last flat. This (if there are more than one flat) will coincide with the second last flat. XVI. Writing the series of flat fifths in two alternate columns, as we did the sharp ones, they will form two sets of notes falling in natural succession from C and F alternatelythus: 0 C 1 F The number of flats required by these key notes being placed beside them, it is evident that if a piece is to be transposed lower in pitch, we must add 2 flats in the signature for each note it is lowered, in order to get the right signature for the key of the new pitch it is to be put into. This, in the case of a piece already written in sharps, would be the same thing as taking off two of the sharps. Similarly in the case of raising a piece a note, which we spoke of in considering the sharps-instead of adding two sharps-if we had the piece originally written in a flat key, the same result would be obtained by taking off two flats. XVII. Another useful rule may be got by comparing the two successions of sharp and flat fifths. (Sharp Keys) . SERIES IX. C, G, D, A, E, B, #F, # C. C, F, DB, bE, bA, bD, bG, bC. Examining this arrangement, it is seen that if any key-note has a certain number of sharps, the same note flattened has a number which is the difference between that number and 7, as its allowance of flats; or, the signatures in sharp keys are the complements to 7 of the signatures in flat keys : Now from this it results that, without altering the notes in which a piece is written, we may at once transpose it a semitone lower or higher by playing it in the complementary number of flats or sharps. Thus, a piece written in 3 sharps may be played as if in 4 flats from the same written score (except any accidental sharp or flat it may contain), and this will lower its whole pitch one semitone Or, if written in 4 flats, it might be raised a semitone by 'being played as if written in 3 sharps, without needing to alter the score (except in any accidental sharps or flats it contains). Often, in instrumental playing, sharp keys may be easier than flat ones, or vice versa, and an immediate change can thus be effected; or in singing, the voice may want a little easing in pitch, which is thus easily given, These results we have arrived at from the useful succession of fifths will, it is hoped, clear the way in sundry difficulties of home music, adding to its easy understanding and so to its pleasure. THE ANATOMY OF THE RIVER-MUSSEL. BY JOHN C. GALTON, M.A. (Oxon) F.L.S. LECTURER ON COMPARATIVE ANATOMY AT CHARING-CROSS HOSPITAL., [PLATE LXII.] "Molluscorum scilicet testas inhabitantium anatomiam instituere, eorumque internam structuram, partium formam et compagem, situs, nexus, atque usus declarare; sive, ut verbo complectar, eorum zoologiam ac physiologiam simul persequi, opus certe pro rei dignitate eximium atque præstantissimum, prout est ceterorum omnium intricatissimum atque difficillimum."-POLI. IN N the POPULAR SCIENCE REVIEW for April 1869, the leading characters of the great sub-kingdom Mollusca were ably sketched by Mr. St. George Mivart, F.R.S., and illustrated by the anatomy of the cuttle-fish. In the present article it is proposed to give an account, as concise and accurate as possible, of the structure and zoological affinities of one of the classes of the above sub-kingdom, namely, the Lamellibranchiata (leafgilled molluscs), as the type of which the common river-mussel (Anodonta cygnea) has been chosen. The Lamellibranchs are the only representatives of one of the two divisions into which, according to Professor Huxley (Hunterian Lectures, 1868), the Mollusca may be conveniently divided, namely, the Anodontophora, or those which are devoid of any "odontophore," or tooth-bearing tongue; the Odontophora comprising the rest of the Mollusca, such as the snails and slugs which breathe by means of gills or of a pulmonary sac, the cuttle-fishes, and the oceanic "sea-butterflies," certain of which, as the Clio Borealis, form the principal part of the food of the baleen-whales. The various species of river-mussel, of which Anodonta cygnea, Unio tumidus, U. pictorum, and U. margaritifer are British representatives, have been classed together in a family termed, by poetical license, "Naiades"river-nymphs. If a river-mussel shared our perplexity, it would doubtless exclaim, in the language of Keats : "Why it is thus, one knows in heaven above: But, a poor Naiad, I guess not." |