The theory of telegraph transmission, in its broadest aspect, involves the many systems which have appeared from time to time. A treatment of them all is much beyond the scope of a paper of this nature, but fortunately a great many can be eliminated by reason of their limited commercial use. The considerations in this paper are limited to the closed-circuit Morse system, which has been practically supreme in American practice for many years. High-speed automatic systems have enjoyed but little use in this country and a theoretical consideration of such transmission, while very interesting, has a limited practical value at the present time. Considering its commercial importance, it is not easy to understand why the theory of Morse transmission has remained so long in a state of apparent neglect. Perhaps this is due in some measure to the difficulty of the subject, but certainly it cannot be ascribed to the lack of interesting or commercially important problems.