Green´s theorem and potentials in a volume conductor

In their recent paper Barr, Pilkington, Boineau and Spach (ibid., vol. BME-13, pp. 88-92, April 1966) present a method for solving the boundary-value problems of interest to electrocardiography based on Green´s theorem. An earlier method was presented Gelernter and Swihart (1964) and the purpose of this note is to point out how it also can be related to Green´s theorem. A more extensive treatment of aspects of this problem is contained in a recent preliminary report by the author (MIT, Research Lab. of Electrollics, Cambridge, MA, Quarterly Progress Rept. 81, pp. 218-226, April 15, 1966. also Biophys. J., January 1967).