In the three last senses or applications, mean is more generally used for medium.

The means or instrument by which any thing is accomplished, conveyed or carried on. Thus money is the medium of commerce; coin is the common medium of trade among all civilized nations, but wampum is the medium of trade among the Indian tribes, and bills of credit or bank notes are often used as mediums of trade in the place of gold and silver. Intelligence is communicated through the medium of the press.

The middle place or degree; the mean. The just medium of this case lies between pride and abjection.

A kind of printing paper of middle size.

mediums; media not being generally, though sometimes used. In philosophy, the space or substance through which a body moves or passes to any point. Thus either is supposed to be the medium through which the planets move; air is the medium through which bodies move near the earth; water the medium in which fishes live and move; glass a medium through which light passes; and we speak of a resisting medium, a refracting medium

In logic, the mean or middle term of a syllogism, or the middle term in an argument, being the reason why a thing is affirmed or denied. Nothing can be honorable that violates moral principle. Dueling violates moral principle. Therefore dueling is not honorable. Here the second term is the medium, mean, or middle term.

Arithmetical medium, that which is equally distant from each extreme, or which exceeds the lesser extreme as much as it is exceeded by the greater, in respect of quantity, not of proportion.