POE KIECHHOFF’S SPECTEAL LINES. 
31 
first differences. Thus I had a complete table of the values of the length of the wave 
of light expressed in Paris inches for every one of Kirchhoff’s lines. Each number was 
then multiplied by 27'0700, and thus I had a complete table of the values of the length 
of the wave of light expressed in millimetres for every one of Kirchhoff’s lines. In 
this state I very carefully revised all the final numbers. This is the table of results 
now offered to the Royal Society. It did not appear necessary to publish a long series 
of results expressed by a measure which is now so nearly obsolete as the Paris inch ; 
although, as will appear below, the possession of those numbers in my own hands has 
proved to be of considerable utility. 
From the description which I have given of the process by which I have computed 
the wave-lengths from Kirchhoff’s measures, it will be perceived that the results are 
not rigorously accurate, unless the same system (whatever it may be) has been rigorously 
followed by Kirchhoff through the whole of his measures. Now Kirchhoff has 
distinctly stated that he did not in every case adapt his prisms carefully to the angle of 
minimum deviation. So far as I could learn by communication (through Professor 
Roscoe) with M. Kirchhoff, no memorandum was preserved on the possible amount of 
the error thus introduced. I was confident, however, as well from the character of 
Professor Kirchhoff as from the absence of any apparent saltus in the measures, that 
the error must be small, perhaps imperceptible. It was a matter of great satisfaction 
to me therefore, after the completion of my work, to be referred to two late series of 
direct measures of wave-length for numerous lines. One is that by Angstrom, published 
in Poggendorff’s ‘ Annalen der Physik und Ohemie,’ CXXIII. Band, p. 498, in which I 
have found 51 lines apparently identifiable with lines measured by Kirchhoff. The 
measures in these series are expressed by the Paris inch ; and the possession of my own 
calculations in terms of the Paris inch, to which I have alluded above, greatly facilitated 
the comparison of Angstrom’s measures with my calculations. The other is that by 
Ditscheiner, published in the ‘ Sitzungsberichte der Mathematisch-Naturwissehschaft- 
lichen Classe der Kaiserlichen (Wiener) Academie der Wissenschaften,’ L. Band, II. 
Abtheilung, 1864, page 340 : it contains direct measures of the wave-length, expressed 
in millimetres, for 107 of the lines measured by Kirchhoff. The comparison of these 
direct measures with my computed values of the wave-length exhibited small discre- 
pancies, of which the greater part arises from discordances between the values for the 
fundamental lines found by Fraunhofer and those determined by Angstrom and Dit- 
scheiner (which those philosophers ascribe to an erroneous evaluation by Fraunhofer 
of his interference-grating) ; a part apparently is produced by faults inherent in every 
process of interpolation among a limited number of values, especially when that inter- 
polation is so extended as to become extrapolation ; but, as I believe, no sensible part, 
or a very small part, can arise from the suspected class of errors in the measures of the 
prismatic dispersion-spectrum. 
I had arrived at this stage of my work, when I became acquainted with Ditscheiner’s 
Essay contained in the £ Sitzungsberichte der Mathematisch-Naturwissenschaftlichen 
f 2 
