The translation used here: Love = metta, compassion = karuna, equanimity = upekkha, sympathetic joy = mudita. I would have preferred to translate mudita as "empathetic joy" rather than "sympathetic joy".
Unbounded love guards compassion against turning into partiality,
prevents it from making discriminations by selecting and excluding and
thus protects it from falling into partiality or aversion against the
Love imparts to equanimity its selflessness, its boundless nature and
even its fervor. For fervor, too, transformed and controlled, is part
of perfect equanimity, strengthening its power of keen penetration and
Compassion prevents love and sympathetic joy from forgetting that,
while both are enjoying or giving temporary and limited happiness,
there still exist at that time most dreadful states of suffering in
the world. It reminds them that their happiness coexists with
measureless misery, perhaps at the next doorstep. It is a reminder to
love and sympathetic joy that there is more suffering in the world
than they are able to mitigate; that, after the effect of such
mitigation has vanished, sorrow and pain are sure to arise anew until
suffering is uprooted entirely at the attainment of Nibbana.
Compassion does not allow that love and sympathetic joy shut
themselves up against the wide world by confining themselves to a
narrow sector of it. Compassion prevents love and sympathetic joy from
turning into states of self-satisfied complacency within a
jealously-guarded petty happiness. Compassion stirs and urges love to
widen its sphere; it stirs and urges sympathetic joy to search for
fresh nourishment. Thus it helps both of them to grow into truly
boundless states (appamañña).
Compassion guards equanimity from falling into a cold indifference,
and keeps it from indolent or selfish isolation. Until equanimity has
reached perfection, compassion urges it to enter again and again the
battle of the world, in order to be able to stand the test, by
hardening and strengthening itself.
Sympathetic joy holds compassion back from becoming overwhelmed by the
sight of the world's suffering, from being absorbed by it to the
exclusion of everything else. Sympathetic joy relieves the tension of
mind, soothes the painful burning of the compassionate heart. It keeps
compassion away from melancholic brooding without purpose, from a
futile sentimentality that merely weakens and consumes the strength of
mind and heart. Sympathetic joy develops compassion into active
Sympathetic joy gives to equanimity the mild serenity that softens its
stern appearance. It is the divine smile on the face of the
Enlightened One, a smile that persists in spite of his deep knowledge
of the world's suffering, a smile that gives solace and hope,
fearlessness and confidence: "Wide open are the doors to deliverance,"
thus it speaks.
Equanimity rooted in insight is the guiding and restraining power for
the other three sublime states. It points out to them the direction
they have to take, and sees to it that this direction is followed.
Equanimity guards love and compassion from being dissipated in vain
quests and from going astray in the labyrinths of uncontrolled
emotion. Equanimity, being a vigilant self-control for the sake of the
final goal, does not allow sympathetic joy to rest content with humble
results, forgetting the real aims we have to strive for.
Equanimity, which means "even-mindedness," gives to love an even,
unchanging firmness and loyalty. It endows it with the great virtue of
patience. Equanimity furnishes compassion with an even, unwavering
courage and fearlessness, enabling it to face the awesome abyss of
misery and despair which confront boundless compassion again and
again. To the active side of compassion, equanimity is the calm and
firm hand led by wisdom — indispensable to those who want to practice
the difficult art of helping others. And here again equanimity means
patience, the patient devotion to the work of compassion.
In these and other ways equanimity may be said to be the crown and
culmination of the other three sublime states. The first three, if
unconnected with equanimity and insight, may dwindle away due to the
lack of a stabilizing factor. Isolated virtues, if unsupported by
other qualities which give them either the needed firmness or pliancy,
often deteriorate into their own characteristic defects. For instance,
loving-kindness, without energy and insight, may easily decline to a
mere sentimental goodness of weak and unreliable nature. Moreover,
such isolated virtues may often carry us in a direction contrary to
our original aims and contrary to the welfare of others, too. It is
the firm and balanced character of a person that knits isolated
virtues into an organic and harmonious whole, within which the single
qualities exhibit their best manifestations and avoid the pitfalls of
their respective weaknesses. And this is the very function of
equanimity, the way it contributes to an ideal relationship between
all four sublime states.