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New Special Instructions
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Wed, 30 Jul 2014 15:58:21 +0200
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1 <?xml version="1.0" encoding="utf-8" ?>
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5 <html>
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7 <head><title></title>
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9 <meta name="generator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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10 <meta name="originator" content="TeX4ht (http://www.cse.ohio-state.edu/~gurari/TeX4ht/mn.html)" />
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11 <!-- xhtml,html -->
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12 <meta name="src" content="Einst_Nacht_de_1912.tex" />
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13 <meta name="date" content="2005-02-25 10:10:00" />
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14 <link rel="stylesheet" type="text/css" href="Einst_Nacht_de_1912.css" />
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15 </head><body >
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17 <!--l. 12--><p class="noindent"><pb/></p>
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18 <div class="center" >
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20 <!--l. 13--><p class="noindent">
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21 </p><!--l. 14--><p class="noindent"><span
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22 class="cmr-12">9.</span><span
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23 class="cmbxti-10x-x-120">Nachtrag zu meiner Arbeit: </span> <br/><span
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24 class="cmbxti-10x-x-120">,,Thermodynamische</span>
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25 <span
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26 class="cmbxti-10x-x-120">Begr</span><span
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27 class="cmbxti-10x-x-120">ündung des photo- </span> <br/><span
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28 class="cmbxti-10x-x-120">chemischen Aquivalentgesetzes&#8220;;</span>
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29 <br/><span
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30 class="cmbxti-10x-x-120">von A. Einstein.</span></p></div>
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31 <div class="center" >
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33 <!--l. 20--><p class="noindent">
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34 </p><!--l. 21--><p class="noindent">--------</p></div>
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35 <!--l. 24--><p class="indent"> In der genannten Arbeit<sup ><span
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36 class="cmr-7">1</span></sup>) wird auf wesentlich thermo-<br/>dynamischem Wege unter Zugrundelegung gewisser durch die <br/>Erfahrung nahe gelegter Annahmen gezeigt, daß bei der photo-<br/>chemischen Zersetzung eines Gasmoleküls durch (verdünnte) <br/>Strahlung von der Frequenz <span
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37 class="cmmi-10"><img
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38 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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39 class="cmr-7">0</span></sub> die Strahlungsenergie <span
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40 class="cmmi-10">h<img
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41 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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42 class="cmr-7">0</span></sub> (im <br/>Mittel) absorbiert wird. Jene Untersuchung bedarf in einem <br/>wichtigen Punkte der Ergänzung. Es wurde nämlich bei <br/>jener Betrachtung die Annahme zugrunde gelegt, daß nur ein
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43 <br/>unendlich kleiner Frequenzbereich photochemisch auf das Gas <br/>zu wirken vermöge. Man erhält deshalb keine Antwort auf <br/>die Frage, ob für die Größe der pro Molekülzerfall absorbierten <br/>Energie die Frequenz der absorbierten Strahlung oder die <br/>Eigenfrequenz des absorbierenden Moleküls maßgebend sei.
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44 </p><!--l. 41--><p class="indent"> Eine Antwort auf jene Frage läßt sich nur gewinnen, <br/>wenn man den Fall ins Auge faßt, daß ein endlicher Frequenz-<br/>bereich auf das Molekül zersetzend zu wirken vermag. Die <br/>Untersuchung dieses Falles wird mir auch durch persönliche <br/>Mitteilung des Hrn. Warburg nahe gelegt, der den photo-<br/>chemischen Zerfall von Ozon untersucht; Hr. Warburg teilte <br/>mir nämlich mit, daß auf das O<sub ><span
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45 class="cmr-7">3</span></sub>-Molekül Strahlung eines <br/>gegen <span
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46 class="cmmi-10"><img
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47 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sub ><span
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48 class="cmr-7">0</span></sub> durchaus nicht verschwindenden Frequenzbereiches <br/>photochemisch wirksam ist.
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49 </p><!--l. 52--><p class="indent"> Wir legen also jetzt der Betrachtung den Fall zugrunde, <br/>daß auf das betrachtete Molekül beliebig viele elementare <br/>Frequenzbereiche wirken, die zusammen einen kontinuierlichen <br/>endlichen Bereich bilden können; <span
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50 class="cmmi-10"><img
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51 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sup ><img
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52 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19120x.png" alt="(1)" class="left" align="middle" /></sup>, <span
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53 class="cmmi-10"><img
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54 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-17.png" alt="n" class="10x-x-17" /></span><sup ><img
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55 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19121x.png" alt="(2)" class="left" align="middle" /></sup> usw. seien die mittleren
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56 <br/>----------
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57 </p><!--l. 60--><p class="indent"> 1) A. Einstein, Ann. d. Phys. <span
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58 class="cmbx-10">37. </span>p. 832. 1912. <pb/>
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59 </p><!--l. 66--><p class="indent">
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60
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61 </p><!--l. 67--><p class="noindent">Frequenzen dieser Elementarbereiche. Wir fügen den in der <br/>ersten Arbeit gemachten Voraussetzungen die hinzu, daß die <br/>Anzahl der pro Zeiteinheit zerfallenden Moleküle gleich sei <br/>die Summe der Anzahl der pro Zeiteinheit zerfallenden Mole-<br/>küle, welche die Strahlungen der einzelnen Frequenzbereiche <br/>für sich allein liefern würden. Dann erhalten wir für die Zahl <br/>der in der Zeiteinheit zerfallenden Moleküle erster Art (vgl.
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62 <br/>Formel (1) p. 834 der ersten Abhandlung)
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63 </p>
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64 <table width="100%"
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65 class="equation"><tr><td><a
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66 id="x1-2r1"></a>
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67 <center class="math-display" >
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68 <img
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69 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19122x.png" alt=" ( ) Z = n1 A(1)r(1) + A(2)r(2)... . " class="math-display" /></center></td><td width="5%">(1a)</td></tr></table>
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70 <!--l. 83--><p class="nopar">
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71 </p><!--l. 86--><p class="noindent">Gleichung (2) für die Anzahl <span
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72 class="cmmi-10">Z</span><span
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73 class="cmsy-10">' </span>der pro Zeiteinheit statt-<br/>findenden Wiedervereinigungen bleibt unverändert gültig.
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74 </p><!--l. 89--><p class="indent"> Auch in dem jetzt betrachteten Falle gibt es den Fall <br/>des ,,gewöhnlichen&#8220; thermodynamischen Gleichgewichtes, für <br/>welchen die Strahlung <span
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75 class="cmti-10">schwarze </span>Strahlung von der nämlichen <br/>Temperatur ist wie die Temperatur des Gasgemisches. Ebenso
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76 <br/>ergeben sich bei gegebener Gastemperatur unendlich viele <br/>Konstitutionen der Strahlung, für welche ,,außergewöhnliches&#8220; <br/>thermodynamisches Gleichgewicht herrschen muß, falls <span
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77 class="cmmi-10"><img
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78 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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79 class="cmr-7">2</span></sub> <span
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80 class="cmmi-10"><img
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81 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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82 class="cmr-7">3</span></sub><img
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83 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19123x.png" alt="/" class="left" align="middle" /> <span
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84 class="cmmi-10"><img
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85 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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86 class="cmr-7">1</span></sub> <br/>einen geeigneten Wert hat. Aber es ist in dem jetzt unter-<br/>suchten Falle <span
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87 class="cmmi-10">Z </span>= <span
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88 class="cmmi-10">Z</span><span
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89 class="cmsy-10">' </span>nicht mehr eine <span
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90 class="cmti-10">hinreichende </span>Bedingung <br/>für das thermodynamische Gleichgewicht. Damit letzteres vor-<br/>handen sei, muß nämlich außerdem gefordert werden, daß <br/>für jedes wirksame Elementargebiet der Strahlungsfrequenz die <br/>pro Zeiteinheit absorbierte gleich der pro Zeiteinheit neu er-<br/>zeugten Strahlungsenergie sei.
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91 </p><!--l. 101--><p class="indent"> Man kann leicht zeigen, daß Fälle des ,,außergewöhnlichen&#8220; <br/>thermodynamischen Gleichgewichtes existieren müssen. Be-<br/>zeichnen wir nämlich mit
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92 </p>
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93 <center class="par-math-display" >
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94 <img
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95 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19124x.png" alt="j10, j20, j30, r0(1), r0(2)... " class="par-math-display" /></center>
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96 <!--l. 114--><p class="nopar">
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97 </p><!--l. 118--><p class="noindent">die Molekularkonzentrationen, bzw. Strahlungsdichten in einem <br/>Falle ,,gewöhnlichen&#8220; thermodynamischen Gleichgewichtes, <br/>wobei sowohl das Gasgemisch, als auch die
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98 wirksame Strahlung <br/>der einzelnen Elementarbereiche die Temperatur <span
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99 class="cmmi-10">T </span>besitzen, <br/>so sind
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100 </p>
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101 <center class="par-math-display" >
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102 <img
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103 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19125x.png" alt="j10, j20, j30, x xr0(1), xr0(2)... " class="par-math-display" /></center>
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104 <!--l. 132--><p class="nopar"> <pb/>
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105 </p><!--l. 139--><p class="indent">
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106
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107 </p><!--l. 140--><p class="noindent">Werte für die Molekülkonzentrationen bzw. für die Strahlungs-<br/>dichten, bei welchen ,,außergewöhnliches&#8220; thermodynamisches <br/>Gleichgewicht bei beliebigem Werte von <span
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108 class="cmmi-10">x</span>
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109 besteht, falls nur <br/>das Gasgemisch die Temperatur <span
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110 class="cmmi-10">T </span>besitzt. Denn es folgt <br/>aus (1a) und (2), daß die Bedingung <span
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111 class="cmmi-10">Z </span>= <span
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112 class="cmmi-10">Z</span><span
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113 class="cmsy-10">' </span>erfüllt bleibt; es <br/>ändert sich ferner nichts an der pro Zeiteinheit erzeugten <br/>Strahlungsenergie z. B. des ersten Bereiches, weil <span
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114 class="cmmi-10"><img
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115 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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116 class="cmr-7">2</span></sub> und <span
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117 class="cmmi-10"><img
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118 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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119 class="cmr-7">3</span></sub> <br/>ungeändert geblieben sind, und es ändert sich auch nichts an <br/>der Zeiteinheit z. B. aus der Strahlung des ersten Elementar-<br/>bereiches absorbierten Energie, weil das Produkt <span
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120 class="cmmi-10"><img
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121 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-11.png" alt="j" class="cmmi-10x-x-11" align="middle" /></span><sub ><span
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122 class="cmr-7">1</span></sub> <span
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123 class="cmsy-10"><sup class="htf"><strong>.</strong></sup> </span><span
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124 class="cmmi-10"><img
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125 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sup ><img
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126 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19126x.png" alt="(1)" class="left" align="middle" /></sup> un-<br/>geändert geblieben ist.
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127 </p><!--l. 150--><p class="indent"> Diese Zustände außergewöhnlichen thermodynamischen <br/>Gleichgewichtes, welche zur Gemischtemperatur <span
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128 class="cmmi-10">T </span>gehören, <br/>sind dadurch ausgezeichnet, daß sich die Dichten
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129 <span
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130 class="cmmi-10"><img
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131 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sup ><img
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132 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19127x.png" alt="(1)" class="left" align="middle" /></sup><span
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133 class="cmmi-10">, <img
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134 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sup ><img
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135 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19128x.png" alt="(2)" class="left" align="middle" /></sup> usw. <br/>der Elementarbereiche zueinander verhalten wie die ent-<br/>sprechenden Dichten <span
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136 class="cmmi-10"><img
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137 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sub ><span
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138 class="cmr-7">0</span></sub><sup ><img
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139 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_19129x.png" alt="(1)" class="left" align="middle" /></sup><span
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140 class="cmmi-10">, <img
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141 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-25.png" alt="r" class="cmmi-10x-x-25" align="middle" /></span><sub ><span
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142 class="cmr-7">0</span></sub><sup ><img
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143 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191210x.png" alt="(2)" class="left" align="middle" /></sup> usw., welche diesen Bereichen <br/>bei der Gemischtemperatur <span
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144 class="cmmi-10">T</span>
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145 beim gewöhnlichen thermo-<br/>dynamischen Gleichgewichte zukommen. Ist diese notwendige <br/>Bedingung für das außergewöhnliche thermodynamische Gleich-<br/>gewicht
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146 </p>
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147 <table width="100%"
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148 class="equation"><tr><td><a
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149 id="x1-3r1"></a>
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150 <center class="math-display" >
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151 <img
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152 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191211x.png" alt="r(1) r(2)- r0(1) = r0(2) usw. " class="math-display" /></center></td><td width="5%">(5)</td></tr></table>
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153 <!--l. 166--><p class="nopar">
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154 </p><!--l. 169--><p class="noindent">erfüllt, so kann man (1a) in folgender Weise umformen:
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155 </p>
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156 <center class="par-math-display" >
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157 <img
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158 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191212x.png" alt=" ( ( ) Z = n A(1)r(1) + A(2) r0(2)r(1) + ... 1 r0(1) ( (1) (2)r0(2) ) (1) = n1 A + A r-(1) + ... r , 0 " class="par-math-display" /></center>
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159 <!--l. 185--><p class="nopar">
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160 </p><!--l. 189--><p class="noindent">oder endlich in kürzerer Form
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161 </p>
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163 <table width="100%"
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164 class="equation"><tr><td><a
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165 id="x1-4r1"></a>
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166 <center class="math-display" >
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167 <img
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168 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191213x.png" alt="Z = A(1)*r(1)n1, " class="math-display" /></center></td><td width="5%">(1b)</td></tr></table>
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169 <!--l. 197--><p class="nopar">
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170 </p><!--l. 202--><p class="noindent">wobei <span
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171 class="cmmi-10">A</span><sup ><img
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172 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191214x.png" alt="(1)" class="left" align="middle" /><span
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173 class="cmsy-7">*</span></sup> nur von <span
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174 class="cmmi-10">T </span>allein (Gemischtemperatur) abhängt.
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175 </p><!--l. 205--><p class="indent"> Unter Benutzung von (1b) und (2) der ersten Arbeit erhält <br/>man statt Gleichnng (3), p. 835 die entsprechende Gleichung
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176 </p>
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177 <table width="100%"
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178 class="equation"><tr><td><a
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179 id="x1-5r1"></a>
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180 <center class="math-display" >
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181 <img
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182 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191215x.png" alt="n n V2V3-= j2j3= A(1)*r(1). nV1 j1 A' " class="math-display" /></center></td><td width="5%">(3a)</td></tr></table>
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183 <!--l. 214--><p class="nopar">
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184 </p><!--l. 217--><p class="noindent">Ist diese Gleichung sowie (5) erfüllt, so besteht ,,außer-<br/>gewöhnliches&#8220; thermodynamisches Gleichgewicht. <pb/>
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185 </p><!--l. 224--><p class="indent">
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186
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187 </p><!--l. 225--><p class="indent"> Haben wir einen Fall außergewöhnlichen thermodyna-<br/>mischen Gleichgewichtes vor uns, so werden wir uns eine <br/>virtuelle Änderung des Systems als zulässig zu denken haben, <br/>bei welcher ein Grammol der ersten Molekülart des Gemisches
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188 <br/>zersetzt wird unter Absorption der Energie <span
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189 class="cmmi-10">N <img
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190 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-22.png" alt="e" class="10x-x-22" /></span><sup ><img
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191 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191216x.png" alt="(1)" class="left" align="middle" /></sup> aus der <br/>Strahlung des ersten Elementarbereiches derart, daß die <br/>Energiemengen der übrigen Elementarbereiche der Strahlung <br/>ungeändert bleiben. Bei dieser virtuellen Änderung muß die
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192 <br/>Bedingung <span
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193 class="cmmi-10"><img
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194 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/cmmi10-e.png" alt="d" class="10x-x-e" /> S</span><sub ><span
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195 class="cmmi-7">total</span></sub> = 0 erfüllt sein wie in dem zuerst be-<br/>trachteten Fall, daß nur Strahlung eines einzigen Elementar-<br/>bereiches photochemisch wirksam sei.<sup ><span
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196 class="cmr-7">1</span></sup>)
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197 </p><!--l. 234--><p class="indent"> Die rechnerische Durchführung stimmt genau überein mit <br/>derjenigen, welche in der Arbeit für den monochromatischen <br/>Fall gegeben ist, mit dem einzigen Unterschiede, daß die auf <br/>die Strahlung sich beziehenden Größen auf den ersten Ele-<br/>mentarbereich zu beziehen sind. Speziell erhalten wir an <br/>Stelle von (5) die Gleichung
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198 </p>
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199 <table width="100%"
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200 class="equation"><tr><td><a
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201 id="x1-6r1"></a>
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202 <center class="math-display" >
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203 <img
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204 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Nacht_de_1912/fulltext/img/Einst_Nacht_de_191217x.png" alt="e(1) = h n(1). " class="math-display" /></center></td><td width="5%">(5a)</td></tr></table>
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205 <!--l. 245--><p class="nopar">
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206 </p><!--l. 249--><p class="indent"> Es folgt also aus den angedeuteten Überlegungen, daß <br/>die pro Molekülzerfall absorbierte Energie nicht von der Eigen-<br/>frequenz des absorbierenden Moleküls sondern von der Frequenz <br/>der den Zerfall bewirkenden Strahlung abhängt. Sollte dies <br/>bei (5a) aber nicht zutreffen, so müßte man meiner Meinung <br/>nach daraus schließen, daß Absorption bzw. Emission der <br/>verschiedenen wirksamen Frequenzbereiche nicht unabhängig <br/>voneinander erfolgen, sondern zwangläufig miteinander ver-<br/>bunden sind. Es wäre dann eben die von uns betrachtete
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207 <br/>virtuelle Verschiebung als eine mit den Elementargesetzen <br/>nicht vereinbare anzusehen.
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208 </p><!--l. 263--><p class="indent"> Prag, Mai 1912.
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209 </p><!--l. 265--><p class="noindent">----------
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210 </p><!--l. 268--><p class="indent"> 1) Dieser Modus wäre nur dann unzulässig, wenn die elementaren <br/>Gesetze der Absorption und Emission so beschaffen wären, daß mit der <br/>Absorption bzw. Emission von Strahlung einer Frequenz Absorption bzw. <br/>Emission anderer Frequenzen zwangläufig verbunden wäre.
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211 </p>
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212 <div class="center" >
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213
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214
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215 <!--l. 274--><p class="noindent">
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216 </p><!--l. 275--><p class="noindent">(Eingegangen 12, Mai 1912.)</p></div>
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217 <div class="center" >
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219 <!--l. 279--><p class="noindent">
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220 </p><!--l. 280--><p class="noindent">----------</p></div>
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222 </body></html>
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