University of Virginia Library

4. IV.

“I was thinking to-day,” said Mr. Churchill
a few minutes afterwards, as he took some papers
from a drawer scented with a quince, and arranged
them on the study table, while his wife as usual
seated herself opposite to him with her work in
her hand,—“I was thinking to-day how dull and
prosaic the study of mathematics is made in our
school-books; as if the grand science of numbers
had been discovered and perfected merely
to further the purposes of trade.”

“For my part,” answered his wife, “I do
not see how you can make mathematics poetical.
There is no poetry in them.”

“Ah, that is a very great mistake! There
is something divine in the science of numbers.
Like God, it holds the sea in the hollow of its
hand. It measures the earth; it weighs the stars;

it illumines the universe; it is law, it is order, it
is beauty. And yet we imagine—that is, most
of us—that its highest end and culminating point
is book-keeping by double entry. It is our way
of teaching it that makes it so prosaic.”

So saying, he arose, and went to one of his
book-cases, from the shelf of which he took down
a little old quarto volume, and laid it upon the
table.

“Now here,” he continued, “is a book of
mathematics of quite a different stamp from ours.”

“It looks very old. What is it?”

“It is the Lilawati of Bhascara Acharya,
translated from the Sanscrit.”

“It is a pretty name. Pray what does it
mean?”

“Lilawati was the name of Bhascara's daughter;
and the book was written to perpetuate it.
Here is an account of the whole matter.”

He then opened the volume, and read as follows:—

“It is said that the composing of Lilawati was
occasioned by the following circumstance. Lilawati
was the name of the author's daughter, concerning
whom it appeared, from the qualities of
the Ascendant at her birth, that she was destined

to pass her life unmarried, and to remain without
children. The father ascertained a lucky hour
for contracting her in marriage, that she might be
firmly connected, and have children. It is said
that, when that hour approached, he brought his
daughter and his intended son near him. He left
the hour-cup on the vessel of water, and kept in
attendance a time-knowing astrologer, in order
that, when the cup should subside in the water,
those two precious jewels should be united. But
as the intended arrangement was not according to
destiny, it happened that the girl, from a curiosity
natural to children, looked into the cup to observe
the water coming in at the hole; when by chance
a pearl separated from her bridal dress, fell into
the cup, and, rolling down to the hole, stopped the
influx of the water. So the astrologer waited in
expectation of the promised hour. When the
operation of the cup had thus been delayed beyond
all moderate time, the father was in consternation,
and examining, he found that a small pearl
had stopped the course of the water, and the long-expected
hour was passed. In short, the father,
thus disappointed, said to his unfortunate daughter,
I will write a book of your name, which shall
remain to the latest times,—for a good name is
a second life, and the groundwork of eternal existence.”

As the school-master read, the eyes of his wife
dilated and grew tender, and she said,—

“What a beautiful story! When did it happen?”

“Seven hundred years ago, among the Hindoos.”

“Why not write a poem about it?”

“Because it is already a poem of itself,—one
of those things, of which the simplest statement is
the best, and which lose by embellishment. The
old Hindoo legend, brown with age, would not
please me so well if decked in gay colors, and
hung round with the tinkling bells of rhyme.
Now hear how the book begins.”

Again he read;—

“Salutation to the elephant-headed Being who
infuses joy into the minds of his worshippers,
who delivers from every difficulty those that call
upon him, and whose feet are reverenced by the
gods!—Reverence to Ganesa, who is beautiful
as the pure purple lotos, and around whose neck
the black curling snake winds itself in playful
folds!”

“That sounds rather mystical,” said his wife.

“Yes, the book begins with a salutation to the
Hindoo deities, as the old Spanish Chronicles
begin in the name of God, and the Holy Virgin.
And now see how poetical some of the examples
are.”

He then turned over the leaves slowly and
read,—

“One-third of a collection of beautiful waterlilies
is offered to Mahadev, one-fifth to Huri,
one-sixth to the Sun, one-fourth to Devi, and six
which remain are presented to the spiritual teacher.
Required the whole number of water-lilies.”

“That is very pretty,” said the wife, “and
would put it into the boy's heads to bring you
pond-lilies.”

“Here is a prettier one still. One-fifth of a
hive of bees flew to the Kadamba flower; one-third
flew to the Silandhara; three times the difference
of these two numbers flew to an arbor;
and one bee continued flying about, attracted on
each side by the fragrant Ketaki and the Malati.
What was the number of the bees?”

“I am sure I should never be able to tell.”

“Ten times the square root of a flock of
geese—”

Here Mrs. Churchill laughed aloud; but he
continued very gravely,—

“Ten times the square root of a flock of
geese, seeing the clouds collect, flew to the
Manus lake; one-eighth of the whole flew from
the edge of the water amongst a multitude of
water-lilies; and three couple were observed
playing in the water. Tell me, my young girl
with beautiful locks, what was the whole number
of geese?”

“Well, what was it?”

“What should you think?”

“About twenty.”

“No, one hundred and forty-four. Now try
another. The square root of half a number of
bees, and also eight-ninths of the whole, alighted
on the jasmines, and a female bee buzzed responsive
to the hum of the male inclosed at night in a
water-lily. O, beautiful damsel, tell me the number
of bees.”

“That is not there. You made it.”

“No, indeed I did not. I wish I had made it.
Look and see.”

He showed her the book, and she read it herself.
He then proposed some of the geometrical
questions.

“In a lake the bud of a water-lily was observed,
one span above the water, and when

moved by the gentle breeze, it sunk in the water
at two cubits' distance. Required the depth of
the water.”

“That is charming, but must be very difficult.
I could not answer it.”

“A tree one hundred cubits high is distant
from a well two hundred cubits; from this tree
one monkey descends and goes to the well; another
monkey takes a leap upwards, and then descends
by the hypothenuse; and both pass over
an equal space. Required the height of the
leap.”

“I do not believe you can answer that question
yourself, without looking into the book,” said
the laughing wife, laying her hand over the solution.
“Try it.”

“With great pleasure, my dear child,” cried
the confident school-master, taking a pencil and
paper. After making a few figures and calculations,
he answered,—

“There, my young girl with beautiful locks,
there is the answer,—forty cubits.”

His wife removed her hand from the book, and
then, clapping both in triumph, she exclaimed,—

“No, you are wrong, you are wrong, my
beautiful youth with a bee in your bonnet. It
is fifty cubits!”

“Then I must have made some mistake.”

“Of course you did. Your monkey did not
jump high enough.”

She signalized his mortifying defeat as if it had
been a victory, by showering kisses, like roses,
upon his forehead and cheeks, as he passed beneath
the triumphal arch-way of her arms, trying
in vain to articulate,—

“My dearest Lilawati, what is the whole
number of the geese?”