Modern engineering employs the use of the cathode-ray oscillograph as a means to solve some of its problems. A Lissajou figure produced on the cathode-ray tube provides a convenient method of determining the phase difference between two sinusoidal variations of the same frequency. The figure is, in general, an ellipse and this note gives the mathematical basis of the method of determining the phase angle in terms of the axes of the ellipse and of the sides of the principal circumscribing rectangle (whose sides are parallel to the injection axes).