The Researches in Spectrum-Analysis in which I have been engaged are opening out into so many lines of work that I think it desirable to communicate to the Royal Society the present state of the inquiry on its most general aspect, and also to enter somewhat into detail on some of the points to which my attention has specially been directed, the more so as the methods employed are such as can be, and I sincerely trust will be, taken up by other workers. To commence, then, by a general statement, I may remark that I have in the first place endeavoured to determine whether the new method of spectroscopic observation, which I have before described to the Royal Society, is really as competent as it promised to be in the quantitative direction, what are the conditions essential to its successful employment, and how far it would take us.