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velocities of stars are functions of their spectral types, and the further interesting fact that the average radial velocity of Keeler's thirteen planetaries was greatly in excess of the average radial velocities of the stars in any of the spectral classes, proclaimed the desirability of entering upon the nebular programme as early as possible. The director in 1912 assigned this work, at Mount Hamilton with the 36-inch refractor, and at Santiago, Chile, with the equipment of the

D. O. Mill? Observatory, to one of his colleagues, but the latter, in 1913, requested to be relieved of the assignment. Mr. Moore, acting astronomer in charge of the D. O. Mills Expedition, was then assigned the duty of observing certain southern nebulae, and Dr. P. W. Merrill was entrusted with starting the observations at Mount Hamilton. These duties were entered upon by both observers in the early summer of 1913. Mr. Moore's return from Chile in August, 1913, and Mr. Merrill'8 acceptance of appointment elsewhere in September, 1913, made other arrangements necessary. Mr. Campbell then assumed direct charge of the problem in both hemispheres, with Mr. Moore as associate from the early summer of 1914 to date. Other observers who have assisted more or less extensively at Mount Hamilton with the photographic exposures are Messrs.

E. S. Haynes, G. F. Paddock, Manuel Selga, W. K. Green, R. F. Sanford, C. D. Shane, F. J. Neubauer, Holger Thiele, and Francois Henroteau. The nebular observations obtained at Santiago, Chile, since early in 1914 have been made by Acting Astronomer R. E. Wilson, in charge of the Expedition, and by his successive assistants, Messrs. R. F. Sanford, A. A. Scott, and C. M. Huffer. Miss A. M. Hobe has assisted prominently in the measurement of the Mount Hamilton plates and has been reponsible for the major part of the computations relating to the nebulae.

Instruments And Observing Conditions

In the prosecution of the programme at Mount Hamilton in the last two years we have had the great advantage of Dr. Curtis's simultaneous photography of the planetary and other nebulae with the Crossley reflector. This has given us, in nearly all recent observations, a prior knowledge of the forms, dimensions, and brightness of the nebulae investigated, and it has also added a good many objects to our programme which would otherwise have been passed over as unsuited to our purpose. The programme in Chile has been pursued at a relative disadvantage in this regard. No doubt a thorough study of the southern nebulae by means of a great reflecting telescope would extend the list of objects available for radial velocity determinations, and, further, the spectrographs observers would use to advantage the detailed results of such a photographic survey.

The observations recorded in the following pages are sufficient evidence that the work has been extensive and arduous. This is the natural consequence of applying the method to a large number of nebulae so faint as to require long exposures, and of obtaining several exposures on each object in order to increase the weights of the observed velocities. It will be noticed that many of the nebulae have been observed more frequently than would naturally be expected. Several factors have made this desirable:

1. The exposure times in the first years were in many cases too short and the results were correspondingly inaccurate. In fact, in those years the 36-inch telescope was frequently not available for longer exposures.

2. The earliest observations were made with a spectrograph containing one light-flint 60° prism and a camera of 16 inches focal length. An appreciable advance in accuracy was obtained by reobserving the same objects with a dense-flint 631»2 ° prism (Jena glass number 0.102). In describing the observations below, the former is referred to as "1-lt. pr. 16 in.," and the latter as "1-pr. 16 in."

3. For the fainter nebulae with diameters larger than the diameters of those called "stellar," vastly greater density of recorded spectrum was obtained from and after early 1915 by replacing the combination of one 63y2° prism and 16-inch camera with another combination containing the three original Mills spectrograph prisms and a 5-inch camera, the linear dispersion remaining essentially unchanged. For equal densities of the monochromatic bright lines on the photographs the 3-prism combination reduced the exposure times to about one-fifth that required by the 1-prism combination. In effect, this permitted the inclusion of a relatively large number of faint nebulae in the programme.

4. The 5-inch lens referred to is a cheap projection lens giving scarcely passable definition. Early in 1915 an order was placed with the Brashear Company for a camera lens of aperture 1% inches and focus not over 6 inches, with thin component lenses and with field of good definition comparatively small. After much experimental work by Professor Hastings and Mr. McDowell, such a lens was supplied to us early in 1916. Its performance is a great improvement over that of the 5-inch lens, in that the well defined lines yield higher accuracy; and on that account some of the earlier exposures were repeated. We gratefully acknowledge the interest of Professor Hastings and the Brashear Company in our problem, and our indebtedness to their successful work.

5. It was found that many of the brighter objects could be observed with three prisms and a 16-inch camera, using exposures less than twice as long as the light 1-prism and 16-inch camera had required, and the observations were repeated in several cases in order to increase the accuracy.

6. In searching for evidences of relative motion within the brighter planetary nebulae— requiring the higher dispersions and various position angles of the slit—there were many repetitions of exposures, and these incidentally yielded results for the radial velocities of the several bodies as a whole.

7. For a few of the brightest nebulae a 32-inch camera and three prisms were used.

8. The temperature ranges were too large in the cases of several early spectrograms, and a considerable number of these were repeated under better conditions.

The observations in Chile began with a spectrograph of one 63^° dense-flint prism (Jena glass 0.102) and an 18-inch camera, attached to the 37-inch Mills reflector. This spectrograph was succeeded by a 2-prism and 8-inch Brashear lens combination, which reduced the exposures for the fainter bright-line spectra to about 30 per cent of those with the 1-prism combination, with only a slight sacrifice of linear dispersion. Still later the same 8-inch camera was occasionally used with 1-prism dispersion. The mechanical attachments to accommodate the shortcamera combinations were designed and constructed at Mount Hamilton.

Readers interested in the various degrees of linear dispersion employed will be able to estimate closely enough from the datum that with the 3-prism 16-inch combination one millimeter of the spectrum at H/3 corresponds to 20.0 Angstrom units.

In general, the comparison spectra were obtained from hydrogen and helium tubes, but in the beginning at Santiago the iron arc was used, and in a very few cases at Mount Hamilton the titanium spark was employed. Nearly all of the work is based quantitatively on the comparison lines :2

He 5015.858 Rayleigh and Eversheim H/3 4861.505 W. E. Curtis

He 4922.112 Rayleigh and Eversheim He 4713.327 Rayleigh and Eversheim

Kilby's wave-lengths of the titanium lines and Kayser's of the iron lines were employed.

The wave-lengths of the nebular lines were assumed to be :2

N, 5007.02 Campbell and Moore N, 4685.95 Wright (nebulae)

N, 4959.09 Campbell and Moore H7 4340.634 Rowland (Sun)

H/3 4861.505 W. E. Curtis (laboratory) H8 4101.89 Wright (Omicron Ceti) 3

The last two lines were used with a few 1-prism plates only. With the 3-prism combinations the field of good definition did not include more than the region 5100-4650A.

2 See Lick Obs. Bull, 9, 6, 1916. s Astroph. Jour., 9, 51, 1899.

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the change from one refracting Bet to another refracting set is made in a few minutes. It is unnecessary to remind the experienced observer that such frequent manipulation of the delicate slit mechanism would be highly objectionable, for various reasons. The same straight slit is therefore used with all the combinations referred to, and it is necessary to construct and employ a separate curvature correction table for each combination.

The fundamental objection to curved lines is that the micrometer wire is expected to bisect areas which are not symmetrical with reference to the wire; and that is always an uncertain process. This is illustrated in figure 1, in which the area EFOH represents the curved line of the nebular spectrum concerned, and the areas ABCD and l.JKL are the two parts of a comparison line of nearly the same wave-length. Theoretically, the micrometer wire is aimed to pass through the point 0 bisecting the width of line rs, for the reading on the nebular line, and through certain points v and w on the median line of the comparison line, for the reading on the latter. The curvature correction is computed on the assumption that BC, FG, and JK are sections of a known parabola, y- = —constant x, whose axis lies on the line RS; and the value of the correction is the abscissa of a point on the curve whose ordinate is vO' or wO'.

The difficulty is encountered in trying to bisect the lines at the points v, 0. and w. In practice the appearance is somewhat as in figure 2. The irregular distribution of silver grains requires the observer consciously or unconsciously to bisect a considerable length of the nebular line and of each inner end of the comparison line. It frequently happens, we think, that the wire is set upon the nebular line in such a position as to make the area on the left side of the wire equal to the area on the right side of the wire, thus in effect ignoring the curvature; and at the same time it happens, we think, that the observer estimates where the middle points of the inner ends of the two sections of the comparison line are and sets the wire upon those points. It is evident that the application of the full curvature correction in such a case must result in over-correction. Careful consideration of the subject in connection with our measures of radial velocities of bright-line nebulae with 3-prism dispersion, when the slit is relatively long and the nebular lines frequently under-exposed, has caused us to fear a systematic error of appreciable size from this source. A quantitative study and solution of the subject appears to be attended with great difficulties. The embarrassments of bisecting unsymmetrical areas could be avoided, and should be avoided whenever practicable, by arranging for straight lines, as illustrated in figure 3.

Generally, the uncertainty in the curvature correction is relatively unimportant, as the entire curvature correction is small for all of the dispersive combinations used in this work except when three prisms and the 5-inch and 6-inch cameras were employed. It is possible that the uncertainty in the curvature correction for the spectrograms obtained with the latter combinations amounts to as much as 1 km. per sec.

Probable Errors Of The Results

The question of the probable error of the observed velocity of each object is not an easy one to answer, partly owing to the variety of conditions under which the individual observations have been made. The reader can judge of the accuracy from the individual results set down for each nebula. Our own opinion of the relative merits of the spectrograms for each object may be read in the column of assigned weights. A fair test of the accuracy attainable with the 3-prism 16-inch camera combination is afforded by the nebula Jonckheere 900 (R.A. = 6" 20m), for which the computed probable error of a single observation is ±0.49 km.; and the probable error of the mean of five observations is about ±0.22 km. The exposure times ranged from 3^6 to 9^5. The nebula J. 320 (R.A. = 5h O"1) is not so favorable a case, for while it is brighter than J. 900, we found J. 320 to be in rapid rotation, and the resulting inclination of the nebular lines, combined with some unavoidable inaccuracy in guiding, is liable to affect the accuracy of the observed velocity of the nebula as a whole. The beautiful planetary N.G.C., 418 (R.A. = 5h 23m) is an extremely favorable case, as this object is very bright, the lines are of good length for accurate bisection, and rotational effects are not in evidence. This object is observable with three prisms and the 16-inch and 32-inch cameras with accuracy equal to that of the most favorable stars. The accuracy obtainable for a number of the brighter planetaries is reduced by the fact that the bright lines are not monochromatic, owing to the presence of factors other than rotation of the individual nebulae as a whole. There are examples of broadened lines, of double lines, of curving and irregular lines, etc. In dealing with such cases the correct values of the radial velocities of the objects must remain in some doubt, and spectrograms of them obtained under different conditions will give varying results; and there seems to be no gain in accuracy as to the velocities of their centers of mass from using the higher dispersions, for obvious reasons. For nebulae bright enough to give fully exposed lines— provided the lines are monochromatic—there is no difficulty in attaining to probable errors of 0.5 km., or less, for single observations, even though the exposures may run up to 10 or 20 hours. On very many plates, unfortunately, the strongest nebular lines are much under-exposed, and the probable errors increase in consequence.

The probable errors of the southern hemisphere observations are in general appreciably larger than those of the Mount Hamilton observations. We refer more especially to the results obtained with the 2-prism 8-inch combination. The definition of the spectrograms secured with this combination is not so good as it should be, and a great many of the spectrograms are underexposed. An examination of the radial velocities obtained for each nebula by the two or more plate-measurers will give a fair idea of the relative weights.

Differential Motions Within The Nebulae

The question of differential motions within the bright-line nebulae has been considered by several astronomers. Keeler's instrumental equipment and methods made the first close approach to success in detecting such motions, as Doppler-Fizeau effects. He observed the spectrum of the inner and brighter parts of the Orion nebula, chiefly the region preceding the Trapezium, for local broadenings or distortions of the lines, but with negative results. He estimated that differential radial velocities as great as 8 km. per sec. in the brighter parts* of the nebular structure would have been detected. Keeler's comment on the character of the lines from the brighter parts of the Orion nebula is that "The lines always appeared fine and sharp; the hydrogen lines from the spectrum tube were not finer and sharper" (p. 199). To anticipate, we may say that observations secured to date, by the more sensitive photographic method, seem to confirm Keeler's conclusion that in the region described by him the differential velocities are not greater than 8 km. per sec.

In 1902 Vogel and Eberhard found evidence of differential velocities in the Orion nebula,5 fairly strong evidence that the radial velocity of the nebular materials at and slightly east of the brightest star (01 Orionis) in the Trapezium was 5 or 6 km. greater positive than the velocity of the materials lying 0f6 west of 0a; but only some slight indications that the velocities of the materials lying from 0'4 to 2'3 west of 8.2 Orionis varied considerably, as the only nebular line on the photograph, Hy, was "in general very weak."

In 1911-14 Messrs. Buisson, Fabry, and Bourget of Marseilles University applied the interferometer method to the measurement of the radial velocities in the brighter regions of the Orio-n nebula,6 with brilliant success. They determined the velocities of fifty-eight points distributed in twelve directions from the Trapezium within a radius of about two minutes of arc. They obtained a mean value of 15.8 km. per sec. for the fifty-eight points, but found inequalities of speed amounting to 10 km. per sec. for parts of the nebula covering very small areas. They concluded also that there are great collective movements for large areas, such that the region northeast of the Trapezium is receding with a speed of about 5 km. per sec. and the region southwest of the Trapezium approaching with a similar speed, both relative to the average radial velocity of the Trapezium region. They concluded that the part of the nebula studied by them has a sort of rotary movement around a southeast-northwest line, but with numerous irregularities interspersed.

* In making micrometer observations for the positions of the bright lines in the Orion nebula, as Keeler has stated, "the slit was always placed on the bright part of the nebula immediately preceding the Trapezium, one of the Trapezium stars being usually kept within the slit at its extreme end. This was done in order to have all the observations refer to one part of the nebula, in case relative motion of the different parts should be subsequently detected." Publ L. O., 3, 197, 1893.

5 Astroph. Jour., 15, 307-9, 1902.

ec. R., Paris Acad., 158, 1269-71, 1914; Astroph. Jour., 40, 241-258, 1914.

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