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Geometrical Quantities of a Parallel Isothermal Surface System and Their Graphical Representations. Dr. Tsunezo Kawasakiya. This paper deals with the theory of analytical expression of geometrical quantities of casting moulds or furnace walls, in which isothermal sufaces are assumed to be parallel. By introducing a new set of coordinates originated by the author, the distance, area and volume of an isothermal surface system are expressed in the most general forms, containing hyperbolic functions and two constants which the writer caHs "form factor" and "discriminating area". The writer defines a geometrical resistance as the definite integral of the reciprocal of area with respect o its distance, and also a geometrical contact resistance as the reciprocal of contact area. Subsequently two integral quantities are given, which are expressed in the most general forms and useful to express the thermal energy stored in an isothermal surface system. Simpler expressions are given for special cases. A universal chart is prepared for representing geometrical quantities and finally a numerical example is given to illustrate he applications of graphical and mathematical calculations.