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annotate texts/XML/diverse/de/Einst_Beric_de_1911.xml @ 27:8dce37600d38

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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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4 <!--http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd-->
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5 <html>
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7 <head><title></title>
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8 <meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" />
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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_Beric_de_1911.tex" />
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13 <meta name="date" content="2005-03-01 19:05:00" />
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14 <link rel="stylesheet" type="text/css" href="Einst_Beric_de_1911.css" />
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15 </head><body >
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17 <!--l. 9--><p class="noindent"><pb/></p>
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18 <div class="center" >
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20 <!--l. 10--><p class="noindent">
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21 </p><!--l. 11--><p class="noindent"><span
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22 class="cmr-12x-x-120">11. </span><span
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23 class="cmbxti-10x-x-144">Berichtigung zu meiner Arbeit:</span> <br/><span
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24 class="cmbxti-10x-x-144">,,Eine neue</span>
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25 <span
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26 class="cmbxti-10x-x-144">Bestimmung der Molek</span><span
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27 class="cmbxti-10x-x-144">ül-</span> <br/><span
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28 class="cmbxti-10x-x-144">dimensionen&#8220;</span><sup ><span
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29 class="cmr-8">1</span></sup>)<span
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30 class="cmbxti-10x-x-144">;</span> <br/><span
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31 class="cmbxti-10x-x-144">von A.</span>
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32 <span
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33 class="cmbxti-10x-x-144">Einstein.</span></p></div>
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34 <div class="center" >
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36 <!--l. 15--><p class="noindent">
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37 </p><!--l. 16--><p class="noindent">----------</p></div>
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38 <!--l. 19--><p class="indent"> Vor einigen Wochen teilte mir Hr. Bacelin, der auf <br/>Veranlassung von Hrn. Perrin eine Experimentaluntersuchung <br/>über die Viskosität von Suspensionen ausführte, brieflich mit, <br/>daß der Viskositätskoeffizient von Suspensionen nach seinen <br/>Resultaten erheblich größer sei, als der in <span
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39 class="cmsy-10x-x-120">§</span>2 meiner Arbeit <br/>entwickelten Formel entspricht. Ich ersuchte deshalb Hrn. <br/>Hopf, meine Rechnungen nachzuprüfen, und er fand in der <br/>Tat einen Rechenfehler, der das Resultat erheblich fälscht. <br/>Diesen Fehler will ich im folgenden berichtigen.
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40 </p><!--l. 26--><p class="indent"> Auf p. 296 der genannten Abhandlung stehen Ausdrücke <br/>für die Spannungskomponenten <span
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41 class="cmmi-12">X</span><sub ><span
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42 class="cmmi-8">y</span></sub> und <span
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43 class="cmmi-12">X</span><sub ><span
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44 class="cmmi-8">z</span></sub>, die durch einen <br/>Fehler im Differenzieren der Geschwindigkeitskomponenten <span
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45 class="cmmi-12">u</span>, <br/><span
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46 class="cmmi-12">v</span>, <span
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47 class="cmmi-12">w </span>gefälscht sind. Es muß heißen:
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48 </p>
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49 <center class="par-math-display" >
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50 <img
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51 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/Einst_Beric_de_19110x.png" alt=" 3 Aq2 3Mq2- Xx = - 2kA + 10kP h5 - 25kP r7 , Xy = 5kP 3(A+Bh)5qj - 25kP 3Mqrj7-, X = 5kP 3(A+C)qz - 25kP 3Mqz-, z h5 r7 " class="par-math-display" /></center>
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52 <!--l. 40--><p class="nopar">
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53 </p><!--l. 44--><p class="noindent">wobei gesetzt ist
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54 </p>
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55 <center class="par-math-display" >
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56 <img
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57 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/Einst_Beric_de_19111x.png" alt="M = Aq2 + Bj2 + Cz2. " class="par-math-display" /></center>
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58
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59 <!--l. 50--><p class="nopar">
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60 </p><!--l. 53--><p class="noindent">Berechnet man dann die pro Zeiteinheit auf die in der Kugel <br/>vom Radius <span
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61 class="cmmi-12">R</span>
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62 enthaltene Flüssigkeit durch die Druckkräfte <br/>übertragene Energie, so erhält man statt Gleichung (7) auf <br/>p. 296:
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63 </p>
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64 <table width="100%"
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65 class="equation"><tr><td>
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66 <center class="math-display" >
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67 <img
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68 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/Einst_Beric_de_19112x.png" alt=" 2 1 W = 2d k(V + 2P). " class="math-display" /><a
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69 id="x1-2r7"></a></center></td><td width="5%">(7)</td></tr></table>
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70 <!--l. 58--><p class="nopar">
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71 ----------
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72 </p><!--l. 62--><p class="indent"> 1) A. Einstein, Ann. d. Phys. <span
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73 class="cmbx-12">19. </span>p. 289 ff. 1906.<pb/>
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74 </p><!--l. 67--><p class="indent">
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75
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76 </p><!--l. 68--><p class="noindent">Unter Benutzung dieser berichtigten Gleichung erhält man <br/>dann statt der in <span
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77 class="cmsy-10x-x-120">§</span>2 entwickelten Gleichung <span
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78 class="cmmi-12">k</span><span
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79 class="cmsy-10x-x-120">* </span>= <span
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80 class="cmmi-12">k</span>(1 + <span
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81 class="cmmi-12"><img
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82 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/cmmi12-27.png" alt="f" class="cmmi-12x-x-27" align="middle" /></span>) <br/>die Gleichung
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83 </p>
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84 <center class="par-math-display" >
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85 <img
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86 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/Einst_Beric_de_19113x.png" alt="k* = k(1 + 2,5f). " class="par-math-display" /></center>
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87 <!--l. 75--><p class="nopar">
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88 </p><!--l. 78--><p class="noindent">Der Viskositätskoeffizient <span
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89 class="cmmi-12">k</span><sup ><span
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90 class="cmsy-8">*</span></sup> der Suspension wird also durch <br/>das Gesamtvolumen <span
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91 class="cmmi-12"><img
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92 src="http://foxridge.mpiwg-berlin.mpg.de/permanent/einstein/annalen/Einst_Beric_de_1911/fulltext/img/cmmi12-27.png" alt="f" class="cmmi-12x-x-27" align="middle" /></span>
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93 der in der Volumeinheit suspendierten <br/>Kugeln 2,5 mal stärker beeinflußt als nach der dort gefundenen <br/>Formel.
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94 </p><!--l. 83--><p class="indent"> Legt man die berichtigte Formel zugrunde, so erhält man <br/>für das Volumen von 1 g in Wasser gelöstem Zucker statt des <br/>in <span
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95 class="cmsy-10x-x-120">§</span>3 angegebenen Wertes 2,45 cm<sup ><span
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96 class="cmr-8">3</span></sup> den Wert 0,98, also einen <br/>vom Volumen 0,61 von 1 g festem Zucker erheblich weniger <br/>abweichenden Wert. Endlich erhält man aus der inneren <br/>Reibung und Diffusion von verdünnten Zuckerlösungen statt <br/>des im Anhange jener Arbeit angegebenen Wertes <span
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97 class="cmmi-12">N </span>= 4,15.10<sup ><span
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98 class="cmr-8">23</span></sup> <br/>für die Anzahl der Moleküle im Grammolekül den Wert <br/>6,56. 10<sup ><span
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99 class="cmr-8">23</span></sup>.
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100 </p><!--l. 90--><p class="indent"> Zürich, Januar 1911.
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101 </p>
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102 <div class="center" >
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103
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104 <!--l. 92--><p class="noindent">
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105 </p><!--l. 93--><p class="noindent">(Eingegangen 21. Januar 1911.)</p></div>
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106 <div class="center" >
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107
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108 <!--l. 96--><p class="noindent">
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109 </p><!--l. 97--><p class="noindent">------------</p></div>
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110
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111 </body></html>
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112
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113
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