  ``Sub-meV'' resolution photoemission spectroscopy was used to study
carbon-substitution dependence on the multiple superconducting gap of Mg(B$_{1
- x}$C$_{x})_{2}$. Two features corresponding to $\sigma $ and $\pi $ gaps are
clearly observed in the raw spectra up to carbon concentration x = 7.5 {%}. The
observed x dependence of the two gaps shows a qualitatively different behavior:
a marked change of the $\sigma $ gap proportional to the $T_{c}$ variation and
a negligible one of the $\pi $ gap. This as well as the temperature dependence
can be explained with the two-band mean-field theory. Implications from the
present study are discussed.
