It shall be unlawful for the owner of any dog to knowingly or willfully allow his dog to urinate or defecate on public property; provided, that urination by a dog on curbs of streets and in alleys, streets or areas posted by the Town Manager as dog exercise areas shall not constitute a violation of this section; and provided, further, that defecation by a dog on public property out of doors shall not constitute a violation of this section if the owner of the dog immediately removes the material defecated and disposes of it in a manner not inconsistent with the provisions of this section.