The spectrum interval sorter recently described by the writer has been considerably modified to increase its accuracy and convenience. Probability considerations of the relative numbers of real and accidental interval coincidences to be expected in typical complex spectra indicate the desirability of applying the combination principle to selected groups of lines, each group to contain not more than a limited number of lines given by their frequency density and by the accuracy with which their frequencies are known. The modified machine greatly facilitates the use of such groups of lines. Sprocket driven perforated paper tape replaces the plain tape previously used, which introduced errors due to mechanical stretching when intervals were recorded which involved a loop of tape greater than four meters in length. With the device in its present form intervals up to 10,000 wave numbers can be recorded with accuracy to ±0.02 wave number. A new system of tape calibration has been introduced, in which a separate punch produces small round holes in the tape at regular intervals, which combine with one another to produce fiducial marks, but do not interfere with the holes representing the spectrum lines. In this way errors due to tape stretch introduced by any cause whatever are apparent at a glance. Electric drive and mercury arc illumination have been provided so that the recording speed has been greatly increased, and the instrument will record when the tape is sent in either direction, thus eliminating rewinding. Separate motors are used for tape drive, record drive, and tape winding, giving great flexibility in the choice of scales for the coordinates wave number and wave‐number interval. Applications of the instrument to the spectra of osmium, iridium, and cerium have been made and have already given results which indicate its value. Its use makes very evident the fact that improved wave‐length measurements are greatly needed for further analyses of the spectra of the rare earths.