90 
THE ASTRONOMER ROYAL, CORRECTED WAVE-LENGTHS 
comparison of them was the following : — From G (wave-length about 0*00043000 millim.) 
to F (49000), although the required corrections are very large, there is no sensible 
o 
doubt on their value ; and the measures of Angstrom and Ditscheiner, where they are 
comparable, agree closely. As far as 49400, their accord is good ; from that point to 
about 51600, Ditscheiner only has given measures. From 51600 to 54000 their 
measures begin to diverge, and from that point to 56000 they are irreconcilable. Single 
observations of each at 59000 (D) agree fairly, and they support this inference from 
Ditscheiner’s measures, that, whatever be the principle adopted in drawing the final 
curve, there must be a cusp at D. I conceive, therefore, that Kirchhoff made some 
important change in the adjustments of his apparatus at that point. From 61000 to 
62000 the two systems of measure cannot be reconciled. Near 65800 (at C) the dis- 
agreement, though smaller, is too large, and near 68900 (at B) it is much larger. After 
this, the only measure is one by Angstrom, for A. 
From this statement it will appear that the adoption of a correction-curve is by no 
means a straightforward process. In the following steps I have been guided in great 
measure by the wish to make as few sinuosities as possible. From G to a point beyond 
E (about 54000) there is no general difficulty, and I have given nearly equal values to 
the two series of points. From 54000 to the cusp at D, and again from the cusp at D 
o 
to C, I have abandoned Angstrom entirely, the points of Ditscheiner giving very good 
curves. But I cannot very well introduce Ditscheiner’s one remaining measure (that 
o 
at B), and I have continued my curve through Angstrom’s two last points, for B and A. 
I need not explain to any person who has had much familiarity with operations of this 
kind, how great has been the advantage of possessing, as basis of comparison, a series 
of numbers computed on a continuous formula, even though that formula be inaccurate. 
Having thus adopted my curve, I measured its ordinates for every 500 in the final 
figures of the subdivisions of millimetres represented by 0*00000004 millim. In order to 
extend the Table so as to give the results for every 100 in the final figures, it was 
necessary, after giving due attention to the progress of the differences preceding and 
following that difference which is to be divided into five parts, to decide on values of 
correction which would produce an harmonious flow in the second differences at the 
reduced intervals. No great difficulty, however, was found in this process. The Table 
thus formed of corrections to the wave-lengths printed in the Philosophical Transactions, 
1868, is the following. 
