The spatial vector and loop allow a more concise description of the heart's total electromotive force at an instant, and throughout the cardiac cycle, than the conventional electrocardiogram and the three-plane vectorcardiogram. The magnitude of spatial vectors and the angles enclosed by these vectors are independent of cardiac position. Their relationship to the cardiac forces is therefore relatively simple. This suggests a promising new approach to the hitherto unrewarding quantitative analysis of the electrocardiogram. With all lead-systems now in common use, the accuracy of quantitative measurement is limited by the errors inherent in Einthoven's hypothesis. These errors are augmented especially with regard to the sagittal component, where vectors are by-products of unipolar chest lead recording as with the ingenious mechanical models of Langner (1952), Urschel and Denton (1952), and Simonson and Ross (1953), and with the electronic method of Donzelot et al. (1950). The phaseshift error, introduced by recording leads separately with a single-channel instrument, is regarded as significant by Holzmann (1945, p. 58) and Burch et al. (1953), and as unimportant by Goldberger (1953). In the present study the frontal lead-pair Y, X and the coronal pair Z, X of the " cube " lead arrangement, were recorded with a two-channel electrocardiograph. The technique of recording has been described (Fischmann and Brown, 1954). Spatial vectors have been determined by correlating frontal and coronal lead-pairs. Lead X, which appears in both lead-pairs, is used to identify synchronous points in the two records. NON-QUANTITATIVE METHOD OF ANALYSIS The orientation of the spatial QRS loop is that of its longest vector. In the scalar component lead record, the peak of the greatest QRS deflection (Qy in Fig. 2A; Qz in Fig. 2B; R'y in Fig. 2C) marks the instant corresponding to this vector (Fischmann and Brown, 1954). Consideration of x, y, and z (voltages in leads X, Y, and Z) at this instant, will give the general orientation of the longest spatial QRS vector. As shown in Fig. 1, positive deflections in lead X mean left-, in lead Y head-, in lead Z forward orientation of the instantaneous vector. Thus for instance in Fig. 2A the longest QRS vector is foot-(Qy), left-(Rx), and forward (Rz) orientated. The order of enumeration indicates the relative size of the three components. The small initial r or q, and terminal r' or s deflections in leads X, Y, and Z can be similarly employed to determine the spatial orientation of initial and terminal vectors; x, y, z corresponding to the peak of the greatest T wave, the orientation of the T loop. Records from a normal subject, and from subjects with left and right ventricular hypertrophy, are shown in Fig. 2, and analysed in the legend. 496
