ON MEASURES
HORSE-POWER.--When work is performed it is designated as horse-power,
usually indicated by the letters H. P.; but the unit of work is called a
_foot pound_.
If one pound should be lifted 550 feet in one second, or 550 pounds one
foot in the same time, it would be designated as one horse-power. For
that reason it is called a foot pound. Instead of using the figure to
indicate the power exerted during one minute of time, the time is taken
for a minute, in all calculations, so that 550 multiplied by the number
of seconds, 60, in a minute, equals 33,000 foot pounds.
FOOT POUNDS.--The calculation of horse-power is in a large measure
arbitrary. It was determined in this way: Experiments show that the heat
expended in vaporizing 34 pounds of water per hour, develops a force
equal to 33,000 foot pounds; and since it takes about 4 pounds of coal
per hour to vaporize that amount of water, the heat developed by that
quantity of coal develops the same force as that exercised by an average
horse exerting his strength at ordinary work.
All power is expressed in foot pounds. Suppose a cannon ball of
sufficient weight and speed strikes an object. If the impact should
indicate 33,000 pounds it would not mean that the force employed was one
horse-power, but that many foot pounds.
If there should be 60 impacts of 550 pounds each within a minute, it
might be said that it would be equal to 1 horse-power, but the correct
way to express it would be foot pounds.
So in every calculation, where power is to be calculated, first find out
how many foot pounds are developed, and then use the unit of measure,
33,000, as the divisor to get the horse-power, if you wish to express it
in that way.
It must be understood, therefore, that horse-power is a simple unit of
work, whereas a foot pound is a compound unit formed of a foot paired
with the weight of a pound.
ENERGY.--Now _work_ and _energy_ are two different things. Work is the
overcoming of resistance of any kind, either by causing or changing
motion, or maintaining it against the action of some other force.
Energy, on the other hand, is the power of doing work. Falling water
possesses energy; so does a stone poised on the edge of a cliff. In the
case of water, it is called _kinetic_ energy; in the stone _potential_
energy. A pound of pressure against the stone will cause the latter, in
falling, to develop an enormous energy; so it will be seen that this
property resides, or is within the thing itself. It will be well to
remember these definitions.
HOW TO FIND OUT THE POWER DEVELOPED.--The measure of power produced by
an engine, or other source, is so interesting to boys that a sketch is
given of a Prony Brake, which is the simplest form of the Dynamometer,
as these measuring machines are called.
[Illustration: _Fig. 133. Prony Brake_]
In the drawing (A) is the shaft, with a pulley (A'), which turns in the
direction of the arrow (B). C is a lever which may be of any length.
This has a block (C'), which fits on the pulley, and below the shaft,
and surrounding it, are blocks (D) held against the pulley by a chain
(E), the ends of the chain being attached to bolts (F) which pass
through the block (C') and lever (C).
Nuts (G) serve to draw the bolts upwardly and thus tighten the blocks
against the shaft. The free end of the lever has stops (H) above and
below, so as to limit its movement. Weights (I) are suspended from the
end of the lever.
[Illustration: _Fig. 134. Speed Indicator_]
THE TEST.--The test is made as follows: The shaft is set in motion, and
the nuts are tightened until its full power at the required speed is
balanced by the weight put on the platform.
The following calculation can then be made:
For our present purpose we shall assume that the diameter of the pulley
(A') is 4 inches; the length of the lever (C), 3 feet; the speed of the
shaft (A) and the pulley, 210 revolutions per minute; and the weight 600
pounds.
Now proceed as follows:
(1) Multiply the diameter of the pulley (A') (4 inches) by 3.1416, and
this will give the circumference 12.5664 inches; or, 1.0472 feet.
(2) Multiply this product (1.0472) by the revolutions per minute. 1.0472
x 210 = 219.912. This equals the _speed_ of the periphery of the pulley.
(3) The next step is to get the length of the lever (C) from the center
of the shaft (A) to the point from which the weights are suspended, and
divide this by one-half of the diameter of the pulley (A'). 36" / 2" =
18", or 1-1/2 feet. This is the _leverage_.
(4) Then multiply the _weight_ in pounds by the _leverage_. 600 x 1-1/2
= 900.
(5) Next multiply this product (900) by the _speed_, 900 x 219.912 =
197,920.8, which means _foot pounds_.
(6) As each horse-power has 33,000 foot pounds, the last product should
be divided by this figure, and we have 197,920.8 / 33,000 = 5.99 H. P.
THE FOOT MEASURE.--How long is a foot, and what is it determined by? It
is an arbitrary measure. The human foot is the basis of the measurement.
But what is the length of a man's foot? It varied in different countries
from 9 to 21 inches.
In England, in early days, it was defined as a measure of length
consisting of 12 inches, or 36 barleycorns laid end to end. But
barleycorns differ in length as well as the human foot, so the standard
adopted is without any real foundation or reason.
WEIGHT.--To determine weight, however, a scientific standard was
adopted. A gallon contains 8.33 pounds avoirdupois weight of distilled
water. This gallon is divided up in two ways; one by weight, and the
other by measurement.
Each gallon contains 231 cubic inches of distilled water. As it has four
quarts, each quart has 57-3/4 cubic inches, and as each quart is
comprised of two pints, each pint has nearly 29 cubic inches.
THE GALLON.--The legal gallon in the United States is equal to a
cylindrical measure 7 inches in diameter and 6 inches deep.
Notwithstanding the weights and dimensions of solids and liquids are
thus fixed by following a scientific standard, the divisions into
scruples, grains, pennyweights and tons, as well as cutting them up into
pints, quarts and other units, is done without any system, and for this
reason the need of a uniform method has been long considered by every
country.
THE METRIC SYSTEM.--As early as 1528, Fernal, a French physician,
suggested the metric system. Our own government recognized the value of
this plan when it established the system of coinage.
The principle lies in fixing a unit, such as a dollar, or a pound, or a
foot, and then making all divisions, or addition, in multiples of ten.
Thus, we have one mill; ten mills to make a dime; ten dimes to make a
dollar, and so on.
BASIS OF MEASUREMENT.--The question arose, what to use as the basis of
measurement, and it was proposed to use the earth itself, as the
measure. For this purpose the meridian line running around the earth at
the latitude of Paris was selected.
One-quarter of this measurement around the globe was found to be
393,707,900 inches, and this was divided into 10,000,000 parts. Each
part, therefore, was a little over 39.37 inches in length, and this was
called a meter, which means _measure_.
A decimeter is one-tenth of that, namely, 3.937 inches; and a decameter
39.37, or ten times the meter, and so on.
For convenience the metrical table is given, showing lengths in feet and
inches, in which only three decimal points are used.
Metrical Table, showing measurements in feet and inches:
METRICAL TABLE, SHOWING MEASUREMENTS IN FEET
AND INCHES
------------------------------------------
------------+--------------+--------------
Length | Inches | Feet
------------+--------------+--------------
Millimeter | 0.039 | 0.003
Centimeter | 0.393 | 0.032
Decimeter | 3.937 | 0.328
Meter | 39.370 | 3.280
Decameter | 393.707 | 32.808
Hectometer | 3937.079 | 328.089
Kilometer | 39370.790 | 3280.899
Myriameter | 393707.900 | 32808.992
------------+--------------+--------------
METRIC SYSTEM, SHOWING THE EQUIVALENTS
IN OUR MEASURES
1 Myriameter = 5.4 nautical miles, or 6.21 statute
miles.
1 Kilometer = 0.621 statute mile, or nearly 5/8
mile.
1 Hectometer = 109.4 yards.
1 Decameter = 0.497 chain, 1.988 rods.
1 Meter = 39.37 inches, or nearly 3 ft. 3-3/8
inches.
1 Decimeter = 3.937 inches.
1 Centimeter = 0.3937 inch.
1 Millimeter = 0.03937 inch.
1 Micron = 1/25400 inch.
1 Hectare = 2.471 acres.
1 Arc = 119.6 square yards.
1 Centaire, or square
meter = 10.764 square feet.
1 Decastere = 13 cubic yards, or about 2-3/4
cords.
1 Stere, or cubic meter = 1.308 cubic yards, or 35.3 cubic
feet.
1 Decistere = 3-1/2 cubic feet.
1 Kiloliter = 1 ton, 12 gal., 2 pints, 2 gills
old wine measure.
1 Hectoliter = 22.01 Imperial gals., or 26.4
U. S. gals.
1 Decaliter = 2 gallons, 1 pint, 2-2/5 gills, imperial
measure, or 2 gals., 2
qts., 1 pt., 1/2 gill, U. S.
1 Liter = 1 pint, 3 gills, imperial, or 1 qt.,
1/2 gill U. S. measure.
1 Decileter = 0.704 gill, imperial, or 0.845 gill
U. S. measure.
1 Millier = 2,204.6 pounds avoirdupois.
1 Metric quintal = 2 hundredweight, less 3-1/2
pounds, or 220 pounds, 7
ounces.
1 Kilogram = 2 pounds, 3 ounces, 4-3/8
drams avoirdupois.
1 Hectogram = 3 ounces, 8-3/8 drams avoirdupois.
1 Decagram = 154.32 grains Troy.
1 Gram = 15.432 grains.
1 Decigram = 1.542 grain.
1 Centigram = 0.154 grain.
1 Milligram = 0.015 grain.