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Notwithstanding the difficulties, however, Archimedes followed out his calculations to the piling up of bewildering numbers, which the modern mathematician finds to be the consistent outcome of the problem he had set himself. But it remains to notice the most interesting feature of this document in which the calculation of the sand-grains is contained.
But now that she had given away all her merit to Gunvanti, she had none left by means of which she could jump across the seven seas. She sat down forlorn by the bank of a river. Then she got up, bathed in the water, and prayed to the god Vishnu. Next she took one hundred and eight sand-grains in her hand, and then walked one hundred and eight times round a peepul tree by the river's edge.
Meanwhile, the glacier continues to recede, and numerous rills, still younger than the lake itself, bring down glacier-mud, sand-grains, and pebbles, giving rise to margin-rings and plats of soil. To these fresh soil-beds come many a waiting plant.
It scarcely needed music to resolve all the incessant waver and shimmer into a dance; but the music came, and, like sand-grains under the magnet, the beautiful atoms swept into stately shapes and tremulous measured activity, "A fine, sweet earthquake gently moved By the soft wind of whispering silks."
"Before my breath, like, blazing flax, Man and his marvels pass away; And changing empires wane and wax, Are founded, flourish and decay. "Redeem mine hours the space is brief While in my glass the sand-grains shiver, And measureless thy joy or grief, When Time and thou shalt part for ever!"
And the priests obtained untold wealth counted out to them. And as the sand-grains of the earth, or as the stars in the sky, or as the rain-drops when it raineth, cannot be counted by anyone, so the wealth Gaya gave away was incapable of being counted by figures.
His Excellency then began to extol the military forces and powers of the princes of Africa: "The Sultan of Timbuctoo has 100,000 fighting men! Wadai has 100,000 warriors! The Sultans of Soudan have innumerable hosts, as the sand-grains of The Desert are innumerable!" He then asked silly questions as to whether the Turks could beat the Christians in fighting.
Meanwhile, the glacier continues to recede, and numerous rills, still younger than the lake itself, bring down glacier-mud, sand-grains, and pebbles, giving rise to margin-rings and plats of soil. To these fresh soil-beds come many a waiting plant.
We need not follow Archimedes to the limits of his incomprehensible numbers of sand-grains. The calculation is chiefly remarkable because it was made before the introduction of the so-called Arabic numerals had simplified mathematical calculations.
The winter snow is a sort of ceiling, lasting half the year; while the pressed surface is made yet smoother by violent winds armed with cutting sand-grains that bear down any shoot which offers to rise much above the general level, and that carve the dead trunks and branches in beautiful patterns. During stormy nights I have often camped snugly beneath the interlacing arches of this little pine.
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