Verniers are divided scales, with their divisions a little smaller than those on the main scale to which they are attached. If a length equal to nine divisions of the main scale be divided into ten parts, then each of these latter will be 1/10 less than the former. In general, n divisions of the vernier are equal to n - 1 divisions of the scale, which enables us to read to the nth part of a division, whatever that may be. If the divisions on the main scale were tenths of an inch we could get hundredths by dividing a length equal to nine of them into ten parts, then the difference between the lengths of these would be 1/10 of 1/10 of an inch, that is, 1/100.

Angular Measurement

The measurement of the distances of the sun, moon, and planets depends upon our knowledge of the properties of triangles. Our knowledge of the size of the earth and other bodies in space depends upon angular measurement. Our knowledge of the mass, volume, and density of the sun, moon, and planets, and even the masses and distances of some of the stars, depends upon our ability to measure angles.

Measurement Of Time

An ancient method of measuring time was by the gnomon, an upright stick in the ground which cast a shadow of the sun, the length and position of which varied according to the time of day, hence the sun-dial. Other methods consisted in chanting psalms, burning candles, and dropping water or sand from one vessel to another, hence clepsydra and hour-glass, etc. Clocks came into use in England in the fourteenth century; but instead of a pendulum a vibrating horizontal bar was employed - DeWyck's clock. Galileo discovered the pendulum, which suggested itself to him by observing a swinging lamp in the Cathedral of Pisa. Huyghens found that the vibrations of a pendulum were not equal for any length of swing; hence the introduction of the cycloidal pendulum. Hooke's anchor escapement was the next advance, which allowed of a smaller arc of swing and eliminated a certain amount of friction, but it is not used in the best clocks because of the recoil. Graham overcame the recoil just mentioned by using pallets whose surfaces were arcs of circles, hence dead-beat escapement. The chronometer escapement has a balance-wheel in place of a pendulum, which thus admits of a more compact arrangement than is possible in a clock with a pendulum; moreover, it will work in any position.

Altitude And Azimuth

The altitude of a celestial object, as a star, is its angular height above the horizon, and its complement - or that which is required to make it equal to a right angle - is called the zenith distance. The azimuth of a celestial object is its angular distance from the north point of the horizon. It is found by drawing an imaginary arc from the zenith point through the object till it cuts the horizon, and then measuring the angular distance between this point and the north point.

The Sphere Of Observation

The appearance of the starry sphere presents different aspects, depending upon the locality of the observer. At Washington the north pole is elevated about 39° above the horizon, at London about 51° above the horizon; this elevation of the pole always being equal to the latitude of the place of observation. The celestial equator being 90° distant from the pole, will cut the horizon of London at an angle of 38°, and that of Washington at about 51°, the northern side in each case being depressed below, and the southern side elevated above, the horizon.


The moon's place, when looked at through a telescope from London and some distant place, as Cape Town, seems to change - that is, the telescopes contain an angle. This contained angle is less when the sun is viewed in the same way, but when stars are looked at similarly the angle disappears altogether - that is, stars have no parallax, while the sun, moon, and planets have parallax, or angular displacement caused by change of position.

Rotundity Of The Earth

The concave heavens; the disappearance of a ship at sea; the extension of the horizon as we ascend high elevations; the frequent circumnavigation of the globe; the earth's shadow cast by the sun upon the moon during an eclipse; the spherical form of the sun, moon, and planets - all confirm our belief that the earth is globular in form.

Magnitude Of The Earth

The size of the earth is found by observing a star in the exact zenith of any place, then traveling along a direct north line, till the star has declined 1° from the zenith, and measuring the distance traversed. This distance would be the length of 1° in miles, and 360 times that length would give the circumference of the earth.

Demonstration Of Earth's Rotation

A heavy body set in motion tends to retain its original plane of motion. Foucault's pendulum consists of a heavy ball at the end of a long wire, supported by a steel pivot on an agate plane. The ball, when set swinging, seems to change its direction of swing across a graduated circle on a table beneath it, but, as we know that the pendulum tends to keep to the same plane of motion, and that there is so little to prevent it from doing so, we conclude it is the earth which is turning on its axis and carrying the table with it. The gyroscope is essentially the same as the pendulum, a heavy rotating disk taking the place of the swinging bob of the pendulum. The rotating disk is supported inside a horizontal ring, this ring being in its turn supported by knife edges resting on steel plates in the circumference of a vertical ring, and this vertical ring is supported by a torsionless thread, so that all the parts are nicely counterpoised and are free to move. A pointer attached to the vertical ring is found to move over a graduated scale at the same rate as the pendulum changed its plane of motion; hence, we conclude that it is the earth which moves, because we know that the rotating disc holds to its initial plane of motion. The rotation of the earth on its axis furnishes us with an invaluable unit of time.