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The difference of the wave-lengths corresponding to the two D lines, as measured in the third and in the fourth spectrum, amounts to 2·226,—that between the wave-lengths corresponding to the two E lines being only 0·395, as measured in the third spectrum.
Fraunhofer has given two different series of values for the wave-lengths of light. The first series was obtained by measurements with wire gratings, and it is upon this that Cauchy founded his calculations in the Mémoire sur la Dispersion. It contains the following numerical values (β):—
Comparing these values with the corresponding ones in the foregoing Table, which I will call the series (a), the following differences (α–β) are obtained:—
The differences increase, as will be seen, towards the violet end of the spectrum, and are there very considerable. This arises from the difficulty, when using gratings so coarse as those employed by Fraunhofer, of accurately distinguishing the dark lines at the violet end of the spectrum.
The best of all the gratings employed by Fraunhofer is, without doubt, that which he denoted as No. 4, and with which he observed the line E even in the thirteenth spectrum. This grating gives, in general, values which agree better with my own. For the lines C, D, and E the agreement is nearly perfect. The grating in question gave, in fact, the values
I conclude from this that the disagreement between the series (α) and (β) must arise principally from errors of observation, which, with the wire gratings used by Fraunhofer, were unavoidable.
The other series of values of wave-lengths given by Fraunhofer is of a somewhat later date. It will be found in Gilbert’s Annalen der Physik, vol. lxxiv., as well as in Herschel’s ‘Optics,’ Schwerd’s Beugungs-Erscheinungen, and other works. This series, on account of its exactitude, appears to have been held by Fraunhofer in greater esteem than the older ones.
It contains the following values (γ)
and gives, when compared with the series (α), the differences (α–γ)
The values of the wave-lengths contained in the series (γ) depend on measurements of the first interference-spectrum of a glass grating which was considerably finer than the one I employed. According to Fraunhofer’s statement, in fact,
e=0·0001223 of a Par. inch.
Since, however, the number of marks in this grating of Fraunhofer’s amounted only to 3601, the breadth reduces itself to
5·2833 Par. lines; and consequently it must have been considerably less luminous than that of Nobert. In another respect, too, Fraunhofer’s grating, although an excellent one, appears to me to have been inferior to that of Nobert; for the line B could not be measured even in the first spectrum, and the lines from C to G were not visible in any of the spectra beyond the second.
Nevertheless, since almost all the differences (α–γ) have the same value, a constant error appears to be indicated, either in my measurements or in those of Fraunhofer. That an error of this character cannot have affected the value of Θ in my measurements, is evident from the fact that the value of this angle was obtained from mutually agreeing observations on four different spectra. The introduction of such an error into. Fraunhofer’s measurements is equally inadmissible, since on calculating the wave-lengths of the lines from C to G (which Fraunhofer also observed in the second interference-spectrum, though he did not introduce them into his calculation), the following mutually according values are obtained from the two spectra:—
It is only for the line G that the difference is somewhat greater.
The reason of the differences (α–γ), therefore, must arise from an erroneous determination of the value of e; which latter may have been caused either by a wrong enumeration of the lines in one of the two gratings, or by an incorrect estimation of their breadth. In order to make the two values of the wavelengths for the line D agree, in the series (α) and (γ), by altering the value of e, the breadth of Nobert’s grating would have to be diminished by
0·0123 of a Par. line =0·001025 of a Par. inch,
or the number of lines in the grating increased by 6.
The same object would be attained by increasing the breadth