. The Philosophical magazine; a journal of theoretical, experimental and applied physics. ry Definitions.—A source of liquid of strengthm is a point at which a volume of liquid ■iirm is supplied perunit time. A sink (or negative source) of equal strength isa ])oint at which liquid disappears at the same rate. A com-bination of a source and sink of equal numerical strength m,at an infinitesimal distance d apart, is a doublet. As this isanalogous to an infinitely small magnet, I shall call rnd themoment of the doublet. The intensity of a doublet is itsmoment divided by its length; it is analogou
. The Philosophical magazine; a journal of theoretical, experimental and applied physics. ry Definitions.—A source of liquid of strengthm is a point at which a volume of liquid ■iirm is supplied perunit time. A sink (or negative source) of equal strength isa ])oint at which liquid disappears at the same rate. A com-bination of a source and sink of equal numerical strength m,at an infinitesimal distance d apart, is a doublet. As this isanalogous to an infinitely small magnet, I shall call rnd themoment of the doublet. The intensity of a doublet is itsmoment divided by its length; it is analogous to the intensityof magnetization of a bar of unit section. The axis of adoublet is the line from the sink to the source. The lines of flow due to any distribution of sources andsinks are the lines of force due to the corresponding magneticpoles. § 2. Let P, P be a source m and sink —m on the straightline OL: TPL = e ; TPL = & ; TP = r ; PP = d. Then the flow through the circle (of which TT is the pro-jection) formed by revolving T round OL is 27rm (cos ^ —cos 6).Fi-. Let P approach P so that PP diminishes indefinitely,md retaining a constant magnitude /i. Then 27rm (cos 6 —cos 6) = 27r/i sin^ 6. Jr. If the source and sink are interchanged, the sign of the flowis reversed ; we may consider /u, as negative in this case. Pulsating Spheres in a Liquid. 115 Let a doublet of moment —fjJ be placed at Q, where //.>yu,.If TQL = </), TQ = r, the flow through TT due to this is -27r/tsin-</)./?•. The equation of a surface ot revolution across which thereis no flow from the doublets at P and Q is 27r(/x sin- 6. /i—ft sin- (f). /)•) = A, a constant. If A = 0, this reduces to the line OL and the sphere If C be the centre of tliis sphere and a the radius,CP . CQ = a- and a = (a^ -1) PQ/2a, where cc^=,. Since the liquid is supposed to be perfect, and the sphereis part of a surface of flow, we may make a material sphereoccupy its place. Hence the effect of
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