  We present a formula expressing Earle's twisted 1-cocycle on the mapping
class group of a closed oriented surface of genus >=2 relative to a fixed base
point, with coefficients in the first homology group of the surface. For this
purpose we compare it with Morita's twisted 1-cocycle which is combinatorial.
The key is the computation of these cocycles on a particular element of the
mapping class group, which is topologically a hyperelliptic involution.
