How to define private class method ruby

cool_class.rb

class CoolClass
  # This is the documentation
  #    # return a string containing Something Cool or Something Coolest !
  #    arg1 = boolean # Default value to true
  #    CoolClass.cool_method # return 'Something Cool'
  #    CoolClass.cool_method(false) # return 'Something Coolest'

  def self.cool_method(arg1 = true)
    return public_method1 if arg1
    private_method1
  end

  class << self
    def public_method1
      'Something Cool'
    end

    private

    def private_method1
      'Something Coolest !'
    end
  end
end

Just to be clear, this is a 'How to' make private class method in ruby.
Very hepfull.