Piper in 1901 discusses five different systems of aperture marking: the old and new Zeiss systems based on actual intensity (proportional to reciprocal square of the f-number); and the U.S., C.I., and Dallmeyer systems based on exposure (proportional to square of the f-number). He calls the f-number the "ratio number," "aperture ratio number," and "ratio aperture." He calls expressions like 8 the "fractional diameter" of the aperture, even though it is literally equal to the "absolute diameter" which he distinguishes as a different term. He also sometimes uses expressions like "an aperture of f 8" without the division indicated by the slash.