st train, Goosey?" said Mad Mathesis,
as they got into the cab. "Couldn't you count better than _that_?"

"I took an extreme case," was the tearful reply. "Our excellent
preceptress always says 'When in doubt, my dears, take an extreme case.'
And I _was_ in doubt."

"Does it always succeed?" her aunt enquired.

Clara sighed. "Not _always_," she reluctantly admitted. "And I can't
make out why. One day she was telling the little girls--they make such a
noise at tea, you know--'The more noise you make, the less jam you will
have, and _vice versa_.' And I thought they wouldn't know what '_vice
versa_' meant: so I explained it to them. I said 'If you make an
infinite noise, you'll get no jam: and if you make no noise, you'll get
an infinite lot of jam.' But our excellent preceptress said that wasn't
a good instance. _Why_ wasn't it?" she added plaintively.

Her aunt evaded the question. "One sees certain objections to it," she
said. "But how did you work it with the Metropolitan trains? None of
them go infinitely fast, I believe."

"I called them hares and tortoises," Clara said--a little timidly, for
she dreaded being laughed at. "And I thought there couldn't be so many
hares as tortoises on the Line: so I took an extreme case--one hare and
an infinite number of tortoises."

"An extreme case, indeed," her aunt remarked with admirable gravity:
"and a most dangerous state of things!"

"And I thought, if I went with a tortoise, there would be only _one_
hare to meet: but if I went with the hare--you know there were _crowds_
of tortoises!"

"It wasn't a bad idea," said the elder lady, as they left the cab, at
the entrance of Burlington House. "You shall have another chance to-day.
We'll have a match in marking pictures."

Clara brightened up. "I should like to try again, very much," she said.
"I'll take more care this time. How are we to play?"

To this question Mad Mathesis made no reply: she was busy drawing lines
down the margins of the catalogue. "See," she said after a minute, "I've
drawn three columns against the names of the pictures in the long room,
and I want you to fill them with oughts and crosses--crosses for good
marks and oughts for bad. The first column is for choice of subject, the
second for arrangement, the third for colouring. And these are the
conditions of the match. You must give three crosses to two or three
pictures. You must give two crosses to four or five----"

"Do you mean _only_ two cr