  Second-order coding rate of channel coding is discussed for general sequence
of channels. The optimum second-order transmission rate with a constant error
constraint $\epsilon$ is obtained by using the information spectrum method. We
apply this result to the discrete memoryless case, the discrete memoryless case
with a cost constraint, the additive Markovian case, and the Gaussian channel
case with an energy constraint. We also clarify that the Gallager bound does
not give the optimum evaluation in the second-order coding rate.
