"Helps by the Way. No. 7. The Greek Prepositions." by Charles H. Welch
in The Berean Expositor circa 1914-15.

Eis. -- This preposition (the opposite of ek, out of, considered in our
last paper), properly answers the question 'whither?' and may be
generally translated "into."

The underlying idea of motion, common to most prepositions, is well
seen in this word.  "Come into the house" (Matt. ii.11).  "Cast into
the fire" (Matt. iii.10).  In Luke x.36 and Acts iv.17 it is translated
"among," but in each case the direction of the motion, the goal, or end
in view, is quite evident.

In Mark xi.8 and Matt. xxvi.6 it is rendered "in," and in Mark viii.23
it is "on."  It sometimes is enough to render the word by "to"
(thitherward) as in John xi.38, "Cometh to the grave."  To translate
the word by "into" would produce a false impression on the mind (cf.
verse 41). So in John iv.5, the Lord came UNTO, but not into Sychar
(see verses 8 and 28).  So again in John xx.1, Mary Magdalene came
UNTO, but not into the sepulchre (see verse 11). The underlying idea of
the direction of motion may be felt in the expression "bind them into
bundles" (Matt. xiii.40).  "Rent into two" (Mark xv.38).

Sometimes eis is best expressed by the word "against," e.g., " Against
the Son of man" (Luke xii.10).  "Sinned against heaven" (Luke xv.18). 
"Trespass against thee" (Luke xvii.3).  When applied to time it
indicates a point of time "against which," "for which," "till which,"
or a period of time "during." "Unto the next day" (Acts iv.3).  "Unto
the end" (John xiii.1).  "Against that day" (2 Tim. i.12).  "For many
years" (Luke xii.19).  The secondary and figurative use of the
preposition signifies aim, purpose, or end, still preserving the idea
of the direction of motion.  "For a testimony" (Matt. x.18).  "For the
remission" (Matt. xxvi.28).  "For good" (Rom. xiii.4).  "To this end"
(Rom. xiv.9).  Eis ti is "Why?", "For what?" (Matt. xxvi.8).  "That ye
may know" (Eph. i.18).

The condition into which something is brought is expressed by eis. 
"Unto an holy temple" (Eph.ii.21).  "Into darkness" (Acts ii.20).

The results of an action.  "Ye come together not for the better, but
for the worse" (I Cor. xi.17).  The preposition sometimes indicates the
object towards which some feeling is directed.  "Use hospitality one to
another" (I Pet. iv.9).  "Lie not one to another" (Col. iii.9).  It
also indicates the person to whom, or thing to which, some statement
refers, as in Acts ii.25, "David speaketh concerning Him," and Eph.
v.32, "I speak concerning Christ and the church."  A desire after
something may be expressed by eis as in Phil. i.23, "Having a desire to
depart" (i.e, unto the departing).

The above are only some of the many ways in which this interesting
preposition is used, but however remote at first the figurative use may
appear from the original meaning of eis, direction of motion will be
found to be the constant fundamental idea.  In combination it occurs in
eisago, "to lead in" (John xviii.16; Heb. i.6); eisakouo, "to hear
favourably" (literally "to hear towards") (Matt. vi.7; I Cor. xiv.21;
Heb. v.7); eiserchomai, eisodos, &c., all of which will repay careful
study.