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1395 lines
76 KiB
1395 lines
76 KiB
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN">
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<!DOCTYPE html PUBLIC "W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN"
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<title>Units in MathML</title>
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<link type="text/css" rel="stylesheet" href="http://www.w3.org/StyleSheets/TR/W3C-WG-NOTE.css">
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</head>
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<body>
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<div class="head">
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<p>
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<a href="http://www.w3.org/"><img width="72" height="48" alt="W3C" src="http://www.w3.org/Icons/w3c_home"></a>
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</p>
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<h1>
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<a id="title"></a>Units in MathML</h1>
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<h2>
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<a id="w3c-doctype"></a>W3C Working Group Note 10 November 2003</h2>
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<dl>
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<dt>This version:</dt>
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<dd>
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<a href="http://www.w3.org/TR/2003/NOTE-mathml-units-20031110/">http://www.w3.org/TR/2003/NOTE-mathml-units-20031110/</a>
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</dd>
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<dt>Latest version:</dt>
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<dd>
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<a href="http://www.w3.org/TR/mathml-units/">http://www.w3.org/TR/mathml-units/</a>
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</dd>
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<dt>Previous version:</dt>
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<dd>
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<span>This is the first version of this Note.</span>
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</dd>
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<dt>Editors:</dt>
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<dd>Douglas Wilhelm Harder - Invited Expert, University of Waterloo</dd>
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<dd>Stan Devitt - Invited Expert, StratumTek</dd>
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</dl>
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<p class="copyright">
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<a href="http://www.w3.org/Consortium/Legal/ipr-notice#Copyright">Copyright</a> © 2003 <a href="http://www.w3.org/"><acronym title="World Wide Web Consortium">W3C</acronym></a><sup>®</sup> (<a href="http://www.lcs.mit.edu/"><acronym title="Massachusetts Institute of Technology">MIT</acronym></a>, <a href="http://www.ercim.org/"><acronym title="European Research Consortium for Informatics and Mathematics">ERCIM</acronym></a>, <a href="http://www.keio.ac.jp/">Keio</a>), All Rights Reserved. W3C <a href="http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer">liability</a>, <a href="http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks">trademark</a>, <a href="http://www.w3.org/Consortium/Legal/copyright-documents">document use</a> and <a href="http://www.w3.org/Consortium/Legal/copyright-software">software licensing</a> rules apply.</p>
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</div>
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<hr>
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<div>
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<h2>
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<a id="abstract"></a>Abstract</h2>
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<p>MathML is an XML application for describing mathematical
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notation, capturing both its structure and content. As such, its
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scope does not extend to include units - determinate quantities
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adopted as standards of measure - which nevertheless, by their
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very nature, occur in an applied mathematical setting. This
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Note makes recommendations and suggestions for how units can be
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incorporated into MathML.</p>
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</div>
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<div>
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<h2>
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<a id="status"></a>Status of this Document</h2>
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<p>
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<em>This section describes the status of this document
|
|
at the time of its publication. Other documents may
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supersede this document. A list of current W3C
|
|
publications and the latest revision of this technical
|
|
report can be found in the <a href="http://www.w3.org/TR/">W3C technical reports
|
|
index</a> at http://www.w3.org/TR/.</em>
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|
</p>
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<p> This document makes recommendations and suggestions for how
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to work with units in MathML. Please report comments and errors
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in this document to <a href="mailto:www-math@w3.org">www-math@w3.org</a>.</p>
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<p>This document has been produced by the W3C Math Working
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Group as part of the <a href="http://www.w3.org/Math/">W3C
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|
Math Activity</a> (<a href="http://www.w3.org/Math/Activity">Activity
|
|
statement</a>). The goals of the Working Group are
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|
discussed in the <a href="http://www.w3.org/Math/Documents/Charter2001.html">
|
|
Working Group Charter</a>. A list of <a href="http://www.w3.org/TR/2003/REC-MathML2-20031021/appendixi.html">participants
|
|
in the W3C Math Working Group</a> is available.</p>
|
|
<p>Publication as a Working Group Note does not imply
|
|
endorsement by the W3C Membership. This is a draft document
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|
and may be updated, replaced or obsoleted by other documents
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|
at any time. It is inappropriate to cite this document as
|
|
other than work in progress. Patent disclosures relevant to
|
|
this Note may be found on the Math Working Group's <a href="http://www.w3.org/Math/Disclosures">patent disclosure
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|
page</a>.</p>
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|
</div>
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<div class="toc">
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|
<h2>
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|
<a id="contents"></a>Table of Contents</h2>
|
|
<p class="toc">1 <a href="#introduction">Introduction</a>
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<br>
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1.1 <a href="#goals">Goals</a>
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<br>
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1.2 <a href="#definitions">Definitions</a>
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<br>
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2 <a href="#display_in_presentation">Display of Units in Presentation MathML</a>
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<br>
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2.1 <a href="#exceptions">Exceptions</a>
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<br>
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3 <a href="#inclusion_in_content">Inclusion of Units in Content MathML</a>
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<br>
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4 <a href="#identifying_in_presentation">Identifying Units in Presentation MathML</a>
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|
<br>
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5 <a href="#identifying_in_content">Identifying Unit Symbols in Content MathML</a>
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|
<br>
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5.1 <a href="#content">Element Content</a>
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|
<br>
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|
5.2 <a href="#encoding">Encoding Attribute</a>
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|
<br>
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|
5.3 <a href="#definitionURL">Definition URL Attribute</a>
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|
<br>
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5.3.1 <a href="#base">Base</a>
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<br>
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5.3.2 <a href="#name">Unit Name</a>
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<br>
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5.3.3 <a href="#context">Context</a>
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|
<br>
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5.3.4 <a href="#country_code">Country Code</a>
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<br>
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5.3.5 <a href="#prefix">Prefix</a>
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<br>
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6 <a href="#compound_in_content">Facilitating the Conversion of Units in MathML</a>
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<br>
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6.1 <a href="#dimension">Dimension</a>
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<br>
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|
6.2 <a href="#SI-equivalent-unit">SI Equivalent Unit</a>
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|
<br>
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6.3 <a href="#system">System</a>
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<br>
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6.4 <a href="#fps">Foot-Pound-Second System of Units</a>
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|
<br>
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|
6.5 <a href="#SI-conversion-factor">SI Conversion Factor</a>
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|
<br>
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6.5.1 <a href="#N4004AF">Examples</a>
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|
<br>
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7 <a href="#conversions">Conversions Using Semantic Information</a>
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|
<br>
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8 <a href="#examples">Examples</a>
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|
<br>
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|
9 <a href="#acknowledgements">Acknowledgements</a>
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|
<br>
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|
</p>
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|
<h3>
|
|
<a id="appendices"></a>Appendices</h3>
|
|
<p class="toc">A <a href="#bibliography">Bibliography</a>
|
|
<br>
|
|
B <a href="#prefixes">SI and IEC Prefixes</a>
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|
<br>
|
|
B.1 <a href="#SI-prefixes">SI Prefixes</a>
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|
<br>
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|
B.2 <a href="#IEC-prefixes">IEC Prefixes</a>
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|
<br>
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|
C <a href="#dimensions">Dimensions</a>
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|
<br>
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C.1 <a href="#base_derived_dimensions">Dimensions with SI Base or Derived Units</a>
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|
<br>
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|
C.2 <a href="#compound_dimensions">Dimensions with Compound SI Units</a>
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|
<br>
|
|
</p>
|
|
</div>
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|
<hr>
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|
<div class="body">
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|
<div class="div1">
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|
<h2>
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|
<a id="introduction"></a>1 Introduction</h2>
|
|
<p>The support of units within MathML <a href="#MathML2">[MathML2]</a> is of primary interest
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|
to those wishing to use MathML to encode measured data. This Note presents a recommendation
|
|
for how to include units in any MathML
|
|
expression. It deals with both the presentation and content representations of units.</p>
|
|
<p>The primary reference for this document is the IEEE/ASTM SI 10-1997
|
|
<em>Standard for the Use of the International System of Units (SI): The Modern Metric
|
|
System</em><a href="#ieee-astm">[ieee-astm]</a>,
|
|
hereafter referred to as <em>the standard</em>.
|
|
This Note only interprets what is defined in the standard and should not be used as a
|
|
replacement.</p>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="goals"></a>1.1 Goals</h3>
|
|
<p>The goals of this Note are to provide suggestions and recommendations
|
|
for encoding the presentation, identification, and inclusion of units in both Presentation
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|
and Content MathML.</p>
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|
</div>
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|
<div class="div2">
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|
<h3>
|
|
<a id="definitions"></a>1.2 Definitions</h3>
|
|
<p>The term
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<em>unit name</em>
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|
refers to the actual name of a unit (for example, meter, feet, torr), while
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|
<em>unit symbol</em>
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|
refers to usually a smaller number of characters used to represent the associated unit
|
|
(for example, m, ft, Torr). Unit symbols are not abbreviations, and abbreviations should never
|
|
be used as symbols.
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|
For example, use <em>A</em> and not <em>amp</em>. For archaic units with no defined symbol,
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|
use the unit name as the unit symbol.</p>
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|
<p>A <em>compound unit</em> is a unit which is written as a product of powers of unit symbols
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|
and constants.</p>
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|
</div>
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|
</div>
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|
<div class="div1">
|
|
<h2>
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|
<a id="display_in_presentation"></a>2 Display of Units in Presentation MathML</h2>
|
|
<p>Section 3.5 of the standard is
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devoted to the style and usage of writing unit names and symbols. The following highlights
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|
the most relevant points brought up in this section and suggests
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|
possible interpretations in MathML.</p>
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|
<p>When writing compound unit names, the standard recommends that they be written in
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|
full English with standard pluralization and spacing, for example,
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|
<em>kilograms per cubic meter</em>
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|
and
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|
<em>meters per second squared</em>. MathML is concerned with the incorporation of
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units into mathematical expressions, and so the unit names are often inappropriate.
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|
It is recommended instead that the unit symbols are used at all times.</p>
|
|
<p>Unit symbols are written in roman (upright) type, are not altered in the plural,
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|
are not followed by a period except at the end of a sentence, and no space
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|
is left between a prefix
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|
and a unit symbol. This is accomplished in MathML by using the
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|
<code>mi</code> element. Single character symbols must be qualified by setting the
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|
<code>mathvariant</code> attribute to <code>normal</code> as otherwise they would be italicized.
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|
For example,</p>
|
|
<div class="exampleInner">
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|
<pre><mi mathvariant='normal'>m</mi> </pre>
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|
</div>
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|
<p>The standard recommends that a raised dot is used to
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|
indicate the product of two units. In Presentation MathML, this may be done through
|
|
the use of the mathematical operator <code><mo>&middot;</mo></code>.
|
|
For example, the newton meter may be expressed as</p>
|
|
<div class="exampleInner">
|
|
<pre><mrow>
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|
<mi mathvariant='normal' class='MathML-Unit'>N</mi>
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|
<mo>&middot;</mo>
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|
<mi mathvariant='normal' class='MathML-Unit'>m</mi>
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|
</mrow> </pre>
|
|
</div>
|
|
<p>A quotient of two or more units may be expressed in one of the following ways:</p>
|
|
<table cellpadding="2" border="2">
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|
<tbody>
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|
<tr>
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|
<th rowspan="1" colspan="1">MathML Source</th><th rowspan="1" colspan="1">Display</th><th rowspan="1" colspan="1">Description</th>
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|
</tr>
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|
<tr>
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|
<td rowspan="1" colspan="1"><code><mi mathvariant='normal' class='MathML-Unit'>J</mi> <mo>/</mo> <mi mathvariant='normal' class='MathML-Unit'>kg</mi></code></td><td rowspan="1" colspan="1"><img src="units/eq_1.png" alt="J/kg"></td><td rowspan="1" colspan="1">J/kg</td>
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|
</tr>
|
|
<tr>
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|
<td rowspan="1" colspan="1"><code><mi mathvariant='normal' class='MathML-Unit'>J</mi> <mo>&middot;</mo> <msup><mi mathvariant='normal' class='MathML-Unit'>kg</mi> <mn>-1</mn></msup><mfrac></code></td><td rowspan="1" colspan="1"><img src="units/eq_2.png" alt="J*kg^-1"></td><td rowspan="1" colspan="1">J·kg<sup>-1</sup></td>
|
|
</tr>
|
|
<tr>
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|
<td rowspan="1" colspan="1"><code><mfrac><mi mathvariant='normal' class='MathML-Unit'>J</mi> <mi mathvariant='normal' class='MathML-Unit'>kg</mi></mfrac></code></td><td rowspan="1" colspan="1"><img src="units/eq_3.png" alt="J over Kg"></td><td rowspan="1" colspan="1">the ratio of J over kg</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>In representing a quotient, do not use more than one solidus (/) in the same expression unless
|
|
parentheses are inserted to avoid ambiguity.</p>
|
|
<p>In expressing a quantity containing a value and a unit symbol, a space shall be left
|
|
between them. In MathML this is achieved by using the mathematical operator
|
|
<code><mo rspace="thickmathspace">&InvisibleTimes;</mo></code>. If the
|
|
default spacing used for <code>&InvisibleTimes;</code> is not acceptable (it is
|
|
often zero), extra space is added in MathML with the
|
|
<code>rspace</code>
|
|
attribute. For example, <code>35 mm</code> may be expressed as</p>
|
|
<div class="exampleInner">
|
|
<pre><mrow>
|
|
<mn>35</mn> <mo rspace='thickmathspace'>&InvisibleTimes;</mo>
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|
<mi mathvariant='normal' class='MathML-Unit'>mm</mi>
|
|
</mrow> </pre>
|
|
</div>
|
|
<p>In expressing a quantity containing a value and a compound unit, the unit should remain
|
|
distinct from the value. For example, in expressing 10 kg·m/s, one would use:</p>
|
|
<div class="exampleInner">
|
|
<pre><mrow>
|
|
<mn>10</mn> <mo rspace='thickmathspace'>&InvisibleTimes;</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<mi mathvariant='normal' class='MathML-Unit'>kg</mi> <mo>&middot;</mo> <mi
|
|
mathvariant='normal' class='MathML-Unit'>m</mi>
|
|
</mrow> <mi mathvariant='normal' class='MathML-Unit'>s</mi>
|
|
</mfrac>
|
|
</mrow></pre>
|
|
</div>
|
|
<p>and not</p>
|
|
<div class="exampleInner">
|
|
<pre><mfrac>
|
|
<mrow>
|
|
<mn>10</mn> <mo rspace='thickmathspace'>&InvisibleTimes;</mo>
|
|
<mi>kg</mi> <mo>&middot;</mo> <mi mathvariant='normal'>m</mi>
|
|
</mrow> <mi mathvariant='normal'>s</mi>
|
|
</mfrac> </pre>
|
|
</div>
|
|
<p>For both unit symbols and compound units, the unit should be the last term in the product.</p>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="exceptions"></a>2.1 Exceptions</h3>
|
|
<p>As MathML may be used in the display of intermediate steps of a calculation, not all
|
|
of the above rules may apply. For example, in finding the speed of a body which moved
|
|
thirty meters in five seconds, the Presentation MathML markup may be:
|
|
|
|
|
|
</p>
|
|
<div class="exampleInner">
|
|
<pre><mrow>
|
|
<mfrac>
|
|
<mrow>
|
|
<mn>30</mn>
|
|
<mo rspace='thickmathspace'>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>m</mi>
|
|
</mrow>
|
|
<mrow>
|
|
<mn>5</mn>
|
|
<mo rspace='thickmathspace'>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>s</mi>
|
|
</mrow>
|
|
</mfrac>
|
|
<mo>=</mo>
|
|
<mn>6</mn>
|
|
<mo rspace='thickmathspace'>&InvisibleTimes;</mo>
|
|
<mfrac>
|
|
<mi mathvariant='normal' class='MathML-Unit'>m</mi>
|
|
<mi mathvariant='normal' class='MathML-Unit'>s</mi>
|
|
</mfrac>
|
|
</mrow> </pre>
|
|
</div>
|
|
<p> which displays as <img src="units/eq_4.png" alt="30 meters in 5 seconds"></p>
|
|
<p>Certain non-SI units have, through common usage, symbols which differ in the
|
|
plural. For example, the pound may be represented by the symbol
|
|
<code>lb</code>
|
|
or
|
|
<code>lbs</code> , depending on the amount being measured. Similarly, 3.2 yards is often
|
|
written 3.2 yds.</p>
|
|
<p>The symbol kWh for the kilowatthour instead of kW·h is also acceptable.</p>
|
|
<p>Exceptions to the requirement that a space separate the quantity and unit are
|
|
the symbols for degree, minute, and second of plane angle. In this case, it would be
|
|
appropriate to use the
|
|
<code>mo</code>
|
|
operator. For example,</p>
|
|
<div class="exampleInner">
|
|
<pre><mn>32</mn>
|
|
<mo>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>°</mi>
|
|
<mn>18</mn>
|
|
<mo>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>'</mi>
|
|
<mn>54</mn>
|
|
<mo>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>"</mi></pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="inclusion_in_content"></a>3 Inclusion of Units in Content MathML</h2>
|
|
<p>In expressing a quantity with units,
|
|
as with Presentation MathML, it is recommended that the unit be the last child of an
|
|
<code>apply</code>
|
|
element which has a
|
|
<code>times</code>
|
|
element as the first child. It is also preferable if compound units are kept
|
|
separate as a nested apply at the end of a product.</p>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="identifying_in_presentation"></a>4 Identifying Units in Presentation MathML</h2>
|
|
<p>The presentation element
|
|
<code>mi</code>
|
|
does not take any attributes which may be used to indicate that it represents a unit. Content
|
|
MathML must be used to identify individual or compound units.</p>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="identifying_in_content"></a>5 Identifying Unit Symbols in Content MathML</h2>
|
|
<p>MathML 2.0 introduced externally
|
|
defined symbols with the
|
|
<code>csymbol</code>
|
|
element. This element allows the author to use identifiers with externally defined semantics.</p>
|
|
<p>The attribute
|
|
<code>definitionURL</code>
|
|
is a pointer to the external definition of the semantics of the symbol. The attribute
|
|
<code>encoding</code>
|
|
gives the syntax of the definition pointed to by the definition URL. Thus, the
|
|
<code>csymbol</code>
|
|
content element as such is the appropriate tool for identifying a symbol as being a unit.</p>
|
|
<p>The
|
|
<code>csymbol</code>
|
|
element should not be used to encapsulate a compound unit. For example, the following unit
|
|
of speed should not be constructed using a single <code>csymbol</code> element:
|
|
<code><csymbol>centimeters per second</csymbol></code>
|
|
or
|
|
<code><csymbol>cm/s</csymbol></code>.</p>
|
|
<p>Such compound units should be represented by explicit products or quotients of
|
|
simple units.</p>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="content"></a>5.1 Element Content</h3>
|
|
<p>The content of the <code>csymbol</code> element may consist of any
|
|
encoding which is desired to represent the unit and is not restricted in any way beyond
|
|
those already set in the MathML 2.0
|
|
specification.</p>
|
|
<p>The symbol g<sub>0</sub>
|
|
or g<sub>n</sub>
|
|
is often used to represent the unit of acceleration due to freefall. The semantics are
|
|
already defined by the attributes, and thus the content may be used to indicate the display
|
|
of this unit.
|
|
For example,</p>
|
|
<div class="exampleInner">
|
|
<pre><csymbol definitionURL='http://.../units/gravity'><msub><mi>g</mi><mi>n</mi></msub></csymbol></pre>
|
|
</div>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="encoding"></a>5.2 Encoding Attribute</h3>
|
|
<p>The <code>encoding</code> attribute is optional and is used to help parse the actual defintion.
|
|
It is only needed if the intention is to actually interpret the definitions by machine.</p>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="definitionURL"></a>5.3 Definition URL Attribute</h3>
|
|
<p>The
|
|
<code>definitionURL</code>
|
|
attribute may be used to uniquely identify a unit. The following is a recommendation for
|
|
a unique definition URL.</p>
|
|
<p>The definition URL is made up of two to five parts:</p>
|
|
<div class="exampleInner">
|
|
<pre>http://<em>base</em>/units/<em>unit name</em>[/<em>context</em>][/<em>country</em>][#<em>prefix</em>]</pre>
|
|
</div>
|
|
<p>where the context, country, and prefix are optional. The use of these parts is
|
|
described below:</p>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="base"></a>5.3.1 Base</h4>
|
|
<p>To this point, no fixed URL has been chosen to represent the
|
|
base of these definition URLs, so for the remainder of this Note, the base will be
|
|
indicated by ellipsis:
|
|
<code>...</code>. For example,</p>
|
|
<div class="exampleInner">
|
|
<pre><csymbol definitionURL='http://.../units/meter'>m</csymbol></pre>
|
|
</div>
|
|
</div>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="name"></a>5.3.2 Unit Name</h4>
|
|
<p>The unit name is spelled in full without any prefix. With
|
|
the myriad of spellings available for each unit name, even within SI, it is recommended
|
|
that the American English spelling with
|
|
standard translations to lower case ASCII characters be used wherever possible. For
|
|
example, the German Fuß and the Ångström should use the definition URLs
|
|
<code>http://.../units/foot/de</code>
|
|
and
|
|
<code>http://.../units/angstrom</code>, respectively.</p>
|
|
<p>In cases where the (nonstandard) unit symbol is an abbreviation of a compound unit name, the
|
|
unit symbol should be used in place of the unit name. For example,
|
|
<em>gallons per minute</em>
|
|
and
|
|
<em>revolutions per minute</em>
|
|
should use the definition URLs should use the definition URLs
|
|
<code>http://.../units/gpm</code>
|
|
and
|
|
<code>http://.../units/rpm</code> , respectively.</p>
|
|
<p>The unit name was chosen over the unit symbol for the definition URL as the name is
|
|
less likely to conflict with other unit names, and unit names tend to be more easily
|
|
converted to ASCII. For example, the symbol for the ohm is Ω (&Omega;).</p>
|
|
</div>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="context"></a>5.3.3 Context</h4>
|
|
<p>The context is used only where the name is insufficient to
|
|
properly qualify the unit either through common usage or an international or scientific
|
|
agreement. No SI base units, derived units
|
|
with special names and symbols, or derived units with special names admitted for reasons of
|
|
safeguarding human health requires a context as they are understood to be the default. Of
|
|
the units in use with and in temporary use with SI, the only which require a context are
|
|
the angular minute and second, <code>http://.../units/minute/angular</code>
|
|
and
|
|
<code>http://.../units/second/angular</code>, respectively.</p>
|
|
<p>An example of where a context is necessary is the U.S. survey mile. The default
|
|
international mile has the definition URL
|
|
<code>http://.../units/mile</code>
|
|
whereas the U.S. survey mile would use the definition URL
|
|
<code>http://.../units/mile/survey/us</code>. In this case, the context is necessary as the standard U.S. mile is equal to the international
|
|
mile.</p>
|
|
<p>Over the years, the definitions of the various SI units have been modified. In most
|
|
cases, the definitions have been made more exact, so previous measurements are
|
|
still valid up to the
|
|
precision of the former definition. The one exception to this is the definition of the
|
|
liter. In 1901, the liter was defined as <em>the unit of volume occupied by a mass of one
|
|
kilogram of pure water at its maximum density and at standard atmospheric pressure.</em>
|
|
The definition of the liter was changed in 1964 to be a special name for the cubic
|
|
decimeter. These two definitions differ by approximately 28 parts per million, and thus
|
|
it is necessary to
|
|
differentiate between these two units. The context of the original liter could be the year the
|
|
definition was made, so the definition URL would be <code>http://.../units/liter/1901</code>.</p>
|
|
<p>A date may be used in other cases where a definition has changed, where the date
|
|
refers to the year the definition in question was made.</p>
|
|
<p>In some cases, a unit
|
|
may have multiple definitions which may be differentiated by the dimension. In this
|
|
case, the dimension could be used as the context. For example, the langley may either
|
|
be defined as
|
|
<img src="units/eq_5.png" alt="cal/cm^2">
|
|
|
|
(surface energy density) or
|
|
|
|
<img src="units/eq_6.png" alt="cal/(cm^2 × min)">
|
|
|
|
(surface power density). The definition URLs for these two units may be
|
|
<code>http://.../units/langley/surface_energy_density</code>
|
|
and
|
|
<code>http://.../units/langley/surface_power_density</code>, respectively.</p>
|
|
</div>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="country_code"></a>5.3.4 Country Code</h4>
|
|
<p>By default, the country is referred to by the ISO 3166
|
|
country codes. In the case of historical units, where possible, the modern successor
|
|
of that country should be used. Where this is not possible,
|
|
ISO 3166-2 Regional codes may be used, again, if possible.</p>
|
|
<p>For example, the definition URL of the Scottish mile would be
|
|
<code>http://.../units/mile/gb-sct</code>.</p>
|
|
<p>This breaks down when referring to ancient units. It would be nonsensical to
|
|
refer to the Roman mile as an Italian mile. In these cases, the adjective form of
|
|
the civilization is used. Some examples are given below:</p>
|
|
<ul>
|
|
<li>
|
|
<p>arabic</p>
|
|
</li>
|
|
<li>
|
|
<p>athenian</p>
|
|
</li>
|
|
<li>
|
|
<p>egyptian</p>
|
|
</li>
|
|
<li>
|
|
<p>greek</p>
|
|
</li>
|
|
<li>
|
|
<p>hebrew</p>
|
|
</li>
|
|
<li>
|
|
<p>ionian</p>
|
|
</li>
|
|
<li>
|
|
<p>persian</p>
|
|
</li>
|
|
<li>
|
|
<p>prussian</p>
|
|
</li>
|
|
<li>
|
|
<p>rabbinical</p>
|
|
</li>
|
|
<li>
|
|
<p>roman</p>
|
|
</li>
|
|
<li>
|
|
<p>talmudic</p>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="prefix"></a>5.3.5 Prefix</h4>
|
|
<p>SI accomodates decimal multiples and submultiples of units
|
|
to be represented by placing prefixes in front of the symbols. The IEC introduced
|
|
prefixes to represent binary multiples of units. A unit with a prefix is represented by
|
|
appending the prefix to the
|
|
definition URL using the fragment identifier <code>#</code>. For the prefix <code>μ</code> (micro)
|
|
use the recommended ASCII equivalent,
|
|
<code>u</code>.</p>
|
|
<p>Examples:</p>
|
|
<table cellpadding="2" border="2">
|
|
<tbody>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Unit Name</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Recommended Definition URL</th>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">centimeter</td><td rowspan="1" colspan="1">cm</td><td rowspan="1" colspan="1"><code>http://.../units/meter#c</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">micrometer</td><td rowspan="1" colspan="1">μm</td><td rowspan="1" colspan="1"><code>http://.../units/meter#u</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">kilogram</td><td rowspan="1" colspan="1">kg</td><td rowspan="1" colspan="1"><code>http://.../units/gram#k</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">kibibyte (1024 bytes)</td><td rowspan="1" colspan="1">KiB</td><td rowspan="1" colspan="1"><code>http://.../units/byte#Ki</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>A full list of prefixes are given in <a href="#IEC-prefixes"><b>B.2 IEC Prefixes</b></a>. Unlike other parts of the
|
|
definition URL, the prefixes should be capitalized where necessary.</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="compound_in_content"></a>6 Facilitating the Conversion of Units in MathML</h2>
|
|
<p>A unit is
|
|
a standard of measurement. In order to convert, for example, 1.35 dynes to newtons, two
|
|
pieces of information are necessary:</p>
|
|
<ol class="1">
|
|
<li>
|
|
<p>The dimension of the unit, and</p>
|
|
</li>
|
|
<li>
|
|
<p>Either:
|
|
</p>
|
|
<ol class="a">
|
|
<li>
|
|
<p>The associated system of units, or</p>
|
|
</li>
|
|
<li>
|
|
<p>The conversion to a known system of units.</p>
|
|
</li>
|
|
</ol>
|
|
</li>
|
|
</ol>
|
|
<p>At this point, the measurement can be converted to any other unit of equal dimension.</p>
|
|
<p>Suppose we wish to convert 15.3 kilometers per hour to feet
|
|
per second. Both are measurements of speed, the second being the unit of speed in the
|
|
foot-pound-second system of units. If we know
|
|
that the conversion of km/h to SI is approximately 0.277778 m/s, then the conversion from m/s
|
|
is the conversion of m to ft over the conversion of s to s, that is, 3.28084. Thus,
|
|
the conversion is 15.3×0.277778×3.28084 ft/s = 13.9436 ft/s.</p>
|
|
<p>Suppose we want to convert 3.532 calorie hours to erg seconds. This problem may be reduced
|
|
to converting the first unit to a common system of units, say SI, and then converting the
|
|
corresponding SI unit to cgs system of units.</p>
|
|
<p>Given that cal·h and erg·s are units of action (the dimension), if we know that
|
|
the conversion of 1 cal·s to SI is 15062.4 kg·m<sup>2</sup>/s. The conversion from SI to cgs is a multiplication by 10<sup>7</sup>. Thus
|
|
3.532 cal·h = 3.532×15062.4×10<sup>7</sup>erg·s = 5.32e11
|
|
erg·s.</p>
|
|
<p>Again, consider converting 83.7 statvolts per centimeter to volts per meter. This
|
|
problem may be reduced to converting a unit in the electrostatic system of units (emu)
|
|
to SI.</p>
|
|
<p>Given that sV/cm is a unit of electric field strength, we may take the
|
|
product of the conversions of corresponding units of mass, length time, and electric
|
|
current to get the conversion to SI.
|
|
This product is 10<sup>-3</sup>×10<sup>-2</sup>/(1<sup>3</sup>×2997924580<sup>-1</sup>) = 29979.2458, and therefore the conversion to SI of 87.3 statV/cm is 29979.2458
|
|
V/m.</p>
|
|
<p>It is always possible to determine all of this information by interpreting
|
|
the MathML appropriately, although by transmitting plain MathML the task may be quite
|
|
difficult. Even a unit as simple as cm/s may be stored in any of three ways:</p>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<divide/>
|
|
<csymbol definitionURL='http://.../units/meter#c>cm</csymbol>
|
|
<csymbol definitionURL='http://.../units/second>s</csymbol>
|
|
</apply>
|
|
|
|
<apply>
|
|
<times/>
|
|
<csymbol definitionURL='http://.../units/meter#c>cm</csymbol>
|
|
<apply>
|
|
<power/>
|
|
<csymbol definitionURL='http://.../units/second>s</csymbol>
|
|
<cn type='integer'>-1</cn>
|
|
</apply>
|
|
</apply>
|
|
|
|
<csymbol definitionURL='http://.../units/kyne'>kyn</csymbol></pre>
|
|
</div>
|
|
<p>In general, it is quite difficult to pick a unit from an expression. This section
|
|
describes a method for facilitating the transmission of unit information by making use of the
|
|
<code>semantics</code>
|
|
element.</p>
|
|
<p>Each <code>semantics</code> element would contain the attribute
|
|
<code>definitionURL="http://.../units/"</code>. The first
|
|
child element would be the unit encoded in either Content or Presentation MathML.</p>
|
|
<p>The remaining annotations may be used to facilitate interpretation and conversion of
|
|
the given unit.</p>
|
|
<ul>
|
|
<li>
|
|
<p>dimension</p>
|
|
</li>
|
|
<li>
|
|
<p>SI-equivalent-unit</p>
|
|
</li>
|
|
<li>
|
|
<p>system</p>
|
|
</li>
|
|
<li>
|
|
<p>SI-conversion-factor</p>
|
|
</li>
|
|
</ul>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="dimension"></a>6.1 Dimension</h3>
|
|
<p>A dimension is something which may be measured. Within the
|
|
scientific community, most objects may be measured in units of length, mass, time,
|
|
electric current, thermodynamic temperature,
|
|
amount of substance, or luminous intensity (base dimensions) or as products of powers of
|
|
these (derived dimensions). Currency may also be taken to be a base dimension in some fields
|
|
such as economics.</p>
|
|
<p>A system of units is a collection of units which assign specific standards of measure
|
|
(units) to a set of base and derived dimensions. Knowing the dimension of that which
|
|
is being measured
|
|
already goes a long way to helping conversions of units. The International System of Units
|
|
(SI) is one such system of units used to describe physical phenomena and has been chosen
|
|
to be the standard of such measurement.</p>
|
|
<p>If the dimension of a unit and the conversion of that unit to SI (see
|
|
<a href="#SI-conversion-factor">SI conversion factor</a> ) are known, then converting
|
|
the given information to any other system of units is straight forward so long as the
|
|
conversion from SI to the target unit is known.</p>
|
|
<p>For example, 4.37 yds may be encoded as:</p>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<times/>
|
|
<cn type='real'>4.37</cn>
|
|
<semantics definitionURL='http://.../units/'>
|
|
<csymbol definitionURL='http://.../units/yard'>yds</csymbol>
|
|
<annotation definitionURL='http://.../dimension/length'/>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'>
|
|
<cn type='real'>0.9144</cn>
|
|
</annotation-xml>
|
|
</semantics>
|
|
</apply> </pre>
|
|
</div>
|
|
<p>Thus, any application reading this data and wishing to convert it to cgs need only
|
|
extract the dimension, the conversion factor, and look up the appropriate conversion
|
|
of the unit of length in
|
|
SI (m) to the unit of length in cgs (cm) to get 4.37 yds = 400 cm.</p>
|
|
<p>The dimension may also be used to encode information which may be lost in the
|
|
representation. For example, while a reasonable SI unit of torque is the
|
|
<code>J/rad</code>, it is common to use the unit <code>N m</code>
|
|
where the second unit is understood to be a radial measure. Some other examples of units
|
|
which may be used to represent different quantites are:</p>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Unit</th><th rowspan="1" colspan="1">Possible
|
|
Quantities</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">coulomb</td><td rowspan="1" colspan="1">electric
|
|
charge, quantity of electricity</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">volt</td><td rowspan="1" colspan="1">electric
|
|
potential difference, electromotive force</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">watt</td><td rowspan="1" colspan="1">power, radiant
|
|
flux</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">newton meter</td><td rowspan="1" colspan="1">energy,
|
|
torque</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>A list of possible dimensions is given in <a href="#dimensions"><b>C Dimensions</b></a>.</p>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="SI-equivalent-unit"></a>6.2 SI Equivalent Unit</h3>
|
|
<p>In this case, the <code>annotation-xml</code> element is the SI equivalent unit, and
|
|
gives a MathML encoding of the equivalent SI unit. This annotation is redundant if the
|
|
dimension of the unit is given, as the conversion from
|
|
the dimension to the equivalent unit is a matter of a table look up, though it may be used
|
|
if an unnamed dimension is being used. For example, the rate of change of power per unit
|
|
of time is an unnamed dimension, thus, for example, one encoding of 30.523 Hp/min may be:</p>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<times/>
|
|
<cn type='real'>30.523</cn>
|
|
<semantics definitionURL='http://.../units/'>
|
|
<apply>
|
|
<divide/>
|
|
<csymbol definitionURL='http://.../units/horsepower'>Hp</csymbol>
|
|
<csymbol definitionURL='http://.../units/minute'>min</csymbol>
|
|
</apply>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-equivalent-unit'>
|
|
<apply>
|
|
<divide/> <csymbol
|
|
definitionURL='http://.../units/watt'>W</csymbol> <csymbol
|
|
definitionURL='http://.../units/second'>s</csymbol>
|
|
</apply>
|
|
</annotation-xml>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'>
|
|
<cn type='real'>12.428331193037837</cn>
|
|
</annotation-xml>
|
|
</semantics>
|
|
</apply> </pre>
|
|
</div>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="system"></a>6.3 System</h3>
|
|
<p>A system of units is a collection of base units and products of
|
|
powers of those units used to measure various physical phenomena.</p>
|
|
<p>A system of
|
|
units is said to be self-consistent if any two products of units within that system which
|
|
have the same dimensions are equal. For example, SI is consistent while UK and US systems
|
|
systems of units are not. For example, in either system, the unit of power, the Hp, is not
|
|
equal to the compound unit lb·ft<sup>2</sup>/s<sup>3</sup>. Neither is the unit of
|
|
force, the pound-force, equal to the compound unit lb·ft/s<sup>2</sup>.</p>
|
|
<p>In general, the system annotation should only be used when the system is
|
|
self-consistent. The following systems are self consistent:</p>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">System Name</th><th rowspan="1" colspan="1">Annotation</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">International System of Units</td><td rowspan="1" colspan="1"><code><annotation definitionURL='http://.../system/SI'/></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">Centimeter-Gram-Second</td><td rowspan="1" colspan="1"><code><annotation definitionURL='http://.../system/cgs'/></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">Electrostatic System of Units</td><td rowspan="1" colspan="1"><code><annotation definitionURL='http://.../system/esu'/></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">Electromagnetic System of Units</td><td rowspan="1" colspan="1"><code><annotation definitionURL='http://.../system/emu'/></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">Atomic System of Units</td><td rowspan="1" colspan="1"><code><annotation definitionURL='http://.../system/atomic'/></code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>The system annotation should be used if the unit is either the default
|
|
unit in the given system for the particular dimension, or is equal to that unit.</p>
|
|
<p>For example, the system annotation may be used for either J or kg·m<sup>2</sup>/s<sup>2</sup>
|
|
but should not be used for kJ. All three could use the energy dimension annotation, but the
|
|
first two would use the SI system annotation whereas the latter would use the SI conversion
|
|
factor XML
|
|
annotation with content <code><cn type="integer">1000</cn></code>.</p>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="fps"></a>6.4 Foot-Pound-Second System of Units</h3>
|
|
<p>Due to the ubiquitous nature of the
|
|
foot-pound-second system of units in some countries some mention of this system of
|
|
units is necessary. It is recommended that the dimension and SI
|
|
conversion factor annotations be used. Some conversion factors between the fps system and
|
|
SI are provided in the following table. Exact conversions are marked in bold.</p>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Name</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">SI Equivalent Unit</th><th rowspan="1" colspan="1">Conversion Factor</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">foot</td><td rowspan="1" colspan="1">ft</td><td rowspan="1" colspan="1">m</td><td rowspan="1" colspan="1"><code>0.3048</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">pound</td><td rowspan="1" colspan="1">lb</td><td rowspan="1" colspan="1">kg</td><td rowspan="1" colspan="1"><code>0.45359237</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">poundal</td><td rowspan="1" colspan="1">pdl</td><td rowspan="1" colspan="1">N</td><td rowspan="1" colspan="1"><code>0.138254954376</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">pound-force</td><td rowspan="1" colspan="1">lbf</td><td rowspan="1" colspan="1">N</td><td rowspan="1" colspan="1"><code>4.4482216152605</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">horsepower</td><td rowspan="1" colspan="1">Hp</td><td rowspan="1" colspan="1">W</td><td rowspan="1" colspan="1"><code>745.69987158227022</code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">pound(-force)s per square inch</td><td rowspan="1" colspan="1">psi</td><td rowspan="1" colspan="1">Pa</td><td rowspan="1" colspan="1"><code>6894.757293</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<p>The conversions of most other fps units may be found by taking products of
|
|
powers of the above conversion factors.</p>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="SI-conversion-factor"></a>6.5 SI Conversion Factor</h3>
|
|
<p>The SI conversion factor <code>annotation-xml</code> encoding
|
|
is a MathML encoding of the conversion factor between that unit and the equivalent SI
|
|
unit of the same dimension. In the previous example, the
|
|
conversion from lbf·ft to J/rad is 3389544870828501/2500000000000000 = 1.3558179483314004.</p>
|
|
<div class="div3">
|
|
<h4>
|
|
<a id="N4004AF"></a>6.5.1 Examples</h4>
|
|
<p>Some examples of using units with the semantics encoding
|
|
are:</p>
|
|
<p>980.665 cm/s</p>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<times/>
|
|
<cn type='real'>980.665</cn>
|
|
<semantics definitionURL='.../units'>
|
|
<apply>
|
|
<times/>
|
|
<csymbol definitionURL='.../units/meter#c'>cm</csymbol>
|
|
<csymbol definitionURL='.../units/second'>s</csymbol>
|
|
</apply>
|
|
<annotation definitionURL='http://.../dimension/speed'/>
|
|
<annotation definitionURL='http://.../system/cgs'/>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'>
|
|
<cn type='rational'>1</sep>100</cn>
|
|
</annotation-xml>
|
|
</semantics>
|
|
</apply></pre>
|
|
</div>
|
|
<p>1 atm = 103.325 kPa</p>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<eq/>
|
|
<apply>
|
|
<times/>
|
|
<cn type='integer'>1</cn>
|
|
<semantics definitionURL='http://.../units/'>
|
|
<csymbol definitionURL='http://.../units/atmosphere'>atm</csymbol>
|
|
<annotation definitionURL='http://.../dimension/pressure'/>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'>
|
|
<cn type='integer'>101325</cn>
|
|
</annotation-xml>
|
|
</semantics>
|
|
<cn type='integer'>1</cn>
|
|
</apply>
|
|
<apply>
|
|
<times/>
|
|
<cn type='real'>101.325</cn>
|
|
<semantics definitionURL='http://.../units/'>
|
|
<csymbol definitionURL='http://.../units/pascal#k'>kPa</csymbol>
|
|
<annotation definitionURL='http://.../dimension/pressure'/>
|
|
<annotation-xml encoding='MathML' definitionURL='http://.../SI-conversion-factor'>
|
|
<cn type='integer'>1000</cn>
|
|
</annotation-xml>
|
|
</semantics>
|
|
</apply>
|
|
</apply></pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="conversions"></a>7 Conversions Using Semantic Information</h2>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="examples"></a>8 Examples</h2>
|
|
<p>The fuel efficency of some cars is as good as 4.4 L/(100 km).</p>
|
|
<div class="exampleInner">
|
|
<pre><mrow>
|
|
<mn>4.4</mn>
|
|
<mo>&InvisibleTimes;</mo>
|
|
<mfrac>
|
|
<mi>L</mi>
|
|
<mrow>
|
|
<mn>100</mn>
|
|
<mo>&InvisibleTimes;</mo>
|
|
<mi mathvariant='normal' class='MathML-Unit'>km</mi>
|
|
</mrow>
|
|
</mfrac>
|
|
</mrow> </pre>
|
|
</div>
|
|
<div class="exampleInner">
|
|
<pre><apply>
|
|
<times/>
|
|
<cn type='real'>4.4</cn>
|
|
<semantics>
|
|
<apply>
|
|
<divide/>
|
|
<csymbol definitionURL='http://.../units/liter'>L</csymbol>
|
|
<apply>
|
|
<times/>
|
|
<cn type='integer'>100</cn>
|
|
<csymbol definitionURL='http://.../units/meter#k'>km</csymbol>
|
|
</apply>
|
|
</apply>
|
|
</semantics>
|
|
</apply> </pre>
|
|
</div>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="acknowledgements"></a>9 Acknowledgements</h2>
|
|
<p>The first editor would like to thank Stan Devitt, Robert Miner, Max
|
|
Froumentin, Laurent Bernardin, and Jacques Carette for helping me with this Note. In
|
|
particular, Dr. Devitt suggested the use of the
|
|
<code>semantics</code>
|
|
element for isolating a unit, and Dr. Miner helped initiate the Note. The first editor would also like to
|
|
thank Jeff Giles for additional comments.</p>
|
|
</div>
|
|
</div>
|
|
<div class="back">
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="bibliography"></a>A Bibliography</h2>
|
|
<dl>
|
|
<dt class="label">
|
|
<a id="ieee-astm"></a>ieee-astm</dt>
|
|
<dd>IEEE/ASTM SI 10-1997
|
|
<em>Standard for Use of the International System of Units (SI): The Modern Metric
|
|
System</em>, IEEE Inc., New York, 1997.</dd>
|
|
<dt class="label">
|
|
<a id="MathML2"></a>MathML2</dt>
|
|
<dd>David Carlisle, Patrick Ion, Robert Miner, Nico Poppelier, <a href="http://www.w3.org/TR/2003/REC-MathML2-20031021/">Mathematical Markup Language (MathML) Version 2.0, second edition</a>, W3C Recommendation 21 October 2003</dd>
|
|
</dl>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="prefixes"></a>B SI and IEC Prefixes</h2>
|
|
<p>Prefixes are used to form names and symbols
|
|
of decimal or binary multiples and decimal submultiples of units. These prefixes or their
|
|
symbols are attached to names or symbols, forming what are
|
|
called <em>multiples and submultiples of units</em>.</p>
|
|
<p>SI prefixes are used to represent decimal multiples and submultiples of units. As 10<sup>3</sup>
|
|
= 1000 ˜ 1024 is approximately equal to 2<sup>10</sup>, it has been common to use SI prefixes to represent binary multiples of
|
|
information units, though this is not universal. For example, in referring to the bit
|
|
rates of a modem, the prefixes indicate powers of 10, not 2. The IEC introduced binary
|
|
prefixes in 1998 to correct the confusion resulting from this.</p>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="SI-prefixes"></a>B.1 SI Prefixes</h3>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Multiplication Factor</th><th rowspan="1" colspan="1">Prefix</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Example</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>24</sup></td><td rowspan="1" colspan="1">yotta</td><td rowspan="1" colspan="1">Y</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#Y">Ym</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>21</sup></td><td rowspan="1" colspan="1">zetta</td><td rowspan="1" colspan="1">Z</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#Z">Zm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>18</sup></td><td rowspan="1" colspan="1">exa</td><td rowspan="1" colspan="1">E</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#E">Em</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>15</sup></td><td rowspan="1" colspan="1">peta</td><td rowspan="1" colspan="1">P</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#P">Pm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>12</sup></td><td rowspan="1" colspan="1">tera</td><td rowspan="1" colspan="1">T</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#T">Tm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>9</sup></td><td rowspan="1" colspan="1">giga</td><td rowspan="1" colspan="1">G</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#G">Gm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>6</sup></td><td rowspan="1" colspan="1">mega</td><td rowspan="1" colspan="1">M</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#M">Mm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>3</sup>
|
|
= 1000</td><td rowspan="1" colspan="1">kilo</td><td rowspan="1" colspan="1">k</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#k">km</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>2</sup>
|
|
= 100</td><td rowspan="1" colspan="1">hecto</td><td rowspan="1" colspan="1">h</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#h">hm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>1</sup>
|
|
= 10</td><td rowspan="1" colspan="1">deka</td><td rowspan="1" colspan="1">da</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#da">dam</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-1</sup>
|
|
= 0.1</td><td rowspan="1" colspan="1">deci</td><td rowspan="1" colspan="1">d</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#d">dm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-2</sup>
|
|
= 0.01</td><td rowspan="1" colspan="1">centi</td><td rowspan="1" colspan="1">c</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#c">cm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-3</sup>
|
|
= 0.001</td><td rowspan="1" colspan="1">milli</td><td rowspan="1" colspan="1">m</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#m">mm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-6</sup></td><td rowspan="1" colspan="1">micro</td><td rowspan="1" colspan="1">μ</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#u">μm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-9</sup></td><td rowspan="1" colspan="1">nano</td><td rowspan="1" colspan="1">n</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#n">nm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-12</sup></td><td rowspan="1" colspan="1">pico</td><td rowspan="1" colspan="1">p</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#p">pm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-15</sup></td><td rowspan="1" colspan="1">femto</td><td rowspan="1" colspan="1">f</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#f">fm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-18</sup></td><td rowspan="1" colspan="1">atto</td><td rowspan="1" colspan="1">a</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#a">am</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-21</sup></td><td rowspan="1" colspan="1">zepto</td><td rowspan="1" colspan="1">z</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#z">zm</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">10<sup>-24</sup></td><td rowspan="1" colspan="1">yocto</td><td rowspan="1" colspan="1">y</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/meter#y">ym</csymbol></code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="IEC-prefixes"></a>B.2 IEC Prefixes</h3>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Multiplication Factor</th><th rowspan="1" colspan="1">Full
|
|
Technical Name</th><th rowspan="1" colspan="1">Prefix</th><th rowspan="1" colspan="1">Symbol</th><th rowspan="1" colspan="1">Example</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>60</sup></td><td rowspan="1" colspan="1">exabinary</td><td rowspan="1" colspan="1">exbi</td><td rowspan="1" colspan="1">Ei</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Ei">EiB</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>50</sup></td><td rowspan="1" colspan="1">petabinary</td><td rowspan="1" colspan="1">pebi</td><td rowspan="1" colspan="1">Pi</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Pi">PiB</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>40</sup></td><td rowspan="1" colspan="1">terabinary</td><td rowspan="1" colspan="1">tebi</td><td rowspan="1" colspan="1">Ti</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Ti">TiB</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>30</sup></td><td rowspan="1" colspan="1">gigabinary</td><td rowspan="1" colspan="1">gibi</td><td rowspan="1" colspan="1">Gi</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Gi">GiB</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>20</sup></td><td rowspan="1" colspan="1">megabinary</td><td rowspan="1" colspan="1">mebi</td><td rowspan="1" colspan="1">Mi</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Mi">MiB</csymbol></code></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">2<sup>10</sup></td><td rowspan="1" colspan="1">kilobinary</td><td rowspan="1" colspan="1">kibi</td><td rowspan="1" colspan="1">Ki</td><td rowspan="1" colspan="1"><code><csymbol definitionURL="http://.../units/byte#Ki">KiB</csymbol></code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
<div class="div1">
|
|
<h2>
|
|
<a id="dimensions"></a>C Dimensions</h2>
|
|
<p>This appendix contains a list
|
|
of suggested values for the <code>definitionURL</code> element for dimensions which may be used in the dimension annotation
|
|
of a semantics group. Also listed is the standard SI unit of that dimension.</p>
|
|
<p>Fragment identifiers are not used, as indices into the dimension pages may later be
|
|
used to identify, for example, the SI unit, e.g., <code>http://.../dimension/length#SI</code>
|
|
</p>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="base_derived_dimensions"></a>C.1 Dimensions with SI Base or Derived Units</h3>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Dimension</th><th rowspan="1" colspan="1">Definition URL</th><th rowspan="1" colspan="1">SI Unit</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">length</td><td rowspan="1" colspan="1">http://.../dimension/length</td><td rowspan="1" colspan="1">m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">mass</td><td rowspan="1" colspan="1">http://.../dimension/mass</td><td rowspan="1" colspan="1">kg</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">time</td><td rowspan="1" colspan="1">http://.../dimension/time</td><td rowspan="1" colspan="1">s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric current</td><td rowspan="1" colspan="1">http://.../dimension/electric_current</td><td rowspan="1" colspan="1">A</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">thermodynamic temperature</td><td rowspan="1" colspan="1">http://.../dimension/thermodynamic_temperature</td><td rowspan="1" colspan="1">K</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">amount of substance</td><td rowspan="1" colspan="1">http://.../dimension/amount_of_substance</td><td rowspan="1" colspan="1">mol</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">luminous intensity</td><td rowspan="1" colspan="1">http://.../dimension/luminous_intensity</td><td rowspan="1" colspan="1">cd</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">amount of information</td><td rowspan="1" colspan="1">http://.../dimension/amount_of_information</td><td rowspan="1" colspan="1">B</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">plane angle</td><td rowspan="1" colspan="1">http://.../dimension/plane_angle</td><td rowspan="1" colspan="1">rad</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">solid angle</td><td rowspan="1" colspan="1">http://.../dimension/solid_angle</td><td rowspan="1" colspan="1">sr</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric capacitance</td><td rowspan="1" colspan="1">http://.../dimension/electric_capacitance</td><td rowspan="1" colspan="1">F</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric charge</td><td rowspan="1" colspan="1">http://.../dimension/electric_charge</td><td rowspan="1" colspan="1">C</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric conductance</td><td rowspan="1" colspan="1">http://.../dimension/electric_conductance</td><td rowspan="1" colspan="1">S</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric inductance</td><td rowspan="1" colspan="1">http://.../dimension/electric_inductance</td><td rowspan="1" colspan="1">H</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric potential difference</td><td rowspan="1" colspan="1">http://.../dimension/electric_potential_difference</td><td rowspan="1" colspan="1">V</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric resistance</td><td rowspan="1" colspan="1">http://.../dimension/electric_resistance</td><td rowspan="1" colspan="1">Ω</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">energy</td><td rowspan="1" colspan="1">http://.../dimension/energy</td><td rowspan="1" colspan="1">J</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">force</td><td rowspan="1" colspan="1">http://.../dimension/force</td><td rowspan="1" colspan="1">N</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">frequency</td><td rowspan="1" colspan="1">http://.../dimension/frequence</td><td rowspan="1" colspan="1">Hz</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">illuminance</td><td rowspan="1" colspan="1">http://.../dimension/illuminance</td><td rowspan="1" colspan="1">lx</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">luminous flux</td><td rowspan="1" colspan="1">http://.../dimension/luminous_flux</td><td rowspan="1" colspan="1">lm</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">magnetic flux</td><td rowspan="1" colspan="1">http://.../dimension/magnetic_flux</td><td rowspan="1" colspan="1">Wb</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">magnetic flux density</td><td rowspan="1" colspan="1">http://.../dimension/magnetic_flux_density</td><td rowspan="1" colspan="1">T</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">power</td><td rowspan="1" colspan="1">http://.../dimension/power</td><td rowspan="1" colspan="1">W</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">pressure</td><td rowspan="1" colspan="1">http://.../dimension/pressure</td><td rowspan="1" colspan="1">Pa</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<div class="div2">
|
|
<h3>
|
|
<a id="compound_dimensions"></a>C.2 Dimensions with Compound SI Units</h3>
|
|
<table border="1" cellpadding="3">
|
|
<thead>
|
|
<tr>
|
|
<th rowspan="1" colspan="1">Dimension</th><th rowspan="1" colspan="1">Definition URL</th><th rowspan="1" colspan="1">Example Compound SI Unit</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">absorbed dose rate</td><td rowspan="1" colspan="1">http://.../dimension/absorbed_dose_rate</td><td rowspan="1" colspan="1">Gy/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">acceleration</td><td rowspan="1" colspan="1">http://.../dimension/acceleration</td><td rowspan="1" colspan="1">m/s<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">action</td><td rowspan="1" colspan="1">http://.../dimension/action</td><td rowspan="1" colspan="1">kg·m<sup>2</sup>/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">angular acceleration</td><td rowspan="1" colspan="1">rad/s<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">angular speed</td><td rowspan="1" colspan="1">http://.../dimension/angular_speed</td><td rowspan="1" colspan="1">rad/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">area</td><td rowspan="1" colspan="1">http://.../dimension/area</td><td rowspan="1" colspan="1">m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">concentration</td><td rowspan="1" colspan="1">http://.../dimension/concentration</td><td rowspan="1" colspan="1">mol/m<sup>3</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">current density</td><td rowspan="1" colspan="1">http://.../dimension/current_density</td><td rowspan="1" colspan="1">A/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">dynamic viscosity</td><td rowspan="1" colspan="1">http://.../dimension/dynamic_viscosity</td><td rowspan="1" colspan="1">Pa·s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric charge density</td><td rowspan="1" colspan="1">http://.../dimension/electric_charge_density</td><td rowspan="1" colspan="1">C/m<sup>3</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric field strength</td><td rowspan="1" colspan="1">http://.../dimension/electric_field_strength</td><td rowspan="1" colspan="1">V/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">electric flux density</td><td rowspan="1" colspan="1">http://.../dimension/electric_flux_density</td><td rowspan="1" colspan="1">C/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">energy density</td><td rowspan="1" colspan="1">http://.../dimension/electric_density</td><td rowspan="1" colspan="1">J/m<sup>3</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">entropy</td><td rowspan="1" colspan="1">http://.../dimension/entropy</td><td rowspan="1" colspan="1">J/K</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">exposure</td><td rowspan="1" colspan="1">http://.../dimension/exposure</td><td rowspan="1" colspan="1">C/kg</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/heat_capacity</td><td rowspan="1" colspan="1">J/K</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">heat flux density</td><td rowspan="1" colspan="1">http://.../dimension/heat_flux_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">irradiance</td><td rowspan="1" colspan="1">http://.../dimension/irradiance</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">kinematic viscosity</td><td rowspan="1" colspan="1">http://.../dimension/kinematic_viscosity</td><td rowspan="1" colspan="1">m<sup>2</sup>/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">linear frequency</td><td rowspan="1" colspan="1">http://.../dimension/linear_frequence</td><td rowspan="1" colspan="1">1/(m·s)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">linear mass density</td><td rowspan="1" colspan="1">http://.../dimension/linear_mass_density</td><td rowspan="1" colspan="1">kg/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">luminance</td><td rowspan="1" colspan="1">http://.../dimension/luminance</td><td rowspan="1" colspan="1">cd/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">magentic field strength</td><td rowspan="1" colspan="1">http://.../dimension/magentic_field_strength</td><td rowspan="1" colspan="1">A/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">mass density</td><td rowspan="1" colspan="1">http://.../dimension/mass_density</td><td rowspan="1" colspan="1">kg/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">molar energy</td><td rowspan="1" colspan="1">http://.../dimension/molar_energy</td><td rowspan="1" colspan="1">J/mol</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">molar entropy</td><td rowspan="1" colspan="1">http://.../dimension/molar_entropy</td><td rowspan="1" colspan="1">J/(mol·K)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">molar heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/molar_heat_mass</td><td rowspan="1" colspan="1">J/(mol·K)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">moment of force</td><td rowspan="1" colspan="1">http://.../dimension/moment_of_force</td><td rowspan="1" colspan="1">J/rad</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">moment of inertia</td><td rowspan="1" colspan="1">http://.../dimension/moment_of_inertia</td><td rowspan="1" colspan="1">kg·m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">momentum</td><td rowspan="1" colspan="1">http://.../dimension/momentum</td><td rowspan="1" colspan="1">kg·m/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">permeability</td><td rowspan="1" colspan="1">http://.../dimension/permeability</td><td rowspan="1" colspan="1">H/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">permittivity</td><td rowspan="1" colspan="1">http://.../dimension/permittivity</td><td rowspan="1" colspan="1">F/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">power density</td><td rowspan="1" colspan="1">http://.../dimension/power_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">radiance</td><td rowspan="1" colspan="1">http://.../dimension/radiance</td><td rowspan="1" colspan="1">W/(m<sup>2</sup>·sr)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">radiant intenstiy</td><td rowspan="1" colspan="1">http://.../dimension/radiant_intensity</td><td rowspan="1" colspan="1">W/sr</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">specific heat capacity</td><td rowspan="1" colspan="1">http://.../dimension/specific_heat_capacity</td><td rowspan="1" colspan="1">J/(kg·K)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">specific energy</td><td rowspan="1" colspan="1">http://.../dimension/specific_energy</td><td rowspan="1" colspan="1">J/kg</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">specific entropy</td><td rowspan="1" colspan="1">http://.../dimension/specific_entroy</td><td rowspan="1" colspan="1">J/(kg·K)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">specific volume</td><td rowspan="1" colspan="1">http://.../dimension/specific_volume</td><td rowspan="1" colspan="1">m<sup>3</sup>/kg</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">surface energy density</td><td rowspan="1" colspan="1">http://.../dimension/surface_energy_density</td><td rowspan="1" colspan="1">J/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">surface power density</td><td rowspan="1" colspan="1">http://.../dimension/surface_power_density</td><td rowspan="1" colspan="1">W/m<sup>2</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">surface tension</td><td rowspan="1" colspan="1">http://.../dimension/surface_tension</td><td rowspan="1" colspan="1">N/m</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">thermal conductivity</td><td rowspan="1" colspan="1">http://.../dimension/thermal_conductivity</td><td rowspan="1" colspan="1">W/(m·K)</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">speed</td><td rowspan="1" colspan="1">http://.../dimension/speed</td><td rowspan="1" colspan="1">m/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">volume</td><td rowspan="1" colspan="1">http://.../dimension/volume</td><td rowspan="1" colspan="1">m<sup>3</sup></td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">volume flow</td><td rowspan="1" colspan="1">http://.../dimension/volume_flow</td><td rowspan="1" colspan="1">m<sup>3</sup>/s</td>
|
|
</tr>
|
|
<tr>
|
|
<td rowspan="1" colspan="1">wave number</td><td rowspan="1" colspan="1">http://.../dimension/wave_number</td><td rowspan="1" colspan="1">1/m</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</body>
|
|
</html>
|