There is clearly no theoretical limit to the resolving power of gratings, even in spectra of given order.
For accurate measurement of the displacements of lines of stellar spectra which are produced by the relative motion of star and observer in the line of sight, a very beautiful instrument has been devised by Dr J.
Vogel of Potsdam introduced the method of photographing stellar and terrestrial spectra on the same plate, and in this way obtained an immense advance in the ease and precision of observation.
To derive the stellar velocity in the line of sight relative to the observer it was then necessary to assume that the normal wave-lengths of the stellar and terrestrial spectra are accurately known.
Complex spectra of stars of the solar type this is by no means the case; for, as Dr Hartmann remarks, " in the first place the lines in these spectra are so numerous that their complete measurement and reduction would require many days, and in the second place a rigorous reduction of such material has hitherto not been at all possible because the wave-lengths of the lines are not known with sufficient accuracy.