Friends:

 

    What is the Tranquillity Link to Awakening?

 

The Tranquillity Link to Awakening (passaddhi-sambojjhanga) has the
characteristic of peace, and the function of stilling, which manifests
as absence of restless trembling. Stillness of feeling, perception and
mental construction is the factor that induces bodily Tranquillity.
Stillness of consciousness itself induces mental Tranquillity.
The proximate cause of Tranquillity is the satisfaction within Joy!
The resulting effect of Tranquillity is the bliss within Happiness!

The Buddha once said: What mental fermentations (āsava) should be
overcome by development? If a Bhikkhu by careful & rational attention
develops the Tranquillity Link to Awakening based on seclusion, based
on disillusion, based on ceasing, and culminating in cool relinquishment,
then neither can mental fermentation, nor any fever, nor any discontent
ever arise in him. MN2 [i 11]

In one who is joyous, the body becomes calm & the mind becomes calm.
The Tranquillity Link to Awakening emerges right there. He develops it,
& for him it goes to the culmination of its development. MN118 [iii 85]

CALMED
Calm is his thought, calm is his speech,
and calm is his deed, who, truly knowing,
is wholly freed, perfectly tranquil and wise.
Dhammapada 96

CONTENT
The one who eliminates discontent, tearing it out
by the roots, utterly cuts it out, such one spontaneously
becomes absorbed in the calm of tranquillity both day & night.
Dhammapada 250

COMPOSED
The one who is tranquil in movement, calmed in speech,
stilled in thought, collected & composed, who sees right
through & rejects all allurements of this world, such one
is truly a 'Peaceful One'.
Dhammapada 378

Further inspirations on the calming & soothing quality of Tranquillity:
http://What-Buddha-Said.net/drops/III/Feeding_Tranquillity.htm