Ham Sa translated as the "Divine Swan" a symbol of purity. Ham Sa is actually an India Goose, a most elegant bird, but called a swan because of the English tradition of denigrating geese.

Sometimes called the So Hum breath. They are actually the same Mantra.  The syllables are reversed according to whether one inhales or exhales first.  According to the grammar of the Sanskrit language, when the syllables are reversed, so becomes sa. Ham Sa is a Mantra Affirming  I AM THAT I AM, a very powerful mantra.

In meditation you mentally repeat this mantra to harmonise with the breath. You may start off with So on the out breath and Ham on the in breath and soon it feels like a circle so you don’t really know what is in or out. So Ham is the natural sound and rhythm of the breath. You repeat this mantra all  the time naturally with every breath you take.

The space between the inward breath of HAM and before the beginning of the outward breath of SO, where the mind is still, is the space of the SELF. As you meditate the silent space may become more extended.

When you reach a point in which the mind is still, it is time to let go of the Mantra and simply BE in the awareness of GOD.

So Ham is found in many religions. Exodus 3:14 It was the I Am That I Am which Moses was given as the name of God. Ham on the IN breath and So on the OUT breath is happening all the time from the first breath you take at birth and the last breath you will  take at your leaving this planet. Becoming a conscious breather it is being aware of this powerful mantra going on all the time, it is happening spontaneously with every breath you take.  You take about 21,000 breaths a day so this mantra is repeated that many times.   It is the prayer of life in this body connecting us to  the Supreme Being, God.