The county commission in all counties of the first class not having a charter form of government, except first class noncharter counties containing any part of a city with a population of three hundred thousand or more, in addition to the power to levy taxes for county purposes, as otherwise provided by law, shall have the power to levy upon all property subject to its taxing powers, an annual tax in an amount not to exceed ten cents on each one hundred dollar valuation for the purpose of operating or maintaining a public county health center or institution.