Earth Air Fire and Water
The Pharmageddon Herbal
Chapter 4 Part 2
The Measure of Things 4.15
Measurements are fundamental to every sphere of human activity. By measure of the greatest to the smallest, we may see the symmetry of things and their relationship to each other irrespective of scale.
Standing at the kerbside, the eye measures, at the brains command; converging vehicle speed, height of kerb to roadside, speed required to cross safely. Go or stay. Multiple calculations of measure at the speed of light. No margin of error, a mistake could be terminal.
In a supermarket aisle reaching for a packet, or scaling a mountain , multiple internal measures, without which, we could not function at the level of complexity required of the human condition.
Our internal measures are unique, as we as individuals are. Moreover our scales of measurement must cope with the exigency of gestation to old age. Quite clearly measurement and number are the first requirement of a civilisation, if it is to function as a higher organism within the whole. A standard measure is created and adhered to. In this way we may refer to a ‘head of state or the ‘military arm’ when speaking of these complex higher organisms of State which are only made possible by number and measure.
There are many different systems of measurement in use throughout the world, with each one having its own standard, the standard being a specific measure to which other things are compared. It will be appreciated that conversion tables, although necessary, are time consuming, cumbersome and prone to user error. In the context of chemistry, medicine or pharmacy, an error could have tragic consequences. Teach yourself the Metric System.
The rapid global expansion of science and technology meant that a coherent global system of units was not only desirable, but very necessary. From 10 fingers and 10 toes, it is not a great intellectual leap to one of our earliest counting machines, the ‘Abacus’ which still finds widespread use in the West for the teaching of place and number in units of 1 to 10.
The Metric System 4.16
The metric or decimal system has a number base of 10. The conversion of related units is convenient because only the decimal point is moved either left or right as the units change.
A coherent metric system was first proposed in Lyon, France around 1690. Just over 100 years later the system was standardised by the Paris Academy of Sciences, and was finally legalised in 1801. Since that time it has undergone various revisions, which are carried out by the International Bureau of Weights and Measures.
We are able to make sense of very large numbers by the use of Powers, Prefix and symbol. For example, a metric billion means 1000 000 000 000 (1 million, million). We may write that number by the use of Power. A billion has 12 zero,s and is written 10^{12} . One million (1000 000) has 6 zero,s and is written 10^{6}. We operate in the same way when dealing with very small numbers, except the decimal point moves to the left and is designated as the negative power and is indicated by a negative sign. E.g. 1 millionth part of (0.000 001) is written 10^{-6}
Powers of 10. Table 4.16A
Symbol |
Number |
Prefix |
Meaning |
Power |
M |
1000 000 |
mega |
million |
10^{6} |
k |
1000 |
Kilo |
thousand |
10³ |
h |
100 |
hecto |
hundred |
10² |
da |
10 |
decca |
ten |
10¹ |
d |
0.1 |
deci |
tenth |
10^{-1} |
c |
0.01 |
centi |
hundredth |
10^{-2} |
m |
0.001 |
milli |
thousandth |
10^{-3} |
µ |
0.000 001 |
micro |
millionth |
10^{-6} |
Number, Power and Indices 4.17
If a number is multiplied by itself, it has been raised to the power of 2, (for example 3 x 3) and may be written as 3^{2}, or if it is raised to the power of 3, (eg. 3 x 3 x 3), it may be written 3^{3} The small number to the right of the of the main number is called the ‘power’ or ‘index’ which states the number of times that a number must be multiplied by itself.
If a number is raised to the power of 2, it is said to be ‘squared’, eg., the area of a house or land is 10 square metres, it can be written as 10^{2} or 10 metre^{2} .
If a number is raised to the power of 3, it is said to be ‘cubed’ eg, the volume occupied by a house is 50 cubic metres, and written, 50³ or 50 metre^{3}
Negative Power or Index 4.18
The negative power indicates how many times a given number must be divided into unity or 1.
Example 3^{-3} means 1 ÷ 3 ÷ 3 ÷ 3, which equals 0.037;
Another example, 10^{-3} means 1 ÷ 10 ÷ 10 ÷ 10 = 0.001.
It may be seen that with negative powers, the decimal point moves to the left of the conversion factor, by the number of places indicated by the index, or power number.
Multiplying by Power 4.19
The same principle applies when multiplying by powers, except the decimal point moves to the right. A comprehensive set of conversion tables will be given, however be warned that the universal scientific notation is metric based. Learn the Metric System!
The International System of Units 4.20
Since 1960 the metric system has been undergoing a gradual refinement of the units used, with the aim of securing uniformity. The new system is called the International System of Units, which is usually abbreviated to S.I. Units.
The importance of the S.I. System cannot be overstated because we can communicate core concepts of any activity in precision language. For the population at large, and for all practical purposes, we can consider the Metric and S.I. systems as identical.
Physical and Base Quantities 4.21
I often say that when you can measure what you are speaking about, and express it in numbers,
you know something about it; but when you cannotexpress it in numbers, your knowledge of it is
of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely,
in your thoughts, advanced to the stage of science, in whatever the matter may be.
William Thomson, 1st Baron, Lord Kelvin.
Lord Kelvin was a British Physicist, who amongst other things formulated the second law of thermodynamics in 1850. He also introduced an absolute temperature scale, the units of which were named the Kelvin.
The S.I. Units can be described as universal currency of concepts, in which inflation or devaluation are not allowed, unless by international agreement. The base unit must accord with whatever is being counted or measured, for instance; give me 100 dollars worth of apples is meaningless, in the context of the number of apples that are purchased.
If, however, $100 will buy 50 kilogram of apples, we then know something about the mass of apples, but nothing about the mass of a single apple. The kilogram is the base unit for mass, therefore, the mass of an individual apple would be a sub-multiple of the kilo-gram, and would be expressed as ‘x’ number of grams.
There are currently 7 base quantities which are defined by the S.I.System.
Table 4.21A Base Quantities and Units
Base Quantity |
Unit Name |
Unit Symbol |
Length |
metre |
m |
Mass |
kilogram |
kg |
Thermodynamic Temperature |
Kelvin |
K |
Time |
second |
s |
Electric Current |
ampere |
A |
Luminous Intensity |
candela |
cd |
Amount of Substance |
mole |
mol |
If we wish to know the volume of the mass, then it would be necessary to use a different base unit, in this case the metre ^{3 }; the volume would then be expressed as a sub multiple of the metre, i.e. centimetres or millimetres cubed. Such units are known as derived units.
Table 4.21B. Selected Derived Units S.I. System.
Physical Quantity |
Derived Unit |
Symbol |
Area |
square metre |
m^{2} |
Volume |
cubic metre |
m^{3} |
Density (mass) |
kilogram /cubic metre |
kg/m^{3} |
Velocity |
metre per second |
m/s |
Pressure |
Pascal |
Pa |
Thermal Conductivity |
watt per metre degree Kelvin |
w/ (m-K ) |
Concentration |
mole per cubic metre |
mol/m^{3} |
Energy, Heat Quantity |
Joule |
J |
Power, Radiant Flux |
Watt |
W |
Heat Flux Density |
Watt per square metre |
W/m^{2} |
Specific Heat Capacity |
Joule per kg Kelvin |
J/kg/K |
N.B. A Pascal = Newton /metre ^{3}
Conversion Factors 4.22
The tables that follow and the values given are those of the International System of Units. (S.I.)
Table 4.22A
Length |
cm |
metre |
km |
in |
ft |
mile |
1 centimetre |
1 |
10 ^{-2} |
10 ^{-5} |
0.3937 |
3.281 x 10 ^{-2} |
6.214 x 10^{ -6} |
1 metre |
100 |
1 |
10 ^{-3} |
39.37 |
3.281 |
6.214 x 10^{ -4} |
1 kilometre |
10^{ 5} |
1000 |
1 |
3.967 x 10^{4} |
3281 |
0.6214 |
1 inch |
2.540 |
0.3937 |
3.937 x 10^{4} |
1 |
8.333 x 10^{ -2} |
1.578 x 10 ^{-5} |
1 foot |
30.48 |
0.3048 |
3.048 x 10^{ 4} |
12 |
1 |
1.894 x 10^{ -4} |
1 statute mile |
1.609 x 10 ^{5} |
1609 |
1.609 |
6.336 x 10^{4} |
5280 |
1 |
Table 4.22B
Area |
metre² |
cm² |
ft² |
in² |
1 square metre |
10^{-2} |
0.3937 |
3.281 x 10^{-2} |
6.214 x 10^{-2} |
1 square centimetre |
10^{-4} |
1 |
1.076 x 10^{-3} |
0.1550 |
1 square foot |
9.290 x 10^{-4} |
929.0 |
1 |
144 |
1 square inch |
6.452 x 10^{-4} |
6.452 |
6.944 x 10^{-3} |
1 |
Table 4.22C
Volume |
metre ^{3} |
cm³ |
litre |
Ft ³ |
in³ |
1 cubic metre |
1 |
10^{ 6} |
1000 |
35.31 |
6.102 x 10 ^{4} |
1 centimetre ³ |
10 ^{-6} |
1 |
1.000 x 10^{-3} |
3.531 x 10^{-5} |
6.102 x 10^{-2} |
1 litre |
1.000 x 10^{-3} |
1000 |
1 |
3.531 x 10 ^{-2} |
61.02 |
1 cubic foot |
2.832 x 10^{ -2} |
2.832 x 10 ^{4} |
28.32 |
1 |
1728 |
1 cubic inch |
1.639 x 10^{-5} |
16.39 |
1.639 x 10^{-2} |
5.787 x 10 ^{-4} |
1 |
Table 4.22D
Speed |
ft/s |
km/hr |
m/s |
miles/hr |
cm/s |
1 foot per second |
1 |
1.097 |
0.3048 |
0.6818 |
30.48 |
1 kilometre per hour |
0.9113 |
1 |
0.2778 |
0.6214 |
27.78 |
1 metre per second |
3.281 |
3.6 |
1 |
2.237 |
100 |
1 mile per hour |
1.467 |
1.609 |
0.4470 |
1 |
44.70 |
1 centimetre second |
3.281 x 10 G ² |
3.6 x 10 G ² |
0.01 |
2.237 x 10 G ² |
1 |
Table 4.22E
Pressure |
atm |
cm Hg |
Pa |
lb/in ² |
1 atmosphere |
1 |
76 |
1.013 x 10^{5} |
14.70 |
1 cm mercury at 0°C |
1.316 x 10^{-2} |
1 |
1333 |
0.1934 |
1 Pascal |
9.869 x 10^{-6} |
7.501 x 10^{-4} |
1 |
1.450 x 10^{-4} |
1 lb per inch |
6.805 x 10^{-2} |
5.171 |
6.895 x 10^{3} |
1 |
Table 4.22F
Power |
BTU/hr |
hp |
Cal/s |
kw |
Watts |
1 BTU/hr |
1 |
3.929 x 10^{-4} |
7.000 x 10^{-2} |
2.930 x 10^{-4} |
0.2930 |
1 horsepower |
2545 |
1 |
178.2 |
0.7457 |
745.7 |
1 calorie/s |
14.29 |
5.613 x 10^{-3} |
1 |
4.186 x 10^{-3} |
4.186 |
1 kilowatt |
3413 |
1.341 |
238.9 |
1 |
1000 |
1 Watt |
3.413 |
1.341 x 10^{-3} |
0.2389 |
0.001 |
1 |
Table 4.22G
Energy |
Btu |
hp/hr |
Joule |
cal |
kW/hr |
1 Btu |
1 |
3.929 x 10^{-4} |
1055 |
252 |
2.930 x 10^{-4} |
1 Horsepower |
2524 |
1 |
2.685 x 10^{6} |
6.414 x 10^{5} |
0.7457 |
1 Joule |
9.481 x 10^{-4} |
3.725 x 10^{-7} |
1 |
0.2389 |
2.778 x 10^{-7} |
1 Calorie |
3.968 x 10^{-3} |
1.559 x 10^{-6} |
4.186 |
1 |
1.163 x 10^{-6} |
1 kilowatt hour |
3413 |
1.341 |
3.6 x 10^{6} |
8.601 x 10^{5} |
1 |
Miscellaneous Factors 4.23
p or pi ,is the 16th letter of the Greek alphabet, and is used as a math symbol that denotes the ratio of the circumference of a circle to its diameter i.e. p = 3.14159.
The diameter of a circle is a straight line from edge to edge, passing through the centre. The radius of a circle is half the diameter. The circumference is the distance around the edge of a complete circle.
Figure 4.23A
r = radius
D = diameter
C = circumference
The Area of a circle. = p r^{2} = 3.14159 x square of radius.
Example. Assume the radius of a circle is 25cm, then the calculation is; r^{2} = r x r = 25 x 25 = 625cm therefore, the area of the circle is 3.14159 x 625 = 1963.49cm².
The volume of a cylinder = p ^{2} x height = p x height x r^{2}, in other words, the area of 1 end x height.
Example. The height of a drum or cylinder is 100cm, then the calculation is; Area = 1963.49 x 100 = 196349cm^{3}.
When measuring area, 2 dimensional space is measured.
When measuring volume, 3 dimensional space is measured.
Example. The area of a rectangle is length x breadth = area. The volume of a cube is length x breadth x height.
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