transformed into a purgatorial discipline, and as
he progressed from course to course Frank's mind was purified as by
fire.

Here is one occasion. There was a small plumcake, and Frank was required
to divide it so that each of the five persons present should have a just
share. Frank began to cut the cake, but by a mistake cut it into six
pieces instead of five.

This miscarriage of justice sent dismay into the hearts of his parents.
They felt that he was at the parting of the ways. It was a great moral
crisis, in which his character was to be revealed. What would Frank do
with that sixth piece of cake? Perhaps--horrible thought!--he might eat
it. From this crime he was saved only to fall into the almost equal sin
of unscientific charity. In order to save trouble he proposed to give
the extra piece to his father, and when questioned he could give no
better reason than that he thought his father liked cake.

"'What right have you to give it to any of us? You were to judge about
the size of the pieces, and you were to take care that we each have our
just share. But you are going to give one of us twice as much as any of
the others.'"

Justice triumphed. "Frank took the trouble to think, and he then cut the
spare bit of cake into five equal parts, and he put these parts by the
side of the five large pieces and gave one of the large and one of the
small pieces to each person, and he then said: 'I believe I have
divided the cake fairly now.' Everybody present said 'yes,' and
everybody looked carefully at each of the shares, and there appeared
exactly the same quantity in each share. So each person took a share,
and all were satisfied."

That is to say, all were satisfied except Frank's mother. She was afraid
that the family meal had not yielded its full educational value.

"'My dear Frank,' said his mother, 'as you have divided the cake so
fairly, let us see how you will divide the sugar that was upon the top
of the cake, and which is now broken and crumbled to pieces in the
plate. We all like sugar; divide it equally amongst us.'

"'But this will be very difficult to do, mamma, because the pieces of
sugar are of such different sizes and shapes. I do not know how I shall
ever divide it exactly. Will it do if I do not divide it quite exactly,
ma'am?'

"'No,' said his mother, 'I beg you will divide it quite exactly.'"

Frank gathered his fragments into five little mounds, and after
carefully measuring their height,