An explanation is given for the difference between the loudness functions of Richards [(1968). “Monaural Loudness Functions under Masking.” J. Acoust. Soc. Amer.44, 599–605] and the experimental curves previously published by Hellman and Zwilocki [(1963). “Monaural Loudness Function of a 1000‐cps Tone and Interaural Summation,” J. Acoust. Soc. Amer.35, 856–865 (1964). “Loudness Functions of a 1000‐cps Tone in the Presence of a Masking Noise,” J. Acoust. Soc. Amer.36, 1618–1627]. It is shown that most of the difference can be attributed to two factors: a bias introduced by the method of magnitude halving and a misinterpretation of the method of numerical magnitude balance.