This paper continues the investigation of a previous ones entitled "Luminous Vapour from the Mercury Arc, and the Progressive Changes in its Spectrum." Several points (it is hoped) are cleared up, and new phenomena are described. Needless to say, much remains to be done. The present work is an instalment only. 1. Conditions for the Appearance of Higher Members of Spectrum Series . It was found that the lines of the diffuse series from M = 12 upwards, 1 p1 - 12 d , 1 p1 - 13 d etc., were seen in the distilled mercury vapour, but not in the arc from which the distilled vapour came. This point has now been examined more closely.