turn the leaves at
random. Before fixing one's eyes on a definite point in the landscape,
it is well to take a summary view of the whole. Page follows swiftly
upon page, telling me nothing. A chapter catches my attention in the
middle of the volume; it is headed, Newton's Binomial Theorem.

The title allures me. What can a binomial theorem be, especially one
whose author is Newton, the great English mathematician who weighed the
worlds? What has the mechanism of the sky to do with this? Let us read
and seek for enlightenment. With my elbows on the table and my thumbs
behind my ears, I concentrate all my attention.

I am seized with astonishment, for I understand! There are a certain
number of letters, general symbols which are grouped in all manner of
ways, taking their places here, there and elsewhere by turns; there are,
as the text tells me, arrangements, permutations and combinations.
Pen in hand, I arrange, permute and combine. It is a very diverting
exercise, upon my word, a game in which the test of the written result
confirms the anticipations of logic and supplements the shortcomings of
one's thinking apparatus.

'It will be plain sailing,' said I to myself, 'if algebra is no more
difficult than this.'

I was to recover from the illusion later, when the binomial theorem,
that light, crisp biscuit, was followed by heavier and less
digestible fare. But, for the moment, I had no foretaste of the
future difficulties, of the pitfall in which one becomes more and more
entangled, the longer one persists in struggling. What a delightful
afternoon that was, before my grate, amid my permutations and
combinations! By the evening, I had nearly mastered my subject. When the
bell rang, at seven, to summon us to the common meal at the principal's
table, I went downstairs puffed up with the joys of the newly initiated
neophyte. I was escorted on my way by a, b and c, intertwined in cunning
garlands.

Next day, my pupil is there. Blackboard and chalk, everything is ready.
Not quite so ready is the master. I bravely broach my binomial theorem.
My hearer becomes interested in the combinations of letters. Not for a
moment does he suspect that I am putting the cart before the horse and
beginning where we ought to have finished. I relieve the dryness of my
explanations with a few little problems, so many halts at which the mind
takes breath awhile and gathers strength for fresh flights.

We try together. Discreetly, so as to