Whenever the Mayor or, in his or her absence, the President of the Council, shall find on the basis of accumulated snowfall that street conditions make it necessary that parking on streets outside of the Business District as referred to in the previous section be prohibited or restricted for snowplowing and snow removal and related purposes, he or she may put into effect a parking prohibition on parts of or all of such streets outside of the Business District by declaring that parking be prohibited for the first 24 hours after snowfall has ended and no vehicle shall be parked on the west and south sides of any such street. For the second 24-hour period after snowfall has ended, no vehicle shall be parked on the north and east sides of any street outside of the Business District.