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Take this or that term, place the + sign before it and forthwith you have the ellipse, the trajectory of the planets, with its two friendly foci, transmitting pairs of vectors whose sum is constant; substitute the sign and you have the hyperbola with the antagonistic foci, the desperate curve that dives into space with infinite tentacles, approaching nearer and nearer to straight lines, the asymptotes, but never succeeding in meeting them.

It varied from twenty-three to fifty-one inches wide, and was at least five or six feet high. Sometimes there is an inner recess in the middle twenty-five to thirty-three inches wide. From the religious scene over such a recess it seems that these were the foci for family worship.

Cork city in these days was known to be one of the foci of disaffection; perhaps it was its chief stronghold. The Metropolis may have given an absolutely larger number of members to the Fenian organization, but in proportion to the number of its population the Southern city was far more deeply involved in the movement.

The disciples of Plato invented conic sections, and discovered the geometrical foci. It was however reserved for Euclid to make his name almost synonymous with geometry. He was born 323 B.C., and belonged to the Platonic sect, which ever attached great importance to mathematics. His "Elements" are still in use, as nearly perfect as any human production can be. They consist of thirteen books.

Piazzi Smyth, who during a prolonged visit to this mountain in 1856 made a careful survey of its form and structure, shows that the great cone is surrounded by an outer ring of basalt enclosing two foci of eruption, the lavas from which have broken through the ring of the outer crater on the western side, and have poured down the mountain.

Others gave no heed to these matters, but were engaged in attracting the attention of the ladies, throwing themselves into attitudes more or less interesting and statuesque, flashing diamond rings, especially when they thought themselves the foci of insistent opera-glasses, while yet another would address a respectful salute to this or that señora or señorita, at the same time lowering his head gravely to whisper to a neighbor, "How ridiculous she is!

From the first law of Kepler, that every planet moves in an ellipse with the sun in one of its foci, he drew the still more general inference that the force by which the planet moves round that focus varies inversely as the square of its distance from the focus.

They are generous, courageous, and ever ready in the hour of danger. But there is a dark side to this picture. They are said to be the foci of political encroachment and intrigue, and to be the centre of the restless and turbulent spirits of all classes.

They are the cause of the bright spots of the moon, while the want of them is what distinguishes the duller portions, usually but erroneously called SEAS. In some parts, bright volcanic matter, besides covering one large patch, radiates out in long streams, which appear studded with subordinate foci of the same kind of energy.

They are the two foci of the ellipse in which moves history; the two shores between which oscillates the tossing tide of humanity. Lord Morley calls them "the two incendiary forces of history, ever shooting jets of flame from undying embers." This explains why the soil of history is so volcanic, so filled with burning lava which time itself has not cooled.