שאינו מאיר ונאחז בפתילה בלי שמן

that it does not shed light nor is it retained by the wick, without oil,

By nature, fire strains upward; it will not remain below unless restrained by a wick or wood, for example. But a wick alone is rapidly consumed, and the fire vanishes quickly. Moreover, the burning wick produces a dim and smoky light, for it consists of material insufficiently refined to be completely absorbed by the flame. Oil, on the other hand, is completely transformed into the flame and absorbed by it; burning steadily, it produced a pure and clear light.

This is what is meant by the Alter Rebbe’s statement that without oil “the flame of the candle (a) does not shed light, (b) nor is it retained by the wick.”

Returning now to the point of the analogy:

וכך אין השכינה שורה על גוף האדם שנמשל לפתילה, אלא על ידי מעשים טובים דווקא

similarly, the Shechinah does not rest upon man’s body, which is compared to a wick, except through man’s performing good deeds.

The body can only act as a wick, not as oil. It is a coarse physical being which will not be absorbed within the light of the Shechinah, but will always remain separate from it. The good deeds that man performs provide the oil.

ולא די לו בנשמתו, שהיא חלק אלוה ממעל, להיות היא כשמן לפתילה

It is evident from the Zohar, however, that one’s soul, although a part of G‑d above, is insufficient to serve as oil for the wick.

A question is implied here. Why should the soul, itself divine, and thus certainly suited to being absorbed within the light of the Shechinah, require anything external (such as good deeds) to serve as oil for that light? Surely the soul itself should constitute the oil!

מבואר ומובן לכל משכיל

But the reason for this — the Alter Rebbe now concludes the sentence begun earlier with the words “The meaning of this analogy” — is clear and understandable to every intelligent person.