This hypothesis states that, if in an acid catalysed reaction, log 10 k 1 (first-order rate constant of the reaction) is linear in H0 (Hammett acidity function), water is not involved in the transition state of the rate-controlling step. However, if log 10 k 1 is linear in log 10 H + then water is involved. This has been shown to be incorrect by Hammett himself.
Source:
PAC, 1994, 66, 1077. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)' on page 1176 (https://doi.org/10.1351/pac199466051077)