Spectroscopic measurements of the helium atom are performed to high precision using an atomic beam apparatus and electro-optic laser techniques. These measurements, in addition to serving as a test of helium theory, also provide a new determination of the fine structure constant α. An apparatus was designed and built to overcome limitations encountered in a previous experiment. Not only did this allow an improved level of precision but also enabled new consistency checks, including an extremely useful measurement in 3He. I discuss the details of the experimental setup along with the major changes and improvements. A new value for the J = 0 to 2 fine structure interval in the 23P state of 4He is measured to be 31 908 131.25(30) kHz. The 300 Hz precision of this result represents an improvement over previous results by more than a factor of three. Combined with the latest theoretical calculations, this yields a new determination of α with better than 5 ppb uncertainty, α-1 = 137.035 999 55(64).