In the first part of the paper asymptotic representations at infinity
of the Green function, of the velocity potential and of the elevation
of the free surface are obtained for the linear problem of the uniform
motion of a pointwise source in a fluid. The advantage of these repre
sentations is that they are uniform with respect to all directions and
depth. This uniformity is achieved due to singling out an additional
wave going to infinity along the track of the source. In the second pa
rt it is proved that the problem of the uniform motion of a submerged
body is solvable for all velocities except, possibly, for a finite num
ber.