Part 2

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.”