + │ │3832 │ .75│ │ │ │ + │ │3829 │ .25│ │ │ │ + │ │3826 │ .16│ │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 20797 │4340 │ .54│_2_, 1, 1 │ │ │ + │ │Hγ │ │ │ │ │ + │α Bootis │4227 │ 1.34│2, 2, _3_ │ │ │ + │ │Ca │ │ │ │ │ + │ │4215 │ .50│_7_, 8 │ │ │ + │ │Sr+ │ │ │ │ │ + │ │4101 │ .74│_2_, 3, _2_ │ │ │ + │ │Hδ │ │ │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 20800 │4877 │ .00│0, 0 │ .00│0, 0 │ + │α Aquilae │4872 │ .12│_5_, 5 │ .12│_5_, 5 │ + │ │4866 │ .36│_6_, 6 │ .30│ │ + │ │4861 │ .71│_1_, 1 │ .70│ │ + │ │Hβ │ │ │ │ │ + │ │4856 │ .45│_5_, 5 │ .45│_5_, 5 │ + │ │4851 │ .20│_5_, 5 │ .20│_5_, 5 │ + │ │4846 │ .15│_3_, 2 │ .15│_3_, 2 │ + │ │4840 │ .09│_7_, 8 │ .09│_7_, 8 │ + │ │ │ │ │ │ │ + │ │4363 │ .06│_1_, 1 │ .06│_1_, 1 │ + │ │4358 │ .11│_4_, 4 │ .11│_4_, 4 │ + │ │4354 │ .16│_4_, 4 │ .16│_4_, 4 │ + │ │4349 │ .21│_4_, 4 │ .21│_4_, 4 │ + │ │4345 │ .39│10, _9_ │ .49│ │ + │ │4340 │ .81│1, _1_ │ .82│ │ + │ │Hγ │ │ │ │ │ + │ │4336 │ .39│10, _9_ │ .49│ │ + │ │4331 │ .21│_4_, 4 │ .21│_4_, 4 │ + │ │4327 │ .16│_4_, 4 │ .16│_4_, 4 │ + │ │4322 │ .07│0, 0 │ .07│0, 0 │ + │ │4318 │ .01│1, _1_ │ .01│1, _1_ │ + │ │ │ │ │ │ │ + │ │4116 │ .03│4, _3_ │ .03│4, _3_ │ + │ │4112 │ .10│5, _5_ │ .10│5, _5_ │ + │ │4109 │ .23│_7_, 8 │ .23│_7_, 8 │ + │ │4105 │ .46│6, _6_ │ .40│ │ + │ │4102 │ .71│1, _1_ │ .70│ │ + │ │Hδ │ │ │ │ │ + │ │4098 │ .50│5, _5_ │ .50│5, _5_ │ + │ │4095 │ .23│7, _6_ │ .17│ │ + │ │4091 │ .10│5, _5_ │ .10│5, _5_ │ + │ │4088 │ .01│1, _1_ │ .01│1, _1_ │ + │ │ │ │ │ │ │ + │ │3986 │ .20│ │ .20│ │ + │ │3983 │ .25│0, 0 │ .25│ │ + │ │3980 │ .32│_2_, 3 │ .30│ │ + │ │3976 │ .43│_3_, 4 │ .40│ │ + │ │3973 │ .81│1, _1_ │ .82│ │ + │ │3970 │ > 1.50│ │ > 1.50│ │ + │ │Hε │ │ │ │ │ + │ │3967 │ .79│_1_, 1 │ .78│ │ + │ │3964 │ .48│_13_, 14 │ .35│ │ + │ │3960 │ .25│_12_, 13 │ .17│ │ + │ │3957 │ .12│_2_, 3 │ .10│ │ + │ │3954 │ .02│ │ .02│ │ + │ │ │ │ │ │ │ + │ │3942 │ .15│ │ .15│ │ + │ │3939 │ .22│_2_, 3 │ .20│ │ + │ │3936 │ .53│_3_, 4 │ .50│ │ + │ │3933 K│ .79│_3_, 2 │ .82│ │ + │ │3930 │ .51│_1_, 1 │ .50│ │ + │ │3927 │ .07│5, _5_ │ .12│ │ + │ │3924 │ .05│ │ .05│ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21640 │4866 │ .07│_7_, _5_, 0, _7_, │ .07│0, 0, 0 │ + │ │ │ │10, 0, 0 │ │ │ + │α Cygni │4861 │ .33│2, 4, _3_, _1_, _3_,│ .32│0, 0 │ + │ │Hβ │ │_1_, 2 │ │ │ + │ │4856 │ .18│4, _3_, _1_, 2, _3_,│ .16│1, _1_, 1 │ + │ │ │ │_1_ │ │ │ + │ │ │ │ │ │ │ + │ │4345 │ .11│1, 1, 1, _1_, _1_ │ .10│0, 0 │ + │ │4340 │ .63│_1_, 2, _16_, 4, 17,│ .67│_2_, 3 │ + │ │Hγ │ │_16_, 2, 7 │ │ │ + │ │4336 │ .21│1, _1_, 1, _1_ │ .21│1, _1_ │ + │ │ │ │ │ │ │ + │ │4105 │ .16│9, 1, _6_, 4, _4_, │ .11│_1_, 1, _1_ │ + │ │ │ │_6_ │ │ │ + │ │4101 │ .63│17, _3_, _16_, 2, 2 │ .56│_8_, 9 │ + │ │Hδ │ │ │ │ │ + │ │4098 │ .37│13, _2_, _7_, 0, _5_│ .31│_1_, 1 │ + │ │ │ │ │ │ │ + │ │3973 │ .25│_5_, 5, 5, 0, _5_, │ │ │ + │ │ │ │0, 7, 2, _5_, 0, _5_│ │ │ + │ │3970 │ .70│15, 5, _5_, _5_, 22,│ .66│_1_, 1, _1_, 1 │ + │ │Hε │ │_8_, _5_, _3_, _5_, │ │ │ + │ │ │ │_3_ │ │ │ + │ │3967 │ .46│24, _4_, _19_, 14, │ .34│_7_, _2_, 8 │ + │ │ │ │_1_, _4_, 16, _14_, │ │ │ + │ │ │ │_16_, 4, 1 │ │ │ + │ │3936 │ .10│20, 0, _3_, _5_, │ .06│_1_, 1 │ + │ │ │ │_5_, 0, 2, _3_, _3_ │ │ │ + │ │3933 K│ .54│13, 1, _7_, 1, _10_ │ .52│3, _5_, 3 │ + │ │3933 │ .37│8, _7_, _7_, _5_, 8,│ .35│_3_, 2 │ + │ │ │ │8, 0, _10_ │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21645 │4877 │ .32│_15_, 15 │ .47│ │ + │δ │4872 │ .42│ │ .42│ │ + │Cassiopeiae│ │ │ │ │ │ + │ │4866 │ .72│_2_, 3 │ │ │ + │ │4861 │ 1.49│_7_, _7_, 23, _7_ │ │ │ + │ │Hβ │ │ │ │ │ + │ │4856 │ .72│_17_, 18 │ .90│ │ + │ │4851 │ .34│_9_, _7_, 16 │ .50│ │ + │ │4846 │ .13│_1_, _3_, 4 │ .17│ │ + │ │ │ │ │ │ │ + │ │4354 │ .31│4, _14_, _16_, 6, 6,│ .31│_16_, 6, 9 │ + │ │ │ │9, 9, _4_ │ │ │ + │ │4349 │ .45│5, _13_, 12, 7, 5, │ .45│_13_, 7, 5 │ + │ │ │ │5, _23_ │ │ │ + │ │4345 │ .81│1, _1_, 24, _6_, │ .75│5, 0, _5_ │ + │ │ │ │_11_, 16, _21_ │ │ │ + │ │4340 │ 1.46│4, 9, _4_, 9, _16_ │ │ │ + │ │Hγ │ │ │ │ │ + │ │4336 │ .84│33, 18, _9_, _14_, │ .86│16, _16_ │ + │ │ │ │_9_, _19_ │ │ │ + │ │4331 │ .55│20, _18_, _5_, 7, │ .50│_13_, 12, 0 │ + │ │ │ │_5_, 5, _3_ │ │ │ + │ │4327 │ .32│20, _15_, _2_, 13, │ .32│_15_, 13, 3 │ + │ │ │ │3, 0, _17_ │ │ │ + │ │ │ │ │ │ │ + │ │4112 │ .34│_2_, _4_, _14_, 8, │ .30│0, _10_, 5, 5 │ + │ │ │ │1, 1, 6, 1 │ │ │ + │ │4109 │ .54│_4_, _12_, _22_, 21,│ .47│_5_, _15_, 3, │ + │ │ │ │_4_, 11, 13 │ │18 │ + │ │4105 │ .88│2, _8_, _18_, _13_, │ .75│5, _5_, 0 │ + │ │ │ │34, 17, _13_, _3_ │ │ │ + │ │4102 │ 1.54│1, 6, _4_, 1, _4_ │ │ │ + │ │Hδ │ │ │ │ │ + │ │4098 │ .86│_4_, _6_, _11_, 29, │ .74│6, 1, 1, _7_ │ + │ │ │ │_11_, _19_, 26 │ │ │ + │ │4095 │ .53│_13_, _8_, _8_, 22, │ .47│_2_, _2_, 3, 3 │ + │ │ │ │_3_, _3_, 14 │ │ │ + │ │4091 │ .33│_11_, _8_, _8_, 17, │ .29│_4_, _4_, 13, │ + │ │ │ │9, _8_, 9 │ │_4_ │ + │ │ │ │ │ │ │ + │ │3976 │ .84│_9_, _4_, _29_, _7_,│ │ │ + │ │ │ │56, _17_, _9_, │ │ │ + │ │ │ │21 │ .68│_13_, 9, _1_, 7│ + │ │3973 │ 1.37│_7_, 23, _32_, 13, 1│ 1.27│_22_, 23 │ + │ │3970 │ 2.15│_5_, 15, _5_, _10_, │ │ │ + │ │Hε │ │12 │ │ │ + │ │ │ │ │ │ │ + │ │3933 K│ 1.48│_23_, _3_, 2, 22, 2 │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21646 │4861 │ .25│ │ .25│ │ + │ │Hβ │ │ │ │ │ + │α │4444 │ .31│_6_, 6 │ .31│_6_, 6 │ + │Cassiopeiae│Ti+ │ │ │ │ │ + │ │4340 │ .42│_5_, 5 │ .42│_5_, 5 │ + │ │Hγ │ │ │ │ │ + │ │4227 │ .83│2, _1_ │ .83│2, _1_ │ + │ │Ca │ │ │ │ │ + │ │4215 │ .71│1, _1_ │ .71│1, _1_ │ + │ │Sr+ │ │ │ │ │ + │ │4101 │ .56│11, _11_ │ .56│11, _11_ │ + │ │Hδ │ │ │ │ │ + │ │3970 │ 2.50│5, _5_ │ 2.50│5, _5_ │ + │ │Hε │ │ │ │ │ + │ │3933 K│ 2.47│ │ 2.47│ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21721 │4861 │ .43│_16_, _11_, 4, 32, │ │ │ + │ │Hβ │ │_11_, 4 │ │ │ + │ │ │ │ │ │ │ + │α Aurigae │4444 │ .21│_9_, _14_, _1_, 11, │ │ │ + │ │Ti+ │ │4, 11, 1 │ │ │ + │ │ │ │ │ │ │ + │ │4340 │ .74│21, 11, 1, _7_, _9_,│ │ │ + │ │Hγ │ │_4_, _12_ │ │ │ + │ │ │ │ │ │ │ + │ │4326 │ .62│13, 5, _10_, 13, 5, │ │ │ + │ │Fe │ │_17_ │ │ │ + │ │ │ │ │ │ │ + │ │4227 │ .57│30, _37_, 5, _7_, 8 │ │ │ + │ │Ca │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4215 │ .36│14, _11_, 1, 4, _6_ │ │ │ + │ │Sr+ │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4101 │ .57│0, _12_, 10, 13, │ │ │ + │ │Hδ │ │_2_, 5, _17_ │ │ │ + │ │ │ │ │ │ │ + │ │3976 │ .53│2, _1_ │ │ │ + │ │3973 │ 1.14│8, _7_ │ │ │ + │ │3970 │ 1.62│13, 5, _17_, 23, │ │ │ + │ │Hε │ │_22_ │ │ │ + │ │3967 │ 1.13│17, _16_ │ │ │ + │ │3964 │ .62│ │ │ │ + │ │3939 │ .80│0, _5_, _5_ │ │ │ + │ │3936 │ 1.27│10, _10_ │ │ │ + │ │3933 K│ 1.67│5, 3, _10_, 0, 5 │ │ │ + │ │3930 │ 1.27│10, _10_ │ │ │ + │ │3927 │ .76│4, _6_, 1 │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21722 │4866 │ .32│5, 0, _10_, 5 │ │ │ + │δ Canis │4861 │ .61│1, 4, _4_ │ │ │ + │ │Hβ │ │ │ │ │ + │Majoris │4856 │ .28│4, _1_, _6_, 2 │ │ │ + │ │ │ │ │ │ │ + │ │4444 │ .76│4, 4, _6_ │ │ │ + │ │Ti+ │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4345 │ 1.12│_7_, 8 │ │ │ + │ │4340 │ 1.12│ │ │ │ + │ │Hγ │ │ │ │ │ + │ │4336 │ 1.21│_9_, 9 │ │ │ + │ │ │ │ │ │ │ + │ │4326 │ .78│_7_, _8_, 2 │ │ │ + │ │Fe │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4227 │ .70│_10_, 10 │ │ │ + │ │Ca │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4215 │ .51│_1_, 1 │ │ │ + │ │Sr+ │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4105 │ .31│1, _1_ │ │ │ + │ │4101 │ .86│_1_, _1_, 1 │ │ │ + │ │Hδ │ │ │ │ │ + │ │4098 │ .21│6, _6_ │ │ │ + │ │ │ │ │ │ │ + │ │3970 │ > 2.25│ │ │ │ + │ │Hε │ │ │ │ │ + │ │ │ │ │ │ │ + │ │3933 K│ > 2.25│ │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21788 │4861 │ .22│0, 3, 3, 3, 3, _10_ │ .25│0, 0, 0, 0 │ + │ │Hβ │ │ │ │ │ + │ß Orionis │4481 │ .22│3, 3, 0, 8, 0, _12_ │ .22│3, 0, 8, 0, │ + │ │Mg+ │ │ │ │_12_ │ + │ │4471 │ .21│4, 4, 1, 9, 1, _11_ │ .16│1, 6, _6_ │ + │ │He │ │ │ │ │ + │ │4340 │ .45│20, _5_, _5_, 15, │ .36│4, 4, _9_ │ + │ │Hγ │ │_5_, _18_ │ │ │ + │ │4101 │ .43│12, _3_, _3_, 12, │ .40│0, 0 │ + │ │Hδ │ │_3_, _13_ │ │ │ + │ │4026 │ .14│3, 1, _2_, 8, _2_, │ .12│0, 0 │ + │ │He │ │_5_ │ │ │ + │ │3970 │ .45│10, 5, 0, 7, _5_, │ .46│4, _1_, 6, _6_ │ + │ │Hε │ │_18_ │ │ │ + │ │3933 K│ .17│_2_, 3, 3, 0, _2_, │ .18│2, 2, _1_, _3_ │ + │ │ │ │_2_ │ │ │ + │ │3889 │ .43│12, 12, _8_, 11, │ .54│1, 1, _2_ │ + │ │Hζ │ │_8_, _18_ │ │ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21789 │4861 │ .23│7, _3_, _1_, _3_ │ .23│7, _3_, _1_, │ + │ │Hβ │ │ │ │_3_ │ + │ε Orionis │4471 │ .31│16, _6_, 1, _11_ │ .20│ │ + │ │He │ │ │ │ │ + │ │4387 │ .24│_2_, _4_, 8, _2_ │ .20│ │ + │ │He │ │ │ │ │ + │ │4340 │ .40│12, _8_, 2, _5_ │ .35│ │ + │ │Hγ │ │ │ │ │ + │ │4116 │ .17│5, _2_, _5_, _2_, 3 │ .17│_2_, _2_, 3 │ + │ │He │ │ │ │ │ + │ │4101 │ .37│5, _5_, 3, _2_ │ .36│_4_, 4, _1_ │ + │ │Hδ │ │ │ │ │ + │ │4097 │ .17│5, _2_, _2_, _2_ │ .15│0, 0, 0 │ + │ │4026 │ .19│1, 1, 1, _4_ │ .17│3, _2_ │ + │ │He │ │ │ │ │ + │ │3970 │ .32│8, _2_, 5, _10_ │ .30│7, _8_ │ + │ │Hε │ │ │ │ │ + │ │3889 │ .33│2, 14, _6_, _11_ │ .33│2, 14, _6_, │ + │ │Hζ │ │ │ │_11_ │ + ├───────────┼──────┼──────────┼────────────────────┼──────────┼───────────────┤ + │MC 21803 │4877 │ .12│3, _2_, _2_, 0, _2_,│ .11│_1_, _1_, 1, │ + │ │ │ │0 │ │_1_, 1 │ + │α Canis │4872 │ .30│25, _8_, _5_, 0, │ .25│_3_, 0, 5, _5_,│ + │ │ │ │_10_, _5_ │ │0 │ + │Majoris │4866 │ .56│11, _4_, _4_, 9, │ .55│_3_, _3_, 10, │ + │ │ │ │_6_, 4 │ │_5_ │ + │ │4861 │ 1.02│18, _7_, _2_, _10_ │ .96│_1_, 4, _4_ │ + │ │Hβ │ │ │ │ │ + │ │4856 │ .67│13, _12_, 0, 13, │ .65│_10_, 2, 15, │ + │ │ │ │_12_, 0 │ │_10_, 12 │ + │ │4851 │ .31│11, _4_, _4_, 1, │ .29│_2_, _2_, 3, │ + │ │ │ │_4_, 1 │ │_2_, 3 │ + │ │4846 │ .13│9, _1_, _3_, _3_, 2,│ .12│0, _2_, _2_, 3,│ + │ │ │ │_1_, _3_ │ │0, _2_ │ + │ │ │ │ │ │ │ + │ │4481 │ .20│5, 0, 0, 0, 0, _8_ │ .18│2, 2, 2, 2, _6_│ + │ │Mg+ │ │ │ │ │ + │ │ │ │ │ │ │ + │ │4354 │ .28│2, _6_, 7, _6_, _1_,│ .31│4, _4_, 1 │ + │ │ │ │4 │ │ │ + │ │4349 │ .45│5, _3_, 2, _3_, _3_,│ .45│2, _3_, 2 │ + │ │ │ │2 │ │ │ + │ │4345 │ .80│10, _5_, 0, _5_, 2 │ .79│1, _4_, 3 │ + │ │4340 │ 1.38│7, _8_, 7, _6_ │ 1.39│6, _7_ │ + │ │Hγ │ │ │ │ │ + │ │4336 │ .83│_1_, 4, _6_, _3_, 2,│ .82│_5_, 3, 3 │ + │ │ │ │2 │ │ │ + │ │4331 │ .43│_3_, _1_, 4, _8_, 4,│ .46│1, 1, _1_ │ + │ │ │ │2 │ │ │ + │ │4327 │ .27│3, _5_, 3, 0, 0, 0 │ .28│2, _1_, _1_ │ + │ │ │ │ │ │ │ + │ │4125 │ .12│10, _7_, _5_, _2_, │ .11│_4_, _1_, 4 │ + │ │ │ │_2_, 3 │ │ │ + │ │4121 │ .20│15, _5_, _5_, _3_, │ .17│_2_, _2_, 4 │ + │ │ │ │_5_, 2 │ │ │ + │ │4116 │ .42│15, _7_, _10_, 0, │ .39│_7_, _7_, 13 │ + │ │ │ │_10_, 10 │ │ │ + │ │4112 │ .60│15, _5_, _8_, 15, │ .52│0, 0, 0 │ + │ │ │ │_8_, _8_ │ │ │ + │ │4109 │ .98│17, _16_, 4, _6_ │ .97│5, _5_ │ + │ │4102 │ 1.45│12, _13_, 17, _15_ │ 1.46│16, _16_ │ + │ │Hδ │ │ │ │ │ + │ │4098 │ 1.04│21, _9_, 2, _12_ │ .97│5, _5_ │ + │ │4095 │ .61│29, _6_, _9_, _9_, │ .53│_1_, _1_, 2 │ + │ │ │ │_6_ │ │ │ + │ │4091 │ .43│14, _3_, _16_, 4, │ .37│_10_, _5_, 15 │ + │ │ │ │_11_, 9 │ │ │ + │ │4088 │ .24│11, _2_, _7_, 1, │ .20│_3_, 0, 2 │ + │ │ │ │_4_, _2_ │ │ │ + │ │4084 │ .12│10, 0, _7_, 0, _7_, │ .08│_3_, _3_, 7 │ + │ │ │ │3 │ │ │ + │ │ │ │ │ │ │ + │ │3986 │ .12│7, 0, _12_, _5_, 10,│ .12│0, _12_, _5_, │ + │ │ │ │2, 0 │ │10, 2, 0 │ + │ │ │ │ │ │ │ + │ │3983 │ .25│7, _2_, _7_, 7, 0, 2│ .25│_2_, _7_, 7, 0,│ + │ │ │ │ │ │2 │ + │ │3980 │ .42│15, _2_, _10_, 12, │ .42│_2_, _10_, 12, │ + │ │ │ │0, _7_ │ │0 │ + │ │3976 │ .66│22, _2_, _5_, 0, │ .58│5, 2, 7, _10_ │ + │ │ │ │_18_ │ │ │ + │ │3973 │ .86│_22_, 13, 8 │ .97│3, _2_ │ + │ │3970 │ 1.47│11, _11_, 18, _11_ │ 1.45│_11_, 20, _9_ │ + │ │Hε │ │ │ │ │ + │ │3967 │ 1.10│20, _8_, 2, _15_ │ 1.02│0, 10, _7_ │ + │ │3964 │ .70│27, _3_, _10_, _5_, │ .64│_5_, _2_, 3, │ + │ │ │ │_15_ │ │_7_ │ + │ │3960 │ .47│23, _2_, _5_, 3, │ .43│2, _1_, 7, _3_,│ + │ │ │ │_7_, _10_ │ │_6_ │ + │ │3957 │ .33│24, 0, _6_, 0, _8_, │ .28│5, _1_, 5, _3_,│ + │ │ │ │_8_ │ │_3_ │ + │ │3954 │ .23│19, 4, _6_, _13_, │ .16│11, 1, _6_, _4_│ + │ │ │ │_11_ │ │ │ + │ │ │ │ │ │ │ + │ │3933 K│ .18│12, 2, _6_, 4, _3_, │ .17│3, _5_, 5, _2_ │ + │ │ │ │_6_ │ │ │ + │ │ │ │ │ │ │ + │ │3889 │ 1.48│7, _9_, 17, _16_ │ 1.55│ │ + │ │Hζ │ │ │ │ │ + └───────────┴──────┴──────────┴────────────────────┴──────────┴───────────────┘ + +9. Table X contains a summary of the results, for line centers only. +Successive columns give the name of the star, the spectral class, the +absolute magnitude, and the drop in magnitudes from background to line +center, for the spectrum lines mentioned at the heads of the columns. +The greater line depth for absolutely brighter stars, at least among +those of the second type, is especially to be noted. + + TABLE X + DROP IN INTENSITY, FROM BACKGROUND TO LINE CENTER, FOR ELEVEN STARS, + EXPRESSED IN STELLAR MAGNITUDES + ┌──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┐ + │ Star │Class │ M │ Hβ │ Hγ │ Hδ │ Hε │ K │ 4227 │ 4215 │ + ├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┤ + │ε Ori │ B0│ │ .23│ .40│ .37│ .32│ │ │ │ + │ß Ori │ cB8│ 5:│ .22│ .45│ .43│ .46│ .17│ │ │ + │α Lyr │ A0│ 0.6│ .95│ 1.43│ 1.60│ 1.68│ .23│ │ │ + │α CMa │ A0│ 1.2│ .96│ 1.39│ 1.46│ 1.47│ │ │ │ + │α Cyg │ cA2│ 4:│ .33│ .63│ .63│ .70│ .54│ │ │ + │α Aql │ A5│ 2.4│ .71│ .81│ .71│ 1.50│ .79│ │ │ + │δ Cas │ A5│ 1.6│ 1.49│ 1.46│ 1.54│ 2.15│ 1.48│ │ │ + │δ CMa │ cF8│ 3:│ .61│ 1.12│ .86│ >2.25│ >2.25│ .70│ .51│ + │α Aur │ G0│ 0.0│ .43│ .76│ .57│ 1.62│ 1.67│ .57│ .36│ + │α Boo │ K0│ 0.3│ │ .54│ .74│ │ │ 1.34│ .70│ + │α Cas │ K0│ 0.0│ .25│ .42│ .56│ 2.50│ 2.47│ .83│ .71│ + └──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┘ + +10. The material contained in Table X is reproduced in Table XI, where +the intensity at the line center is expressed in terms of percentage of +the background intensity, instead of in stellar magnitudes. The +“background intensity,” as defined in Section 6, is the intensity that +the background would have if the line were not present. It is noteworthy +that, for the great majority of the lines, the residual intensity at the +line center is greater than 30 per cent of the background intensity. + +11. The material presented above constitutes the first systematic study +of the contours of strong absorption lines. In view of the preliminary +nature of the work the discussion has been devoted for the most part to +presentation of method. Extended discussion seems at present to be +premature, and only a few points need be mentioned. + +Probably the chief interest of Table X lies in the result that the +maximum intensity drop from background to line recorded for any of these +stars is 2.50 magnitudes, corresponding to a light loss of ninety per +cent. Except for the supergiant cF8 star and the Ca+ absorption for α +Cassiopeiae and Hε for δ Cassiopeiae, the light remaining at the center +of the line is at least fifteen per cent of the background intensity. On +the average for all these strong absorption lines there is something +like twenty-five per cent of the background light remaining at the +center of the lines. The significance of these residual intensities will +be discussed in a later publication, when the forms of the lines as +shown by the data of Table IX will also be considered. + + TABLE XI + RESIDUAL INTENSITIES AT LINE CENTERS, EXPRESSED AS PERCENTAGES OF + BACKGROUND INTENSITY + ┌───────┬───────┬───────┬───────┬───────┬───────┬───────┬──────┬──────┐ + │ Star │ Class │ Hβ │ Hγ │ Hδ │ Hε │ K │ 4227 │ 4215 │ + ├───────┼───────┼───────┼───────┼───────┼───────┼───────┼──────┼──────┤ + │ε Ori │ B0│ 81│ 69│ 71│ 74│ │ │ │ + │β Ori │ cB8│ 82│ 66│ 67│ 65│ 86│ │ │ + │α Lyr │ A0│ 42│ 27│ 23│ 21│ 81│ │ │ + │α CMa │ A0│ 41│ 28│ 26│ 26│ │ │ │ + │α Cyg │ cA2│ 74│ 56│ 56│ 52│ 61│ │ │ + │α Aql │ A5│ 51│ 47│ 51│ 25│ 48│ │ │ + │δ Cas │ A5│ 25│ 26│ 24│ 14│ 26│ │ │ + │δ CMa │ cF8│ 57│ 36│ 45│ <13│ <13│ 52│ 63│ + │α Aur │ G0│ 67│ 50│ 59│ 22│ 21│ 59│ 72│ + │α Boo │ K0│ │ 61│ 51│ │ │ 29│ 52│ + │α Cas │ K0│ 79│ 68│ 60│ 10│ 10│ 47│ 52│ + └───────┴───────┴───────┴───────┴───────┴───────┴───────┴──────┴──────┘ + +For the wider lines, especially those that are strong and heavily +winged, the intensities derived in this paper are probably of the right +order. Probably, however, the dispersion used is too small to reproduce +satisfactorily the detail at the centers of lines as narrow as those of +such stars as α Cygni and β Orionis. The difficulty introduced does not +involve inaccuracy of plates, microphotometer, or process of +measurement; it is concerned solely with the fact that the spectral +region examined is so narrow that, with the dispersion used, the grain +of the plate is not fine enough to reproduce the spectral detail. The +same difficulty would prevent any recognition of the double reversal of +the solar H and K lines, if they were studied with the present +dispersion. + +Whatever the dispersion used, the same qualification must be made in +discussing the results; probably the dispersion would have to be greatly +increased before the measured effective line depth becomes much greater +for narrow line stars. + +Relative effective line depth, derived from numerous spectra made with +the same dispersion, is still, however, of considerable significance. It +permits us to recognize differences of surface gravity, and to form an +idea of relative chromospheric depths for different classes of stars. + + + SUMMARY + +1. The investigation deals with the determination of the depth and +contour of prominent absorption lines in the spectra of stars of various +classes. + +2. The spectra used were made with the 16-inch refractor of the Harvard +Observatory, using two prisms and a special set of apertures. + +3. Results are presented for eleven stars, of spectral class ranging +from B0 to K0. + +4. The spectra were analyzed under uniform conditions by means of the +Moll thermoelectric microphotometer. The resolving power of this +instrument is such that no integrating effect need be considered in +discussing the results. + +5. The microphotometer tracings were measured with reference to fiducial +lines representing “darkness” and “clear film,” and to a line, +representing the continuous background, drawn across the absorption +lines. + +6. The intensity drop from continuous background to line was deduced +graphically from the measures. + +7. The accuracy of the results is discussed in detail. + +a. The reliability of the plates, as judged from qualitative +reproduction of detail, and from the consistency of the numerical +results, is satisfactory. Effects of stray light are of negligible +magnitude, and in this respect slit spectra appear to have no advantage +over objective prism spectra. + +b. Effects of poor focus are measurable, but small. Spectra that are in +such poor focus as to cause appreciable inaccuracy would be rejected +from visual inspection. + +c. The accuracy of the microphotometer tracings is in general +satisfactory. Tracings showing abnormal deflections from “darkness” to +“clear film” are not susceptible of correction, and are omitted in +deriving results. + +d. The measures upon the tracings are also of satisfactory accuracy. + +8. The differences in intensity between the continuous background and +various points along the line contour are tabulated for the eleven stars +under discussion. + +9. The general results for the intensities at the centers of lines show +an interesting relation to absolute brightness; the brighter stars have, +in general, lines that cut more deeply into the background. 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