There are so many lead systems of vector-cardiography and their loops vary so much from each other that a great deal of inconvenience arises in the clinical use of vectorcardio-gram (VCG). In order to remove this inconvenience, the author worked out a mutual transformation theory of VCGS based on BURGER'S conception of lead vector to acquire a transformation equation by which a VCG of any lead system could be transformed into a VCG of any other lead system. Mutual Transformarion Theory of VCG When lead vectors of two lead systems A and B are represented by Ai and Bj respectively, the following equation can be induced according to the general principles of vector: Ai=Σ^^3__(j=1)(A←B)<ij>Bi ( 1 ) The i is 1, 2 or 3 ; A1 corresponds to the lead vector A^^→x, A^^→2 to the one A^^→y, and A^^→3 to the one A^^→z. The same is the case with j. The (A←B)ij is transformation coefficient. Equation ( 1 ) holds good whether A^^→i; and B^^→j are orthogonal or oblique respectively. If we get the scalar product of the heart vector H^^→t at a given moment by the lead vec-tor A^^→i, there follows the equation below: H^^→t·A^^→i=Σ^^3__(j=1)(A←B)ijH^^→t·B^^→j (2) H^^→t·A^^→i according to the definition of lead vector, represents the potential differences of the scalar electrocardiograms (SECGs) of Lead System A at a given moment, and so is replaced with VAit· In the same way, H^^→t·B^^→j is replaced with VBit· Thus, the following equation results from Equation (2) : VAit=Σ^^3__(j=1)(A←B) ijVB<jt≥ ( 3 ) The transformation coefficients being computable from SECGs, it is prossible to transform the SECGS of Lead System B into that of Lead System A by using Equation (3). When the electric action of the heart is assumed to be caused by an electric dipole, Equation (3) holds good generally.
