usual association (which is reflected in most languages) of light with joy (cf. with the R. светлое настроение; светло на душе).
The meaning of the adjective sad in Old English was "satisfied with food" (cf. with the R. сыт(ый) which is a word of the same Indo-European root). Later this meaning developed a connotation of a greater intensity of quality and came to mean "oversatisfied with food; having eaten too much". Thus, the meaning of the adjective sad developed a negative evaluative connotation and now described not a happy state of satisfaction but, on the contrary, the physical unease and discomfort of a person who has had too much to eat. The next shift of meaning was to transform the description of physical discomfort into one of spiritual discontent because these two states often go together. It was from this prosaic source that the modern meaning of sad "melancholy", "sorrowful" developed, and the adjective describes now a purely emotional state. The two previous meanings ("satisfied with food" and "having eaten too much") were ousted from the semantic structure of the word long ago.
The foot of a bed is the place where the feet rest when one lies in the bed, but the foot of a mountain got its name by another association: the foot of a mountain is its lowest part, so that the association here is founded on common position.
By the arms of an arm-chair we mean the place where the arms lie when one is setting in the chair, so that the type of association here is the same as in the foot of a bed. The leg of a bed (table, chair, etc.), though, is the part which serves as a support, the original meaning being "the leg of a man or animal". The association that lies behind this development of meaning is the common function: a piece of furniture is supported by its legs just as living beings are supported by theirs.