mild: [OE] Mild goes back ultimately to Indo- European *meld-, *mold-, *mld-, which denoted ‘softness’ and also produced English melt and Latin mollis ‘soft’, source of English mollify and mollusc. From it was derived the Germanic adjective *milthjaz, whose modern descendant has shown remarkable formal stability: German, Dutch, Swedish, Danish, and English all share the word mild. => melt, mollify, mollusc, smelt
mild (adj.)
Old English milde "gentle, merciful," from Proto-Germanic *milthjaz- (cognates: Old Norse mildr, Old Saxon mildi, Old Frisian milde, Middle Dutch milde, Dutch mild, Old High German milti, German milde "mild," Gothic mildiþa "kindness"), from PIE *meldh-, from root *mel- "soft," with derivatives referring to soft or softened materials (cognates: Greek malthon "weakling," myle "mill;" Latin molere "to grind;" Old Irish meldach "tender;" Sanskrit mrdh "to neglect," also "to be moist"). Originally of persons and powers; of the weather from c. 1400, of disease from 1744. Also in Old English as an adverb, "mercifully, graciously."
Mild goes further than gentle in expressing softness of nature; it is chiefly a word of nature or character, while gentle is chiefly a word of action. [Century Dictionary]