Holtzmann's Law is a Proto-Germanic sound law originally noticed by Adolf Holtzmann in 1838.
The law affects the "doubling" or Verschärfung of PIE * -y- and * -w- to Proto-Germanic * -jj- and * -ww-, which further "hardened" to -ggj-/-ggv- in Northern and to -ddj-/-ggw- in Eastern dialects, while in West Germanic the group results in a diphthong.
The conditions of the sound change were long debated, since there is a seemingly random distribution of affected and unaffected words. At first, dependence on word accent was assumed, parallel to Verner's Law. One currently accepted solution, first proposed by Smith (1941), postulates dependency on the presence of a PIE laryngeal.
According to Lehmann (2007), the lengthening occurs as in the contexts of PIE * -VwH-, * -iyH-, * -ayH-, * -aHy- (where V is any short vowel, and H is any laryngeal).
An example is Old Norse tryggva "make trusty", Gothic triggwa "alliance", Old High German treuwa "faith", all from Proto-Germanic * triwwō, PIE * drewā.
The egg word is problematic: Gothic * addjis (Crimean Gothic ada), Old Norse egg, Old High German ei, Old English ǣg may be from Proto-Germanic * ājjam, PIE * oh₂yom. The plurals Old Norse eigir, Old English ǣgru exhibit an s-stem, Proto-Germanic * ajjaz-.[1]
Some linguists (e.g. Joseph Voyles)[1] hold that Holtzmann's Law represents two separate and independent sound changes, one applying to Gothic and another to Old Norse, rather than being a common innovation. This is supported by James Marchand's[2] observation that a Runic inscription (niuwila on the Naesbjaerg bracteat of the 5th century) and an early loan into Finnish (kuva "picture", cf. Gothic skuggwa) do not exhibit this change. If true, this would prevent Holtzmann's law being used as an example of early Gotho-Nordic unity, in which context it is often cited. Voyles's explanations of the changes do not involve laryngeal theory.
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