Apparatus of use in solving field equations of the laplace type by analogue methods

摘要

942,101. Variable resistors. K. W. E. GRAVETT. Sept. 21, 1962, [Oct. 13, 1961], No. 36751/61. Heading H1S. [Also in Division G4] Apparatus for solving a Laplace field equation, e.g.- of a two dimensional or superficial system comprises a supported film of high silver content photo-sensitive material which has been exposed to light, developed, and fixed, having a shape geometrically similar to the system, and of an electrical conductivity for each element dependent on the extent of exposure of such element; the exposure being such that the relative values of conductivity between distinct elements of the film correspond to the relative values of the property affecting the strength of the field existing between corresponding parts of the system; there being provided means for applying an electrical potential between spaced locations of the film and means for determining the electrical potential or potential gradient at any desired part of the film. A photographic plate 1 which has been exposed to light, developed, and fixed is provided with fixed electrodes 2, 3 of silver paste which are connected to a fixed direct voltage 4; the conductivity of the film between different elements of the plate having been regulated in accordance with the varying values of the property affecting the strength of the field in the system by exposure to projected images of differing brightness or through light obturating masks. The potential at any point of the plate is determined by applying thereto a variable electrode 5 (e.g. a lead pencil) connected through galvanometer 6 to the slider of a potentiometer 8 across the voltage source. Equipotential lines may be plotted by setting the slider to a series of predetermined potential values and tracing lines on the film with the electrode at which 6 is undeflected, and spot potential values may be obtained by positioning the electrode and adjusting the potentiometer for a null reading at each point. A symmetrical three-dimensional field equation may be represented by using a film whose conductivity has a continuing over-riding gradation from one side to the other obtained by exposure through a suitable filter, and an asymmetrical field equation may be represented by using plural conducting films with electrodes connected in parallel. Circular and nonplanar, e.g. curved films may be employed for special problems.