scalar adj.

[weighing instrument] early 15c., extended to the whole instrument from the earlier sense of "pan of a balance" (late 14c.); earlier still "drinking cup" (c. 1200), from Old Norse skal "bowl, drinking cup," in plural, "weighing scale."

This is from a noun derivative of Proto-Germanic *skæla "to split, divide" (source also of Old Norse skel "shell," Old English scealu, Old Saxon skala "a bowl (to drink from)," Old High German scala, German Schale "a bowl, dish, cup," Middle Dutch scale, Dutch schaal "drinking cup, bowl, shell, scale of a balance"), from PIE root *skel- (1) "to cut."

The connecting sense seems to be of half of a bivalve ("split") shell used as a drinking cup or a pan for weighing; compare scallop, which is from the same root. But according to Paulus Diaconus the "drinking cup" sense originated from a supposed custom of making goblets from skulls (see skull). Scales as a name for the zodiac constellation Libra is attested in English from 1630s.