The curve to be analyzed, which must be drawn to a specified scale, as is explained later, is placed underneath the machine; the handles h are grasped with the fingers, and the stylus s is caused to trace the curve, which requires movements in two directions. The machine as a whole rests on rollers which permit it to be moved to and from the operator in the direction of the amplitude of the curve, and the stylus is attached to a carriage which rolls along a transverse track t in the direction of the length of the curve.

The instrument shown has five integrators; each sphere, made of glass, rests on a roller so that when the curve is traced, the sphere is rotated on a horizontal axis by an amount proportional to the amplitude of the curve; two integrating cylinders with dial indexes rest against each sphere at points 90° apart, Fig. 75, and, by means of a wire and pully w are given rotation about a vertical axis proportional to the movement along the axis of the curve.

While each sphere rolls only in amplitude, the cylinders sliding around the sphere take up components of the amplitude motion which are proportional to the sine and cosine of the phase change respectively. The first integrator turns once around its sphere while the tracer moves over one wave length of the fundamental curve, that is, while the stylus is being moved the length of the track t, the next integrator turns twice, and the others three, four, and five times in the same interval. In this manner one tracing gives the ten coefficients, five sines and five cosines, of the first ten terms of the complete Fourier equation of the curve.

In the Henrici analyzer the sizes of the various parts are so proportioned that the effects of the constant factors of the amplitude terms are mechanically incorporated in the dial readings, which are, without reduction (except for the factor n, mentioned below), the actual amplitudes in millimeters of the components of the curve traced.

When the stylus has been moved over one wave length of the fundamental, it must have moved over two wave lengths of the second component, three of the third, and so on; then the integrator for the second component has integrated two waves, and the dial readings are twice the required coefficients; in general, the readings of the nth integrator are n times too large.