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Lingua aspera . . . . . . . . . . . . Praeoperculum squamosum, limbo

denticulato, nudo. Operculum squamosum, integrum, inerine. Interoperculum nudum, minutissime denticulatum. Caput epunctatum. Squamae aspera . . . . . . . . . . . Cirri duo ad symphysin maxillae inferioris. Suborbitaria eroso-dentata. Pinna Dorsalis et Analis nudae, basi in sulco sita, antice elevatae: spinis tenuibus, paucis. Pinna caudalis furcata, squamosa. Pinnarum Ventralium radio primo molli, flexili, articulato nec spinoso-pungente; ultimo libero.

Caeca numerosissima, parva. s. temuia, densissime fasciculata.

Vesica natatoria mediocris, simplex, elliptica.

D. 5 + 36

P. l 4-16 v. 17. . . . . . . . W. 1 + 6 . . . . . . . .

M. B. 4 . . . . . Vert". 29. . . . . . .

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BRAMA.
(B. Raii Bl.)

Exteriores uniseriati. .. Interiores - la scobinati Maxillae. * I in fascia Dentes J superioris angusta. . . In fascia Palati angusta. Womeris Nulli. Maxillae ș Biseriati, fascia ininferioris termedia angusta.

Lingua laevis . . . . . . . . . . . . . .

Praeoperculum squamosum, limbo integro, nudo.

Operculum squamosum, integrum, inerme.

Interoperculum squamosum, integrum.

Occiput, nucha,ambitusqueoculorum minutissime punctati.

Squamae laves . . . . . .

Cirri nulli . . . . . . .

Suborbitaria integra . . .

Pinna D. et A. squamosae, antice elevatae: spinis tenuibus, paucis.

Pinna caudalis furcata, squamosa.

Pinnarum Ventralium radio primo (spina) brevi, tenui, vix pungente, haud articulato; ultimo libero.

Caeca quinque; duobus longis, tribus brevibus.

Vesica natatoria nulla.

5 +VIII
C. gr. . . - - -

M. B. 7 . . . .
Wert”. 43. (41, Cuv. et Val.)

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ORD. MAILACOPTERYGIANAF.

Fam. Pleuronectidae (“Poissons plats,” Cut.)

GEN. RHOMBUS, Cuv.
S.S. ii. Oculi remoti; superiore subpostico.

Sp. R. maderensis, Nob.

R. corpore ovali; latere sinistro scabriusculo, etuberculato, olivaceofusco, ferruginascente, annellis punctorum albidorum ocellatim picto: pinnae dorsalis analisque radiis inclusis, indivisis: dentibus minutis, uniseriatis: maxillae superiore ambituque oculorum antice tuberculato-cornutis.

D. 91 – 95; A. 69 – 71 ; C. 15 – 17. P. sinistra 10 v. 11; dextra 9 v. 10. V. sin. 6; dext. 5 v. 6. R. maderensis, nob. in Proceedings of the Zool. Soc. 1833. 1. p. 143. TAB. VI. f. 1. magn", nat".

f. 2. Ejusdem pars anterior lateris dextri.

Hab. rarior in statione navium prope urbem Funchalensem. Ad Insulam Portús Sancti frequentior dicitur.

FUNCHAL, MADE IRA,
July 24, 1834.

Vol. VI. PART I. C C

IX. On Fluid Motion, so far as it is expressed by the Equation of Continuity. By S. EARNshaw, M.A. of St John's College.

[Read March 21, 1836.]

THE difficulty of this subject is so universally admitted, that I hope it will be received as a sufficient excuse for bespeaking the reader's indulgence should any thing occur, in the course of this paper, which he may judge not sufficiently borne out by the arguments on which it is sought to be established.

Though the subject of this communication is by no means new, yet what is brought forward in it will be found to possess some novelty both as to the results obtained, and the manner of treating the subject. Hitherto, nothing more could be done, beyond investigating the differential equations of fluid motion, than to endeavour to generalize the results obtained from a particular integral of the equation of continuity d. p + d, p + d. p = 0. It is manifest, however, that the results of such generalization from a particular case, how skilfully soever deduced, must at least be clogged with some degree of uncertainty, and be therefore in some measure unsatisfactory. But in consequence of the discovery of the general integral of the equation

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not only is the difficulty of the subject shifted farther from the threshold of our researches, being reduced to that of interpreting this integral, but we are able to proceed with a much greater degree of generality.

Vol. VI. PART II. D D

GENERAL PROPERTY.

1. If in a fluid medium we describe a surface whose differential equation is uda + v.dy + widz = 0, the motion of each particle through which this surface passes is in the direction of the normal at the point where the particle is situated.

u, v, w are the velocities, estimated parallel to the co-ordinate axes, of the particle whose co-ordinates are ar, y, x. Let there be another particle in the surface very near to this; and let its co-ordinates be a +da, y + dy, z + dz; and let ds be their distance from each other; by a, 3, y denote the inclinations of ds to the axes. Let also P be the velocity of the former particle, and by a′, so, y denote the inclinations of the direction in which V takes place to the three axes.

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and since, from the nature of the case, neither P nor ds is equal to Zero, ... cos a' cos a + cos 3 cos G + cos y cos y = 0.

But the left hand member expresses the cosine of the inclination of V to do, which being equal to zero, P and ds must be at right angles to each other; that is, the motion of - the particle whose coordinates are w, y, z, takes place in a direction perpendicular to the surface whose equation is

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We may simultaneously draw surfaces of this nature through all parts of the fluid in motion, and shall thus obtain the direction of the motion of every particle. It is manifest that these surfaces are very analogous to the level-surfaces, which occur in investigations concerning the equilibrium of heterogeneous fluids.

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