Editing Mass (section)

=== Weight as an amount ===
{{main|Weight}}
[[File:El pesado del corazón en el Papiro de Hunefer.jpg|right|thumb|Depiction of early [[balance scales]] in the [[Papyrus of Hunefer]] (dated to the [[Nineteenth dynasty of Egypt|19th dynasty]], {{circa|1285 BCE}}). The scene shows [[Anubis]] weighing the heart of Hunefer.]]

The concept of [[wikt:amount|amount]] is very old and [[Prehistoric numerals|predates recorded history]]. The concept of "weight" would incorporate "amount" and acquire a double meaning that was not clearly recognized as such.<ref name=":0" />

{{Blockquote|text=What we now know as mass was until the time of Newton called “weight.” ... A goldsmith believed that an ounce of gold was a quantity of gold. ... But the ancients believed that a beam balance also measured “heaviness” which they recognized through their muscular senses. ... Mass and its associated downward force were believed to be the same thing.|author=K. M. Browne|title=The pre-Newtonian meaning of the word “weight”}}

Humans, at some early era, realized that the weight of a collection of similar objects was [[Proportionality (mathematics)|directly proportional]] to the number of objects in the collection:
: <math>W_n \propto n,</math>
where ''W'' is the weight of the collection of similar objects and ''n'' is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant [[ratio]]:
: <math>\frac{W_n}{n} = \frac{W_m}{m}</math>, or equivalently <math>\frac{W_n}{W_m} = \frac{n}{m}.</math>

An early use of this relationship is a [[balance scale]], which balances the force of one object's weight against the force of another object's weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields.  Hence, if they have similar masses then their weights will also be similar.  This allows the scale, by comparing weights, to also compare masses.

Consequently, historical weight standards were often defined in terms of amounts.  The Romans, for example, used the [[carob]] seed ([[Carat (unit)|carat]] or [[siliqua]]) as a measurement standard.  If an object's weight was equivalent to [http://std.dkuug.dk/JTC1/SC2/WG2/docs/n3138.pdf 1728 carob seeds], then the object was said to weigh one Roman pound.  If, on the other hand, the object's weight was equivalent to [[Ancient Roman units of measurement|144 carob seeds]] then the object was said to weigh one Roman ounce (uncia).  The Roman pound and ounce were both defined in terms of different sized collections of the same common mass standard, the carob seed.  The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was:
: <math>\frac{\mathrm{ounce}}{\mathrm{pound}} = \frac{W_{144}}{W_{1728}} = \frac{144}{1728} = \frac{1}{12}.</math>