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(iv) MEASURES OF TIME.

The sidereal day is the period in which the earth turns once on its axis, and is equal to 86,164 mean solar seconds.

The earth goes round the sun in one tropical year of 365-24224 mean solar days or 31,556,929 mean solar seconds.

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If a straight line be kept constantly in a plane with one end centered at a fixed point, and be then caused to revolve with a motion like the hand of a clock, it moves through an angular space called a round in making one revolution.

One-fourth of a round is called a quarter-round or rightangle. (Cf. Euc. Bk. 1. Defin. x.)

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A radian is the angle between two radii of a circle, which comprise between them an arc of the circle equal in length to the radius.

1 radian = 57.29578° 3437-747′ = 206,264.8" nearly,

=

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2. Rectangular parallelopiped edges a, b, c. V = abc.

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PHYSICS AND CHEMISTRY.

(9) MASS, VOLUME, DENSITY AND WEIGHT.

The mass of, or quantity of matter in, a body remains constant so long as nothing is added to or taken from the body, and is proportional to the volume and density conjointly. Two bodies are of equal mass, if equal forces applied to them produce in equal times equal changes of velocity.

The density (4) of a body is measured by the number of units of mass contained in the unit of volume of it.

Hence in the metric system the density of a solid or liquid is measured by the number of grams in one cubic centimetre of it, or by the number of kilograms in one litre of it.

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Thus 1000 c.c. of copper A9, contain 1000 × 9 = 9000 grams, and 1000

1000

of
grams copper occupy 9

111.1 c.c.

Since 1 c.c. of water at the temperature of 4o C. contains 1.000013 grams, the density of a solid or liquid is measured very nearly by the number of times it is heavier or lighter than an equal volume of water at the temperature of 4o C.

Thus cast-lead is 11.35 times heavier than water, and its true density is 11.35 × 1·00001311.35014755.

This correction is so small that it may be neglected in all ordinary cases.

*In the English system if a cubic foot be taken as the unit of volume, the density of a body is measured by the

number of pounds in one cubic foot of it; and the number of times a body is heavier or lighter than an equal volume of water at 62°F. is spoken of as its specific gravity. Since a cubic foot of water at 4°C. weighs 62-425 lbs., the density of a substance is nearly 62.4 times its specific gravity.

Thus, the specific gravity of mercury is 13.55, but its density is 848.75.

The mass of a body is in practice usually measured by its weight, that is, by the attraction of the earth upon it, which is equal to the mass of the body multiplied by g, the velocity which it would acquire by falling freely in vacuo for a second under the influence of the attraction of the earth.

W = Mg (where g = 981 c.m. in London).

Since the force of gravity, though always the same at the same place, increases in passing from the Equator to the Pole, because in the latter case the body is nearer the centre of the earth, and also the centrifugal force acting upon it becomes less, the weight of a body varies according to its geographical position and to its distance above the sea-level.

If then masses at different places were compared by estimating the weights of the bodies by means of a springbalance, a correction for the difference of the force of gravity would have to be introduced. But in chemistry masses are usually compared by the number of standard pieces of metal (weights) on which the earth exercises an equal attraction. Hence in a balance masses and not weights are in reality estimated.

The word weight is often wrongly used when mass is really meant, e.g. a gram or a pound is a unit of mass and not a unit of weight.

The Chemical Balance, by which the equality of masses is determined, consists of a lever with equal arms, hence

when the instrument is in equilibrium the mass in one pan is equal to the mass in the other pan.

In very exact experiments the chance of error arising from any inequality in the length of the arms may be obviated by two methods.

(i) In the method of counterpoise, the substance is placed in one pan, and shot, sand, &c. are placed in the other pan to counterpoise it. The substance is then removed, and weights are put into the pan to balance the counterpoise.

1

(ii) In the method of double-weighing, the substance is placed in one pan and balanced by weights, W, in the other. The substance is then changed into the other pan, and balanced by weights W, in the first pan. If a, b be the lengths of the arms of the balance and x the true mass of the substance :

and

or

and

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if the difference between W, and W, be small,

x = 1⁄2 (W1 + W ̧) nearly.

1

grams

in one pan,

Thus a crucible is found to weigh 19.76 and 19.74 grams in the other, find its true mass.

=

/19-76 x 19-7419-74999, or very nearly 19.75 grams.

From the relations between volume, density, and mass given above, many important questions connected with changes in volume and density, when metals are alloyed

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