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SIMMS

1759

SIMPLE HARMONIC MOTION

elected, and eight appointed, representatives. He selected York (since 1834 Toronto) as the capital. He took great interest in making surveys and locating roads, one being even now sometimes spoken of as Governor's Road. Simcoe County and Lake are called after him. A monument to his memory has been erected in Queens Park, Toronto, in sight of the new parliament buildings.

Simms, William Gilmore, American historian, novelist and poet, was born at Charleston, S. C,, April 17, 1806, and died there on June n, 1870. In early life he studied law, but abandoned it for journalism and, later, for literature. He specially devoted himself to writing a series of 17 volumes of fiction, including romances of colonial life, romantic tales of revolutionary incidents in South Carolina, of which he wrote a history, a geography of the state and an account of South Carolina in Revolutionary times. He for several years was a member of the legislature, and filled other political offices. He had, besides a fertile mind, a vivid imagination and the power of writing an interesting and realistic novel; he also wrote verse, of which a compilation exists. Of his novels perhaps the most notable are The Yemassee, Guy Rivers, Pelayo, Carl Werner, The Scout, The Partisan, Count Julian, Mellichampe and Border Beagles. His best, as it is his longest, poem is entitled Atalantis: a Drama of the Sea. See Geo. W. Cable's Life in the American Men of Letters Series.

Simonides (st-mon'%-dez), a Greek lyric poet (B. C. 556-469), a native of the island of Ceos, though early in his career he appears to have been banished and took up his residence partly in the Peloponnesus, with occasional visits to the court of Hiero of Syracuse as well as to the ruling families (the Scopadae in particular) of Thessaly. He became famous by his dirges, epigrams and funeral inscriptions in honor of those who fell in the Persian Wars as well as in praise of the Athenians who took part in the notable struggle. The chief theme of his song was, in an especial manner, the devotion of Leonides and his 300 at Thermopylae. In his finished versification, as well as in the choice and variety of his themes, his song has been compared to that of Tennyson. Especially fine are his meter, language and thought. Another of his name is the Greek poet Simonides or Semonides of Amorgos, a native of Samos (about B. C. 660). Only fragments of his work, however, have come down to us.

Simoom (si-moom') or Simoon, a hot, suffocating wind, common in the deserts of Africa and Arabia. It is very much like a cyclone, with a calm center surrounded by whirling blasts of very hot air, the whole moving slowly from south to north or from east to west. It often

carries along columns of sand, and is indicated by a purple atmosphere. ^ It is very injurious both to men and animals, causing severe pain and a feeling of suffocation. It lasts only for a few minutes, not more than 20 at the most, and occurs in spring and summer. See SCIROCCO.

£im'ple Harmon'ic Mo'tion is the projection of   uniform  circular  motion  upon  a ~                  diameter of the

circle. Referring to the accompanying figure, let P be a point moving with uni-Iform speed in the 'circumference of the circle. From the point P, in each of its successive positions, imagine a perpendicular let fall upon the diameter there shown. The motion of the foot of this perpendicular H to. and fro along the diameter is a simple harmonic motion, and is often indicated by the letters S. H.^M.

The circle in which we have imagined the point P to move is called the circle of reference. The radius of this circle is known as the amplitude of the S. H. M. The time occupied by one round trip of the point H to and fro across the diameter is called the period of the S. H. M. The angle between the radius OP and the radius from which angles are measured in this circle is called the phase of the S. H. M. The value of the phase at the instant from which time is measured is called the epoch of the S. H. M. The distance of the point H from the center of the circle at any instant is called the displacement of the S. H- M.

Any S. H. M. is completely described only when we know four things about it, namely: (i) the amplitude; (2) the period; (3) the phase at any time, t; and (4) the direction of motion of the point P in the circle of reference. If we denote the amplitude by A, the period by T, the phase by 0 and the displacement at any instant, t, by x, then the equation of S. H. M. is

x «Acos. -Tp-t

211*

where -7^t=Q

No one motion in nature is more frequently met with than S. H. M. The motion of a freelv suspended pendulum-bob is practically simple harmonic. A ball suspended by a vertical, spiral spring oscillates up and down in a vertical line with a S. H. M. Air-particles set in motion by a tuning fork vibrate to and fro witJa

SIMPLE HARMONIC  MOTION