ÿþ<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <HTML> <HEAD> <title>0@04>:A, ?@54AB02;O5<K9 1>;LH8<8 48=>702@0<8</title> <meta name="description" content="1JOA=O5B, ?>G5<C 48=>702@K 8 ?B5@>702@K ?@54AB02;ONB =0CG=K9 ?0@04>:A."> <meta name="keywords" content="1@0E8>702@, ?B5@>702@, 48=>702@, B5>@8O"> </HEAD> <BODY> <TABLE BORDER=0 CELLSPACING=0 CELLPADDING=10 WIDTH=850> <TR> <TD> <CENTER><IMG SRC="Header1.jpg" WIDTH=960 WIDTH=146 ALIGN="center" alt="Page Header"></CENTER> <CENTER> <A HREF="scaling_ru.html"><IMG SRC="brown3-R-pc.jpg" alt="Link to Scaling properties"></A> <A HREF="index_ru.html"><IMG SRC="brown3-R-hp.jpg" alt="><0H=OO AB@0=8F0"></A> <A HREF="solution_ru.html"><IMG SRC="brown3-R-nc.jpg" alt="Link to Solution to Dinosaur Paradox"></A> </CENTER> <BASEFONT SIZE=4 COLOR=BLACK FACE="Times New Roman"> <CENTER><H1>2) 0@04>:A, ?@54AB02;O5<K9 1>;LH8<8 48=>702@0<8</H1></CENTER> <P><CENTER><H2>@8<5=5=85 =0CG=>3> ?>4E>40 4;O ?>=8<0=8O 48=>702@>2</H2></CENTER> <IMG SRC="brachiosaurus.jpg" HEIGHT=345 WIDTH=441 ALIGN="right" alt="Picture of Brachiosaurus"> <P ALIGN=JUSTIFY> ?@>H;>9 3;025 ?@82>48;>AL >1JOA=5=85 >A>15==>AB59 <0AHB018@>20=8O 0;8;5>, :>B>@K5 ?>:07K20NB, GB> @07<5@K 8<5NB 7=0G5=85. 4=0:> :>340 <K 2>72@0I05<AO =0704 2 ?@>H;>5 2 57>7>9A:CN M@C, <8@ 48=>702@>2 >:07K205BAO <038G5A:8< <5AB><, 345 :0:8<-B> C4828B5;L=K< >1@07>< =5 459AB2CNB 70:>=K =0C:8. > 2A59 25@>OB=>AB8, 5A;8 1K 8A:>?05<K5 48=>702@K =8:>340 =5 1K;8 1K =0945=K, =0CG=>5 A>>1I5AB2> C65 402=> 1) 2:;NG8;> 1K CG5=85 0;8;5> >1 >A>15==>ABOE <0AHB018@>20=8O 2 ?@>3@0<<C M;5<5=B0@=>3> =0CG=>3> >1@07>20=8O 8 2) ?@8H;> 1K : 70:;NG5=8N, GB> A0<K5 :@C?=K5 87 =K=5 682CI8E =075<=KE 682>B=KE O2;ONBAO ?@545;L=> 1>;LH8<8 ?> @07<5@0<. 4=0:> MB8 =0CG=K5 8458 4> A8E ?>@ =5 ?@8=OBK, ?>B><C GB> CG5=K5 ?>AB02;5=K 2 BC?8: D0:B>< ACI5AB2>20=8O 2 ?@>H;>< 48=>702@>2 8 ?B5@>702@>2 8A:;NG8B5;L=> 1>;LH8E @07<5@>2. <P ALIGN=JUSTIFY>865 ?@82545=K G5BK@5 ?@8G8=K, >1JOA=ONI85, ?>G5<C ACI5AB2>20=85 1>;LH8E 48=>702@>2 8 ?B5@>702@>2 ?@54AB02;O5B =0CG=K9 ?0@04>:A: <OL ALIGN=JUSTIFY><B> <LI>54>AB0B>G=0O ?@>G=>ABL :>AB59 4;O ?>445@60=8O 25A0 1>;LH8E 48=>702@>2<BR> <LI>54>AB0B>G=0O <KH5G=0O A8;0 4;O B>3>, GB>1K 1>;LH85 48=>702@K <>3;8 ?>4=8<0BLAO 8 ?5@542830BLAO<BR> <LI>54>?CAB8<> 2KA>:>5 :@>2O=>5 402;5=85 8 =03@C7:0 =0 A5@4F5 >G5=L 2KA>:8E 48=>702@>2<BR> <LI>@8=F8?K 0M@>48=0<8:8, ?>:07K20NI85 GB> ?B5@>702@K =5 <>3;8 ;5B0BL</B> </OL> <CENTER><H2>0AA0 70C@>?>40</H2></CENTER> <P ALIGN=JUSTIFY>> B>3>, :0: <K @0AA<>B@8< 0@3C<5=BK, :0A0NI85AO ?@>G=>AB8 :>AB59 8 <KH5G=>9 A8;K, =5>1E>48<> >F5=8BL <0AAC :@C?=59H8E 48=>702@>2  70C@>?>4>2. <P ALIGN=JUSTIFY>0C@>?>4K 1K;8 A0<K<8 :@C?=K<8 87 :>340-;81> ACI5AB2>202H8E =075<=KE 682>B=KE. ?0B>702@ 8<5; >1KG=CN 4;O 48=>702@>2 D>@<C A 1>;LH8<8 704=8<8 :>=5G=>ABO<8 ?> A@02=5=8N A ?5@54=8<8, 48?;>4>: 1K; AE>6 A 0?0B>702@><, => 8<5; 1>;55 4;8==CN H5N 8 E2>AB, 0 1@0E8>702@, 8725AB=K9 B0:65 :0: «?;5G8ABK9 OI5@», 8<5; E0@0:B5@=CN >A>15==>ABL  53> ?5@54=85 :>=5G=>AB8 1K;8 4;8==55 704=8E. @><5 MB8E =081>;55 8725AB=KE ?@54AB028B5;59 70C@>?>4>2, ACI5AB2>20;> <=>65AB2> 4@C38E :@C?=KE, AE>68E <564C A>1>9 70C@>?>4>2, @07;8G=KE ?> =08<5=>20=8O<, B0: :0: ?0;5>=B>;>38 A>@52=CNBAO 70 ?@02> =0E>645=8O A0<KE 1>;LH8E =075<=KE 682>B=KE. ;O A@02=5=8O @07<5@>2, <0AAK 8 A8;K, <K 1C45< @0AA<0B@820BL 1@0E8>702@0. <P><center><IMG SRC="dino5.jpg" alt="Sauropod"></center> <P ALIGN=JUSTIFY>'B>1K ?>;CG8BL ?@81;878B5;L=>5 7=0G5=85 <0AAK 682>B=>3>, >?@545;8< <0AHB01=K9 :>MDD8F85=B ?CB5< ?>8A:0 AE>68E ?> D>@<5 682>B=KE, 0 70B5< A@02=5=85< 8E AE>68E ?@87=0:>2, :0:, =0?@8<5@, 2KA>BC ?;5G. 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"0:65 ?@54AB02LB5 @07@57 <KHFK: ?;>I04L A@570 ?@O<> ?@>?>@F8>=0;L=0 <KH5G=>9 A8;5. !8;0 <KHF 8 :>AB59, ?@>?>@F8>=0;L=0O ?;>I048, 42CE<5@=K9 0B@81CB. > <0AA0 B5;0  DC=:F8O >1J5<0, B@5E<5@=K9 0B@81CB. !;54>20B5;L=>, >B=>A8B5;L=0O A8;0 682>B=KE, >B=>H5=85 A8;K : <0AA5, C<5=LH05BAO A @07<5@>< 682>B=>3>: A0<K5 :@C?=K5 682>B=K5 8<5NB =08<5=LHCN >B=>A8B5;L=CN A8;C. <P ALIGN=JUSTIFY>'B> :0A05BAO >B=>A8B5;L=>9 ?@>G=>AB8 :>AB59, 1>;LH85 682>B=K5 =0<=>3> 1>;LH5 @8A:CNB ?>;><0BL A2>8 :>AB8, G5< <5=LH85 682>B=K5. 5@>OB=>ABL B>3>, GB> ?>;><:0 :>AB59 A>:@0B8B 687=L 682>B=>3>, 4>AB0B>G=> 25;8:0 4;O 1>;LH8E 682>B=KE. ><8=8@CNI85 284K 8<5NB B5=45=F8N M2>;NF8>=8@>20BL ?> =0?@02;5=8N : 1>;LH8< @07<5@0<. > 1>;LH0O 25@>OB=>ABL A;><0==KE :>AB59, >:07K20NI8E 2;8O=85 =0 1>;LH8E 682>B=KE, <>65B 1KBL D0:B>@><, :>B>@K9 2 :>=5G=>< AG5B5 >3@0=8G8205B 8E @07<5@K. <P ALIGN=JUSTIFY>0?@8<5@, ?@87>2>9 A:0:C= <>65B ;53:> A;><0BL =>3C ?@8 1535. 1KG=> MB> A;CG05BAO 2 =86=59 G0AB8 ?5@54=8E =>3. > 2>7<>6=> B0:65 ?>2@5645=85 4@C38E G0AB59 ?5@54=8E 8 704=8E =>3. -B> ?>:07K205B, GB> ?>2@5645=8O - =5 @57C;LB0B A?5F8D8G5A:>3> 8<5NI53>AO A;01>3> CG0AB:0 2 =>30E. !:>@55 MB> ?>A;54AB28O BO65;>3> 25A0 682>B=>3>, ?@>872>4OI53> C40@K, ?@52KH0NI85 ?@>G=>ABL <0B5@80;0 :>AB59 =>3. <P ALIGN=JUSTIFY>@C3>9 ?>:070B5;L B>3>, GB> MB8 500 :8;>3@0<<>2K5 682>B=K5 ?@81;865=K : ?@545;C @07<5@>2, MB> ?@>1;5<K, 2>7=8:0NI85 :>340 ?@54?@8=8<0NBAO ?>?KB:8 2K;5G8BL MB8E 25;8:>;5?=KE 682>B=KE, ?>A;5 B>3>, :0: >=8 ;><0NB =>38. >H048 G0AB> A?OB AB>O, GB> O2;O5BAO C40G=K< M2>;NF8>==K< A?>A>1>< 2K6820=8O, B0: :0: >=8 <>3CB 1KAB@> C1560BL >B E8I=8:>2. > 5A;8 ;>H04L <>65B AB>OBL =0 B@5E 74>@>2KE =>30E 8 45;05B MB> 4>2>;L=> 4;8B5;L=>5 2@5<O, ?5@5=03@C7:0 74>@>2KE =>3 <>65B ?@825AB8 : @0728B8N ;0<8=8B0. A:>@5 AB>OBL =0 74>@>2KE =>30E AB0=5B B0: 65 1>;L=>, :0: 8 =0 A;><0==>9 =>35. 0G0ABCN 1>;55 G5;>25G=> C<5@B28BL ;>H04L, G5< >AB028BL 55 AB@040BL ?>A;54=85 4=8. <P><IMG SRC="race_horses.jpg" HEIGHT=299 WIDTH=446 ALIGN="right" hspace=10 vspace=5 alt="A Horse Race"> <P ALIGN=JUSTIFY> B> 2@5<O :0: 4>AB0B>G=> ;53:> ?>:070BL, GB> A0<K5 1>;LH85 682>B=K5 8<5NB A0<CN =87:CN >B=>A8B5;L=CN ?@>G=>ABL :>AB59 8 A0<CN =87:CN >B=>A8B5;L=CN <KH5G=CN A8;C, B@C4=55 >?@545;8BL A0<KE 1>;LH8E ?> @07<5@C =075<=KE ?>72>=>G=KE. <P ALIGN=JUSTIFY> E>BO A:0:>2K5 ;>H048  :@C?=K5 682>B=K5, >=8 40;5:> =5 A0<K5 1>;LH85 87 =075<=K5 ?>72>=>G=K5. ;5945A40;LA:85 ;>H048-BO65;>2>7K 25AOB >:>;> >4=>9 B>==K, GB> 2 420 @070 1>;LH5 <0AAK B8?8G=>3> A:0:C=0. "8?8G=K9 65 A0<5F 0D@8:0=A:>3> A;>=0 8<55B <0AAC A5<L B>==. <P ALIGN=JUSTIFY>5=LH0O <KH5G=0O A8;0 1>;LH8E 682>B=KE =0 A0<>< 45;5 O2;O5BAO 8E ?@58<CI5AB2><, B0: :0: >3@0=8G8205B 8E 0:B82=>ABL, GB> <>65B ?>2;5GL 70 A>1>9 2>7<>6=>ABL ?>;><0BL :>AB8. 530O 1>;55 <54;5==>, 0 2 A;CG05 A> A;>=0<8, 1530O 1>;55 <54;5==> 8 =5 ?@K30O, A0<K5 :@C?=K5 =075<=K5 682>B=K5 >1KG=> 871530NB 1>;55 2KA>:8E C40@=KE A8;, GB> <>65B ?>2;5GL ?>;><:C =>3. <P><IMG SRC="buffalo2.jpg" HEIGHT=251 WIDTH=320 ALIGN="left" hspace=10 vspace=5 alt="Buffalo"> <P ALIGN=JUSTIFY>>AB8 ;><0NBAO, :>340 402;5=85 =0 :>ABL ?@52KH05B ?@545; ?@>G=>AB8 <0B5@80;0 :>AB8. 'B>1K ?>=OBL, GB> 1>;LH85 682>B=K5 1>;LH5 @8A:CNB ?>;><0BL :>AB8, <K <>65< A@02=8BL 402;5=85 =0 :>AB8 =>3 682>B=KE, ?@8 CA;>288 B>3>, GB> >=8 =0E>4OBAO 2 A?>:>9=>< ?>;>65=88 8 B>;L:> ?>445@6820NB A2>9 25A <P ALIGN=JUSTIFY>amount of cross sectional supporting bone area is determined. "01;8F0, ?@82545==0O =865, ?>:07K205B ?@54AB028B5;L=CN 2K1>@:C <;5:>?8B0NI8E, @0A?>;>65==KE ?> <5@5 2>7@0AB0=8O >B =08<5=LH8E : =081>;LH8<. <5O ?@82545==K5 40==K5 4;8=K >:@C6=>AB59 :>AB59 ?5@54=8E 8 704=8E =>3, >?@545;8< ?;>I04L ?>?5@5G=>3> A5G5=8O :>AB59. 02;5=85, >:07K205<>5 =0 :>ABL, 2 B> 2@5<O, :>340 682>B=>5 AB>8B, <>65B 70B5< 1KBL @0AAG8B0=> 45;5=85< 25A0 682>B=>3> =0 ?;>I04L ?>?5@5G=>3> A5G5=8O :>AB8. >A;54=89 AB>;15F A?@020  MB> 402;5=85 =0 =>38 682>B=>3>, :>340 >=> AB>8B. <P><CENTER> <H3>02;5=85 =0 :>AB8 =>3 <;5:>?8B0NI8E, :>340 >=8 AB>OB</H3> <TABLE BORDER="5" CELLPADDING="3"> <TR> <TH>;5:>?8B0NI55</TH><TH>;8=0 >:@C6=>AB8 ?5@54=8E =>3<BR>(mm)</TH><TH>;8=0 >:@C6=>AB8 704=8E =>3<BR>(mm)</TH><TH>@81;878B5;L=0O >1I0O ?;>I04L :>AB8 <BR>(mm^2)</TH><TH>5A 682>B=>3><BR>(N) </TH><TH>02;5=85 2 <><5=B AB>O=8O <BR>(N/M^2 E5)</TH> </TR><TR> <TD Align="center">C3>20O <KHL</TD><TD Align="center">5</TD><TD Align="center">5</TD><TD Align="center">4</TD><TD Align="center">0.5</TD><TD Align="center">1</TD> </TR><TR> <TD Align="center">>@A:0O A28=:0 </TD><TD Align="center">10</TD><TD Align="center">15</TD><TD Align="center">29</TD><TD Align="center">3.8</TD><TD Align="center">1.3</TD> </TR><TR> <TD Align="center">!5@0O 15;:0</TD><TD Align="center">10</TD><TD Align="center">13</TD><TD Align="center">24</TD><TD Align="center">3.9</TD><TD Align="center">1.6</TD> </TR><TR> <TD Align="center">!5@0O ;8A8F0</TD><TD Align="center">28</TD><TD Align="center">26</TD><TD Align="center">130</TD><TD Align="center">39</TD><TD Align="center">3.0</TD> </TR> <TD Align="center">=>B</TD><TD Align="center">30</TD><TD Align="center">28</TD><TD Align="center">150</TD><TD Align="center">50</TD><TD Align="center">3.3</TD> </TR> <TD Align="center">OB=8ABK9 ;5>?0@4</TD><TD Align="center">45</TD><TD Align="center">41</TD><TD Align="center">330</TD><TD Align="center">140</TD><TD Align="center">4.2</TD> </TR> <TD Align="center">>;:</TD><TD Align="center">62</TD><TD Align="center">62</TD><TD Align="center">680</TD><TD Align="center">470</TD><TD Align="center">6.9</TD> </TR> <TD Align="center">52</TD><TD Align="center">104</TD><TD Align="center">94</TD><TD Align="center">1700</TD><TD Align="center">1400</TD><TD Align="center">8.1</TD> </TR> <TD Align="center">>;O@=K9 <54254L</TD><TD Align="center">158</TD><TD Align="center">135</TD><TD Align="center">3820</TD><TD Align="center">4390</TD><TD Align="center">11.5</TD> </TR> <TD Align="center">!;>=</TD><TD Align="center">459</TD><TD Align="center">413</TD><TD Align="center">33700</TD><TD Align="center">57800</TD><TD Align="center">17.1</TD> </TR> </TABLE> </CENTER> <CENTER><H4> <P ALIGN=JUSTIFY>AE>4=K5 40==K5, 4;8=0 >:@C6=>AB8 ?5@54=8E 8 704=8E =>3 8 <0AA0 :064>3> 682>B=>3> 27OBK 87 Anderson, J. F., Hall-Martin, A., and Russell, D. A. 1985. "Long-Bone Circumference and Weight in Mammals, Birds, and Dinosaurs," Journal of Zoology, London (A) 207: 53-61 <BR>;>I04L @0AAG8B0=0 :0: (CF2 + CR2)/2PI, ;>I04L :>AB59 = ;>I04L * 5/9, ?@8=8<0O 2> 2=8<0=85 ?>;CN A5@548=C :>AB59, !B@5AA 2 ?>;>65=88 AB>O = 5A / ;>I04L :>AB8 </H4></CENTER> <CENTER><IMG SRC="standing_stress.jpg" HEIGHT=341 WIDTH=801 hspace=5 vspace=5 alt="Graph of Standing Stress as a Function of Weight"></CENTER> <CENTER><H4>!@02=820O <;5:>?8B0NI8E, :>340 >=8 =0E>4OBAO 2 ?>;>65=88 AB>O, :>AB8 1>;LH8E 682>B=KE ?>425@30NBAO 1>;LH5<C 402;5=8N, G5< <5=LH8E 682>B=KE. >;LH85 <;5:>?8B0NI85 =0E>4OBAO ?>4 1>;LH8< @8A:>< A;><0BL A2>8 :>AB8, G5< <5=LH85 682>B=K5. </H4></CENTER> <P ALIGN=JUSTIFY>02;5=85 =0 :>AB8 <>65B 1KBL 2> <=>3> @07 1>;LH5, :>340 682>B=>5 ?@875<;O5BAO ?>A;5 ?045=8O. 02;5=85 =0 :>AB8 2 :>=F5 ?045=8O >1KG=> 7028A8B >B B>3>, :0: 25;8:> 682>B=>5, 8 A :0:>9 2KA>BK >=> ?0405B. 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BAN40 >G5284=> 70:;NG5=85, GB> 70C@>?>4K 8 4@C385 :@C?=K5 48=>702@K ?@54AB02;ONB =0CG=K9 ?0@04>:A. <CENTER><H2>@>1;5<0 :@>2O=>3> 402;5=8O</H2></CENTER> <P ALIGN=JUSTIFY>=>385 8AA;54>20B5;8 704020;8AL 2>?@>A><, :0: :@>2L 1@0E8>702@>2 <>3;0 ?>ABC?0BL : 3>;>25. 0: @5H5=85 MB>9 ?@>1;5<K, 1K;8 2K428=CBK =5A:>;L:> @07;8G=KE 38?>B57. 4=8 ?0;5>=B>;>38 ?@54?>;030;8, GB> 1@0E8>702@K 8<5;8 <0AA82=>5 A5@4F5, :>B>@>5 <>3;> A>74020BL =5>1E>48<>5 4;O ?>4=OB8O :@>28 402;5=85. @C38< ?@54?>;>65=85< 1K;> B>, GB> 2 ?@>F5AA5 M2>;NF88 1@0E8>702@K ?>;CG8;8 =5A:>;L:> @0A?>;>65==KE A @02=K<8 8=B5@20;0<8 A5@45F 2 >1;0AB8 H58, @01>B0NI8E :0: =0A>A=0O A8AB5<0. > =081>;55 ?>?C;O@=>9 84559 O2;O5BAO ?@54?>;>65=85, GB> 1@0E8>702@K =8:>340 =5 ?>4=8<0;8 3>;>2C, 0 2<5AB> MB>3> <>3;8 42830BL 55 =0704 8 2?5@54 3>@87>=B0;L=>. <P><CENTER><IMG SRC="brachiosaurus3_blood.jpg" HEIGHT=300 WIDTH=815 hspace=5 vspace=5 alt=""></CENTER> <P><IMG SRC="blood_pressure2.jpg" HEIGHT=315 WIDTH=235 ALIGN="right" hspace=10 vspace=5 alt="A person having their blood pressure taken"> <P ALIGN=JUSTIFY>A5 MB8 38?>B57K 2>7=8:;8 87 ?@>1;5<K, A2O70==>9 A 2KB0;:820=85< :@>28 =0 1>;LHCN 2KA>BC.  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"0:8< >1@07><, 8<55BAO ?0@04>:A =0;8G8O 682>B=>3>, A;>65==>3> B0:8< >1@07><, GB>1K 53> 3>;>20 4>AB830;0 <0:A8<0;L=>9 2KA>BK, => A5@4F5 :>B>@>3> =5 A?>A>1=> ?>AB02;OBL :@>2L : 53> 3>;>25. <P><CENTER><H3><A HREF="mailto:questions@dinosaurtheory.com">>H;8B5 A>>1I5=85, 5A;8 C 20A 5ABL 2>?@>AK, 2K E>B8B5 2K@078BL ?>445@6:C, 8;8 70?;0=8@>20BL ?@575=B0F8N </A></H3></CENTER> <P><CENTER><A HREF="mailto:questions@dinosaurtheory.com"><IMG SRC="e-mail2.gif" HEIGHT=50 WIDTH=50 alt="Sending mail"></A></CENTER> <P><CENTER><H4>-B>B <0B5@80; 70I8I5= 02B>@A:8<8 ?@020<8. <P ALIGN=JUSTIFY>>?8@>20=85 8 @0A?@>AB@0=5=85 40==>3> <0B5@80;0 2 =587<5=5==>< 2845 @07@5H5=> ?@5?>4020B5;O<, 0 B0:65 ABC45=B0< :0: 3>AC40@AB25==KE, B0: 8 G0AB=KE CG51=KE 702545=89</H5></CENTER> <P><CENTER> <A HREF="solution_ru.html"><IMG SRC="brown3-ds.jpg" alt="Link to Solution to Dinosaur Paradox"></A> <A HREF="index_ru.html"><IMG SRC="brown3-hp.jpg" alt="><0H=OO AB@0=8F0 "></A> </CENTER> </TD> </TR> </TABLE> </BODY> </HTML>