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That no appreciable errors can have thereby arisen in the mean values thus obtained—values which may be regarded as true for 15° C. and the mean barometric pressure—is readily seen on calculating the magnitudes of these corrections. Assuming the refraction-coefficient of air to be
to be a constant magnitude, independent of temperature
and pressure, and the value of e, moreover, to hold for 15° C., w. obtain the following corrected value:—
whence we conclude that the correction for log λ amounts to
+ 0·45 (t°–15°)–0·14 (H–0m·76),
expressed in units of the fifth decimal place.
Accordingly a change of 2 degrees in temperature produces a change of 2″ in the value of the angle Θ, if Θ be assumed equal to 25°; this error is comparable with the error of adjustment itself. For smaller values of Θ the error will of course be smaller.
The angle Θ is also subject to a correction dependent upon the absolute motion of the instrument in the direction of the path of the incident ray; this correction, however, is almost inappreciable for the observations upon which the numerical values in the following Table are founded.
The wave-lengths are, like those of Fraunhofer, expressed in units whose magnitude is equal to 0·00000001 of a Par. inch.
Table I.—Wave-lengths, inths of a Paris inch.
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)