Dear Joe,

Thank you for your response. I have interspersed some remarks.

on 2003-07-15 10.18, Joseph B. Reid at [EMAIL PROTECTED] wrote:

> Pat Naughtin wrote in USMA 26339:
>> 
>> I favor the idea of renaming the right angle as the 'quad' (with milliquads,
>> microquads etc.) as the basis for the best choice for practical angle
>> measurements in SI. If you would like me to elaborate on this let me know
>> and I will send you a short essay on the quad.
>> 
>> As a matter of interest, an angle of 1 milliquad would subtend a distance of
>> 785 millimetres at a distance of 1 kilometre.
> 
> I am confused. I get that at 1 km an angle of 1 quad would be
> subtended by �/2 km, and hence a milliquad would be subtended by �/2
> m = 1.571 m.

Thanks Joe. You are right. I made a calculation error. I should have said.
'As a matter of interest, an angle of 1 milliquad would subtend a distance
of 1571 millimetres or 1.571 metres at a distance of 1 kilometre.

> What is the diference, if any, between 1 milliquad and 0.1 grade, grad or gon?

A quad is the name that I have given to a right angle and this is in keeping
with many European languages. I chose the word quad because it is short for
quadrant and, as a single syllable word it lends itself to being coupled
with prefixes as in milliquad and microquad.

The Dent Dictionary of Measurement (J M Dent 1994) defines grad and grade as
follows:

** begin quote
grad (arc measure] One-hundredth of a right-angle or quadrant, alternatively
known as a gon. 

1 grad = 0.9 (nine-tenths of a) degree
100 grads = 90 degrees
200 grads = 180 degrees
400 grads = 360 degrees

The unit is used particularly in the calculation of a course in maritime
navigation, and for locating a vessel's position at sea.

The name of the unit relates to a grade (see below); as a gon, the term
derives from the ancient Greek for 'angle' (as in polygon; akin to English
knee).

grade [maths] Primarily another word for DEGREE and, in many European
languages, the only word for 'degree'. [Etymologically, both grade and
degree derive from Latin (de)gradus 'step (down)'.]

Despite the potential confusion, however, the term is additionally an
alternative for GRAD or gon (nine-tenths of a degree).

In the United States, the word grade is also used as a synonym for GRADIENT.
** end quote

It seems to me that there is a real need for a simple unambiguous unit for
angle that can be understood by those who have to use angle measures
everyday in their work eg. carpenters, paper hangers, and tailors. I don't
think that the grad, grade, or gon fits the description of being simple and
unambiguous.

As I said, I think of a quad as a 'right angle', and I think that a quad
meets both of the above criteria � it is both simple and unambiguous.

That is why I believe that the quad would be a suitable unit, either as an
SI base unit, or, if that idea is too radical for the CGPM, then as a unit
that would replace the degree in 'Table 6 Non-SI units accepted for use with
the International System' (page 105). This would place the quad in a similar
position to the litre, the hour, the tonne, and the bel. If we choose the
latter course then I see no need to remove the radian from 'Table 3. SI
derived units with special names and symbols' (page 100) as the radian has a
useful place within the mathematical framework of the SI. However, in
considering these options I very much favor the idea of the quad being the
SI base unit of the quantity 'plane angle' and if this was done we would
have to reconsider the place of the radian.

So to get back to your question,

> What is the diference, if any, between 1 milliquad and 0.1 grade, grad or gon?

and to answer in the original context:

At a distance of 1 kilometre:

1 degree                    would be subtended by 17.453 metres.
1 grad, grade, or gon would be subtended by 15.708 metres.
so
0.1 grad, grade, or gon would be subtended by 1.571 metres.
and
1 milliquad                would be subtended by  1.571 metres.

There is no diference between the numerical value of 1 milliquad and 0.1
grade, grad or gon, but there is a profound difference in how these could be
understood by users and potential users of the SI. Keep in mind that the
issues of units of plane angle have been confusing people all around the
world since the 1790s and before.

It is interesting in this context to refer to the 'Instructions for Authors'
for 'Metrologia', the world's leading metrology journal published by the
BIPM. At one point they say, 'Authors must employ the International System
of Units, for which the prime reference is Le Syst�me International d'Unit�s
(SI), published by the Bureau International des Poids et Mesures, F-92312
S�vres Cedex, France' and at another point they say that 'Half-tone
photographs . . . should be trimmed at right angles'.

Do they mean that we should use the SI unit 'radians' within the articles we
write but use the non-SI 'right angles' when we prepare our photographs. I
think I detect some confusion here.

Cheers,

Pat Naughtin LCAMS
Geelong, Australia
-- 

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