INTER-RELATIONSHIP of the FOUR BRAHMA VIHARAS
Here are some excerpts from a beautiful treatise by Nayanaponika Thera, from his Vision of the Dhamma:
Equanimity includes all the other three BV’s and pervades them fully, just as they fully pervade and perfect equanimity.
Love (Metta) imparts to Equanimity its selflessness its boundless nature and even its fervor.
Compassion guards Equanimity from falling into a cold indifference, and keeps it from indolent or selfish isolation.
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.
Equanimity rooted in insight is the guiding and restraining power for the other three sublime states. It guards Love and Compassion from being dissipated in vain quests and for going astray in the labyrinths of uncontrolled emotion.
Equanimity, even-mindedness gives to love an even unchanging firmness and loyalty. It endows it with the great virtue of Patience. It 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 ay dwindle away due to the lack of a stabilizing factor
Isolated virtues if unsupported by other qualities which give the 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.