<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">  <!--Converted with jLaTeX2HTML 2002 (1.62) JA patch-1.4 patched version by:  Kenshi Muto, Debian Project. 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est <!-- MATH  $\Delta \rho = \rho_{1}-\rho_{2}$  --> <IMG  WIDTH="97" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"  SRC="img243.png"  ALT="$ \Delta \rho = \rho_{1} - \rho_{2}$">, est donn&#233; par (voir figure&nbsp;<A HREF="node35.htm#fig:gra_03_002">3.2</A>): <P></P> <DIV ALIGN="CENTER"><!-- MATH  \begin{equation} \Delta g_{z} = 	\frac{ G \pi R^2 \Delta \rho }{z (1 + (x/z)^2 )} 	\left[ 		\frac{1}{  			\left( 1 +  				\frac{ ( x^2 + z^2 ) }{ (y + L)^2 }  			\right)^{1/2}} 		- 		\frac{1}{ 			\left( 1 +  				\frac{ ( x^2 + z^2 ) }{ (y - L)^2 } 			\right)^{1/2}} 	\right]  \end{equation}  --> <TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><IMG  WIDTH="433" HEIGHT="82" ALIGN="MIDDLE" BORDER="0"  SRC="img273.png"  ALT="$\displaystyle \Delta g_{z} = \frac{ G \pi R^2 \Delta \rho }{z (1 + (x/z)^2 )} \... ...\frac{1}{ \left( 1 + \frac{ ( x^2 + z^2 ) }{ (y - L)^2 } \right)^{1/2}} \right]$"></TD> <TD NOWRAP WIDTH="10" ALIGN="RIGHT"> (3.8)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P>  <P>  <DIV ALIGN="CENTER"><A NAME="fig:gra_03_002"></A><A NAME="2383"></A> <TABLE> <CAPTION ALIGN="BOTTOM"><STRONG>Figure 3.2:</STRONG> </CAPTION> <TR><TD> <DIV ALIGN="CENTER"><IMG  WIDTH="516" HEIGHT="351" ALIGN="BOTTOM" BORDER="0"  SRC="img274.png"  ALT="\includegraphics[width=4.5in]{figures/gra_03_002.eps}"> </DIV></TD></TR> </TABLE> </DIV>  <P> Si le cylindre est infiniment long (<IMG  WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"  SRC="img275.png"  ALT="$ L &gt; 10~z$">), alors l'&#233;quation se simplifie pour donner: <P></P> <DIV ALIGN="CENTER"><!-- MATH  \begin{equation} \boxed{ \Delta g_{z} = \frac{ 2 G \pi R^2 \Delta \rho } 	{z (1 + (x/z)^2)} } \end{equation}  --> <TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><IMG  WIDTH="161" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"  SRC="img276.png"  ALT="$\displaystyle \boxed{ \Delta g_{z} = \frac{ 2 G \pi R^2 \Delta \rho } {z (1 + (x/z)^2)} }$"></TD> <TD NOWRAP WIDTH="10" ALIGN="RIGHT"> (3.9)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P>   <P> avec un maximum en <IMG  WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"  SRC="img245.png"  ALT="$ x=0$"> donn&#233; par: <P></P> <DIV ALIGN="CENTER"><!-- MATH  \begin{equation} \Delta g_{max} = \frac{ 2 G \pi R^2 \Delta \rho }{z} \end{equation}  --> <TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><IMG  WIDTH="147" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"  SRC="img277.png"  ALT="$\displaystyle \Delta g_{max} = \frac{ 2 G \pi R^2 \Delta \rho }{z}$"></TD> <TD NOWRAP WIDTH="10" ALIGN="RIGHT"> (3.10)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P>   <P> En utilisant ces derniers r&#233;sultats et, de la m&#234;me mani&#232;re que pour la sph&#232;re, on a, au point <IMG  WIDTH="63" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img248.png"  ALT="$ x = x_{1/2}$">, en posant <!-- MATH  $C = 2 \pi G R^2$  --> <IMG  WIDTH="87" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"  SRC="img278.png"  ALT="$ C = 2 \pi G R^2$">: <BR> <DIV ALIGN="CENTER"> <!-- MATH  \begin{eqnarray} \Delta g 	& = & \frac{ \Delta g_{max} }{2} \nonumber \\ \frac{ C \Delta \rho }{ z (1 + (x_{1/2}/z)^{2}) } 	& = &  	\frac{1}{2} \frac{C \Delta \rho }{z} \nonumber \\ \frac{ 1 }{ (1 + \left[ \frac{x_{1/2}}{z} \right]^{2}) } 	& = &  	\frac{1}{2} \nonumber \\ (1 + \left[ \frac{x_{1/2}}{z} \right]^{2}) 	& = &  	2 \nonumber  \end{eqnarray}  --> <TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100%"> <TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG  WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"  SRC="img251.png"  ALT="$\displaystyle \Delta g$"></TD> <TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG  WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img26.png"  ALT="$\displaystyle =$"></TD> <TD ALIGN="LEFT" NOWRAP><IMG  WIDTH="55" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"  SRC="img279.png"  ALT="$\displaystyle \frac{ \Delta g_{max} }{2}$"></TD> <TD WIDTH=10 ALIGN="RIGHT"> &nbsp;</TD></TR> <TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG  WIDTH="121" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"  SRC="img280.png"  ALT="$\displaystyle \frac{ C \Delta \rho }{ z (1 + (x_{1/2}/z)^{2}) }$"></TD> <TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG  WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img26.png"  ALT="$\displaystyle =$"></TD> <TD ALIGN="LEFT" NOWRAP><IMG  WIDTH="54" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"  SRC="img281.png"  ALT="$\displaystyle \frac{1}{2} \frac{C \Delta \rho }{z}$"></TD> <TD WIDTH=10 ALIGN="RIGHT"> &nbsp;</TD></TR> <TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG  WIDTH="97" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"  SRC="img282.png"  ALT="$\displaystyle \frac{ 1 }{ (1 + \left[ \frac{x_{1/2}}{z} \right]^{2}) }$"></TD> <TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG  WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img26.png"  ALT="$\displaystyle =$"></TD> <TD ALIGN="LEFT" NOWRAP><IMG  WIDTH="16" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"  SRC="img256.png"  ALT="$\displaystyle \frac{1}{2}$"></TD> <TD WIDTH=10 ALIGN="RIGHT"> &nbsp;</TD></TR> <TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG  WIDTH="99" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"  SRC="img283.png"  ALT="$\displaystyle (1 + \left[ \frac{x_{1/2}}{z} \right]^{2})$"></TD> <TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG  WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img26.png"  ALT="$\displaystyle =$"></TD> <TD ALIGN="LEFT" NOWRAP><IMG  WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img260.png"  ALT="$\displaystyle 2$"></TD> <TD WIDTH=10 ALIGN="RIGHT"> &nbsp;</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P>  <P> <P></P> <DIV ALIGN="CENTER"><!-- MATH  \begin{equation} \boxed{ z = x_{1/2} } \end{equation}  --> <TABLE CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><IMG  WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"  SRC="img284.png"  ALT="$\displaystyle \boxed{ z = x_{1/2} }$"></TD> <TD NOWRAP WIDTH="10" ALIGN="RIGHT"> (3.11)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P>  <P> La profondeur du cylindre est trouv&#233;e directement par la valeur de <IMG  WIDTH="33" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"  SRC="img249.png"  ALT="$ x_{1/2}$">. De plus, le cylindre donne une amomalie plus large que celle d'une sph&#232;re (voir figure&nbsp;<A HREF="node35.htm#fig:gra_03_003">3.3</A>).  <P>  <DIV ALIGN="CENTER"><A NAME="fig:gra_03_003"></A><A NAME="2424"></A> <TABLE> <CAPTION ALIGN="BOTTOM"><STRONG>Figure 3.3:</STRONG> </CAPTION> <TR><TD> <DIV ALIGN="CENTER"><IMG  WIDTH="516" HEIGHT="223" ALIGN="BOTTOM" BORDER="0"  SRC="img285.png"  ALT="\includegraphics[width=4.5in]{figures/gra_03_003.eps}"> </DIV></TD></TR> </TABLE> </DIV>  <P> <HR> <!--Navigation Panel--> <A NAME="tex2html830"   HREF="node36.htm"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A>  <A NAME="tex2html826"   HREF="node33.htm"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A>  <A NAME="tex2html820"   HREF="node34.htm"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A>  <A NAME="tex2html828"   HREF="node1.htm"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A>   <BR> <B> suivant:</B> <A NAME="tex2html831"   HREF="node36.htm">3.1.3 Le cylindre vertical</A> <B> monter:</B> <A NAME="tex2html827"   HREF="node33.htm">3.1 Modle simple</A> <B> pr&eacute;c&eacute;dent:</B> <A NAME="tex2html821"   HREF="node34.htm">3.1.1 La sphre</A>  &nbsp <B>  <A NAME="tex2html829"   HREF="node1.htm">Table des mati&#232;res</A></B>  <!--End of Navigation Panel-->  </BODY> </HTML> 
