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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
of Fraunhofer’s grating by
0·00061 of a Par. inch,
or by diminishing the number of lines by 5.
That the second decimal is wrong in the above breadth (= 9·0155 lines) of Nobert’s grating is not probable; far more so is the supposition of an error of about half this magnitude in the estimation of the breadth of Fraunhofer’s grating, especially since the microscope, forty years ago, had not reached its present high degree of perfection. Fraunhofer, moreover, was compelled to strengthen the extreme lines of his grating, in order to see them more distinctly when measuring, a circumstance which may possibly have affected the positions of these two lines.
Besides the fact that my measurements agree with the results which Fraunhofer obtained by means of the grating No. 4, there is another reason in favour of the assumption that the differences (α–γ) arise from an incorrect value of e in Fraunhofer’s glass grating. For the above-cited memoir of Fraunhofer’s contains measurements made with another glass grating for which e had the considerably greater value of
0·0005919 of a Paris inch.
Fraunhofer made no use of these measurements, probably because this grating proved to be far less perfect, the spectra on one side of the axis being twice as intense as those on the other. On calculating these measurements, however, we obtain the following values corresponding to the lines from D to G:—
These values, compared with the series (α), indicate a constant difference; here, however, the differences amount only to
1·25, 1·14, 1·13, 1·63,
or to about one-third of those last given.
Now, since this last grating was nearly five times as coarse as the former, and probably also broader, it must have been easier to determine accurately its corresponding e. This circumstance