The synchronous machine has a long history of development, analysis and usage. Now almost all large generators are synchronous generators, which are synonymous with AC generators. They have generally saliency of magnetic poles, which makes machine inductances timely variant and makes their analyses complicated and difficult. The conventional theories have not provided adequate analytical results of the machine and they still leave the machine analysis somewhat in confusion. The spiral vector method, which has been proposed by the author, will be applied in this paper to analysis of transient phenomena of the machine. It was reported in the recent proceedings.3) But this time the new idea of “damped inductance” will be introduced to further the SV theory of the synchronous machine.