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Re: A weighty subject



I would like to clarify and summarize this thread. The conventional
definition of weight is, e.g., as stated in "A Textbook of the
Principles of Physics" by Alfred Daniell, Macmillan & Co, New York
and London, 1894:

The remaining fundamental idea involving measurement is that
of *Mass* or *quantity of Matter*. The notion implied in this
term is quite distinct from that of Weight. The weight of a
certain quantity of matter depends upon the presence and
nearness of other matter, which attracts it according to the
well-known law of Gravitation. This may, and even within our
terrestrial observation, does vary; the effect of gravity on a
given mass - that is to say, its Weight - is greater as we near
the poles than it is at the equator; and the weight of a
substance varies, therefore, according to local causes, while
the quantity of matter in it remains the same. Cæteris paribus,
however, equal masses will everywhere counterpoise one another
in a balance, and we may define the *unit of mass* as that
quantity of matter which will counterpoise in a balance a
certain standard mass known as a standard Pound or Gramme.

I believe this definition is substantially equivalent to the
definitions in all textbooks which have made significant market
penetration in the English speaking world. It is very definite
and complete; it is not wrong.

I would appreciate direction to the definition of weight which
has the official sanction of some authoritative body, e.g. BIPM
or IUPAP. I have not been able to locate one. If such a
definition exists then I will be informed by it and adjust my
terminology appropriately, but until I see I am *wrong* I will
continue to teach my students my students that the appropriate
approximation to apply in laboratories anywhere, including on
Earth's surface, is that all objects are acted upon by
noncontact forces proportional to their respective masses, and
I will call the (vector) constant of proportionality g, and the
forces themselves I will refer to as the "weights" of those
objects. I will point out that I can measure the weight of an
object in static equilibrium in the laboratory using a scale,
with the direction of the weight defined as being downward.

Thus the weight W of any object in the laboratory is given by

W = mg

g is called "the acceleration of gravity" and on Earth is
mostly due to Earth's gravitational attraction for the object.

It is important to realize that this constitutes an operational
definition of g which conforms to the geophysicist's meaning
of "the acceleration of gravity", conforms to his measurements
of this quantity, and *it is not equal to the gravitational
field strength in the laboratory*.

Since the latter definition is more accurate and more useful
than the conventional definition, and if it does not disagree
with some externally mandated meaning for the term "weight", I
advocate its adoption in future textbooks. I maintain that it
does no violence to any of the Newtonian physics instruction we
do, it is conceptually simpler than the conventional definition,
and it is less wrong!

I await citation of the authoritative definition of weight. I
already gave my own, the OED, and I will add that Webster's
Ninth New Collegiate Dictionary and many others concur. They
all say that the weight of an object is what it weighs.

What benefit is there to being out of step with this meaning?

Leigh