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Grassmann's law, named after its discoverer Hermann Grassmann, is a dissimilatory phonological process in Ancient Greek and Sanskrit which states that if an aspirated consonant is followed by another aspirated consonant in the next syllable, the first one loses the aspiration. The descriptive (synchronic) version was described for Sanskrit by Panini.

Here are some examples in Greek of the effects of Grassmann's Law:

• [t^hu-oː] θύω 'I kill an animal'
• [e-tu-t^heː] ἔτυθη 'it was killed'

• [t^hrik-s] θρίξ 'hair'
• [trik^h-es] τριχές 'hairs'

• [t^hap-sai] θάψαι 'to bury (aorist)'
• [t^hapt-ein] θάπτειν 'to bury (present)'
• [tap^h-os] τάφος 'a grave'
• [tap^h-e] ταφή 'burial'

In the reduplication which forms the perfect tense in both Greek and Sanskrit, if the initial consonant is aspirated, the prepended consonant is unaspirated by Grassmann's Law. For instance [p^hu-oː] φύω 'I grow' : [pe-p^huː-ka] πεφυκα 'I have grown'.

The fact that deaspiration in Greek took place after the change of Proto-Indo-European *b^h, d^h, g^h to /p^h, t^h, k^h/, and the fact that no other Indo-European languages have Grassmann's law, show that Grassmann's law developed independently in Greek and Sanskrit; it was not inherited from PIE.^{[citation needed]}

Cases like [t^hrik-s] ~ [trik^h-es] and [t^hap-sai] ~ [tap^h-ein] illustrate the phenomenon of diaspirate roots, for which two different analyses have been given.

In one account, the "underlying diaspirate" theory, the underlying roots are taken to be /t^hrik^h/ and /t^hap^h/. When an /s/ (or word edge, or various other sounds) immediately follows, then the second aspiration is lost, and the first aspirate therefore survives ([t^hrik-s], [t^hap-sai]). If a vowel follows the second aspirate, it survives unaltered, and therefore the first aspiration is lost by Grassmann's Law ([trik^h-es], [tap^h-ein]).

A different analytical approach was taken by the ancient Indian grammarians. In their view, the roots are taken to be underlying /trik^h/ and /tap^h/. These roots persist unaltered in [trik^h-es] and [tap^h-ein]. But if an /s/ follows, it triggers an "aspiration throwback" (ATB), in which the aspiration migrates leftward, docking onto the initial consonant ([t^hrik-s], [t^hap-sai]).

Interestingly, in his initial formulation of the law Grassmann briefly referred to ATB to explain these seemingly aberrant forms. However, the consensus among contemporary historical linguists is that the former explanation (underlying representation) is the correct one.

In the later course of Sanskrit, (and under the influence of the grammarians) ATB was applied to original monoaspirates through an analogical process. Thus, from the verb root gah 'to plunge', the desiderative stem jighak^ha- is formed. This is by analogy with the forms bubhutsati (a desiderative form) and bhut (a nominal form, both from the root budh 'to be awake', originally PIE *[b^hud^h-]).

Grassmann's Law is also known to occur in Ofo, an extinct and underdocumented Siouan language. The law is found in compounds such as the following:

• o´skha "the crane" + afhaⁿ´ "white" : oskạfha "the white egret"

A similar phenomenon occurs in Meitei (Tibeto-Burman) in which an aspirated consonant is deaspirated if preceded by an aspirated consonant (including h) in the previous syllable. The deaspirated consonants are then voiced intervocalically.

• thin- "pierce" + -khət "upward" : thingət "pierce upwards"
• səŋ "cow" + khom "udder" : səŋgom "milk"
• hi- "trim" + -thok "outward" : hidok "trim outwards"

• Chelliah, Shobhana L. (1997). A grammar of Meithei. Berlin: Mouton de Gruyter. ISBN 0-19-564331-3.
• de Reuse, Willem J. (1981). Grassmann's law in Ofo. International Journal of American Linguistics, 47 (3), 243-244.
• Sag, Ivan. A. (1974) "The Grassmann's Law Ordering Pseudoparadox," Linguistic Inquiry 5, 591-607.