In 1880 we described, simultaneously with Dr. Huggins, a series of lines forming the strongest part of the spectrum of water, and again, in 1882, a second, less strong and more refrangible series, forming a second section of the same spectrum. Subsequently, M. Deslandres discovered a third still weaker and more refrangible series, beginning at a wave-length 2610·3. We find, however, that the spectrum does not end there, but extends both on the more refrangible and on the less refrangible sides to a considerable distance. By employing a large spectroscope with a single calcite prism and a long exposure we have obtained photographs of the spectrum of the oxy-hydrogen flame, showing closely set lines from wave-length 2268 to 4100, with traces of lines beyond those limits. The whole spectrum appears to consist of a succession of rhythmical series of lines, the lines of each rhythmical series being stronger and more closely set at the more refrangible end of the series and becoming weaker and wider apart towards the less refrangible end. The strongest of these series are those first described, those on either side of them becoming fainter as they are more remote, until the highest series gave us a measurable photograph only after an exposure of five hours. In most cases two series begin near together and overlap one another, producing a complication which cannot easily be unravelled, and the overlapping appears in some cases to extend to more than two series. M. Deslandres states (‘Comptes Rendus,’ vol. 100, p. 854,) that the first band of the water spectrum ( i. e. , the group beginning at a wave-length about 3063) includes a series of rays which reproduce, line for line, at the same distances and with the same relative intensities, the band A of the solar spectrum; and that the second band ( i. e. , the group beginning at a wave-length about 2811) includes a series corresponding to B, and that in the third α may be found to be reproduced. He does not state at what wave-lengths in these bands we are to look for the more refrangible edges of A, B, and α respectively; and we have not been able to make out such an exact correspondence between the lines of the water spectrum and those of A, B, and α as M. Deslandres’ words seem to imply. Nevertheless, the similarity of the grouping is very remarkable, as may be seen from the accompanying map, on which are given the lines of A, on a scale slightly reduced from Professor Piazzi Smyth's solar spectrum, side by side with the lines of the water spectrum. The correspondence of B and of α to certain lines of the higher groups is less striking. We have no doubt that the peculiar arrangement of the lines, commencing at the more refrangible end with some closely set lines and continued in a series of doublets, is in all these cases the result of a general law.