Richard Jackson wrote:
An empirical equation is one that is not based on theory, only observations. The equation is arbitrary, in the sense that it was not derived from fundamental theory, but it does describe the observations in question.
Yep. That saves me from some typing. 
Stuart
[Reminded me of the debate in Working with numbers or variables with Units - there are a few discussions about empirical equations in there.]
Yep. That saves me from some typing.
Is your answer to me any shorter than the one to Philip would have been? 
From the first volumes of the Transactions of the American Society of Civil Engineers (just an example), units have been printed in roman. The following excerpt is taken from Volume 2, published in 1874:
You will notice that:
- pound units (lbs) are typed in roman. (Units are in roman throughout the Transactions)
At the same time, notice that:
- intermediate numerical values are shown;
- variables are not unnecessarily repeated in the second equation; (u⁴ is a typo, it should read u₄)
- the symbol for multiplication is ・ when used with variables and ✕ when used with numbers.
The last point is mentioned, 142 years later, in the current International System of Units:
In the year 1900, Gustave Eiffel published a voluminous book describing the main structural and mechanical aspects of design, construction and operation of the Eiffel Tower. Here is where it gets crazy. Units are printed in italics both in the text and in calculations!
Wow! At least, I won my own challenge and please don’t tell me that Eiffel did not know what is was doing.
But today units must be printed in roman. It all about standards and legislation. At first, governments are expecting that the changeover to SI will be done on a voluntary basis. Eventually though, companies that do not abide by the law may be subject to fines. Boards of Professional Engineers may not appreciate the fact that engineers do not document their work in the most appropriate way. The ISO certification of some engineering firms could be jeopardized. Who knows, but then you will be arguing with these people, not with me.
Sorry if I "mislead you" into thinking that the purpose of my thread was to debate about lawsuits.
Back to units:
- If a sentence is in italics, like this one, it would make sense to have units in italics, for example 1 mm = 0.001 m.
- Units could be in any font, for example 1 km = 1000 m, as long as it is that of the sentence.
I found an occurrence of units in blue, bold, italics, in “Quotations of Brainy Smurf”:
If a sentence is in italics, like this one, it would make sense to have units in italics, for example 1 mm = 0.001 m.
I thought you were in favor of abiding to the rules.... ISO 80000-1 says (paragraph 7.2.1):
"Symbols for units are always written in roman (upright) type, irrespective of the type used in the rest of the text."
And ISO 80000-2 adds that an explicitly defined function is printed in roman (upright), such as sin, exp, ln etc.
as are mathematical constants such as e and pi
and also well defined operators.
This means that also the equals sign must be upright!
Further: Numbers expressed ion the form of digits are always printed in Roman (upright) style.
So it must be:
Even if a sentence is in italics, like this one, the units, digits and standard operators must still be in upright font, for example: 1 mm = 0.001 m.
Luc
LucMeekes wrote:
I thought you were in favor of abiding to the rules....
Of cause not. Rules are only for my students.
LucMeekes wrote:
So it must be:
Even if a sentence is in italics, like this one, the units, digits and standard operators must still be in upright font, for example: 1 mm = 0.001 m.
You are right. It is Eiffel's fault, he misled me.
In Russian the word "roman" is not a font, but a literary work - роман, a novel - the novel of Leo Tolstoy's "War and Peace" for example.
I read this discussion as a novel about units - the novel "Units general and in Mathcad partial". The chapter 1 "Angles and units: to be or not to be?"
Dominique Bauer wrote:
Units in roman
“The International System of Units”, now adopted throughout the world, specifies which units to use and how to write them. Defined in the SI Brochure , it is clear on the subject:
Chapter 5: Writing unit symbols and names, and expressing the values of quantities
Unit symbols
Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. They are printed in lower-case letters unless they are derived from a proper name, in which case the first letter is a capital letter.
The National Institute of Standards and Technology (NIST), an agency of the U.S. Department of Commerce, has published “The NIST Guide for the use of the International System of Units”, which is also clear on the subject:
Chapter 6. Rules and Style Conventions for Printing and Using Units
6.1.1 Typeface
Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text. (See also Sec. 10.2 and Secs. 10.2.1 to 10.2.4.)
where Sections 10.2 and 10.2.1 to 10.2.4 restate and explain the rule.
Essentially, units are written in roman in order to distinguish them from variables which are written in italics. For example, "m" is a variable whereas "m" is a unit. Please refer to one of the above publications for more details. Note that the color of the font for units (as well as for numbers, variables, etc.) is not addressed in these documents..
In Mathcad, displaying units in a color different than that of variables is a good way to distinguish them even better. However, displaying them in italics is unnecessary and wrong.
References
The “SI Brochure” is available in English at http://www.bipm.org/en/publications/si-brochure/.
“The NIST Guide for the use of the International System of Units” is available at http://www.nist.gov/pml/pubs/sp811/.
Here's another item from NIST:
Typefaces for Symbols in Scientific Manuscripts
