The diagrammatic figure illustrates the principle involved. The vertical full lines represent ordinates of a curve of which the

abscissae are Oa1, Oa2, etc. Let now all these vertical lines be rotated round the points O, a1, a2, etc., while retaining their original lengths, through the same angle θ. The curve passing through the new positions of the end points is now to be referred to the tilted axis Oy0 and the line OAB, drawn at right angles thereto. If we put OC = X, CD = Y, and let X′, Y′, be the corresponding coordinates with reference to the tilted axis we get