XXI. A freehand graphic way of determining stream lines and equipotentials
Lucy Richardson · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · 1908
I. On the need for new methods.II.The first idea of freehand solution and confirmation of its accuracy.III.The conditions which the solution of ~72V=0 must satisfy in order that it may be determinable by a single graph.(a) When the guiding lines are normal to a family of surfaces.Possible types--test cases.(5) Thin shells.(e) Screw symmetry--example.IV.Points and lines of equilibrium.V. Equations other than Laplace's--varlable conductivity.~I.Boundary conditions.uMiscellaneous notes on draughtsmanship.u Estimation of errors.I.The Need for _/Ve~ Methods.T HE Laplacian differential equation bW bW.bW = ohas received an extraordinary amount of atfention during the last century owing to the great number of physical quantities, the space distribution of which can be determined from its integrals.The analytical integrals hitherto obtained by such means as Fourier series, Bessel functions, spherical and other harmonics make it possible to determine the distribution when the boundary conditions bear relation to certain simple types of surface, such as parallelipipeds, cylinders, spheres, ellipsoids, anchor rings, &c.Now for physical research this is well enough.It is usually possible to arrange the instruments so that the parts involved-are of these simple forms.The wires may be wound in circular rings of small cross-section, as in Helmholtz's galvanometer.The pieces of substance for the measurement of specific properties may be shaped into square bars, as in Forbes's experiments on the flow of heat.Or, as in Kelvin's