This hypothesis states that, if in an acid catalysed reaction,

(first-order
rate constant of the reaction) is linear in

(Hammett
acidity function ), water is not involved in the
transition state of the
rate-controlling step. However, if

is linear in

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
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.