Electrical Axis of the Human Heart. 



55 



from a consideration of the simple trigonometrical ratios of a varying axial 

 angle. 



The transverse lead is the simplest to consider, and its simplest case is that 

 of the horizontal heart in which the axial angle during quiet respiration is 

 90°. In this position, regarding the heart as forming (electrically) a 

 horizontal lever, it is evident that with this type of heart the transverse 

 electrical effect has its maximum value, and that the effect must be 

 diminished by either rise or fall of the diaphragm ; the diminution will be 

 proportional to the sine of the altered axial angle. Taking as unity or 

 10 this maximal value with the chest at rest, we shall have the altered 

 values = 9-8, 9-4, 87, 77, 6'4, 5-0, if with fall of the diaphragm the angle 90° 

 is changed to 80°, 70°, 60°, 50°, 40°, 30°. 



Thus the theoretical alterations of magnitude in the transverse lead with 

 alterations of the axial angle must be in ratio with the numerical values of 

 the sines of the altered angle. And as the reference curve to which to com- 

 pare our observations we have the simple curve of sines : — 



1736 3420 5000 6428 7660 8660 9397 9848 10000 

 at 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 



The superior leads, right and left, come next in order of simplicity. The 

 former (mouth and right hand), as stated in 1889, is " weak," being most 

 nearly in accordance of direction with the direction of the equator ; the latter 

 is " strong," being most nearly in accordance of direction with the direction 

 of the current-axis. The angle EML (fig. 1) is taken as being = 90°. In the 

 case of the horizontal heart with the axial angle = 90° it is evident that 

 the electrical effects along MR, ML, are equal and opposite, with values 

 = + RL(cos 4o ) 2 = + 50. With the axial angle altered + 10° by respira- 

 tion the effects become : — 



Along MR = 100 cos (45°+ 10°) x cos 45° = 40, 

 and along ML = 100 cos (45°- 10°) x cos 45° = 58. 



With a perfectly vertical heart, i.e. with an axial angle = 0°, the effects 

 are again equal, viz., 100(cos 45°) 2 = 50. 



The theoretical alterations of magnitude of the superior leads with 

 alterations of the axial angle must be in numerical ratio with the cosines 

 of the altered angle. We have as the reference curve to which to com- 

 pare our observations, a simple sine curve formed by the tabular values 

 of cosines multiplied by a constant factor to correct for projection between 

 RL and the two sides MR, ML — in this case multiplied by cos 45°. The 

 electromotive values for the superior leads for values of the axial angle from 

 0° to 90° are thus :— 



