  We present in a detailed manner the scaling theory of irreversible
aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$, as
well as a minor generalisation thereof. In this case, it is possible to
evaluate the scaling function exactly. By this we mean that it is expressed as
the unique solution of an ordinary differential equation with given boundary
conditions. This can be solved numerically to high accuracy, making a highly
detailed analysis of the scaling behaviour possible. The results confirm the
far more general results of earlier work concerning a general scaling theory
for so-called reaction rates of Type III. On the other hand, the behaviour of
large aggregates at fixed time, that is, not in the scaling limit, which had
been up to now analysed in an approximation valid in the limit of small times,
can be determined more precisely in this case, and is shown to display subtle
differences from the small-time approximation.
