Ever notice that when you use up most of the bar soap that the suds
are harder and harder to produce?  Why is that?

Here's my assumption: The amount of suds produced is proportional to
the amount of the soap surface exposed to water. Therefore, as the bar
gets smaller the is less soap available to the water to make suds, so
fewer suds are produced.

I theorize that the difficulty of raising a good lather from a used-up
bar of soap has to do with the inability to position the bar properly
in one's hand. You can't hold it and rub it as well, so it's hard to
get a nice amount of foam out of it.

When my soap gets thin and skimpy, I put it into a small nylon net
drawstring bag with other smallish pieces of soap. The lather is
superb, and the nylon net makes a great body-scrubber.

I really don't believe that the mere physical change of the soap bar
can account for the change in the suds or texture of the resulting
suds-less smeary stuff that you can get from it.

I suspect that there is a different composition core in the bar soap
at its center, and that the outer layers are the more suds producing
soap.  I'm hoping that someone in the know about such things would
confirm this with the typical anatomy of a bar of soap.

Likely some soap manufactures use a different formula for the interior
of the bar, but I think most brands are uniform throughout. The
moisture content will increase near the end if the bar is exposed to
water as much as 1/2 the time. This could result in part of the bar
being converted to soap scum.  Neil