The accompanying map of the solar spectrum between the limits of λ 7150 and λ 10,000 is made from photographs taken with the diffraction gratings, and is more complete in every respect than the map from λ 7600 to λ 10,000 which appeared in the Phil. Trans, for 1880, under the title of “The Method of Mapping the Least Refrangible End of the Spectrum.” In the map which accompanied the paper above referred to the scale numbers attached to the different lines have more accuracy than the wave numbers, and it was to correct the latter that the new series of photographs have been taken. It is my intention at some future and indeterminate time to publish the photographs of this region in connexion with Professor Rowland’s new photographic spectrum which he has in hand, and these will show the minute features of the spectrum down to a wave-length of nearly double that shown; but as the wave-lengths adopted for the visible spectrum by Professor Rowland differ slightly from those given by Ångström, I Lave thought it better to publish the part which, is to supersede the map of 1880 on the latter scale, leaving the discussion of the true wave-numbers to a later period. It must be recollected at the time the first map of this region was made that the photographic process employed was comparatively new—that is to say, it had been brought to its true state of perfection but a short time. Four years have elapsed since then, and much experimental work has been undertaken in connexion with it; and moreover the instrumental defects which were then present have been remedied to a large extent, new apparatus having been procured and finer gratings having been employed.