SPECTROSCOPIC MEASUREMENTS The need for some means of expressing the positions of lines in the spectrum is sufficiently evident. In the more common forms of spectroscope the observing telescope is provided with cross-threads which can be brought into coincidence with any given spectrum line, and the position of the telescope is then read off on a graduated circle. Such readings will evidently give the relative positions of the lines on an arbitrary scale, but read ings for the same lines on different instruments will not be directly comparable. Similarly, when dealing with photographs it is only possible to measure directly the relative positions in arbitrary units.
Measurements of spectra which have been observed or photographed become directly comparable with each other when they have been converted to the scale of wave lengths of the light which produces them. The credit of intro ducing this scale into spectroscopy is due to A. J. Angstrom, who mapped the spectrum of the sun in terms of wave-lengths in 1868. The same procedure was subsequently adopted by his colleague Thaler' in connection with the spectra of the elements, and since that time the positions of spectrum lines in all spectro scopic tables have been stated in wave-lengths. The unit of wave-length in spectroscopy is the ten-millionth of a millimetre, or
centimetre. It is called the tenth-metre
m.) or "angstrom," and is now ordinarily indicated, when necessary, by writing A after the figures indicating the wave-lengths. In these units, the visible spectrum ranges from about 3,900A at the violet limit to about 7,600A in the extreme red. When it is stated, for example, that the wave-length of the red line of hydrogen is 6,562.79A, it is to be understood that it amounts to 6,562.79x
cm. Wave-lengths, especially in connection with the invisible infra-red part of the spectrum, are also often ex pressed in terms of the micron (p.), which is one-thousandth of a millimetre ; thus the wave-length of the red hydrogen line might be written 0.656279,u.
Absolute wave-lengths cannot be determined directly by the use of prisms, but are determined by observations made with diffraction gratings or by interference methods. In ordinary spectroscopic work, however, whether with prisms or gratings, no attempt is ever made to determine the wave-lengths directly.
The wave-lengths required are deduced by interpolation between standard lines which have previously been determined with sufficient accuracy.
More especially in connection with investi gations of regularities in spectra it is important to express the positions of spectrum lines in "wave-numbers" instead of in wave-lengths. The most fundamental figures in this connection for theoretical purposes are the "oscillation frequencies," since these are independent of the medium through which the light passes. Oscillation frequency may be defined as the number of waves which pass a given point in one second, and is equal to the velocity of light (c) divided by the wave-length (X) in vacuo, i.e., n= c/X. Since the velocity of light is very great (nearly 300,00o kilometres per second), and the wave-lengths very small, oscillation frequencies are represented by extremely large numbers. Thus, for red light of wave-length 6,5ooA the frequency is about 462 billions per second, while for violet light of wave-length 4,200A it is 713 billions per second. Difference in colour, it will be noticed, depends upon difference in the fre quency of the waves that reach the eye. These oscillation fre quencies are not directly measurable but can be deduced from the measured velocity of light combined with measurements of wave-lengths. They are unsuitable for ordinary spectroscopic use on account of their great magnitude. It is accordingly the practice to replace the actual frequencies by "wave-numbers," represent ing the numbers of waves in the length of a centimetre. Since the wave-number is dependent on the wave-length, it will vary with the medium in which the vibrations are propagated, and in the calculation of wave-number from wave-length it is therefore necessary to express the wave-length in vacuo. If a wave-length has been measured in air it must be corrected to vacuum con ditions for the determination of the corresponding wave-number. This correction is based upon measurements of the refractive index of air for different wave-lengths, and convenient tables have been prepared for its application. When corrected to vacuum in this way the calculated wave-numbers are strictly proportional t o the corresponding oscillation frequencies.