UC-MRLF The First Deslandres' Group of the Positive Band Spectrum of Nitro- gen, under High Dispersion A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RAYMOND T. BIRGE IXIVERSITY OF WISCONSIN '9*3 The First Deslandres 5 Group of the Positive Band Spectrum of Nitro- gen, under High Dispersion A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY RAYMOND T. BIRGE UNIVERSITY OF WISCONSIN 1913 THE FIRST DESLANDRES' GROUP OF THE POSITIVE BAND SPECTRUM OF NITROGEN, UNDER HIGH DISPERSION BY RAYMOND T. BIRGE This paper is a preliminary discussion of the First Deslandres' Group of the band spectrum of nitrogen, based mainly upon photo- graphs taken by the author in the second order of a 21 -foot concave grating, from \5ooo to \68oo. The bands are almost completely resolved into lines, and the discussion in this paper is concerned with the relations between the lines forming the three principal heads of the bands. INTRODUCTION The positive band spectrum of nitrogen has been the subject of a large number of investigations. Under low dispersion the apparent regularity of the bands, both in position and in appear- ance, is very striking. The violet end of this spectrum can easily be photographed under high dispersion, but because of the rela- tively low intensity in the longer wave-lengths, this portion had not previously been resolved into its component lines in a satis- factory manner. Von der Helm 1 made the latest attempt. The two objects of his investigation, with his success in accomplishing them, are stated as follows: 1. tlbersicht iiber den gesamten Teil des in Frage kommenden Spectrums, inbesondere iiber die Lage der Bandenkopfe. 2. Genaueres Studium einzelner Banden. Den ersten Teil der Aufgabe darf ich als gelost betrachten; am zweiten bin ich leider fast vollig gescheitert. Von der Helm gives a complete discussion of relevant previous work on nitrogen, together with the possible results of such an investigation, and the first eight pages of his article could well form the introduction to this paper. The First Deslandres' Group of bands extends from X 5100 out into the infra-red. Measurements on the heads of individual 1 Zeitschr. f. wiss. Phot., 8, 405, 1910. 50 GIFT POSITIVE BAND SPECTRUM OF NITROGEN 51 bands have previously been made to X 9100. The results seem to show that the spectrum consists of a series of band groups, each of which is most intense at the center, and diminishes in intensity toward either side. Kayser's Handbuch* gives only three groups, which he calls a, b, and c. Other groups of longer wave-length have since been found, arid it appears now that there are six groups in all, which will be designated a to / respectively. Group a i . 06 /A (?) Group b 9101 ( ?) to 7887 Group c 7887 to 7059 Group d 7059 to 6185 (Kayser's a group) Group e 6186 to 5485 (Kayser's b group) Group/ 5632 to 5126 (Kayser's c group) Group /is quite different from the others. It has two intensity maxima, one at X 5200 and the other at X 5475. This would indi- cate two groups, but as the spacing is the same in both, it has been customary to classify them together. This group also overlaps considerably on group e. The author obtained, besides the exposures on the large grating, one on a Hilger constant deviation spectroscope, extending to X 7650. From this point to X 9100 we have only the measurements of Croze. 2 Coblentz, 3 in connection with other infra-red work, has recorded positions of maximum intensity at 0.546, 0.667, -75> 0.90, and i.o6ju. These are very evidently the approximate positions of maximum intensity in the several band groups. The reading at i . 06 ju points to the existence at this point of another group, which we have called group a. In making this investigation the author had two objects in view: (i) to determine whether or not the bands in any one group were identical; (2) to determine, in case there were any similarities, whether corresponding lines in successive bands would fit into a Deslandres' series or other arithmetical relation. The results of the study made thus far indicate that out of the 250 or more lines composing each band, at least 50 of the strongest are related to corresponding lines in other bands, and that the relationship is approximately that expressed by Deslandres' Law: 1 Handbuch der Spectroscopie, 5, 828. 2 Comptes rendus, 150, 860, 1910. 3 Physical Review, 22, i, 1906. 629 52 RAYMOND T. BIRGE where a, b, and c are constants, and m takes successive integral values. EXPERIMENTAL ARRANGEMENTS Atmospheric nitrogen, free from oxygen, carbon dioxide, and water- vapor, was used as a source. Hence the inert gases of the atmosphere were present, but the only lines due to them which have thus far been noted are a few of the stronger argon lines of the red spectrum. There is no trace of helium X 5876. Traces of mercury diffused into the spectrum tube from the pressure gauge, but only the three strong lines at X 5790, X 5769, and X 5461 appear, the last enormously overexposed. The nitrogen was electrically excited in a Goetze "Type C' spectrum tube. The emission from the capillary of such a tube, in a " head-on" direction, appears to be the most intense, per unit cross-section, now obtainable. The electrical excitation was furnished by the secondary of a large induction coil, the primary being run on no volts A.C., 1.5 amperes. The nitrogen was introduced at about 5 mm pressure and used until the pressure fell to about i mm, low enough to cause a slight diminution of the radiation. Refilling of the tube was necessary only once in 24 to 36 hours. The tube was placed accurately "head-on" to the slit of the grating, 60 cm away. A double convex lens of 15 cm focus pro- duced on the slit a sharp image of the end of the capillary, some- what more than i mm in diameter. This usual arrangement was now varied by introducing, at a distance of 12 cm from the slit, a double concave cylindric lens of 1 2 cm focus, placed with its axis horizontal. This caused the circular image on the slit to be drawn out into a vertical line some 2 cm in length. The use of such a cylindric lens in spectrum work has been advocated by Humphreys, 1 but I know of no definite statement of the advantages and disadvan- tages incident to its use. The action of the cylindric lens is greatly to reduce the vertical aperture of the cone of rays proceeding from the slit. With the particular lenses used, it is possible, with a source of light less than approximately 2 mm in diameter, to reduce the vertical aperture, at the grating, to less than the length of the grating rulings. Thus 1 Astrophysical Journal, 18, 324, 1903. POSITIVE BAND SPECTRUM OF NITROGEN 53 the cross-section of the cone of light at the grating, instead of being a 75-cm circle, is reduced (roughly) to an ellipse of 75 cm horizontal diameter, but with a vertical diameter of 5 cm or less. The gain in intensity of the middle point of the astigmatic image at the camera is theoretically =15. The actual increase, deter- 5 cm mined experimentally, was thirteen fold. If now the source is made 4 mm in diameter, instead of 2, the amount of light actually striking the grating, using the cylindric lens, is scarcely increased at all. But with the ordinary arrange- ment, the amount would practically be doubled. Hence the advantage of the cylindric lens is proportionally decreased. For sources more than 2 cm in diameter, there is no appreciable advan- tage in using a cylindric lens. The chief disadvantage attendant upon its use is the necessity of accurate adjustment. The centers of the tube, convex lens, concave lens, and slit should all lie accurately in the horizontal plane formed by the center of the grating and of the camera. With this condition fulfilled, and the cone of light falling symmetrically upon the grating, a raising or lowering of the cylindric lens of even one-tenth of a millimeter is sufficient to throw an appreciable por- tion of the light entirely below or above the rulings of the grating. Because of the excess of radiation in a " head-on" direction, the illumination of the grating is far from uniform; but this is true even when the cylindric lens is not used. Such a non-uniformity is liable, however, to cause a shift of the lines of the comparison spectrum relative to those under investigation. The actual shifts found in many cases, between the iron and nitrogen lines, are believed to be due primarily to this cause. As a comparison source I used an iron arc of the Pfund 1 type, run on 200 volts, 5 amperes, with iron and carbon electrodes. It worked in a very satisfactory manner. The exposures were made in the second order, and both the second-order and coincident third- order international iron normals were used, the measurements in the ultra-violet being those of Buisson and Fabry, 2 not yet offi- cially adopted as standards. No relative shift of orders could be detected on those plates where both the second- and third-order normals were present. 1 Astro physical Journal, 27, 296, 1908. * Ibid., 28, 169, 1908. 54 RAYMOND T. BIRGE Whenever two normals fell near together and were both of suitable intensity for an accurate setting, the agreement was perfect. When one or both lines were overexposed the disagreement might be anything from 0.007 A down. This was taken to indicate that the secondary international normals, when overexposed, do not necessarily broaden symmetrically. The much greater uni- formity in intensity of the normals between X 3500 and X 4500 thus makes them preferable for use, and this fact, coupled with the great faintness of the normals from X 5900 into the red, caused the author to use only the coincident third-order normals in the region X 5900 to X 6800. In order to eliminate the exceedingly strong violet bands of nitrogen, an 8 per cent solution of potassium chroma te 5 mm thick was employed. The absorption of this solution sets in at about X 5200 and this accounts for the rapid decrease in intensity below this point. (See Plate III.) Although the head of the \3576 band is a thousand times as intense, photographically, as that of any band under investigation, no trace of it appears on the exposures. Fluorescein was tried as an absorbent and found quite ineffective. For the exposures from X 5000 to X 5900 the Cramer Instanta- neous Isochromatic plates were employed, while from X 5800 to X 6900 both Cramer " Spectrum" and Wratten & Wainwright "A" Panchromatic were used. For the one exposure on the Hilger spectroscope, from X 6800 to X 7700, I used a Wratten & Wain- wright "B" Panchromatic plate. The strongest portion of the spectrum, from the photographic standpoint, is that from X 5700 to X 5800. The X 5804 band is fully three times as intense as that at X6623, the only one which von der Helm appears to have obtained sufficiently intense for meas- urement. The region from X 5500 to X 5900 was accordingly photographed first, using 12X1^ inch plates, and the usual Row- land type of comparison shutter. All other exposures were made with 18X2^ inch plates, using a comparison shutter, mounted independent of the camera. In making exposures several days in length, the greatest prob- lem is a proper control of temperature. Fortunately for the author, the large grating of the University of Wisconsin is mounted inside a double-walled room, built in turn entirely inside an ordinary room. POSITIVE BAND SPECTRUM OF NITROGEN 55 The temperature in this outer room was kept constant within a few tenths of a degree by suitable electrical heating. This enabled the temperature of the grating to be kept constant within a few hundredths of a degree. The grating temperature was read on an accurate mercury thermometer, mounted in metallic contact with the side of the grating. Other thermometers were laid in a slot in the iron beams forming the slit-grating-camera triangle. A small change of temperature in this triangle is immaterial, so long as all parts remain at an equal temperature. For the grating, however, a constant temperature is indis- pensable, the change of wave-length at a given point on the camera plate being proportional, to first-order effects, to the change in the width of the grating space. 1 Holtz 2 seems to question this, and spends some time searching for other causes for the observed shift of lines with temperature. The mounting of the grating at the University of Wisconsin is such as to exclude the chief sources of error which he mentions, and it was found experimentally that the shift was exactly that computed from the change of temperature and the coefficient of expansion of the grating. A change of o?oi C. in the grating temperature will shift a line (at X 5000) about o . ooi A. During the exposures the tempera- ture was never allowed to leave a o?i C. range, and during any one exposure the average variation from the mean temperature varied, in different exposures, from o?oi5 to o?o35 C. The broadening of the lines was thus always less than o.oi A. Not only the temperature, but the barometric pressure as well, causes a shift of the spectrum. A change of i mm in pressure will shift the lines 0.002 A. With frequent total pressure variations of 2 cm, sufficient to cause a 0.04 A broadening of the lines, it becomes necessary to eliminate this change also. This was done by arbitrarily changing the temperature. A i cm rise of pressure is compensated by a o?i5 lowering of temperature. The mean temperature mentioned above, which I endeavored to hold con- stant, refers to the initial temperature, properly corrected for subsequent change in barometric pressure. The time of exposure varied from 66 to 120 hours. The slit- 'See Baly, Spectroscopy, p. 241, 1912 edition. 2 Zeitschr. /. Wiss. Phot., 12, 101, 1913. 56 RAYMOND T. BIRGE width varied from o.oi to 0.04 mm, being usually 0.02 mm. The theoretical resolving power of the grating (a 6-inch, 14, 43 8-line grating), for the slit- width used, was actually obtained on all exposures except those in the red where, in the second order, the grating has a somewhat poorer definition. The spectrum was photographed on eight different plates, two for each region. These regions were (i) X 6goo-X 6300, (2) X 6400- X 5800, (3) X 5900-X 5500, (4) X 56oo-X 5000. For regions (i) and (2), one was a Cramer plate, the duplicate a Wratten & Wainwright plate. No plates were exact duplicates, as the slit-width and time of exposure were varied. One 85 -minute exposure was made on a Hilger spectroscope, for the region X 68oo-X 7700. A one-minute exposure is sufficient, on this instrument, for the shorter wave- lengths. The spectroscope was calibrated with the argon spectrum, and the readings obtained for nitrogen are probably correct to i A. All of the plates obtained with the large grating are usable save one in the X 6300-X 6900 region which dried very unevenly. The duplicate plate, however, is the best that I have, and the readings obtained from it are believed to be as trustworthy as those in any portion of the spectrum. The work that has thus far been completed is as follows: 1 . The lines in the immediate vicinity of the three conspicuous " heads" of each band have been measured, and their wave-lengths computed, on all plates. 2. The regions X 55oo-X 5900 and X 630O-X 6900 have been completely measured and computed. There are about 6400 lines between X 5000 and X 6800, and 274 in the X 6623 band, in which von der Helm measured 119. There appear to be fully as many in all the other bands, although in most cases the number actually measured is much less, owing to the smaller intensity and shorter length of the bands. The measurements were made on a 55-cm Geneva dividing engine. The screw was carefully calibrated by the author and is believed to have no unknown errors greater than o . 002 mm. In order to test the evenness of drying of the plates, the international secondary standards were first corrected for non-normality of the dispersion and errors of the screw, and were then fitted as nearly as possible to a linear scale. Only standards of suitable intensity POSITIVE BAND SPECTRUM OF NITROGEN 57 were used, those overexposed being evidently untrustworthy. In the case of one plate in the X 63OO-X 6900 region, the average devia- tion of all the normals from a linear scale was less than o . 002 A. This was taken to indicate that the screw had been correctly cali- brated. On other plates there was a general drift from such a linear scale, very evidently due to uneven drying. It seldom exceeded 0.015 A and by drawing a smooth curve through the plotted read- ings of the normals, the correction for this was easily made. When the wave-length determinations of one plate were com- pared with those of a duplicate plate, there generally appeared a constant difference between them. This difference varied from o.oi A to 0.04 A on different sets of plates. It was considered due to the uneven illumination of the grating, as already explained. Fortunately, however, we have interferometer measurements of the three mercury lines present on my plates. By means of the ghosts and satellites of these lines, it was possible to determine their position with great accuracy, in spite of their overexposure. This settled the absolute wave-lengths from \5ioo to \5goo. One plate in each of the other two regions was then found to agree per- fectly in the overlapping portions. I thus had a full set of plates in complete agreement, and the duplicate plates were then given the proper constant correction to make them also agree. The values of the wave-length of any one line, as determined on different plates, then seldom differed by more than o . 01 A. Several settings were made on each line, and as the nitrogen lines are fairly sharp, the average experimental error of setting scarcely exceeds 0.003 A. It is hoped, therefore, that the relative error of all save very faint or hazy lines is less than 0.005 A, and that the abso- lute wave-lengths are in general correct to o.oi A. Table I gives the wave-lengths of 872 lines forming the three principal heads of the bands. The lines in the vicinity of all the heads given by von der Helm were measured, although in several cases there is no real head present. Several other heads not given by von der Helm were noted and measured. These so-called "heads" are caused by the proximity of several heavy lines, accom- panied by more or less continuous radiation. The measurements, in all cases, cover this region of continuous radiation, which is indicated in the table by braces. Frequently the haze is due 58 RAYMOND T. BIRGE merely to the scattering of light in the photographic film, but in most cases it is apparently a true radiation. The three main heads of a band, out of the five that appear with low dispersion, are designated I, II, and IV. The bands themselves are designated in two ways: first, by the division into groups (a to/), the individual bands of each group, from red to violet, being designated by Arabic numerals; the second method of designation is that proposed by Cuthbertson 1 and formulated mathematically by Deslandres. 2 In this arrangement the position of the first head of each of the entire set of 57 bands is given as a function of two independent parameters, p and n. The value of these parameters, for each band, is given immediately below the designation of the band according to the first arrangement. The first integer refers to the value of p, the second to n the values being those of Deslandres. 3 The three columns in the table are: (i) Intensity; lines marked " ?" are so faint as to preclude an accurate determination of wave-length; (2) wave-length on the International System (I. A.), at i5C., 760 mm; (3) character of the line. In this regard the following abbreviations are used: s., especially sharp. b., broad. b.'d., broad, probably double. d., certainly double. h., hazy. h.r., haze on the red side (due to one or more fainter components on that side). h.v., haze on violet side, n.s., a non-symmetric line due to two or more components of unequal intensity. The setting was made on the center of gravity of the system. k., the line at which a "head " apparently starts, a., argon. Von der Helm's value for the wave-length in air for the general position of the head, together with the frequency in vacuo, is given to the right of the designation of the head. *PhU. Mag. (6), 3, 348, 1902. a Comptes rendus, 134, 747, 1902. 3 See Baly, Spectroscopy, p. 620, 1912 edition. POSITIVE BAND SPECTRUM OF NITROGEN TABLE I 59 I 2 3 i 2 3 i 2 3 /Id 4 / 6787.91 U8-53 117,728. i /IId 5 / 6694-95 \47-52 \ 1 4,93 2. 6 3 4 2 2 4 4 i 3 2 66l3.l88 .cs6i 12.878 759 524 .244 .001 11.722 -603 h.r. h. h. s. (i 2 I 2 6788.614 243 .101 87.970 .834 .712 515 .270 k. f 4 2 I 2 3 2 I I ( 3 13 3 6694.911 775 553 391 .226 93-774 .610 474 -367 .242 92.849 k. /n.s. 1 h.v. b. /IVd6 / 6594.425 146-51 1 15,160. i /lid 4 / 6778.35 \48~53 Ii4,748.9 1 4 6 3 2 6594.418 175 93 739 -598 155 92.568 423 91.936 .781 k.b. h.v. i i {I 2 I I 2 2 6779.972 78.821 .623 .448 77-949 .538 .288 76.874 .661 k. /IVd 5 / 6675.01 \47-52 \ 14,977- 2 {I 4 2 2 3 i (4 14 6674.908 634 -236 .074 73-8i7 .615 .446 72-954 -852 k.b. b. /Id 7 / 6544-81 145-50 115,275.2 /IVd 4 / 6758.98 l48-$3 \ 14,791 -2 f/3 \3 i 1 5 4 2 6 e 4 4 6544.881 .716 .598 432 -237 095 43 942 714 .616 .460 251 k. h. 2 2 /I \I 2 I (i i 4 6759.243 58.054 57.807 .665 355 .067 56.721 .611 325 55-948 k. rid 6 / 6623.534 146-51 115,093.6 4 2 2 ' 4 4 2 5 I 1 b 6623.574 - .417 .281 . 1 20 22.915 795 -658 395 .130 21.971 -838 k.b. b.h. b.h. n.s. s. /lid 7 / 6535.50 \45-5o 115,296.8 fid 5 / 6704.45 \47-52 1 14,911.4 6 3 4 3 4 3 4 i 4 6535-655 . no 34-924 .627 .482 .188 .028 33-754 305 .127 s. d. h.r. /h.r. Ih.v. b. 3 2 I 3 3 3 3 3 4 6704.755 634 514 363 .132 03.879 .630 .376 .227 k. h.d. /IId6 f 6614.023 146-51 \ 15,115.0 6 ft 3 6614.031 13-789 .678 5i4 k. h. 6o RAYMOND T. BIRGE TABLE I Continued I 2 3 i 2 3 i 2 3 riv (AiR) (vacua) DIFFERENCE DIFFERENCE / 16 34-37 5126.81 19,499.86 107.88 / 15 35-38 5I55-32 19,391.98 0.27 108.15 / 14 36-39 5184-24 19,283.83 I . 22 109.37 / 13 37-40 5213-81 19,174.46 1.27 110.64 / 12 38-41 5244.07 19,063.82 i-39 112.03 / ii 39-42 5275-07 18,951.79 i-49 H3-52 / 10 40-43 5306.86 18,838.27 1.32 114.84 / 9 41-44 5339-41 18,723.43 i .58 116.42 / 8 42-45 5372.82 18,607.01 1.65 118.07 / 7 43-46 5407 13 18,488.94 1.50 H9-57 / 6 44-47 5442.32 18,369.37 1.62 121 . 19 / 5 45-48 5478.47 18,248.18 1-63 122.82 / 4 46-49 55 T 5-59 18,125.36 i .64 124.46 / 3 47-50 5553-73 18,000.90 i-55 126.01 / 2 48-51 5592-88 17,874.89 0.52 126.53 / i 49-52 5632-75 17,748.36 e 15 35-39 5484.34 18,228.65 141.19 e 14 36-40 5527-I5 18,087.46 0.46 I4I-65 e 13 37-41 5570.78 17,945.81 0.69 142.34 e 12 38-42 5615-32 17,803.47 0.83 143-17 e ii 39-43 5660 . 84 17,660.30 1.07 144.24 e 10 40-44 5707.46 17,516.06 1.02 145.26 e 9 41-45 5755-19 17,370.80 1.23 146.49 e 8 42-46 5804.13 17,224.31 1.40 147.89 e 7 43-47 5854-40 17,076.42 1.32 149.21 e 6 44-48 5906.01 16,927. 21 I .46 150.67 74 RAYMOND T. BIRGE TABLE IV Continued DESIGNATION A FREQUENCY FIRST SECOND (Am) (vacuo) DIFFERENCE DIFFERENCE P n e 5 45-49 5959-05 16,776.54 i-43 152.10 e 4 46-50 6013.57 16,624.44 1-52 153 62 3 47-$I 6069.66 16,470.82 $! 155 *3 tf 2 48-52 6127.37 16,315.69 1.41 156.54 I 49-53 6186.73 16,159.15 <* 12 40-45 6185.22 16,163.09 175.18 d II 41-46 6253.00 15,987.91 i-35 176.53 d 10 42-47 6322.82 15,811.38 1.03 I77-56 <* 9 43-48 6394-63 15,633 82 I. 21 178.77 d 8 44-49 6468 . 60 15,455 05 1-36 180.13 <* 7 45-50 6544-88 15,274.92 i 34 181.47 d 6 46-51 6623.57 l5,093-45 1.28 182.75 <* 5 47-52 6704.75 14,910.70 i-43 184.18 <* 4 48-53 6788.61 14,726.52 1.8 186.0 rf 3 49-54 6875-5 14,540.5 192.9 d 2 50-55 6968.0 14,347-6 186.4 d i 51-56 7059.6 14,161.2 c 8 43-49 7059 . 6 14,161.2 208.2 ' 7 44-50 7165.0 13,953-0 209.2 c 6 45-51 7274.0 13,743 8 208.5 5 46-52 7386.1 13,535-3 215-4 c 4 47-53 7505-6 i3,3i9-9 208.4 c 3 48-54 7624.8 i3,iii-5 198.5 (?) C 2 49-55 7742- (?) 12,913- (?) 237- (?) C I 50-56 7887. 12,676 6 8 43-50 7887 12,676 246 POSITIVE BAND SPECTRUM. OF NITROGEN TABLE TV Continued 75 DESIGNATION A. (AIR) FREQUENCY (vacua) FIRST DIFFERENCE SECOND DIFFERENCE p n b 7 44-5 1 8043 12,430 244 b 6 45-52 8204 12,186 240 b 5 46-53 8369 11,946 241 b 4 47-54 8541 11,705 223 b 3 48-55 8707 11,482 253 b 2 49-5 6 8903 11,229 244 b i 50-57 9101 10,985 In groups d and e it is occasionally doubtful what line forms the beginning of a new band. In the first heads of the/ group, however, there appears an extremely heavy doublet, the successive pairs of lines having not only the same relative intensity, but also a con- stant frequency difference. The doublets thus form two simple series, of which that of longer wave-length has been used for the / group of Table IV. In / i only one member of the doublet is present that of shorter wave-length. Hence it does not fit well with the other lines in Table IV. I give in Table V the simple series formed from the more refrangible member of the doublet. The first nine terms of this series can be fitted into the ordinary Deslandres' formula v=A+B(m+c) 2 (2) with an average difference between observed and computed values of 0.005 A. For the less refrangible member of the doublet the corresponding average difference is 0.006 A, and the constants for this latter series are: ^4 = 22,900.627 B= 0.8000 c= + 0.260 w = 8o to 72 The beginning of the deviation from Deslandres' Law occurs, in both series, at a point of minimum intensity at/ 10 (X 5306). 7 6 RAYMOND T. BIRGE TABLE V DESIGNATION A (Are) FREQUENCY (vacua] FIRST DIFFERENCE SECOND DIFFERENCE P / I 49-52 5632.754 17,748.361 127.701 / 2 48-51 5592.514 17,876.062 1.669 126.032 / 3 47-50 5553-362 18,002.094 I 597 124-435 / 4 46-49 55I5.239 18,126.529 1.629 122.806 / 5 45-48 5478.124 18,249.335 1.607 121.199 / 6 44-47 5441.981 18,370.534 1.615 119.584 / 7 43-46 5406.785 18,490.118 I-57I 118.013 / 8 42-45 5372.496 18,608.131 1.584 116.429 / 9 41-44 5339 089 18,724.560 1-544 114.885 / 10 40-43 5306.529 18,839.445 1-479 113.406 / IT 39-42 5274-777 18,952.851 1-379 112.027 / 12 38-41 5243-782 19,064.878 1.448 110.579 / 13 37-40 5213-540 I9,I75.457 1. 197 109.382 / 14 3 6 -39 5183 970 19,284.839 1-364 108.018 / is 35-38 5155.095 19,392.857 At this same point the frequency difference of the doublet also begins to diminish. For these two reasons it appears that the / group consists really of two groups, having a point of coincidence at X 5306. Table VI gives the frequency difference of the doublets for the en tire /group. I have thus far been unable to find any other strong series lying within the heads of the / group. In the d and e groups, however, there are at least 15 series, distributed among the three heads. In most of these the second difference remains approxi- mately constant for six or eight terms; in a few it forms more nearly an arithmetical progression, the third difference being con- stant. Such a relation can be satisfied by adding one more term to Deslandres' Law, so that it reads: v = A +B(m+c) 2 +C(m+c)s . (3) POSITIVE BAND SPECTRUM OF NITROGEN TABLE VI 77 DESIGNATION ft ft /4 /a /6 /7 i Difference ( in ) I-I73 I-I93 I . 167 1-157 i . 161 1 .176 1.123 \ A / DESIGNATION /9 /io /" / /I3 /I4 /IS Difference ' I.I27 i.:75 I .064 1-059 1-034 I .OC6 0.876 In the fifteen series the average difference of experimental and calculated values is slightly more than o.oi A. In some cases it is over 0.02 A and evidently exceeds the experimental error of measurement. The lines forming the doublets in/ are very difficult to measure correctly, because of their great intensity, and the nearness of adjacent lines. Yet they fit into series better than any other set of lines. Hence the deviations from formulae (3) or (2), in the case of other series are real, and not due to experimental errors. The spacing arrangement in different series varies slightly, so that series often tend to cross one another, and this gives successive heads an entirely different appearance. This can best be shown by the five series in heads IV d. These five series include nearly two- thirds of all the lines present in these heads, and, with two excep- tions, every strong line. Series 5 and e start from the same line and gradually diverge. Series 6, at the fifth term, breaks into a doublet, the components of which in turn diverge. The middle of the doublet is used for the last two terms. Such a sudden splitting of a line into a doublet is common in the series found in band spectra, and there are numerous examples of it in the spectrum under investigation. The five series are given in Table VII. The foregoing portion of Section II has been concerned simply with the law followed by individual simple series, each being considered entirely independently. There are also -relationships RAYMOND T. BIRGE TABLE VII IV d a (Air) Frequency (vacua) First Difference Second Difference 6758.054 14,793.111 184.265 6674 . 908 14,977.376 1.460 182.805 6594.418 15,160. 181 I-3I2 181.493 6516.403 15,341.674 1-340 180.153 6440 . 768 15,521.827 1-349 178.804 6367.416 15,700.631 1.251 177-553 6296. 212 15,878.184 1.020 176.533 6226.978 16,054.717 I . 165 175 368 6159.692 16,230.085 IV d ft 6757.355 14,794.642 184.242 6674.236 14,978-884 1-383 182.859 6593 739 15,161.743 1.411 181.448 65I5-759 i5,343-i9i 1.322 180.126 6440.150 I5,523-3I7 1.311 178.815 6366.808 15,702.132 1-234 177-581 6295.606 15,879-713 1.127 176.454 6226.416 16,056.167 I. 012 175-442 6159.114 16,231 .609 IV d 7 6756.666 14,796.151 184.127 6673.615 14,980.278 1.320 182.807 6593 -155 15,163.085 1.340 181.467 6515.181 15,344.552 1.352 180.115 6439 590 15,524.667 1.272 178.843 6366.252 15,703.510 1.306 177.537 6295.077 15,881.047 POSITIVE BAND SPECTRUM OF NITROGEN 79 TABLE VII Continued IV d 8 A (Air) Frequency (vacua) First Difference Second Difference 6755.948 I4,797-724 184.040 6672.954 14,981 . 764 1-368 182.672 6592.568 15,164.436 1-393 181.279 6514.687 15,345.715 1-435 179.844 6439.220 l5,525-559 1.304 178.540 6366.010 15,704.099 IV d e 6755-948 14,797.724 184.268 6672.852 14,981.992 1.491 182.777 6592.423 15,164.769 1.293 181.484 6514.459 15,346.253 1-374 180.110 6438.887 15,526.363 1.273 178.837 6365 . 564 15,705.200 between the spacing arrangement of simple series in different band groups. This can best be studied from the standpoint of the Cuth- bertson arrangement. In a two-parameter formula such as (i) there may be included one line from each band in the entire spectrum. It therefore com- prises several simple series. The entire set of simple series, one for each band group, satisfying separately and collectively such a two- parameter formula I call a " complete" series. When the lines of any complete series are regrouped to form the p and n progressions , it appears that formula (i) is not the correct functional form. Table VIII shows this clearly. In this table I give only the average frequency intervals of the two progressions, using the data given in Table IV. 8o RAYMOND T. BIRGE TABLE VIII FIRST PROGRESSION SECOND PROGRESSION p = CONST ANT n = CONST ANT First Second First Second n Frequency Difference Frequency Difference P Frequency Difference Frequency Difference 54 49 1615.0 1432.3 53 25-6 48 27-3 1589-4 1405.0 52 29.9 47 28.0 1559-5 1377 5i 28.9 46 27-8 1530 -6 1349 2 50 29.0 45 2 7 .8 1501.6 1321.4 49 29.6 44 28.0 1472.0 1 293 4 48 29.6 43 28.6 1442.4 . 1264.8 47 29.7 42 28.5 1412.7 1236.3 46 29.9 4i 28.9 1382.8 1207.4 45 30.2 40 29.4 1352.6 1178.0 44 30 3 39 29-7 1322.3 1148.3 43 30.8 38 30-3 1291.5 1118.0 42 31.2 37 31.0 1260.3 1087.0 4i 31-6 36 31.0 1228.7 1056.0 40 32-4 35 33 4 1196.3 IO22.6 39 3i-3 34 1165.0 38 34-5 "30.5 37 The second difference is an approximate arithmetical progression and requires a function of the type given in formula (3). Instead of formula (i) we must therefore use: v=A+B(n+c i y+r(n+c l )*+C(p+c 2 )*+s(p+c 2 )* . (4) Since the variation of both n and p has the same functional form, it follows that the variation of both together, such as we find in a simple series, has also this same form. For that reason it is possible to combine two simple series in order to determine the constants of a complete series. The two conditions imposed upon such a pair of POSITIVE BAND SPECTRUM OF NITROGEN 81 simple series are: (i) each simple series must fit formula (3); (2) both simple series must have the same third difference. In formula (3) this third difference equals 6C; in (4) it is 6(r+s). It is therefore the same for both simple series. When the constants of a complete series are thus determined, all other simple series in- cluded in the complete series have definite predicted positions. If we now choose the simple series given in Table IV, using only the band groups for which we have accurate measurements (groups /, e, and part of d), it appears that all three simple series satisfy condition (i), but no two of them satisfy condition (2). It is therefore impossible to group them together into a complete series satisfying formula (4) , and so the first lines of the first heads of all bands do not satisfy the Cuthbertson arrangement. Another way of stating this is that -the several First Progressions are not identical with one another. This was evident in compiling Table VIII. There are eight intervals in this table whose values can each be derived from two different First Progressions (and similarly for the Second Progressions) , using only accurate data. For these eight intervals the average difference of the two values is 0.2 A, more than ten times the experimental error. In the I heads of the d group there are three heavy lines in all. The two of shorter wave-length form a doublet of the same con- stant frequency difference as that in the / group. This suggested the combination of these two series of doublets into two com- plete series, which should differ from one another only by a con- stant value. It appears that the two simple series formed from the doublets in the d group are compatible with those of the / group, and so this rearrangement into complete series is possible. The simple series in the d group, of shorter wave-length, is given in Table IX. Using the two simple series given in Tables V and IX, we get the following constants for the complete series. The derivation is rather laborious, and the computations were not made by a strictly least-squares method : A =22,108.476 r =+0.0245 B= 18.0562 s= .0254 C = + 17-2474 * = + .3365 C a =-\- .7222 82 RAYMOND T. BIRGE For p and n the derived values are respectively three and four units lower than Deslandres' values, which I have consistently used in designating the bands. This shows not only that the values of c r and c 2 (which define the " phase" of a series) are meaningless without more accurate data, but also that no deductions can be drawn from the exact value of p n for any band group. TABLE IX DESIGNATION A FREQUENCY FIRST SECOND (AIR) (vacua) DIFFERENCE DIFFERENCE P d 4 48-53 6787.712 14,728.479 184.174 d 5 47-5 2 6703.879 14,912.653 1 . 291 182.883 d 6 46-51 6622.658 15,095 536 1.306 181.577 d 7 45-50 6543.942 15,277.113 1-335 180.242 d 8 44-49 6467 . 634 15,457-355 i 352 1 78 . 890 d 9 43-48 6393.636 15,636.245 I . 2IO 177.680 d 10 42-47 6321.797 15,813.925 For eight terms from the / group, and seven from the d group, the average difference (obs. calc.) is 0.005 A. For the less re- frangible member of the doublet we have 4 = 22,107.315 The other constants remain the same. For 14 terms the average difference (obs. calc.) is o.oi A. By means of the constants given above we can obtain the theoretical position of corresponding simple series in all other band groups. From the position of the component simple series, in the heads of the d and / groups, we snould expect the predicted series in the b and c groups to lie just to the violet of the rough measurements of the first heads in those groups. This is found to be the case, within the limits of experimental error. In the e group, however, where we have accurate data, there is no series in the predicted position. All series in I e have a slightly different spacing arrangement, and one of them gradually crosses the pre- dicted series. POSITIVE BAND SPECTRUM OF NITROGEN 83 Thus the only Cuthbertson arrangement I have been able to get is between alternate rather than adjacent groups. As already pointed out, k \ ^(p~\-n)\ and / { =%(pn)\ are the parameters in the von der Helm arrangement, corresponding to p and n in the Cuthbertson arrangement. In this latter arrangement the first heads of all the bands are represented by integral values of p and n. In the von der Helm arrangement integral values of k give a simple series. If, however, we keep k constant, and give / successive integral values, we get corresponding first heads only in every alternate band group. (See series k = constant on Fig. i.) For the intermediate groups / has the value of an integer plus one-half, and cannot be satisfied by integral values of p and n. Therefore we might expect to find related simple series only in every alternate group. I have at present no other numerical evidence either for or against this view. The previous discussion shows that many more lines can be fitted into series on the von der Helm arrangement than on the Cuthbertson. This naturally follows from the fact that each simple series involves only one parameter, while the Cuthbertson arrangement involves two. The individual series in different band groups should have related spacing arrangements, given implicitly by formula (4). The data show, however, that the relation is in general not accurate within the limits of experimental error. One further point of interest is the continuity of successive band groups. The heads of the last band of one group practically coincide with those of the first band of the succeeding group. In this connection the band at X 6186 is the most interesting in the entire spectrum. In this band we have at 6186.7 a head which agrees in its general position and appearance with the designation I e i ; similarly at 6185 . 2 a head Id 12. The entire appearance of the band is that of a d band, and it is doubtful whether the e group is represented save by I e i, although I have recorded in Table I the lines in the vicinity of the theoretical position of II e i and IV e i. In the case of the e and / groups, the theoretical position of I e 1 6 is 5443.3, almost coinciding with the strong 1/6 head at 5442.3. Deslandres records I e 16 but there seem to be no lines 84 RAYMOND T. BIRGE at this point resembling an e head. Again, however, the rough theoretical positions of these two heads almost coincide. For the other groups the coincidences are at 7059.6 and 7887. The data are so inaccurate here that the positions will fit equally well in either of the adjacent band groups. Considering that we have at least approximate coincidences at the four points mentioned above, several interesting relations follow. The values of p and n at these points are: p n p n p n p n 43-50 2 j 43-49 | 40-45 j 34-38 50-56 / 51-56 3 ( 49-53 4 I 44-47 Since the coincidence is between two heads of different band groups, the two values of p n at each point differ by unity. Two other unexpected facts, however, are: (i) that the discontinuity in p increases by unity at each succeeding point of coincidence; and (2) that the number of bands between points of coincidence in- creases by four, from group to group. This is also shown in Fig. i. The coincident points are indicated by vertical dotted lines. The length of these lines gives the discontinuity in p. The number of bands between them is seen to increase by four, as one goes from red to violet. In group c there are six, in d ten, and in e fourteen bands. If this rule were followed farther to the red we should expect only two bands in 6, between the coincident bands 46-53 and 43-50. This would be the last group, the next one, by rule, having zero length. On the violet side we should expect nine more bands (including the coincident ones) in the / group, 25-28 coinciding with 36-38 of an unknown g group, and so on. In the next (ti) group the last of the 26 predicted bands would have />= i, w=o. Since the correct value of p n for any band group is indeterminate to at least one integer, it seems natural to suppose that all values of p should be raised by one integer. We should then have a complete plan for the First Deslandres' Group. It would start, theoretically, at p = o, w = o, and would consist of seven groups of bands. The first head of some band near the end of each group would coincide approximately with the first head of a band in the next group. The number of bands POSITIVE BAND SPECTRUM OF NITROGEN 85 between coincidences would diminish by four, in each succeeding group. Some groups run past the points of coincidence and so overlap on each other. Although groups g and h do not appear in the ordinary spectrum, Goldstein 1 believes he has seen the First Deslandres' Group, under certain low-temperature conditions, extending into the blue. Other investigators have been unable to verify this. Group h should start at X 4430 and extend to X 4530. Group g should extend from this latter point to X 4890, and/ from X 4890 to X 5442 . 8. SECTION III Under high dispersion successive bands have a very similar appearance, and this not only suggested to the author the formation of simple series, but also indicates the validity of the von der Helm arrangement of the bands. The general intensity of successive bands also varies continuously through a group of bands. All simple series were formed from lines of the same general appearance, and of a continuously varying intensity. The large number of possible series with approximately the same spacing is also good evi- dence of a connection between successive lines. A few bands in group e have been measured and plotted beneath one another. It is these bands (X 59OO-X 5700) that indicate the existence of some 50 simple series of lines, superimposed upon a much larger number of unrelated lines. Below X 5700 all of the e series die out, save only those in the first heads. In the d group, however, the series extend to the last regular d band at X 6185, and perhaps farther. In the case of the / group there seem to be no conspicuous series save the two mentioned in the first heads. This portion is the most irregular of the entire spectrum. The only exceptions to the general rise and fall of intensity in the bands of one group are two very strong heads at X 7072 .8 and X 6968.0. The latter lies at the predicted position of I d 2. The former lies somewhat to the red of I c 8. There is no apparent reason why either one should be strong. On the other hand, all changes in appearance of the bands under changing physical conditions point to the Cuthbertson 1 Goldstein, Phys. Zeitschr., 6, 14, 1905. 86 RAYMOND T. BIRGE arrangement as the one indicating the actual physical connection between the sources of the radiation. Fowler 1 has shown that the spectrum of the active modification of nitrogen shows certain of the bands of the First Deslandres' Group greatly intensified, while the others are very faint or entirely lacking. The three strongest bands are those at X 6253, X 5804, and X 5407 (# = 46; ^ = 41, 42, and 43), while the weaker bands on each side are those at X 6323, ^5 8 54> ^5442 (w = 475 = 42, 43> 44) and at X6i85, X 5755, and X 5373 (# = 45, /> = 4O, 41, and 42). Fowler has pointed out this evidence in favor of the Cuthbertson arrangement. The fact that apparently the entire band is increased in intensity may point to a further relation, not included in the Cuthbertson. It would be very interesting to photograph this spectrum under high dispersion and to note whether all the lines of a band were intensi- fied, or only those belonging in series. Angerer 2 has made an exhaustive study of the First Deslandres' Group at low temperature. I have made no critical study of his results, and cannot well do so until I have my own measurements completed. Several points, however, are worth noting. At low temperature the heads of a band are far more intense, relative to the rest of the band, than at ordinary temperature. This is especially true of the III heads which, at high temperature, escape detection in many bands not having been measured at all by von der Helm. But they are particularly strong at low tempera- ture. This would point to an independence between the series lying within the heads of the bands, and other series. At low temperature the entire spectrum is relatively much fainter than at room temperature. Aside from two small groups of lines in the green, the only exceptions to this statement are the first heads of the three bands X6623, X 6070, and X 5593 (^ = 51; = 46, 47, and 48). The second of these is even more intense at low temperature, while the other two are fully as intense. Here again we have evidence in favor of the Cuthbertson arrangement. There is one additional fact pointing to a general relationship between the heads of all the bands. The frequency difference of 1 Fowler, Proc. Roy. Soc., 85 A, 377, 1911. 3 Ann. d. Phys., 32, 549, 1910. POSITIVE BAND SPECTRUM OF NITROGEN 87 the rough position of the I and IV heads is a constant for all bands from X 5100 to X 9100, although the length of the bands more than doubles within this range. The maximum variation of the differ- ence is 7 units (from 2 = 68 to 61). The frequency difference of the I and II heads, except in the / group, is also practically constant. I cannot recall having previously seen this fact explicitly stated. This relation of the heads is what we should expect if the bands were composed of a number of identical series of lines. It seems evident that all possible series have very closely the same spacing, but it is also certain that the spacing is not identical. Sections II and III may be summarized in the statement that numerical relationships among the lines of the First Deslandres' Group favor the von der Helm method of grouping, while changes in the bands under varying physical conditions of the source all point to the Cuthbertson method as the significant one. CONCLUSIONS 1. The First Deslandres' Group of the positive band spectrum of nitrogen consists really of two spectra, one composed of a large number of superimposed series of lines, the other quite irregular. 2. The similarity in the spacing of all series gives the banded appearance of the spectrum, the length of a band being the distance between two successive lines of each series. 3. The so-called " heads" of the bands are formed by groups of particularly heavy lines, accompanied by more or less con- tinuous radiation. 4. It is possible to fit a greater number of lines into the simple series of the von der Helm arrangement of bands than into the more complex two-parameter formula indicated by the Cuthbertson arrangement. All physical changes in the spectrum, however, favor the latter arrangement. 5. Simple series of lines, running through one band group of the von der Helm arrangement, obey Deslandres' Law for at least the first few bands, but later show a large and systematic deviation from it. 6. The First and Second Progressions of the Cuthbertson arrangement fit approximately into a formula containing both 88 RAYMOND T. BIRGE the second and third powers of the parameter, but will not fit the simpler second-power formula of Deslandres' Law. 7. The successive band groups have certain heads which approximately coincide, and these points of coincidence show regularities which enable the entire set of bands of the First Des- landres' Group to be arranged so as to indicate a definite plan for the group. The experimental part of the investigation is the resolving, for the first time, of the 39 bands between X 5000 and X 6800 into about 6400 lines, and the measurement of a portion of these lines with an average error of o.oi A or less. In conclusion the author wishes to express his thanks to Pro- fessor C. E. Mendenhall for the many helpful suggestions offered during the progress of this investigation. DEPARTMENT OF PHYSICS UNIVERSITY OF WISCONSIN August 1913 7 DAY USE RETURN TO DESK FROM WHICH BORROWED PHYr"*'* ' E *ARY This publication is due on the LAST DATE stamped below. RB 17-60m-8,'60 (B3395slO)4188 .General Library University of California Berkeley