Both Uses of

correspond
in
Frankenstein - 1831 version

You must pardon me if I regard any interruption in your correspondence as a proof that your other duties are equally neglected.
p. 56.4 *

correspondence = communication by writing letters

I remembered also the necessity imposed upon me of either journeying to England or entering into a long correspondence with those philosophers of that country whose knowledge and discoveries were of indispensable use to me in my present undertaking.
p. 157.5

Definitions:

(1) (correspond as in: corresponding time period)
connect or fit together by being equivalent, proportionate, or matched

(Two things are equivalent if they have the same or very similar value, purpose, or result.)
(2) (correspond as in: corresponding by email)
communicate -- typically by writing letters or email

A corresponding secretary is an officer of an organization who is responsible for managing the organization's correspondence and keeping a record of it.
(3) (correspondence as in: a correspondence course)
done from afar

For example, a corresponding member or a correspondence course.

This sense of corresponding arose because people who lived in distant cities and could not be present for meetings, could communicate by sending written communications.
(4) (correspondent as in: foreign correspondent of the paper)
a reporter or other representative -- typically from a foreign country or with a particular expertise