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Schmidt (1959) speculated that the star formation rate is proportional to a power
of the surface density of the interstellar medium
where the power seems between 1 and 2 around the solar vicinity.
If , the star formation rate is thought to be determined by the collision rate
of interstellar clouds.
At that time Schmidt showed us .
On the other hand, if the gas passing through the galactic arms forms stars,
the star formation rate seems proportional to the gas surface density and the arm-to-arm
Thus this predicts .