This is a crystal American Pioneer Oil Lamp. The height, to the top of the metal connector is 9". The base diameter is 3 & 5/8". The design is similar to the most common electric lamps and the lower half of the vases. The globe in the first picture is not original to the lamp.
Per Bill Quillin - "I also cannot be positive that this was originally an oil lamp, or the connections were modified to make it so, but it is the only oil lamp I have found in the American Pioneer pattern."