The following may be regarded as typical: - (t) Largest aperture; necessary corrections are - for the axis point, and sine condition; errors of the field of view are almost disregarded; example - highpower microscope objectives.

But the quarrel, known as the controversy de auxiliis gratiae, was brought to an end by Pope Paul V., who closed the debates and adjourned his decision sine die.

Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.

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But Cyprian of Carthage said long ago, Consuetudo sine veritate vetustas erroris est; and the bare fact of previous existence is no argument for the re-introduction of obsolete and antiquated institutions and theories.

Fourier's theorem asserts that such a curve may be built up by the superposition, or addition of ordinates, of a series of sine curves of wave-lengths X, IX, 3A, 4A...

The enforcement of these reforms, however, was postponed sine die owing to the revolution which transformed the Ottoman Empire into a constitutional state; and the powers, anticipating an improvement in the administration of Macedonia by the new government, withdrew their military officers in the summer of 1908.

The legislatures of Connecticut and Rhode Island, and town meetings in Cheshire and Grafton counties (New Hampshire) and in Windham county (Vermont) accepted the invitation, and the convention, composed of 12 delegates from Massachusetts, 7 from Connecticut, 4 from Rhode Island, 2 from New Hampshire and 1 from Vermont, all Federalists, met on the 15th of December 1814, chose George Cabot of Massachusetts president and Theodore Dwight of Connecticut secretary, and remained in secret session until the 5th of January 1815, when it adjourned sine die.

An intimate collaboration with England and France was a conditio sine qua non for Czechoslovakia.

As spring merges into summer, sunny days become more frequent; the ever-increasing breadth of beeforage yields still more abundantly, and the excitement among the labourers crowding the hives increases, rendering room in advance, shade and ventilation, a sine qua non.

Ii.) that the abnormal values of the variation observed in the wood-built ships of his day was due to deviation of the compass caused by the iron in the ship; that the deviation was zero when the ship's head was near the north and south points; that it attained its maximum on the east and west points, and varied as the sine of the azimuth of the ship's head reckoned from the zero points.