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A gallon of water at 62° F. weighs 10 lbs. or 70000 grains.
A cubic inch of water at 39° F. weighs 252.88 grains.

A cubic foot of water at 39° F. weighs 62.425 lbs. or 998.8 ozs.

A pound of water occupies 0162 of a cubic foot.

1000000 volumes of water at 39° F. become 1001118 volumes at 62° F.

Measures of Mass.

The Imperial Standard pound avoirdupois is the mass in vacuo of a certain piece of platinum.

1 grain avoirdupois and Troy..

437.5 grns. = 1 ounce avoirdupois (oz.).

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16 ozs. = 1 pound avoirdupois (lb.). 1792 ozs. = 112 lbs. = 1 hundredweight (cwt.).

7000 grns. grns.

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5760 grains = 1 ounces Troy = 12 pound Troy. 1 ounce Troy = 1.097 ozs. avoirdupois.

1 lb. avoirdupois = 1.215 pounds Troy.

1 ton of water occupies 224 gallons or 35.88 cubic feet.

(ii) THE METRIC SYSTEM.

In the metric system all the measures are multiplied by 10 and its powers, multiples being shown by prefixing a Greek numeral; and also divided by 10 and its powers, submultiples being shown by prefixing a Latin numeral.

Measures of Length.

The metre is the length of a certain bar of platinum

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1000000 m.m, = = 100000 c.m. = 10000 d.m. = 1000 m.

=

100 dekam.

=

10 hectom.

=

1 kilometre.

The metre was constructed to be the 10000000 of the quadrant of the globe passing through Paris. According to the best modern results however this quadrant really measures 10001472.5 times the length of the standard metre, which is preserved at Paris.

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Measures of Volume or Capacity.

1 cubic centimetre (c.c.).

1000 c.c. = 1 cubic decimetre (a litre).

1000000 c.c. 1000 litres = 1 cubic metre (a stere).

=

Measures of Mass.

A kilogram is the mass of a certain piece of platinum in

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The kilogram was intended to be the mass of one cubic decimetre of water measured at 4° C. But it is found that the mass of 1 c.c. of water at 4° C. is 1.000013 grams.

For the conversion of English to Metric and of Metric to English measures see Table II.

*(iii) THE C.G.S. SYSTEM.

Nearly all the quantities, with which physical science deals, can be expressed in terms of three fundamental units, of which the most convenient are :

a definite length-the Centimetre.

a definite mass-the Gram.

a definite time-the Second.

Surface is expressed in square centimetres, and volume in cubic centimetres. The gram, the unit of mass, is very nearly the mass of the unit-volume of water at 4° C.

The C.G.S. unit of force is the dyne. It is the force, which acting on a gram for a second, generates in it a velocity of 1 centimetre per second.

Thus, if a body falls in vacuo at Greenwich for 1 second, the velocity is found to be at the rate of 981.17 centimetres per second. Or the force exerted upon a body at Greenwich by the attraction of the earth is g = 981·17 dynes. At Paris g= 980-94 dynes.

The C.G.S. unit of work is called the erg. It is the amount of work done by a dyne working through the distance of 1 centimetre.

The C.G.S. unit of energy is also the erg, since energy is measured by the amount of work which it represents.

If a body the mass of which is m grams fall through a distance h centimetres; the working force is the action of gravity upon the mass of the body = gm dynes, which, multiplied by the distance passed through, gives mgh ergs as the work done. But the velocity acquired is such that v2gh. Hence mgh = mv2.

The kinetic energy of a mass of m grams with the velocity of v centimetres per second is mv2 ergs.

In cases in which great accuracy is not required, it is usual to consider gravity as a force constant at all positions on the earth's surface, and to reckon work by a mass lifted through a certain distance in opposition to gravity.

Thus a kilogram-metre is the work done in lifting a kilogram through a metre in opposition to gravity.

L. C. A.

A kilogram-metre = 100000 × g ergs.

2

A foot-pound is the work done in lifting a pound through a foot in opposition to gravity.

A foot-pound = 13825 × g ergs.

A horse-power is the power of doing work at the rate of 33000 foot-pounds per minute or 550 foot-pounds per second, it is equal to 7.46 × 10° ergs per second.

X

Since only one unit for each measure is used in the C.G.S. system, the easy and rapid expression of large multiples and of small sub-multiples is a matter of great importance.

The prefix micro- is used to express division by a million; a microdyne is the millionth of a dyne: the prefix mega- or megal- is used to denote multiplication by a million; a megalerg is a million ergs.

In expressing small or large multiples of the unit in figures it is most convenient to write them as one figure of whole numbers, followed by decimals, and multiplied by the requisite negative or positive power of 10.

and

Thus 324,000,000,000 is written 3.24 x 10",

•000 003 24

as

3.24 × 10-6.

The power of 10 used is the characteristic of the common logarithm of the expression.

These multiples of 10 are easily expressed in words, thus 10 grams is spoken of as a gram-nine, and 10-9 grams is spoken of as a ninth-gram.

The prefix mega- is equivalent to the affix -six, and the prefix micro- to the prefix sixth-.

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