Spectroscopic Measurements

Standard Wave-lengths.

The primary standard of wave length in modern spectroscopy is based upon interferometer measurements of the red line of cadmium, under standard con ditions, in relation to the standard metre. The unit of wave length thus arrived at is called the International Angstrom, and is very close to metre. The standard conditions are air at I 5° C and 76o mm. pressure, g= 980.67, and the wave-length of the red cadmium line, adopted by international agreement, is then 6,438.4696I.A. This has been deduced from the work of C. Fabry and A. Perot, and is in close agreement with the value determined by A. A. Michelson. (See INTERFEROMETER.) The older spectroscopic tables are on the scale of Rowland, which was based upon slightly erroneous absolute wave-lengths for the two yellow lines of sodium ; such tabulated spectra can be approxi mately corrected to the international scale by subtracting quan tities ranging from 0.25 at 7,000A to 0.06 at 1,950A.

The most useful secondary standards, especially for work with large instruments, are provided by the arc spectrum of iron, which includes many hundreds of lines. Many of these have been measured with respect to the red cadmium line in various labora tories, and a number of secondary standards for general use have been recommended by the International Astronomical Union (Transactions, vol. III., 1929).

Interpolation of Wave-lengths.

The secondary standards, which have thus been determined by interferometer methods may obviously be used for the determination of the positions of lines in any other spectra by interpolation, employing ordinary spectro graphs. For this purpose, photographs are taken of the source under examination through one portion of the slit, and an arc spectrum of iron through one or both of the adjacent portions, so that two spectra in juxtaposition, or slightly overlapping, are obtained as illustrated in Plate II., fig. 5. Lines of other elements thus become, in turn, available for use as tertiary standards, and may be used with instruments which give too small a dispersion to resolve satisfactorily the complicated spectrum of iron.

When a prismatic spectrum is used, the dispersion increases rapidly as the wave-length diminishes, and simple linear inter polation between standards will not give correct results. When the spectra do not permit of very accurate measurement, the interpolation may be performed graphically, using measurements of the lines under investigation and a number of lines of known wave-length in conjunction. The same procedure may be adopted for measurements of a photograph with a finely divided scale, if a comparison spectrum which includes lines of known wave length has also been impressed on the plate, or if a sufficient number of known lines are included in the spectrum under exam ination.

For more accurate determinations, photographs are measured with a photo-measuring micrometer. This consists of a micro

scope of moderate or low power which can be made to traverse the photograph by means of an accurate screw of small pitch, so that the cross-threads are brought successively into coincidence, with the desired lines; the positions of the lines are then read off on a scale which counts complete turns of the screw, and a divided drum head which registers fractions of a turn. As before, lines of known wave-length, which are generally provided by a com parison arc spectrum of iron, must be included in the measure ments. Interpolation may then be most conveniently performed with the aid of a formula first proposed by A. Cornu and after wards brought into more general notice by J. Hartmann. The wave-length, X, and the scale reading, s, are here supposed to be Three lines of known wave-length, and the corresponding scale readings are thus required in order to determine the constants C and So; one should be chosen near each end, and the other near the middle of the region investigated.

The wave-lengths so determined will not be quite exact, because the formula does not accurately represent the dispersion of the spectrum on the plate, except over a small range. The imperfec tion of the formula, however, can be corrected by including a number of well distributed known lines in the measurements. The differences between the calculated and known values of these lines are then plotted to give a "curve of errors," which can be used to give the corrections to the calculated wave-lengths of the lines under observation. This procedure might, of course, be adopted with any approximate formula, but the Cornu-Hartmann formula has the advantage that the corrections are small.

The dispersion in spectra produced by gratings is much more uniform—that is, the spectra are more nearly normal—than in those produced by prisms. By certain arrangements, the scale of a grating apparatus can be made quite normal for visual obser vations, but in all photographs there is a slight departure from a uniform scale. Interpolation may then be made by following the procedure which has been outlined for prismatic spectra, except that the Cornu-Hartmann formula is replaced by a linear interpolation formula, such as X= X0-1-bs, where and s can be calculated from two of the standard lines which are included in the measurements. The necessary corrections for lack of normality are then given by a curve of errors similar to that described for prismatic spectra.

A good photographic map of the iron arc spectrum, which is indispensable in practical spectroscopy, has been prepared by C. Fabry, ranging from X2,327 to X6,7oo. A small portion of this is reproduced in Plate II., fig. 4 ; approximate wave-lengths can be read off from the map and the corresponding accurate wave lengths obtained from tables.