Modern Engineering Thermodynamics

1.5 How Do We Measure Things? 7
being measured in units of feet or meters has nothing to do with any physical law. It is solely dependent on the
creativity and ingenuity of people. Therefore, whereas the basic concepts of dimensions are grounded in the fundamental
logic of descriptive analysis, the basic ideas behind the units systems are often grounded in the roots
of past civilizations and cultures.
ANCIENT UNITS SYSTEMS
Intuition tells us that civilization should have evolved using the decimal system. People have ten fingers and ten toes, so the
base 10 (decimal) number system would seem to be the most logical system to be adopted by prehistoric people. However,
archaeological evidence has shown that the pre-Egyptian Sumerians used a base 60 (sexagesimal) number system, and ancient
Egyptians and early American Indians used a base 5 number system. A base 12 (duodecimal)
number system was developed and used extensively during the Roman Empire. Today, mixed
remains of these ancient number systems are deeply rooted in our culture.
A fundamental element of a successful mercantile trade is that the basic units of commerce
have easily understood subdivisions. Normally, the larger the base number of a particular
number system, the more integer divisors it has. For example, 10 has only three divisors
(1, 2, and 5), but 12 has five integer divisors (1, 2, 3, 4, and 6) and therefore makes a considerably
better fractional base. On the other hand, 60 has an advantage over 100 as a
number base because the former it has 11 integer divisors whereas 100 has only 8.
Hand
Cubit
The measurements of length and time were undoubtedly the first to be of concern to
prehistoric people. Perhaps the measurement of time came first, because people had to
know the relationship of night to day and understand the passing of the seasons of the
year. The most striking aspect of our current measure of time is that it is a mixture of
three numerical bases; decimal (base 10) for counting days of the year, duodecimal (base
12) for dividing day and night into equal parts (hours), and sexagesimal (base 60) for
dividing hours and minutes into equal parts.
Nearly all early scales of length were initially based on the dimensions of parts of the adult
human body because people needed to carry their measurement scales with them (see
Figure 1.6). Early units were usually related to each other in a binary (base 2) system. For
example, some of the early length units were: half-hand = 2 fingers; hand = 2 half-hands;
span = 2 hands; forearm (cubit) = 2 spans; fathom = 2 forearms, and so forth. Measurements
of area and volume followed using such units as handful = 2 mouthfuls, jack = 2
handfuls, gill = 2 jacks, cup = 2 gills, and so forth.
Pace
Foot
FIGURE 1.6
Egyptian man with measurements.
Weight was probably the third fundamental measure to be established, with the development of such units as the grain
(i.e., the weight of a single grain of barley), the stone, and the talent (the maximum weight that could be comfortably
carried continuously by an adult man).
CRITICAL THINKING
Where are Roman numerals still commonly used today? How would technology be different if we used Roman numerals
for engineering calculations today?
NURSERY RHYMES AND UNITS
Many of the Mother Goose nursery rhymes were not originally written for children but in reality were British political
poems or songs. For example, in 17th century England, the treasury of King Charles I (1625–1640) ran low, so he imposed
a tax on the ancient unit of volume used for measuring honey and hard liquor, the jack (1 jack = 2 handfuls). The response
of the people was to avoid the tax by consuming drink measured in units other than the jack. Eventually, the jack unit
became so unpopular with the people that it was no longer used for anything. One of the few existing uses of the jack unit
(Continued)