  We have investigated the ac susceptibility of the spin triplet superconductor
Sr$_2$RuO$_4$ as a function of magnetic field in various directions at
temperatures down to 60 mK. We have focused on the in-plane field configuration
(polar angle $\theta \simeq 90^{\circ}$), which is a prerequisite for inducing
multiple superconducting phases in Sr$_2$RuO$_4$. We have found that the
previous attribution of a pronounced feature in the ac susceptibility to the
second superconducting transition itself is not in accord with recent
measurements of the thermal conductivity or of the specific heat. We propose
that the pronounced feature is a consequence of additional involvement of
vortex pinning originating from the second superconducting transition.
