794 
intensity of the unweakened line, is, however, not 100, but smaller, 
and the diminished intensities are all of them smaller in the same 
ratio. Accordingly each of the points of CD must be displaced to 
points where the intensity is smaller in a definite ratio, the value 
of the blackening being retained. As the abscissa represents log i, 
this means a shifting of the points of CD of the same amount 
towards the left. The amount of this shifting is not known a priori, 
but must be chosen so that after the displacement to C’ D’ the 
points of CD lie as much as possible between those of AB. This 
process may be repeated for still fainter lines, and in this way a 
curve of blackening may be constructed ranging from the smallest 
to the greatest of the occurring intensities, and of which many points 
are fixed, though only six spectra with known ratios of intensities 
have been reproduced. 
By the aid of this curve of blackening the intensity at any point 
of another spectrum reproduced on the same plate, may be found. 
3. Determination of position. To determine the position a spectrum 
of comparison has been placed under every spectrum, except under 
that which served for the determination of the curve of blackening. 
These comparison-spectra were photographed at the same position 
of the echelon, so that a definite line of these spectra indicates a 
definite position ') in the image plane of the echelon. 
The position of a detinite line was measured by the determination 
of the distance from this line to a definite line of the comparison 
spectrum with a Zxiss comparator. It is sufficient to measure this 
distance for one line of the spectrum with the comparator, and 
determine the position of the other lines from their mutual distance. 
This is found from the registered curves of the spectra, when once 
the ratio has been determined of the distances of two correspond- 
ing points on the photographic plate and on the registering paper. 
This ratio is a characteristic constant of the micro-photometer. The 
order of magnitude of the error in the localisation was 0.5 °/, of 
the distance of two orders, which amounted to 2 mm. 
4. Results. No exact agreement can be expected on comparison 
of formula (1) with the observations. When the light traverses the 
echelon obliquely, this formula only holds in first approximation. 
In this case @ represents the angle of the light with the optical 
') By position and intensity of a line here and elsewhere the position and intensity 
of the maximum blackened part of the line should be understood. The error 
mentioned on p. 791, therefore, plays a part. 
