Old English milde "gentle, merciful," from Proto-Germanic *milthjaz- (source also of 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 from root *mel- (1) "soft."
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]