Cases like ~ and ~ 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 /tʰrikʰ/ and /tʰapʰ/. When an /s/ (or word edge, or various other sounds) immediately follows, then the second aspiration is lost, and the first aspirate therefore survives (, ). If a vowel follows the second aspirate, it survives unaltered, and therefore the first aspiration is lost by Grassmann's Law (, ).
A different analytical approach was taken by the ancient Indian grammarians. In their view, the roots are taken to be underlying /trikʰ/ and /tapʰ/. These roots persist unaltered in and . But if an /s/ follows, it triggers an "aspiration throwback" (ATB), in which the aspiration migrates leftward, docking onto the initial consonant (, ).
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 that an assumption of ATB would require multiple root shapes for the same basic root in different IE languages whenever an aspirate follows in the next syllable — e.g. d for Sanskrit, t for Greek, dh for Proto-Germanic and Proto-Italic (which have no dissimilation) — whereas the theory with an underlying aspirate allows for a single root shape with dh for all languages.
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 /ɡah/ ('to plunge'), the desiderative stem /jiɡʱakʰa-/ is formed. This is by analogy with the forms /bubʱutsati/ (a desiderative form) and /bʱut/ (a nominal form, both from the root /budʱ/ 'to be awake'), originally PIE *bʰudʰ-).
The linguist Ivan Sag has pointed out an advantage of the ancient Indian theory, namely that it explains the fact that there are no patterns like hypothetical " ~ ", which are not ruled out by the underlying-diaspirate theory. However, ATB fails to account for reduplication patterns seen in roots with initial aspirates, such as Greek 'I put' with an unaspirated reduplicated consonant, and so ATB needs to be enhanced with a stipulation that aspirates reduplicate as their unaspirated counterparts. From a diachronic standpoint, the absence of these patterns in Greek is explained by the Proto-Indo-European constraint against roots of the form *T...Dʰ-.
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