Asymptotic Methods in Resonance Analytical Dynamics 1st Edition Eugeniu Grebenikov

Asymptotic Methods in Resonance Analytical
Dynamics 1st Edition Eugeniu Grebenikov pdf
download
https://ebookfinal.com/download/asymptotic-methods-in-resonance-
analytical-dynamics-1st-edition-eugeniu-grebenikov/
Explore and download more ebooks or textbooks
at ebookfinal.com

We believe these products will be a great fit for you. Click
the link to download now, or visit ebookfinal
to discover even more!
Hierarchical Methods Hierarchy and Hierarchical Asymptotic
Methods in Electrodynamics 1st Edition V. Kulish
https://ebookfinal.com/download/hierarchical-methods-hierarchy-and-
hierarchical-asymptotic-methods-in-electrodynamics-1st-edition-v-
kulish/
Analytical Fluid Dynamics 3rd Edition George Emanuel
https://ebookfinal.com/download/analytical-fluid-dynamics-3rd-edition-
george-emanuel/
Analytical and Computational Methods in Electromagnetics
Ramesh Garg
https://ebookfinal.com/download/analytical-and-computational-methods-
in-electromagnetics-ramesh-garg/
From Finite Sample to Asymptotic Methods in Statistics 1st
Edition Pranab K. Sen
https://ebookfinal.com/download/from-finite-sample-to-asymptotic-
methods-in-statistics-1st-edition-pranab-k-sen/

Analytical methods for Kolgomorov equations 2nd Edition
Lorenzi
https://ebookfinal.com/download/analytical-methods-for-kolgomorov-
equations-2nd-edition-lorenzi/
Analytical and numerical methods for vibration analyses
1st Edition Wu
https://ebookfinal.com/download/analytical-and-numerical-methods-for-
vibration-analyses-1st-edition-wu/
Analytical Solution Methods for Boundary Value Problems
1st Edition A.S. Yakimov
https://ebookfinal.com/download/analytical-solution-methods-for-
boundary-value-problems-1st-edition-a-s-yakimov/
Solutions Manual for Recursive Methods in Economic
Dynamics Claudio Irigoyen
https://ebookfinal.com/download/solutions-manual-for-recursive-
methods-in-economic-dynamics-claudio-irigoyen/
Methods in molecular biophysics structure dynamics
function 1st Edition Igor N. Serdyuk
https://ebookfinal.com/download/methods-in-molecular-biophysics-
structure-dynamics-function-1st-edition-igor-n-serdyuk/

Asymptotic Methods in Resonance Analytical Dynamics
1st Edition Eugeniu Grebenikov Digital Instant Download
Author(s): Eugeniu Grebenikov, Yu. A. Mitropolsky, Y.A. Ryabov
ISBN(s): 0415310083
Edition: 1
File Details: PDF, 2.09 MB
Year: 2004
Language: english

Asymptotic Methods in
Resonance Analytical
Dynamics
Stability and Control:Theory, Methods and Applications
Volume 21
E.A. Grebenikov
Russian Academy of Sciences
Moscow, Russia
Yu. A. Mitropolsky
National Academy of Sciences of Ukraine
Kiev, Ukraine
Yu. A. Ryabov
Moscow Institute of Auto and Highway Construction
Moscow, Russia
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London NewYork Washington, D.C.
Copyright © 2004 CRC Press LLC

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with
permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish
reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials
or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical,
including photocopying, microÞlming, and recording, or by any information storage or retrieval system, without prior
permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works,
or for resale. SpeciÞc permission must be obtained in writing from CRC Press LLC for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identiÞcation and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
© 2004 by CRC Press LLC
No claim to original U.S. Government works
International Standard Book Number 0-415-31008-3
Library of Congress Card Number 2003069583
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
Library of Congress Cataloging-in-Publication Data
Grebenikov, E. A. (Evgeniæi Aleksandrovich)
Asymptotic methods in resonance analytical dynamics / by Eugeniu Grebenikov, Yu. A.
Mitropolsky, and Y. Ryabov.
p. cm. — (Stability and control ; v. 21)
Includes bibliographical references and index.
ISBN 0-415-31008-3 (alk. paper)
1. Averaging method (Differential equations) 2. Differential equations—Asymptotic
theory. 3. Resonance—Mathematical models. I. Mitropol§skiæl, ëIìU. A. (ëIìUriæi
Alekseevich), 1917- II. Rëiìabov, ëIìU. A. (ëIìUriæi Aleksandrovich) III. Title. IV.
Series.
QA372 .G715 2004
515¢.35—dc22 2003069583
TF1684_Disc.fm Page 1 Wednesday, January 21, 2004 11:24 AM

Introduction to the Series
The problems of modern society are both complex and interdisciplinary. Despite the
apparent diversity of problems, tools developed in one context are often adaptable to
an entirely different situation. For example, consider the Lyapunov’s well known
second method. This interesting and fruitful technique has gained increasing signi-
fycance and has given a decisive impetus for modern development of the stability
theory of differential equations. A manifest advantage of this method is that it does
not demand the knowledge of solutions and therefore has great power in application.
It is now well recognized that the concept of Lyapunov-like functions and the theory
of differential and integral inequalities can be utilized to investigate qualitative and
quantitative properties of nonlinear dynamic systems. Lyapunov-like functions serve
as vehicles to transform the given complicated dynamic systems into a relatively
simpler system and therefore it is sufficient to study the properties of this simpler
dynamic system. It is also being realized that the same versatile tools can be adapted
to discuss entirely different nonlinear systems, and that other tools, such as the vari-
ation of parameters and the method of upper and lower solutions provide equally
effective methods to deal with problems of a similar nature. Moreover, interesting
new ideas have been introduced which would seem to hold great potential.
Control theory, on the other hand, is that branch of application-oriented mathema-
tics that deals with the basic principles underlying the analysis and design of control
systems. To control an object implies the influence of its behavior so as to accomplish
a desired goal. In order to implement this influence, practitioners build devices that
incorporate various mathematical techniques. The study of these devices and their
interaction with the object being controlled is the subject of control theory. There
have been, roughly speaking, two main lines of work in control theory which are
complementary. One is based on the idea that a good model of the object to be
controlled is available and that we wish to optimize its behavior, and the other is
based on the constraints imposed by uncertainty about the model in which the object
operates. The control tool in the latter is the use of feedback in order to correct for
deviations from the desired behavior. Mathematically, stability theory, dynamic
systems and functional analysis have had a strong influence on this approach.
Volume 1, Theory of Integro-Differential Equations, is a joint contribution by
V. Lakshmikantham (USA) and M. Rama Mohana Rao (India).
Volume 2, Stability Analysis: Nonlinear Mechanics Equations, is by A. A. Martynyuk
(Ukraine).
Volume 3, Stability of Motion of Nonautonomous Systems: The Method of Limiting
Equations, is a collaborative work by J. Kato (Japan), A. A. Martynyuk (Ukraine) and
A. A. Shestakov (Russia).

Volume 4, Control Theory and Its Applications, is by E. O. Roxin (USA).
Volume 5, Advances in Nonlinear Dynamics, is edited by S. Sivasundaram (USA) and
A. A. Martynyuk (Ukraine) and is a multiauthor volume dedicated to Professor
S. Leela (USA).
Volume 6, Solving Differential Problems by Multistep Initial and Boundary Value
Methods, is a joint contribution by L. Brugnano (Italy) and D. Trigiante (Italy).
Volume 7, Dynamics of Machines with Variable Mass, is by L. Cveticanin (Yugo-
slavia).
Volume 8, Optimization of Linear Control Systems: Analytical Methods and Compu-
tational Algorithms, is a joint contribution by F. A. Aliev (Azerbaijan) and V. B. La-
rin (Ukraine).
Volume 9, Dynamics and Control, is edited by G. Leitmann (USA), F. E. Udwadia
(USA) and A. V. Kryazhimskii (Russia) and is a multiauthor volume.
Volume 10, Volterra Equations and Applications, is edited by C. Corduneanu (USA)
and J. W. Sandberg (USA) and is a multiauthor volume.
Volume 11, Nonlinear Problems in Aviation and Aerospace, is edited by S. Sivasun-
daram (USA) and is a multiauthor volume.
Volume 12, Stabilization of Programmed Motion, is by E. Ya. Smirnov (Russia).
Volume 13, Advances in Stability Theory at the End of the 20th Century, is edited by
A. A. Martynyuk (Ukraine) and is a multiauthor volume.
Volume 14, Dichotomies and Stability in Nonautonomous Linear Systems, is a colla-
borative work by Yu. A. Mitropolsky (Ukraine), A. M. Samoilenko (Ukraine) and
V. L. Kulik (Ukraine).
Volume 15, Almost Periodic Solutions of Differential Equations in Banach Spaces, is
a collaborative work by Y. Hino (Japan), T. Naito (Japan), Nguyen Van Minh (Viet-
nam) and Jong Son Shin (Japan).
Volume 16, Functional Equations with Causal Operators, is by C. Corduneanu
(USA).
Volume 17, Optimal Control of the Growth of Wealth of Nations, is by E. N. Chukwu
(USA).
Volume 18, Stability and Stabilization of Nonlinear Systems with Random Structure,
is a joint contribution by I. Ya. Kats (Russia) and A. A. Martynyuk (Ukraine).
Volume 19, Lyapunov Functions in Differential Games, is by V. I. Zhukovskiy
(Russia).
Volume 20, Stability of Differential Equations with Aftereffect, is a joint contribution
by N. V. Azbelev (Russia) and P. M. Simonov (Russia).
Volume 21, Asymptotic Methods in Resonance Analytical Dynamics, is e a colla-
borative work by E. A. Grebenikov (Russia), Yu. A. Mitropolsky (Ukraine) and
Yu. A. Ryabov (Russia).
Due to the increased interdependency and cooperation among the mathematical
sciences across the traditional boundaries, and the accomplishments thus far achieved
in the areas of stability and control, there is every reason to believe that many
breakthroughs await us, offering existing prospects for these versatile techniques to
advance further. It is in this spirit that we see the importance of the ‘Stability and
Control’ series, and we are immensely thankful to Taylor & Francis and Chapman &
Hall/CRC for their interest and cooperation in publishing this series.

!$#%'()$+*%)(,!(+*%-$# ,!#.$*/$0#.,10122)2#.3$42#/5
3$+*%)6!,!#%)+%7(,8$42#)+3$#%99$:2)#$# $#%2$#.#%$#.,80;,!=#%$#%$+)$#%?$5
,!=#%$#%$+)2#.@:(3$(%ACBD42# 0(#%(*/#DE=#/F2*G:22H#%$)#/$42!,2CEIJ$42# H#.$?3$
EK22)2#. !$#%L4(L,!$H#%$42#,!#%H#%)2#% EDNM +,!#2?#1EK22$OF!3$#
()$+* (, :2#%$+*%)P!()$+*J#/$42!,2$4(3J*%Q0# 2)#%#%$#.,QQ#/=#.*G$H#K*/15
2:!$#%9)?$$42%A
B6$2?N$;?H#$42#%RN?#%2#%),!#.$*/$!$72#*%S$#%T$4(3 2*G$+*%))))
22$OF!3$#L#/$42!,29$# */($$:(*G$#.,80'$42#Q$#%3$;2$(*/2)#AKBD42+#.(D$4(3
U 'V2$+)22$OF!3$W+#%423MX*42#%WEI1$42#Y2$02)#%;7K(,Z$42#%7K0
#.(E9$#%3$(%7$42#Y,2,!$VE9$#%$1EL,!=#%$#% U 2$#.) ,!#%1$[$42#
2$+)22$OF!3$'$#EI:2(,A-BD42#9$#%$^]$#%3$(_ +K:2(,!#%$!,42#%$#L #%$42#%
:(*%*/#.$H#22$OF!3$(%7(TN*4(YE :(*%*/#.$H# $(EI$3$( E-24(#H3$5
02)#.%7J1YEI:2(*G$()D#%$#. M $4W$#%$,!#.*/$#.2?YWH3):2#A[`2$R$42#N42+$$+*%)
#.*G.7$42# U 22$OF!3$MD-*/(+,!#%$#.,1 ):!$E# )2#.2$02)#%
a42#%(*/#Y$42#$#%$b)2#.$c.3$d#/$42!,(eG7D$WM 42+*4f#[)) EI:2(*G$( a2$5
$()$$42#L))=(#/$#%Ge-,!#/$#%$2#.,'M $42N$42#9EI#%MK$g1E62#TD2$42#%
#%$:2$0(3$h$42#%$[MK#%$#,2,!#.,A;`2 #/F22)#7CM 42)#N$:(,!2?;$42#'$*/))+3$(LE
$42#3$42#%3$+*%)J#%(,!:2):2ji#%MD$S*/(+,!#%$#.,;$42#))J$*/))+3$(Tk aIl e9E-$42#
#%(,!:2):2;7(mA#A(1)2#. 2$02)#%XEC$42#LEI$
nk;oSp q%kZrfsQt
M 42#%$#Lpt$su$# */(%A-BD42+ )2#. #.@:(3$;#%$H#. K$42# 2$+)C22$OF!3$
EID$42# 22)2#. #.@:(3$
nv oSp q v rfs
w/x

y.zz {L|}6~JJ€9C‚ƒJJƒ6„Iƒ6|†J‡Y‡|OJƒ6†JƒJˆ=|N€‰ƒ6†J{LŠˆ
$4(3,!#.$*/$0#.K$*/))+3$( v aIl e EJ3$42#%3$+*%)=#%(,!:2):2;722D2#.*/#.$$$)))
;H3):2#A
‹6?2?# ,!+,Q$42# $#KM 42#%*/(+,!#%$2?T#.*/:2)+C#%$:2$0(3$(C$42#D2)+2#/$
$42$#%#/5Œ0!,!W2$02)#%:2(,!#%)) #%$:2$0(3$(%AŽŒ'MD$42#%$4(3$42#Y!$#%E
,!=#%$#%$+)#.@:(3$(KEC$42#LEI))3M 2?1EI$XMDD)H#.,
n‘ oSp q ‘ r“’ aIl eGt
M 42#%$# ‘ +F57C#%?45T $#%!5”,!#%(() H#.*G$.76p•$42#'H#.*G$QE9*/( EI$#/5
@:2#%(*/#.%7((,8’ aIl eD1H#.*G$5mEI:2(*G$Y– 5Œ#%$!,!+*TM $4;$#.#.*GD$ l A
— 2$42#%Y22$*4d$V22)2#.82$02)#%˜)H2?+8M 42#%7LN$42#h2$+) !5
2$OF!3$7=$42#'):!$hED;!$#%™+Tg#%[$4(3Q+ 822)2#.L02:!Q#.$#%$+))
]$2)#%_'!$#%š$4(Y$42#2$+)C2#ATBD42+T2)U #.,!$#%›*%Y0#0!2#.,Y0
,!=#%$#%-#/$42!,2%702:! (*/#K$42#K$#.JE=‹6?2?#K(,œL:($%73$*/))+3$$L!,!#%)+
E6*/#%)#.$+)(#.*4(2+*%J$42#9#/$42!,EOH#%?2? a $422?eE#%$!,!+* K@:(5
#%$!,!+*EI:2(*G$(K0#%2?1Q(KE$42#L()$+*$$:(*G$:2$#9E$42#T#.@:(3$(-MD
E$#%h:(#.,A‹63$#%.7(,($+*/:2)+$);23MD,2O!%7OH#%?2?'#/$42!,2TS*/02(3$
M $4h!$$+* $#%2$#.#%3$( aY$42#1#%(#QE žJ(*%2Ÿ#Oe MK#%$# :(#., $42#0(+*
*/($$:(*G$H#D#.(JE=)H2?T$$+*%3$#D2$02)#%JE=()$+*%)2,!(+*%%73EI$)c%#.,
N$42#L)+2?:(?#9EC,!=#%$#%$+)=#.@:(3$(%ABD42+K0#.*%#L$02)#9$4(2g! $$42#LMK$g
EiQAiQA(K?):203H8$42#¡.¢£¤%7M 42#%$#T$42# 2$02)#%XEC22)2#. 2$02)#%¥)H2?
MDKEI$:2)+3$#.,; 2$02)#%¥EC$(EI$3$NEC$42# 2$+)C,!=#%$#%$+)#.@:(3$(
$L2#%MV2)U #.,75”*%))#.,*/($+Q#.@:(3$(%AJ¦(*/#K$42#*42+*/#KE=*/($+
#.@:(3$(T+ $02$$7=2#*%[g#h!$)*42+*/# a#A?(A=EI$›$42#(,!
EJ$42#%9)H302)72 $42#Q2$OF!'E-):!$( E*/($+8#.@:(3$(D$$42#
EC$42# 2$+)6!$#%;7!D$42# #/§'*/#%(*/'EJ:2#%$+*%)=#/$42!,222)#.,N$1$42#%'eK$4(3
,!#/$#%$2#.-$42#L*/$$#.(,!2?L$(EI$3$E24(#9H3$+02)#.%ACŽŒK+ #.1$1423M
$4(3DE$42#L,!=#%$#%$+)#.@:(3$(K$#9M $$#%'8Q2$)(EI$¨'$42#Q©K:(*4#%(#7
$42#%d$42#YEI:2(*G$($4(3'#%EI$$42#[*4(2?#;ELH3$+02)#.$3$+EI#!$#%bE
@:(5Œ)2#. !$#%D U 5Œ,!#%D($+),!#%$H33$H#.%A
`2$•$42##.*GE?#%#/$$+*-$#%$2$#/3$73$42#K$(EI$3$QE2$+)2#.@:(35
$($N*/($+;#.@:(3$(*%Y0#$#%$2$#/$#.,; $42#*42+*/#QE-24(#(*/#
9!$)EI $42#Q?H#%;2$02)#%;72E#/$$+*%(,82$;ADBD42#L$(EI$3$
E6#.@:(3$( #.( $42#L#.*4EI $42#L?#%#/$$1$4(3D?H#.-$42#L2)#. ,!#.$*/$!$
$[$42#Y*/(+,!#%$#.,Z2$02)#%;AWK:!1$42#Y2)#.,!#.$*/$!$ET2$02)#%,!#.12
#.Y$4(3$42##/$42!,YE-):!$Y4(0#%#%YEI:2(,ABD42#%$#/EI$#79$:2)#7(T+2)
$#.(02)#N*/02(3$ZE9$#%3$Z2$!*/#.,!:2$#.QM $4V[:(*%*/#.$EI:2)D*42+*/#NE $42#
2$+) 22$OF!3$[(,[M $4[$42#:(#E EŠQ)?$$42L(,h*/(*GL2$?
$4(3*%Z?:($#%#1$42#N#/§'*/#%(*/hED$42#8*/($$:(*G$SE9W22$OF!3$#):!$
M $4;2$#.$*/$0#.,8*%*/:2*/A
¦$42#Q#.*4NEID$42#Q!$)?#%#/$$EI #.*4Y#.*/U *L2$02)#%¥E()$+*%)
,!(+*%+ */22#.*G$#.,1M $4$42# U (,!2?QE#:20($$:!$E=H3$+02)#.J$4(3 02(,2
$42# )+,24(#DH3$+02)#.CM 42+*4$42# 2$+)2,!#.$*/$!$1E($42# 2$02)#%ª+J,!#7M $4
2#%M«24(#H3$+02)#.LSM 42+*4h$42#2$02)#%j+Q,!#.$*/$0#.,h0h8#/$42!,h$4(3Q+Q15
2)#. a.723$42#%.7!9*/H#%2#% EID$42#Q$#.#.*42#%GeGAŽŒEMK#Q:(*%*/#%#.,8Y)H2?1$42#

¬ ‡|‚.†Cˆ=| y.zzz
#.@:(3$( ,!#/$#%$22?Q$42#T:20($$:!$'EH3$+02)#.%7MK#90!'*/H#%2#% $#%)+3$(
02(,!2?$42# 2$+)24(# (*/#LM $48$42# 2#%M2#A
— Y#/F2*/#%))#%9)):($3$;EJ$42++ $42#QMK#%))5Œg23M N$42$#%#/5Œ0!,!82$02)#%¥E-(35
)$+*%)=,!(+*%%AJ®#%$# $42#EŠ:(-2$02)#%«E6)),!#%2(3$!*%*/:2$$#.,EI-$42#
U $#7M 42+*4'+ '#.$#%(*/#$42#9D3$*G$H#3$42#%3$+*%)0!¯#.*G-EIK$#.#.*4
8$42# U #%)+,8EJ$#.((*/#L()$+*T,!(+*%%A
¦))C,!#%2(3$DMK#%$# U T,!+$*/3H#%$#.,NZ¡3°3±²08‹62)+*/# M 42#%Y42#$:(,!#.,
$42#N$SE³:22$#%1(,Z¦!3$:2$W$:2(,[$42#8¦:2A;ŽŒQ$:2$2#.,S:!Q$4(31))K,!#/5
2(3$ a0#%)3M¨MK#'M ))K?H#$42#%1,!#/)#.,W,!#.$*/$!$eL)#.,h$H#%$[
#.*/:2)+$$#.L$42#$hE-$42#.#2)+2#/%7M 42+*4S*/:2)+,2 0##/F!2)+2#.,0;$42#
:!(,!2?3$42#%3$+*/+(DEC$42# ( aŠ´ )#%.72‹6?2?#7!‹60#%(,N$42#%eGA
BD42#N1+Q$4(3$42#8$(QE2)+2#/1(,W$3$#%))$#. a.73$42#%.7C$42#%*/5
,!(3$#.L(,[H#%)!*/$#.e4(OH#NH#%$Y*/2)#/F[(3$:2$#(,h*%[0#3$42#%3$+*%))
$#%2$#.#%$#.,'$42#EI$¨E6:2)$2)#T`2:2$#%D#%$#.%7mA#A$42#9EI$¨E6*/02(3$
ED') aLE$#%S[ U 2$##/GeE #%$!,!+*1$(9M $4S,!=#%$#% #%$!,2T.7
M 42+*4N+K$42#L$#7M $4;,!=#%$#%KEI$#.@:2#%(*/#.%Aµ9:())D+K$02)#9$*42#90(+*
L$#%LEI$#.@:2#%(*/#.9$4(3$#1)+$?#1@:($$#. */($#.,M $4[$42#$42#%TEI$#.@:2#%!5
*/#.%A-`2 #/F22)#7!N$42#LMK5Œ2)+2#/D2$02)#% a ¦:2P2)+2#/P2)+2#/GeK+D$02)#T$
*42#QMKN0(+*QEI$#.@:2#%(*/#.T*/$$#.(,!2?$N$42#OH#%?# #%$!,2TE-$42#12)+2#/%7
$#%H):!$V$:2(,S$42#¦:27K0#%2?[$42#YOH#%?#N2?:2)+1H#%)!*/$#.1E$42#%$
)2?Q42#%)!*/#%$$+*$02%A — $$2#%-*%))($42#.#T0(+*DEI$#.@:2#%(*/#.-$42#LOH#%?#D5
$(%AT¦$$+*G$);#.g2?(7OH#%?#L$(E2)+2#/99$3$#%))$#.T$# 2T*/(.7
02:!Q90(#%$H33$(9423M 7$42#%*4(2?#H#%$;)3M )7=mA#A$42#%$#1)3M•EI:2(*G$(TE
$#A
ŽŒE8$42# MK5Œ2)+2#/ 2$02)#%X$42#Q0(+*TEI$#.@:2#%(*/#.$# */)#%)8*/#%(:202)#7
K+-$42#%$4(3KMK#9*/#9*/$$J$42#92$02)#%«E6)),!#%2(3$%AC3$42#%3$+*%))
$42#[#/=#.*G8E))T,!#%2(3$'423Mf$42#EŠ*GN$4(38d$42#h):!$('EL$42#
#.@:(3$(JE2)+2#/$ $7$#%2$#.#%$#.,Q0`2:2$#%#%$#.%73#%$!,!+* $#%$2#.
M $4Y*/#/§'*/#% M 42#L,!#%2(3$ $#L*/)#T$c%#%$(7 ;$42#% MK,2%7#%$!,!+*
4($2+*%DM $4;)+$?#L2)$:(,!#.2#..A
ŽŒE-$42#%$#1+L[#/F2*GT3$()J*/#%(:202);E$42#0(+* EI$#.@:2#%(*/#.%7)2#.
EI:2(*G$(QEK$#O[)+Y2#. S$42#'):!$( a($#.,SED#%$!,!+*EI:2(*G$(
M $48H#%$)+$?#92)$:(,!#.eGAŽ”N2)+2#/$$7#/=#.*GD!*%*/:2 $4(3DN24!+*%D$#
*%))#.,N$#.((*/#T#/=#.*G%72)g#T$42# $#.(D$*/))+3$(KE6MK#%(,!:2):2 M $48$42#%
EJ:(#%(;)!*%3$#.,N;*/842$c%)=$!,A
Ž”'$42# *%#9EEI$#.@:2#%(*/$#.((*/#.%7#%)#%#%KE62)+2#/$$02K(,$42#% !5
?:2)+DH#%)!*/$#. :2(,!#%$?1?$#.3D*4(2?#. M 42+*488*/(3$H#%)42K$#L$#%$H3)+
$# ,!§'*/:2)$',!+$2?:2+48EI$š#.*/:2)+.7!mA#A2)2#. EI:2(*G$( EC$#AK`2 #/F22)#7
S$42#'*%#E ³:22$#%(,Z¦!3$:2$h$42#%OH#%?#$Z*4(2?#.L;$4(3Q3H#%¡.¤¤
#.T$42#%S$#)Q+,!#%$+*%)$#.*/:2)+ $ANŽŒMDT$42+*/*/:2(*/#$4(3
2$!$#.,‹6?2?#T$Ng#[3$#%!.7=423MK#%H#%90$H#72$8*/($$:(*GT$42#%$
E$42#T$'E6³:22$#%D(,N¦!3$:2$'M $4'$42#TOH#%?# $(-'$42#9EI$«E6)2#.
EI:2(*G$( EC$#A
i3MWMK#KM ))2,!#.$*/$0#K$42#D$#.:2)C0!2#.,0Q‹62)+*/#K1$#D,!#/)mA — *%*/,!2?
$;$42#0(#%$H33$(T,!#0[$$2#%Th$42#'#.*/(,[4()EDEK$42#Y¡.±3$4S*/#%$:2$7

y.z¶ {L|}6~JJ€9C‚ƒJJƒ6„Iƒ6|†J‡Y‡|OJƒ6†JƒJˆ=|N€‰ƒ6†J{LŠˆ
$42#OH#%?#Q$[E ¦!3$:2$ a42#%)!*/#%$$+*2?:2)+TH#%)!*/;E ¦!3$:2$[#%Q,2O2e+
·J¸¹º
» r¨¡O¼¤½½Š¾²¿3²À²¿!t(,E ³:22$#%L+ ·J¸¹º
q r¼¢¢½½Š¾¡O¼±£À2¡A9ŽŒL+9#.8$8*%)+*/:2)+3$#
$4(3 ·J¸¹º
q ·J¸¹º
» rÁ¼!¾²±££¼ÀNÂÁ¿¼!76mA#A$42#'OH#%?#Q$(LEK$42#2)+2#/Q$#
3$())')*/#%(:202)#A
`2$Á$42+ $#%)+3$N EI))3MK$4(3
¼ ·J¸¹º
qÄÃ ¿ ·J¸¹º
» r Ã ² ½½¾¤2¡.À¿¤£ r Ã ¤2¾¤¤¤¤2¡.¢²!°¼¿,=¾
BD42#*/$$#.(,!2?Z,!=#%$#%$+)#.@:(3$(1EI$42#)2?$:(,!#YEQ¦!3$:2$ a@:(!5
$fÅ» e(,f³:22$#% a@:($dÅq e1g2?*%*/:2'E :!$:()T3$*G$(4($42#
EI$
Æ Å»
Æ l r ÇÈ
É
Ê ÈËÊÌÍJÎ ÇÈ
s Ê ÈËÊÌ */ amÏ »GÐ» o Ï q Ð q eGt
Æ Åq
Æ l r Ç Ì
É
Ê ÈËÊÌÍJÎ Ç Ì2Ñ Ê È$ËÊÌ */ amÏ »GÐ» o Ï q Ð q eGt
M 42#%$# Ð» t Ð q $#1EI:2(*G$(,!#%#%(,!2?YWY*/2)+*%3$#.,[MDO a423MK#%H#%.76)Q)!5
#.$)2e-N$# l (,N'$42#L)2?$:(,!#. Å» t$Åq $42#%#%)H#.%A-BD42#L()$+*L$$:(*G$:2$#TE
$42#L*/#/§'*/#%Ks Ê ÈËÊÌ t
Ñ Ê ÈËÊÌ +K)+QH#%$*/2)+*%3$#.,702:!DN22$OF!3$# $42#%$#.
$42#%N*%'0# */(+,!#%$#.,'D*/(%ACŽŒE6MK#TM $$#L$?$:( */)#.,'!$#%ÁEC,!=#%5
#%$+)#.@:(3$(LEK2)+2#/$,!(+*%%7QM ))g#$42#EI$™ED8:2)$EI$#.@:2#%(*/
$$Z!$#%^M $4d)3M¥(,ZEŠH3$+02)#.%7-(,V*/(#.@:2#%$)Zs Ê ÈËÊÌ 7
Ñ Ê ÈËÊÌ $#
$#%2$#.#%$#.,N0N3MK#%#%$#.DM $4Y$#.#.*G $')3MÒH3$+02)#.K$4(3T$#L42#%$#L$42# 3$
E2$42#D3¯J#%+3F!#.E2$42#D2)+2#/%ÓO$02%ACK#.+,!#.%73J+Cg23M $4(3s Ê ÈËÊÌ 7
Ñ Ê ÈËÊÌ
,!2+4;@:2+*g)#%2:2?4NM $4N(*/$#.#9E ÔÏ » ÔtOÔÏ q Ô7!(,ND+ )+K$12$#
$4(39$42#*/#/§'*/#%9s Ê ÈËÊÌ $#Q2$$()$'$42#$E ³:22$#%.7=(,
Ñ Ê È$ËÊÌ $
$42#$LE ¦!3$:2$ABD42+ #.(T$4(3L$42#'*/#/§'*/#% s Ê ÈËÊÌ $#22$OF!3$#%)Y£
$¿$#.L)+$?#%9$4(
Ñ Ê ÈËÊÌ A1®#%(*/#1Q42:2)+,[0##/F!#.*G$#.,$4(3L$42##/=#.*G E-$42#
*4(2?#LEJÅ» +D?$#.3$#%DM $48$# $4(N$4(3EC$42#Q*4(2?#TEÅq A
Ž”[$42#g23M [$42#%$#.TEK2)+2#/$;$ a0$4S!,!#%$S(,2$#%H:(T2#.e
'+'423M $4(3M $42“[$#Y$#%$H3)#%H#%) ,!#.*%,!#.)2? amA#A ,!:2$2?W#%H#%)
$#%H):!$(KE³:22$#%(,Y¦!3$:2$;$:2(,'$42#¦:2e
Õ Ð» aIl e•Â ·J¸¹º
» l o Ð» Ë¹ t
Ð q aIl e•Â · ¸¹º
q l o Ð q Ë¹ t aŒÖ e
M 42#%$# ·J¸¹º
» t ·J¸¹º
q )'#/F2*G$)V*/(*/+,!#YM $4d$42#H3):2#.EQOH#%?#N$(0!5
2#.,,!$#.*G$)NEI$š0(#%$H33$( 3H#%9*/#%$:2$#.%ADŽŒE-MK#$:2# $4(3Ls Ê ÈËÊÌ 7
Ñ Ê ÈËÊÌ
$#*/(%7C(, Ð» aIl eG7 Ð q aIl e $##/F!2$#.$#.,[0YEI$:2)+# aŒÖ eG76$42#%ZQ8$#.:2)QE

¬ ‡|‚.†Cˆ=| y%¶
$#%?3$8E6$42# #.@:(3$(KEID$42# )2?$:(,!#LMK# 0!
Å» aIl e r“s ¹ Ë¹ l o ÇÈ
É
Ê È$ËÊÌ$ÍJÎ ÇÈ
s Ê ÈËÊÌ ×amÏ » ·J¸¹º
» o Ï q ·J¸¹º
q e l o Æ »$Ø
Ï » ·J¸¹º
» o Ï q ·J¸¹º
q
t
Åq aIl e r
Ñ ¹ Ë¹ l o Ç Ì
É
Ê ÈËÊÌÍJÎ Ç Ì Ñ Ê ÈËÊÌ ×amÏ » ·J¸¹º
» o Ï q ·J¸¹º
q e l o Æ q Ø
Ï q ·J¸¹º
q o Ï » ·J¸¹º
»
t
Æ » 7 Æ q $# */(%A
K#/EI$#9‹62)+*/#7$42#L*/($$:(*G$E$42#%$#.-E2)+2#/$1$N$:2(,1$42#
¦:2$$2#%C*/ U 2#., $42#%#%)H#.C$9$#%$JM $4$42# ))#.:23$1(,!+*/#.
Ï » t Ï q rÙ¡t¼ a*/#%2)M $42:!8S$?$:(13$42#%3$+*%)¯:($U *%3$fE :(*4f
$$:2(*%3$E$42##%$#.eG72)+*/$):222?T$4(3 ))!$42# $#%22? :2(,2-$#
2#%?)?02);)) a2$# $4(39$42++ $42#1$:(3$;$4(3T!*%*/:2 ;$42#1*%# E$42#%$#.
EJ$8EJ$42#% 02?2)+2#/eGA-®3MK#%H#% ‹62)+*/#9EI:2(,N$4(3 $42# 4($2+*
s Î=Ú Ëq ×a ¼ ·J¸¹º
qÄÃ ¿ ·J¸¹º
» e l o Æ »$Ø
¼ ·J¸¹º
qÄÃ ¿ ·J¸¹º
»
t
*/$$;$;EI$#% +,!#.%74( ;H#%$Y)+$?#2)$:(,!#',!:2#$;$42#'))2#.$LE $42#
,!#%2(3$C¼ ·J¸¹º
q¨Ã ¿ ·J¸¹º
» M 42+*4 +%7.#A?(A7%MK,!#%=E!?2$:(,!# a£¤¤K$#.e))#%
$4($42#,!#%2(3$K¼ ·J¸¹º
q o;¿ ·J¸¹º
» ACŽŒE ·J¸¹º
» (, ·J¸¹º
q 4(,12-0#%#%3$())Q)
*/#%(:202)#73$42#%1$42# M $$#%4($2+*KMK:2)+,14(OH#K4(,L))(2)$:(,!#7(,
T*/:2)+,80#Q?2$#.,N;$42#L$42#%$72)g#Q‹62)+*/#ÓKEI$#%$:222#%D4(,;,!2#AD¦'‹62)+*/#
EI:2(,$4(3-$42#9$#.((*/# ·J¸¹º
» ·J¸¹º
q Â“¼1¿L$#.:2)-$42#T2#.(*/# E 4($2+*
M $4f[)+$?#82)$:(,!#7D(,M 42#%$42+4($2+*NMDg#%$S*%*/:2$42#
$42#%$E$42#T$'EJ¦!3$:2$N(,N³:22$#%KD02$:2?4 $42#9$42#%$(,0(#%$H33$(
$'*/(3$H#L*/(*/,A
BD4:(%7!‹62)+*/#9EI:2(,'$4(3K$42# OH#%?#92?:2)+KH#%)!*/$#.KEJ¦!3$:2$;(,N³:22$#%
*/)2?5Œ#%$!,#%$:2$0(3$(-M $4$42#T#%$!,E6±££ #.-(,M $4NH#%$)+$?#
2)$:(,!#.%AŽŒE $42#%h$#12Q*%*/:2$#.,YEI.7$42#,!+$*/$#%((*/#.T[$42#)2?$:(,!#0#/5
MK#%#% $42#-$42#%$ (,L$42# 0(#%$H33$(E=¦!3$:2$ OL$#.*4Q¿¤½½Š7(, Ã ¼¤½½(, $#
EIL³:22$#%.ATŽŒTMDT:(*4[,!#%H+3$(E-$42#Q$42#%$8EI$Û0(#%$H33$(D$4(3 $:2#.,
$#.#.*42#%%7(0#.*%:(#QEI$š$42#1LE-H#%MªE-0(#%$H33$()C$$272$42#.#$#
2$4202$H# :2%A
®+$$+*%));$42#'))5”,!#%2(3$T2$02)#%™#%#%$?#.,h,!:2$2?8$42#$:(,![E $42#
$hh$42#'¦:2P!³:22$#%P2¦!3$:2$[2$02)#%;7$42:2?4S$$2#%923Mª$#%)+3$#1 $
$42#Y2$02)#%bM $4¨]2H#%$4($(_[$#.((*/#AdŽ”?2#8EI'S#%$4(3$42#
OH#%?#1$(QE9¦!3$:2$Z(,Z³:22$#%1$##.@:()-$ ·J¸¹º
» r›¡¡.¢½½Š¾±²£2¡O¼¼!7 ·J¸¹º
q r
¼¢¢½½Š¾¡.¤°°3¢¿3²(¡7T$#.#.*G$H#%)ANBD42#%Á¼ ·J¸¹º
qÜÃ ¿ ·J¸¹º
» r Ã ¤½½Š¾¤¤¤¤¤¤2¡.¢27L(,[$42#%h$42#
03H#4($2+*JMK:2)+,L4(OH#Q2)$:(,!#¡.¤¤K$#.)+$?#%.AŽ” $42+4$42#/$+*%)*%#
$42#L)2?#%$!,'MK:2)+,0#T#.@:()$1±££¤¤ #.%7(,$42# ,!+$*/$#%((*/#.-N)2?$:(,!#.
a0#.*%:(#$42#$#%$Ýs Î=Ú Ëq ×a ¼ ·J¸¹º
qÞÃ ¿ ·J¸¹º
» e l o Æ » Ø MD92Tg#%$8*%*/:2T
$42#L$42#%$2e MK:2)+,8$#.*4N(*/(*/#%H302)#LH3):2#.%72$:2(,8±£ßL(,;¼£ß3A

y%¶.z {L|}6~JJ€9C‚ƒJJƒ6„Iƒ6|†J‡Y‡|OJƒ6†JƒJˆ=|N€‰ƒ6†J{LŠˆ
‹62)+*/#ÓLH#.$?3$(L$;$42#'$42#%$ED$42#'$ZE¦!3$:2$W(,S³:22$#%
42:2)+, 0#K$#%?,!#., 6Q:!(,!2?T*42#%H#%#%6E(3$42#%3$+*%C(,Q*/#%)#.$+)#/5
*4(2+*%%73$42#%1$#K3MK#%EI:2)2()$+*%)$)+%AJBD42#%Q4(,2:! T:20#%EEI:2(,2#%)
2$02)#%Q0#/EI$#3$42#%3$+*/+((,Z$$2#%%à6$42#N)H2?YED$42#.#N2$02)#%
4(D#%2$+*42#.,N22)N*/)+$+*%)=3$42#%3$+*%%7202:!9)+!,!#%$83$42#%3$+*%%A
— E$#%6$42# ,!+$*/3H#%$9E$42#K))5”,!#%2(3$#/=#.*GC0L‹62)+*/#7O(,L($+*/:2)+$)
8$42#¡.¢3$48*/#%$:2$7$42#TMK1)2#.DEC$#.#.*4'0#%?N$423M 72*/)#.$)#/F!2$#.$#.,'02:!
$?4$)8*/22#.*G$#.,NM $4;#.*48$42#%.A
BD42# U )2#E=H#.$?3$*%0#9*%))#.,$$2+*%)mA6ŽŒ )#.$42#9,!#%H#%)!5
#%6E!#/$42!,26(, ,!$#.*G6*/($$:(*G$LE222$OF!3$#):!$(E$42#-2$02)#%
E-*/#%)#.$+)#.*4(2+*%M 42#%$#L$42#%$# +9$#.((*/#LEJEI$#.@:2#%(*/#. a$42#*/#%(:235
02)“E1OH#%?#Y$(8“$42# U ;2)+*/#Oe'E1*/#%)#.$+)T0!,!#.%Ó $02)T$A
á #.@:2$#.,hE $42#'):!$(TMD ;:!§'*/#%$)[2$#.*/+#,!#.$*/$!$hED$#.)J$(%7
?#%2#%))NM $42[)$#.,Y02:!T)+$?# #%2:2?4;$#$#%$H3)mA Ž”Y3$42#%3$+*%)$#%$
D+D@:2#.$'E$42#L*/($$:(*G$'E6!$$+*9):!$( E6,!=#%$#%$+)=#.@:(3$(
E2)+2#/$N,!(+*%Y!$$+*%))')+$?#L$#Q$#%$H3) aE,!#%9â aIã Î » eeGA
— $$2#%%72#T?4$O74(OH#T:(*%*/#.$EI:2))N)H#.,$42+D2$02)#%XE6#%$:2$0(3$
$42#%$WEI'2'H#%$4($d$#.((*/#.10#.(ET$42#[*/)+$+*%)#%$#.M 42+*4dMK#
:2(,!#%(,$Q0#T()$+*%)(#/F!2$#.$(JEI-$42#9$#.@:2$#.,1H3$+02)#.$4(3D*/#.*G5
:2)+.7=$$?2#/$$+*(,[F!#.,#%$:2$0(3$(%7mA#A=$42#1E $42#EI$
Ñ
ä l 7 02:!
1$:2)#Q)+$42#Q#.*/:2)+(,NF!#.,NEI:2(*G$(
s l Ê amÏNå ¤eGt æ l Ê ä lçamÏNå ¤eG¾
© )+$+*%)6#%$:2$0(3$Y$42#%$NEI9$42#,!#.$*/$!$E-)+$?#Q2)+2#/%Ó=$02)65
$Y$:2(,$42#¦:2;MDD2)N,!#%H#%)#.,N0 ´ :2)#%.7© )+:!.72‹6?2?#7‹62)+*/#7
œL:($%72‹# è#%$$#%.7!(,;i#%MD*/0A
— 2$42#%)2# EH#.$?3$LL$42# ))5”,!#%2(3$2$02)#%Ò+3$42#%3$+*%)
$42#%$#/$+*%)mà )#.-'@:()3$H#()!+JE=$42#9):!$(E,!=#%$#%$+)(#.@:(3$(
E-*/#%)#.$+)60!,!#.%Ó$7(,;;$42#1*/($$:(*G$;E-:(*4#%$#.D$4(3L$#Q*/H#%5
?#%9#%$42#%[Y!$$+*%))N)+$?#T$#$#%$H3); U 2$#Q$#Q$#%$H3)mA
`2$š$42#()$+*%)6#/F!2$#.$(DEIT#%$:2$0(3$(9*/($$:(*G$#.,;0;#.(9E */)+$5
*%)$42#%$72EI))3M */)#.$)'#%2:2?48$4(39*/)+$+*%)#%$#. $#L:($02)# U 2$# $#
$#%$H3)C:!+,!#1E-M 42+*4$42#%,!N2L*/$$#.(,8$8$#.)62)+2#/$;$[,!:2#$
$42#12$#.#%(*/#E #.*/:2)+T(,YF!#.,#%$:2$0(3$($42#1#%$#.%ATBD42#%$#/EI$#Q #%#%
(3$:2)-$h#.*4hEI:(*4Z3$42#%3$+*%) #/$42!,2$4(31MK:2)+,Z))3M¨:( $[0!
()$+*8#/F!2$#.$( a03H#;))m7 EI$42#)3MX$() H3$+02)#. ‘ e$4(3N,!S2
*/N$#%$ 2$$()($ l Ê amÏNå ¤eGA
‹62)+*/#LMDD$42# U $'(O83$#%$8$$42#,!OM 0(*g!DE*/)+$+*%)#%$#.(,
#/$42#Q0!¯#.*G$H#LE U (,!2?'):!$( EJ2)+2#/$N$;#.@:(3$(D;$42# EI$¥E
$$?2#/$$+* #%$#. aE$42#92#%H02)#9#.*/:2)+$#%$¨E=$42#EI$p l )MDO!2$#.#%
#/F!2$#.$( EI 2)+2#/$')2?$:(,!#.D+D29*%*/:2$#.,'EIGeGA
Ž”8$42#'¡.¢3$4Y*/#%$:2$N:20#%EJ$#%$g302)#LH#.$?3$(KMK#%$#Q*%*/2)+42#.,
aŠé #%)2#/.7 i#%MD*/07J‹(,2$#.,.7KœT)+,!#%eG7g2?1$02)#$[$#%2$#.#%Q$42#85
):!$(QE 2)+2#/$[2$02)#%QLEI$)-$$?2#/$$+*#%$#.%A;BD42#'02$?4Q3$42#/5

¬ ‡|‚.†Cˆ=| y%¶.zz
3$+*%)+,!#.NEKžJ(*%2Ÿ#Q$42#22)+*%02)YED!$$+*$#%2$#.#%3$Y$42#%$
a2$#.,'(,',!#%H#%)#.,042#%)Ee$Q$42#T2$02)#%-EC®9)$2+N,!(+*% )5
)3MK#.,L$42#D:!$42C$T,!#.$*/$0#K42+6EŠ:(6MK$gQêë/ìhíë/îIï2ð.ñOòðóôë/õëGòGîmöŠ÷3õ2íëôï2÷3ø(öŠôGò
EI$™N:22U #.,h(,!T$42#1#/$42!,2LE-$42#$:(,!EK()$+*%)J,!(+*%T2$0!5
)#%$4(3T?4T#%#%›,!=#%$#%T#.$#%(*/#Q(,;EI$;A9BD4(2g! $$42#3$42#%3$+*%)
?#%2:(JEžJ(*%2Ÿ#7.2-2)Q$#.((*/#D()$+*%)!,!(+*%J$#.*42#.,11:2(:2$($#.,
)#%H#%)m702:!KEŠ*GKQ$*/#%$U **G$2$?ªMDJEI$:2)+3$#.,1EI$42#T()$+*%E=$42#
¼¤3$4;*/#%$:2$A
ù 2#KE2$42#K$#%$#.$2?92#%M,!$#.*G$(C+6$42#Dú — aúL)?$3HP — $2)+,P!Y#%Ge
$42#%$))3M 2?Q:(-$1*/($$:(*GK#/F2*G a'$42#T#%(#9E6*/H#%$?#%(*/#Oe):!$(-E$42#
®9)$2+Z,!(+*%L$#%?:2)+LM $4S$#.#.*G $YY))(#/$#%.7Z2$#E $42#
2#%?3$H#Y(*GNEL$42#[))T,!#%2(3$d$42#[*/(,!$('E */H#%$?#%(*/#;E
S U 2$#'*4(SED*%22+*%)J$(EI$3$(T?H2?;#/F2*GQ):!$(Lh$42#).A
ú — Û$42#%$1,!#9K$02)# $1)H# N'#/F2*G MK,!2?L$42#92$02)#%«E602)
EDN4$42#/$+*%)J2)+2#/$!$#% aL3$42#%LL*/ U ?:23$eG7M 42+*4h42:2)+,0#
$#.*/?2c%#.,hQ;$#%$g302)#*42#%H#%#%QED!,!#%$S3$42#%3$+*%%A8µ!EI$:2(3$#%)7
$42#.#h$#.:2)8$#[WEŠN(22)+*%02)#$V:28)+8!$#%û0#.*%:(#[8,!(+*%)
(#/$#% a2)+2#/$$#.%7603H#))eL,!Y2$3$+EI$42##.$3$( E ú —
$42#%$A
®3MK#%H#%6MK:2)+,L0#-(*/$$#.*G$9*/$#%(,9$4(3J!$$+*J#/$42!,2 $#.((*/#
()$+*%),!(+*%D$#9;13$#TEC*/2)#/$#%2#.$%ABD42+D+K#.#.*/+))2$+*/#.02)#T
$42#N*/($$:(*G$SE):!$( E,!=#%$#%$+)-#.@:(3$( E()$+*%) ,!(+*%%7CmA#A
[*/($$:(*G$H#Q#.@:(3$;$42#%$A — !,!#%$Y$#.#.*42#%,!$#. E :(*4'*/2:!$#%
$#.)c.3$E9$42#!$$+*8@:()3$H#N$42#%$WEL,!=#%$#%$+) #.@:(3$(1$4(3
MK:2)+,d))3M¥:($Z:(#()$+*%) #%3$((,d?242+*%)K$)+EI:2))A•®3MK#%H#%
L$:2$(T:!T$4(3T$42#.#1+$:2#.L$#1*/)#%)Y$!*/+3$#.,YM $4$42#5”*%))#.,;2$02)#%›E
!$$+*N$42#%$S02EI:2*%3$V$42#;2#%?40$42!,ZET)3MKP,!#%QEI$#.@:2#%(*/Z$#.5
((*/#.%7!(,M $4'$42#T2$02)#%¨E6$#.*%)+*/:2)+3$E$42#92$+)*/(,!$(K3D#.*4N$#%
E$42#T$#%3$(%AJŽ”N$42#%KMK,2%7N$#.((*/#9()$+*%)=,!(+*% + $02)#9$
EI$:2)+3$# #L2$02)#%K$4(39#%#%Á$:(D:2$?#%.
üKý$ðþ/õë/í«ÿ3AJ‹#/J:2)$EI$#.@:2#%(*/ !$#%•E(,!=#%$#%$+)#.@:(3$(0#D#.*/U #.,
$$:(%7= MK#%))J $42#*/$$#.(,!2?2$+)J*/(,!$(%A ŽT$02)# $N*/($$:(*G
H3$+QE9!$$+*$42#%$S:(*4Z$4(331#.*4W$#%ZE $42#'$(EI$3$h$42#
$#%3$($#N2c%#.,0Z*4(2?2?$42#;2$+) */(,!$(™BD42#;(MK#%+1#.%A
Y$#%3H#%.7$42#%$#L#/F!+D;()$+*T)?$$42Á))3M 2?:(K$1#/F!2$#.$ $42#L2#%MÒ2$+)
*/(,!$(K$42$:2?4N$42# )+,82#.%72(,NH+*/#LH#%$2A
BD42+ )?$$42X+D#.)'2)#%#%$#.,8Y*/2:!$#%.A
üKý$ðþ/õë/íANŽ”S$42#N*/($$:(*G$hE !$$+*1$42#%$[0[#.( E :(*%*/#.$H#
*4(2?#.E-H3$+02)#. L+92#/F!#.,!#%9$8#.*/EI;0#/EI$#%4((,;$42#1()$+*Q$$:(*G$:2$#
E$42#L#.@:(3$(K3D#.*48$#%7!02:!K$42+ 42:2)+,'0#L,!#/$#%$2#.,'EI$X#T*/(,!$(
E#.*41$#%3$2$2c.3$Ah# 4(OH#,!#%H#%)#.,)?$$42ªE=0!22?
:(*4L2c.3$Q*/(,!$(=EI2+*%)2$02)#%E$#.((*/#()$+*%),!(+*%%A
— )?$$42L$[)H#1$42#N03H#/5Œ#%$2#.,[2$02)#% 4(OH#'*%))#.,hEI$4h$42#N!5
#.(*/#EL$42#S*/(*/#%!NE $42#[02EI:2*%3$fE EI$'EL$42#h()$+*%)$42#%$VE
#%$:2$0(3$(DE,!=#%$#%$+)#.@:(3$(DM $4Y))(#/$#%.A

y%¶.zzz {L|}6~JJ€9C‚'ƒJJƒ6„Iƒ6|†J‡Y‡|OJƒ6†JƒJˆ=|N€‰ƒ6†J{LŠˆ
üKý$ðþ/õë/íASBD42#8,!#%H#%)2#%1E9*/($$:(*G$H#':2#%$+*%)P!()$+*#/$42!,2E
$42#Q*/($$:(*G$8EJ#%$!,!+*L(,8@:(5Œ#%$!,!+*L):!$(K$2$02)#%DEC$#.((*/#
()$+*%),!(+*%K$4(3:(#Q*/H#%$?2?1()$+*L)?$$42 (,8$#L2)#%#%$#.,
Y*/2:!$#%.7!:(2?0)+*T2$?2?1(*g3?#.%A
BD42#.#2$02)#%-$#*G$:())$42#9:20!¯#.*G E=$42+ 2?24Ah#9$# H#.$?35
2?$42#L2$#%$#. E6$42#L):!$(KE6:2)$EI$#.@:2#%(*/$#%?:2)+D!$#%KEC,!=#%$#%$+)
#.@:(3$(LED()$+*%),!(+*%L[$42#'$:2!$hE $42#2$#.#%(*/#1E EI$#.@:2#%(*/
$#.((*/#.Y$42#1#%H):!$2$!*/#.$ aM $4$42#*4(2?#QE l eGALµ9#.,YEI9$42+92:2$#
$#K$42# OH#%?2?92$(*/2)#7!$$+*K$#%2$#.#%3$Q1$42##%(#KEžJ(*%2Ÿ#7O(,
*/H#%$?2? $#%3$'2$!*/#.,!:2$#. E6‹2:223HP!žJ(*%2Ÿ#A — */($$:(*G$H#9!$$+*
$42#%$'))3M :(K$10!N;N#/F!2)+*/()$+*EI$Á$#%3$(KEC,!#%KM $4
$#.#.*GC$9$42# ))(#/$#%.7.g2?T$L*%*/:26$42# 03H#/5Œ#%$2#.,L2c.35
$Y*/(+,!#%3$(%A
Ž”8$42+2?24;:20#%E22)2#. $*/))+3$( */(*/#%$2#.,8M $422)+*%35
$($#L*/(+,!#%$#.,A

/Ä
BD42#K:!$42MK:2)+, )g#$#/F!2$#.$$42#%C(*/#%$#-?3$$:(,!#$ $42# #%0#%6E$42#Ká :(5
+ — *%,!#%E¦!*/#%(*/#. ¦=AžJA2i3Hg3H(, é AèA — 23H=7#%0#%DE6$42# i93$()
— *%,!#%;ED¦!*/#%(*/#.9E µg2# — AZA¦!)#%2gEI9$42#% ,!H+*/#1(,*/#%
,!#9'$42#T*/:2#E$#%#.3$#.,',!+$*/:($(-$42#T2?24Ó-*/$#%.Ah#9MK:2)+,
)g#$8#/F!2$#.$T:2L(*/#%$#1?3$$:(,!#Q$ — A— A:2gNEIT$42#$?2c.3$(,
$*/#%$U *L#.,!$2?E6$42#L$#/FEC$42# 0g=A
`2$:2(3$#%)'$42#:!$42 4(,8$42#Q2$:228E-,!+$*/:($2?EI:2(,2#%)62$0!5
)#%9E-3$42#%3$+*%9(,Y#.*4(2+*%%7(,;$42#%T:!$:()J*/2)#%#%$$#.(,,!#/5
#%(,!#%(*/#.M $4[*%,!#%+*/+;‹-AŽGA=¦#.,!3H=7(,;MK# #/F!2$#.$ :242#.EI#%)9?3$$:(,!#L$
42;A
h#9MK:2)+,')+Q)g#$$#%(,!#% $4(2g!-$1‹-A2© 42#%$2#/g33¯27!¦=AúL$(27!¦=A!á$425
H3)3H3;(,hiQA#%Q3H3'EIL$42#% 42#%)SS2$#%($2?N$42+ ´ 2?)+4h#.,!$A'`C())7
MK#TM +4'$1*g23M )#.,!?# $42#L*/#%3$'ECBCO)K(,'`2(*/+%7!(,$Q$4(2g$42#%
EID$42#%(3$#%(*/# (,8:2(,!#%(,!2?(A
w/xw

Contents
Introduction to the Series
Preface
Acknowledgments
1 Preliminaries
1.0 Introduction
1.1 Main Symbols
1.2 Asymptotic Series and their Properties
1.3 Poincaré’s Theorem on Asymptotic Approximations of Solutions
of Differential Equations
1.4 Geometric Interpretation of Solutions of Oscillating Systems
1.5 On the Method of Characteristics for Quasi-Linear First-Order
Partial Differential Equations: Method of Characteristics
1.6 Iterative Variant of the Poincaré–Lyapunov Small Parameter
Method
1.6.1 Simple iterations
1.6.2 Iterations with quadratic convergence
1.7 Comments and References

2 Averaging Principle for Multifrequency Systems
of Differential Equations
2.0 Introduction
2.1 Mathematical Averaging Principle
2.2 Classification of Systems of Differential Equations where
Resonances are Possible
2.3 The Basis of the Asymptotic Theory for Locally Nonresonance
Systems
2.4 Initial Conditions for Comparison Equations
2.5 Averaging Operator for Time-Independent Disturbances
2.6 Asymptotic Theory of Systems with Their Paths Passing through
Resonance Points
2.7 The Algorithm of Joining of Resonance and Nonresonance Path
Sections
2.8 Periodic and Quasi-Periodic Oscillations in the Van der Pol
Oscillator System
2.9 Study of Multifrequency Systems with Their Solutions
Not Remaining Close to Resonance Points
2.10 Study of Multifrequency Systems Belonging to Class II
2.11 Multifrequency Systems with Their Solutions Not Leaving
the Neighborhood of a Resonance Point
3 Some Resonance Problems of Nonlinear Mechanics
3.0 Introduction
3.1 Newtonian Three-Body Problem
3.2 The Problem of Justification of the Averaging Principle
in the Bounded Newtonian Three-Body Problem
3.3 Construction of Explicit Solutions of Averaged Differential
Equations of the Bounded Three-Body Problem in the Case
of Resonance
3.4 Quasi-Periodic Solutions of Resonance Hamiltonian Systems

3.5 Motion of a Geostationary Satellite
3.6 Averaging Method in the Theory of Partial Differential Equations
3.7 Energy Method of Construction of Amplitude–Phase Equations
3.8 Averaging Method and Maximum Principle in Boundary Value
Problems
4 Numerical–Analytic Methods
4.0 Introduction
4.1 Construction of Lyapunov Transform for a Linear System
with Periodic Coefficients
4.1.1 Construction of matrices L(t) and W by means of series
4.1.2 Construction of matrices L(t) and W by means of iterations
4.1.3 Interpolation formulae for Lyapunov transform matrices
4.2 Construction of Green and Lyapunov Matrices
4.2.1 Noncritical case
4.2.2 Example
4.2.3 Critical cases
4.3 Direct Numerical–Analytic Method of Construction of Periodic
Solutions
4.4 Construction of Periodic Solutions in Hill’s Problem of Lunar
Motion
4.5 Numerical–Analytic Construction of Mathieu Functions
4.5.1 Algorithm construction
4.5.2 Computational layout
4.5.3 Quick-Basic program
4.5.4 Comments on the program
4.6 Algorithm for Construction of Solutions of the Plane Bounded
Three-Body Problem
4.6.1 Initial differential equations of the problem
4.6.2 Basic equations for the coefficients of the sought solution
4.6.3 Construction of a solution by the method of simple iterations

4.6.4 Construction of a solution by the method of iterations with
quadratic convergence
4.7 Numerical–Analytic Implementation of Krylov–Bogolyubov
Transform
References

!$#$%(')
*,+.-0/213546/879:-0; =-0/2;?87@3A14B-0/2; C@0; D=3=CEFD=7 -0/2; D=7 -014 7G7+87GH:3A13I70;J@1K@; +L-0/87 -B70;
+2;(4;(303070HMENC@O-0/2;3P-67 -0; DQ; +R-QCE-0/2;4C@+R-0; +R-63OCES-0/2;BG7 -0; Q46/879:-0; 63 T7@3OUV; GGW7@3X-0/2;
D=71+3AHYDOC@G3 TR920C@9; A-01;(3VCE$3A; 01;(3V7@3AHYDQ9:-0C-0141+5-0/2;F3A; +83A;ZCE$[C@1+84 72];@^3_:;`8+21-01C@+T
7+8_a-0/2;bD=71+M9C@1+R-63CE-0/2;Q4G7@303A14 7GcHR792d2+2C K@e:[C@1+84 72];-0;(46/2+21fRd2;OENC@F_:1g; 0; +R-017G
;(fRd87 -01C@+83OUS1-0/L3AD=7GGV98767DQ;-0; (hi*j-Q3A; ; D=3b1DQ9C@A-67+R-O-0CMJ@1K@;B7aENd2GGS3P-67 -0; DQ; +R-QCE
-0/2;E)7DQC@d83S[C@1+84 72];-0/2; C@0; DkC@+B-0/2;;l:13P-0; +84;CE7@3AHYDQ9:-0C-014F3AC@Gd:-01C@+83SCEC@6_:1+870H
_:1g; 0; +R-017G;(fRd87 -01C@+83 T83A1+84;1+-0/2;`863P-92G7@4;1-133A; G_:C@DkENC@d2+8_B1+aDQC:_:; 0+D=7 -0/2;m
D=7 -014 3ZCYC@n:3Z7+8_?1+?-0/2;Q3A;(4C@+8_a1-+2; ;(_23Z3AC@DQ;b;(303A; +R-017G$4C@DQDQ; +R-63ZUS/2; +i3P-0d8_:HY1+2J
DOd2G-01EN0;(fRd2; +84HI3AH:3P-0; D=3oCEC@6_:1+870HQ_:1g; 0; +R-017G;(fRd87 -01C@+83 hpW/2;ZD=7 -A-0; VD=71+2GHI4C@+:m
4; 0+83Z-0/2;QK 7Gd2;QCE-0/2;Q-01DQ;Q1+R-0; 0K 7GUS1-0/21+iUS/2146/i1-13F9CR303A12G;b-0Cd83A;Q7@3AHYDQ9:-0C-014
792920Cql:1D=7 -01C@+83CEr;l27@4s-V3AC@Gd:-01C@+83CEt_:1g; 0; +R-017G8;(fRd87 -01C@+83 TY7+8_=7G3AC-0/2;-0/2; C@0;-014 7G
7+8_B9267@4s-014 7G; 00C@63W7@4 4C@DQ987+YHY1+2JX-0/2CR3A;X792920Cql:1D=7 -01C@+83 h
*,+a-0/2;Q3P-0d8_:HaCE-0/2;Q3ACm,4 7GG;(_BJ@; +2; 67G1u ;(_;(fRd87 -01C@+?CEo7@3AHYDQ9:-0C-014X9; A-0d2087 -01C@+
-0/2; C@0HavNC@WwF0HYGC K@e:xVC@J@C@GHYd2C KFJ@; +2; 67G1u ;(_Q;(fRd87 -01C@+y-0/2;ZDQ;-0/2C:_ICEt46/8767@4s-0; 013P-014 3
ENC@W`863P-AmjC@6_:; o987A-017Gr_:1g; 0; +R-017Gr;(fRd87 -01C@+83V/87@3V920C K@;(_Q-0CQ;FK@; 0HQ;g;(4s-01K@;F;(4 7d83A;
1-7GGC U3d83-0CI`8+8_?;l27@4s-F3AC@Gd:-01C@+83CE;(fRd87 -01C@+83CEo7+YHa792920Cql:1D=7 -01C@+T7+8_-0/2; 0;m
ENC@0;7 -V;(7@46/I3P-0; 9ICEr-0/2;1-0; 67 -01C@+83UV;_:CX+2C-V1+R-00C:_:d84;7+I; 00C@1+R-0C-0/2;Z7@3AHYDQ9:-0C-014
792920Cql:1D=7 -01C@+aCE-0/2;=3AC@Gd:-01C@+hpW/213F7@303A; A-01C@+?13F4C@00;(4s-Z7 -FG;(7@3P-ZENC@Z0C-670HDOd2G-01m
EN0;(fRd2; +84H?3AH:3P-0; D=3ZCEV_:1g; 0; +R-017G;(fRd87 -01C@+83ZUS1-0/i3AGC U7+8_aE)7@3P-FK 70172G;(3 h*,+MC-0/2;
UVC@6_23 TC@+2;Q4 7+M307qHB-0/87 -F-0/2;bD=7 -A-0; 4C@+84; 0+83Z3AH:3P-0; D=3ZCEV_:1g; 0; +R-017G;(fRd87 -01C@+83Z3A;-
C@+zD=7+YHRm,_:1DQ; +83A1C@+87GW-0C@01{TWUS1-0/.-0/2; 1501J@/R-Amj/87+8_|DQ; DO; 63I;l:920;(303A;(_|YH.}2C@d201;
_:1KY13A12G;3A; 01;(3 T7+8_~-0/2; 1OEN0;(fRd2; +841;(3b_:; 9; +8_:1+2JiC@+L3AGC U3P-67 -0;BK 70172G;(3XC@+2GH@hi*j-
13-0C53Ad846/M3AH:3P-0; D=3S-0/87 --0/2;M€A0;(3AC@+87+84;4C@+8_:1-01C@+830I70;9;(4d2G17(TC@-0/2;O;(fRd21K 7G; +R-
‚

ƒ „F†t‡ˆ‰Šˆ$‹IŒˆŒtYŽNŒtarŠqˆŒtŒ‘5‰r’Œt„FŽ)‘Š
€A920C@2G; D“CEW3AD=7GG_:; +2C@DQ1+87 -0C@630=-0/87 -O70;X-0/2;=D=71+MC@83P-67@4G;Q_:d201+2Ja4C@+83P-00d84s-01C@+
CE$-0/2; 1S;l27@4s-3AC@Gd:-01C@+83VYH51-0; 67 -01C@+BDQ;-0/2C:_23 h
pW/2;(3A;70;_:1g; 0; +R-017Gr;(fRd87 -01C@+83WCEt-0/2;FENC@0D
”@•
”@–a—.˜r™ v•tšA›š ˜ y š
”@›
”@– —Lœ v• y$ ˜ž v•tšA›š ˜ y š
vPŸ@¡2Ÿqy
US/2; 0; •tš ™ 70;¢5m,_:1DQ; +83A1C@+87GK@;(4s-0C@63 T ›š ž š œ|£ m,_:1DQ; +83A1C@+87GK@;(4s-0C@63CE$¤d84G1_:;(7+
3A987@4;@T7+8_ ˜ 13O7?3AD=7GGo9CR3A1-01K@;I98767DQ;-0; (h¥i;IUS1GGW7G3AC?7@303Ad2DQ;=-0/87 -X-0/2;501J@/R-Am
/87+8_¦DQ; DO; 63ICEb3AH:3P-0; D§vPŸ@h¡2hŸqy=70;M_:1g; 0; +R-0172G;i7|3Ad:¨I41; +R-B+Yd2DO; BCEX-01DQ;(3
US1-0/?0;(3A9;(4s--0C • 7+8_ › 1+M3AC@DQ;¦vN¢k £ yjm,_:1DQ; +83A1C@+87G$_:C@D=71+?©ªW«¬Tr ®mj9; 01C:_:14
US1-0/¯0;(3A9;(4s-F-0C › 7+8_i0; J@d2G7FUS1-0/~0;(3A9;(4s--0C ˜ 7 --0/2;=9C@1+R- ˜z— ¡2hIpW/2;=K@;(4s-0C@
œ v• y — vœ ‚ v• y š š œ ¬rv• yAyB13S4 7GG;(_M°N±2²b³6´qµs¶)·V¸6¹0²6º»8²¼·¶)²sµ½ ²6·°,¾ ¹sh
pW/2;D=7 -0/2; D=7 -014 7G8-0/2; C@0HbCEt3Ad846/53AH:3P-0; D=3 T:_:d2;-0CX-0/2;Z/21J@/IK 701;-PHbCEr-0/2;Z920C@9:m
; A-01;(3$CE3AC@Gd:-01C@+83_:;-0; 0DQ1+2;(_XYHF-0/2;W+2C@+2G1+2;(701-PHFCE2-0/2;WK@;(4s-0C@Am{ENd2+84s-01C@+83 ™ v•tšA›š ˜ ysT
ž v•tšA›š ˜ ysTY7+8_Q_:d2;S-0CF-0/2;9CR303A12G;SC:4 4d200; +84;vN1+b-0/2;920C:4;(303CE-0/2;_:HY+87DQ14 7G2; K@Cm
Gd:-01C@+¿CE-0/2;i3AH:3P-0; DIy=CEO3ACm,4 7GG;(_z3AD=7GGF_:; +2C@DQ1+87 -0C@63 TS135+2C-4C@DQ92G;-0;@TS-0/2C@d2J@/
1-M13;(303A; +R-017GGH¿7@_:K 7+84;(_rhÁÀY1+84;Âct792G7@4;@^3B-01DQ;¯-0/2;¯;g;(4s-?CE=3AD=7GGX_:; +2C@DQ1+87 m
-0C@63?/87@3M; ; +Ãd2+8_:; 63P-0CYC:_Ä7@3?-0/2;L7929;(767+84;¯1+ÄENC@0DOd2G7;¯ENC@?-0/2;L792920Cql:1D=7 -0;
3AC@Gd:-01C@+ÆÅ• v–sš ˜ ysTBÅ› v–sš ˜ ysT?CEO7|3AD=7GGm,_:; +2C@DQ1+87 -0C@63I3AH:3P-0; DÈÇÉ-0/2;i304 7G75920C:_:d84s-
v{Ê š œ v• v–sš ˜ yAyAysTUS/2; 0;XÊ5137+1+R-0; J@67Gr1+8_:;lBK@;(4s-0C@(T27+8_ • v–sš ˜ yW13W-0/2; • mj920CËP;(4s-01C@+
CE-0/2;b3AH:3P-0; D“3AC@Gd:-01C@+hpW/2;b3AD=7GG+2;(303CE-0/2;OENd2+84s-01C@+|v{Ê š œ ySDQ;(7+83S-0/87 -ENC@Z3AC@DQ;
K@;(4s-0C@63~Ê — v{Ê ‚ š š Ê@¬2yM7+8_~3AC@DQ;b9C@1+R-63CEo-0/2;I3A987@4;bCES3AC@Gd:-01C@+83 Tr-0/2;bEN0;(fRd2; +:m
41;(3 œ ‚ v• v–sš ˜ yAy š š œ ¬rv• v–sš ˜ yAyB70;Z67 -01C@+87GGHI4C@DQDQ; +83Ad2672G;C@S7GDQCR3P-S4C@DQDQ; +:m
3Ad2672G;@T:1{h;@h
v{Ê š œ v• v–0ÌÍ š ˜ y0yAyÎ¦¡ šÏ–0ÌÍÐ~Ñ¡ š:ÒFÓ
Ô YKY1C@d83AGH=ENC@-0/2;X;l:13P-0; +84;XCE0;(3AC@+87+84;(3W1-Z13+2;(4;(303070H=-0/87 - £ 3A/2C@d2G_+2C-;
G;(303V-0/87+?:h¥z/YH=-0/2; +a_:CI3AD=7GG_:; +2C@DQ1+87 -0C@63W7929;(7sÕ
c;-Zd830; K@; A--0C=-0/2;b3AH:3P-0; DÖCE_:1g; 0; +R-017G$;(fRd87 -01C@+83OvPŸ@h¡2hŸqyS7+8_a4C@+83P-00d84s--0/2;
4G7@303A14 7G`863P-792920Cql:1D=7 -01C@+5YH=-0/2;FENC@0DOd2G7
•×‚PØ v–sš ˜ y — •8Ù ˜
Ú
Û
Ù ™ v•8Ù@šA›Ù@š ˜ y ”@Ü
— •8Ù ˜Ý – ˜ÁÞß,à ßAá ‚
™ à v•8ÙRš ˜ y
â v{Ê š œ Ù y ;l:9rã â v{Ê š œ Ù y – â v{Ê šA›Ù y6ä š
US/2; 0; å
Ê
å
—æÊ ‚ æ zç ç çq æÊ@¬ æš Ê Í — ¡ šsè Ÿ šsè š šêé — Ÿ š š £
*jEt-0/2;F1+21-017Gr9C@1+R-Xv•8ÙRš2›Ù yo13S3Ad846/I-0/87 -W-0/2; 0;FC:4 4d263W7+5;l27@4s-S0;(3AC@+87+84;Z7 -V-0/2;
1+21-017G$-01DQ;ëv{Ê š œ Ù y — ¡2T-0/2; + Ý¯ì— ¡2TF7+8_a-0/2;OENd2+84s-01C@+ • ×‚PØ v–sš ˜ ysTF;(3A1_:;(3Z/87qKY1+2J
9; 01C:_:14F3Ad2DQD=7+8_23 T27G3ACQ4C@+R-671+83o-0/2;3A;(4d2G7V-0; 0D ˜Ý – 920C@9C@A-01C@+87G8-0C – h*jE7 -V-0/2;

í YŽN„FŽNŒtŽîrŠ ï
1+21-017G$-01DQ;ëv{Ê š œ Ù yÎÄ¡ÃvN1{h;@h-0/2; 0;O13Z7+M7GDQCR3P-Z;l27@4s-0;(3AC@+87+84;qyVENC@F7GG$K@;(4s-0C@63ZÊ
EN0C@Dð3AC@DQ;B3Ad283A;-QCE1+R-0; J@; 63OñsòNó,ôT-0/2; +ÂENC@b;l27@4s-0GH~-0/2CR3A;5K@;(4s-0C@63-0/2;a7DQ92G1-0d8_:;(3
CE9; 01C:_:14FENd2+84s-01C@+83C@+ • ×‚PØ D=7qHB;(4C@DQ;O7021-06701GH5G70J@;@T87+8_ENC@Z7GGtC-0/2; Z3Ad2Dbm
D=7 -01C@+BK@;(4s-0C@63WÊI9; 01C:_:14ENd2+84s-01C@+83WUS1GGr/87qK@;F3AD=7GG7DQ92G1-0d8_:;(3 T23A1+84;ZENC@V-0/2; D-0/2;
K 7Gd2;(3FCEZv{Ê š œ Ù yZ70;b+2C-X3AD=7GG{hbõ4s-0d87GGHa-0/2;=3A1-0d87 -01C@+M13F; K@; +MDQC@0;Q4C@DQ92G14 7 -0;(_rT
;(4 7d83A;7DQ92G1-0d8_:;(31+Q-0/2;S-001J@C@+2C@DQ;-0014oENd2+84s-01C@+83=;l:9rã â v{Ê š œ Ù y – ä?_:; 9; +8_Q+2C-oC@+2GH
C@+=-0/2;K 7Gd2;(3CEov{Ê š œ Ù ysTR2d:-S7G3ACC@+=-0/2;K 7Gd2;(3CEr-0/2;Z}2C@d201; V4CY;¨I41; +R-63 ™ à v•8Ù@š ˜ y
-0/87 -(TYJ@; +2; 67GGHb3A9;(7nY1+2J8TY_:;(40;(7@3A;SUS1-0/I-0/2;J@0C US1+2J+2C@0D
å
Ê
å ö
-0/2; 0;ENC@0;S`8+87GGHO-0/2;
7DQ92G1-0d8_:; ™ à@÷ v{Ê š œ Ù y_:; 9; +8_23C-0/?C@+ ™ à v•8ÙRš ˜ y7+8_C@+|v{Ê š œ Ù yshZÀYd846/M7I4C@DQ92G1m
4 7 -0;(_Q920C:4;(303CE7+=1+840;(7@3A;SC@V_:;(40;(7@3A;SCE-0/2;Z7DQ92G1-0d8_:;(3CEr/870DQC@+214WENd2+84s-01C@+83o7@3
;(70GHa7@31+?-0/2;O`863P-792920Cql:1D=7 -01C@+aD=7n@;(31-_:1¨I4d2G-Z-0C3P-0d8_:H-0/2;b; /87qKY1C@ZCE-0/2;
3AC@Gd:-01C@+83 • v–sš ˜ y š› v–sš ˜ ysT2+2C-W-0C=DQ; +R-01C@+B/21J@/2; AmjC@6_:; W792920Cql:1D=7 -01C@+83 h
}$1+87GGH@TYUV;Z1+84Gd8_:;F1+aøo/879:-0; FŸ-0/2;Z1-0; 67 -01C@+5K 7017+R-VCE-0/2;F987A-WCE-0/2;Z-0/2; C@0H
CEC@6_:1+870H5_:1g; 0; +R-017Gt;(fRd87 -01C@+83 T2nY+2C US+a7@3W-0/2;O[C@1+84 72];se:cHR792d2+2C KbDQ;-0/2C:_rhSpW/2;
920C@9CR3A;(_|1-0; 67 -01C@+83=4 7+L;?;(7@3A1GH|7GJ@C@01-0/2DQ1u ;(_rTV7+8_Â-0/213I13Q1GGd83P-067 -0;(_LYH|3AC@DQ;
;l27DQ92G;(3W1+Møo/879:-0; Sù8húC-0;F-0/87 -SDQCR3P-CEt-0/2;920C@2G; D=3S3A/2C US+B1+B-0/21346/879:-0; 70;
7G3AC_:;(30401;(_?YH?DOd2G-01ENd2+84s-01C@+87G3AH:3P-0; D=3ZCEW_:1g; 0; +R-017G;(fRd87 -01C@+83ZUS1-0/MENd2+84s-01C@+83
9; 01C:_:14BUS1-0/L0;(3A9;(4s-b-0CME)7@3P-=92/87@3A;BK 70172G;(3 › To7+8_ÂEN0;(fRd2; +841;(3b_:; 9; +8_LC@+L3AGC U
K 70172G;(3 • h
)üûÃý2')¦þrÿo
Ÿ@hc;-W-0/2;Z0;(7Gr¤d84G1_:;(7+53A987@4;ZCE$_:1DQ; +83A1C@+ £ ;_:; +2C-0;(_IYH Z¬T27+8_=-0/2;Zd2+21-670H
4C@DQ92G;l=3A987@4;YH I¬húC@0D=3CEK@;(4s-0C@o3A987@4;(3 Z¬=7+8_ I¬O-0/87 -VUV;70;J@C@1+2JF-0COd83A;
70;7@3VENC@GGC U3
å
•
å
—

¬
Þà ‚ æ• à æ
š
å
•
å
— 3Ad29
‚ à ¬ æ• ¬ æš
å
•
å
—
¬
Þà ‚ æ• à æ
:hpW/2;b3A987 -017G$_:C@D=71+83Z¬a7+8_I¬BUS1GG;b_:; +2C-0;(_aYH©¬C@¬hZpW/2;O1+8_:;l
3A/2C U3V-0/2;X_:1DQ; +83A1C@+BCE7Q_:C@D=71+BC@7Q3A987@4;@h
hIpW/2;I_:10;(4s-5vjøV7A-0;(3A17+yZ920C:_:d84s-CEV-PUVC`8; G_23US1GG;I_:; +2C-0;(_iYH©ªW«¬ —
©ª©¬¦C@a©ªW«¬ — ãYv•tšA› y • Ð ©ª šA› Ð ©¬äRh
ù8h ˜ ; K@; 0HYUS/2; 0;F_:; +2C-0;(3S7Q3AD=7GGr+2C@+2+2; JR7 -01K@;F98767DQ;-0; (h
hpW/2;3AHYDOC@G! _:; +2C-0;(3-0/2;SC@+2;m,3A1_:;(_O-067+83PENC@0D=7 -01C@+Bv)3Ad283P-01-0d:-01C@+ysTY7+8_O-0/2;
3AHYDOC@G# _:; +2C-0;(3V-PUVCm,3A1_:;(_iv)_:10;(4s-7+8_51+YK@; 63A;qyo3Ad283P-01-0d:-01C@+T8;@hJ8h • %$• T'(%$2h
) hpW/2;+2C@0D CE$-0/2; £ m,_:1DQ; +83A1C@+87Gr1+R-0; J@; SK@;(4s-0C@aÊ — v{Ê ‚ š š Ê@¬2y5134 7G4d2G7 -0;(_
YHI-0/2;FENC@0DOd2G7
å
Ê
å
—æÊ ‚ æ zç ç çq æÊ@¬ æš Ê Í — ¡ šsè Ÿ šsè š šêé — Ÿ š š £

Discovering Diverse Content Through
Random Scribd Documents

with barrels, with one of those huge specimens of humanity (and beer)
moving along like a clumsy tower by its side. “Like him; and Orlando was
quite young, you know, not so very big—like me, when I am grown up.”
“You don’t know what you will be when you are grown up, you silly
little boy. Perhaps you will never grow up at all,” said Lucy, somewhat
against her conscience improving the occasion.
Jock stood for a moment with wide open eyes. Then resumed:
“I sha’n’t be big or fat like that fellow—when I am about seventeen, or
perhaps twenty-two, and never taught to box or anything. I would have
gone in at him,” cried Jock, throwing out his poor arm, with a very tightly
clinched woolen glove at the end of it, “just like Orlando, just like this; and
down he’d go, like, like—” But imagination did not serve him in this
particular. “Like Charles did,” he concluded, with a dropping of his voice,
which betrayed a consciousness of the failure, not in grammar, but in force
of metaphor. Jock’s experience did not furnish any parallel incident.
“You must never fight when you grow up,” said Lucy. “Gentlemen never
do; except when they are soldiers, and have to go and fight for the queen.”
“Does the queen want to be fighted for?” said Jock. “If any fellow was to
bully her or hit her—”
“Oh,” cried Lucy, horrified, “nobody would do that, but people
sometimes go against the country, Jock, and then the people that are
fighting for England are said to be fighting for the queen.”
Jock’s mind, however, went astray in the midst of this discourse. There
passed the pair in the road a very captivating little figure—a small boy,
much smaller even than Jock, with long fair locks streaming down his
shoulders, in the most coquettish of dresses, mounted upon a beautiful
cream-colored pony, as tiny as its rider. What child could pass this little
equestrian and not gaze after him? The children sighed out of admiration
and envy when they saw him, for he was a very well-known figure about
Farafield; but the elders shook their heads and said, “Poor child!” Why
should the old people say “Poor child!” and the young ones regard him with
such admiring eyes? It was little Gerald Ridout, the son of the circus
proprietor. Nobody was better known. As he rode along, the most daring
little rider, on his pretty little Arab, which was as pretty as himself, with his
long flowing curls waving, there could have been no such attractive
advertisement. The circus traveled for a great part of the year, but its home

was in Farafield, and everybody knew little Gerald. Jock fixed his
glistening eyes upon him from the moment of his appearance—eyes that
shone with pleasure and sympathy, and that wistful longing to be as
beautiful and happy, which is not envy. There was nothing of the more
hateful sentiment in little Jock’s heart, but because he admired he would
have liked to resemble, had that been within his power. He followed the
child with his eyes as long as he was visible. Then he asked, “Do people
who are rich have ponies, Lucy?” with much gravity and earnestness.
“Very often, dear, and horses too; but that poor little fellow is not rich,
you know.”
“I should like to be him,” said Jock.
“A little circus-boy? to ride upon the stage, and have all the most horrid
people staring at you?”
“And jump through the hoop, and gallop, gallop, and have a pony like
that all to myself. A—h!” Jock cried with a long-drawn breath.
“Would you like a pony so very much, Jocky? Then some day you shall
have one,” said his sister in her tranquil voice. “I will buy you one when I
am rich.”
“Are you soon going to be rich?” said the little boy doubtfully. Like
wiser people, he preferred the smallest bird in the hand to a whole aviary in
the dim and doubtful distance. But Lucy had not a very lively sense of
humor. She knew the circumstances better than he did, and said, “Hush!
hush!” with a little awe.
“Not for a very long time, I hope,” she said.
Her little brother looked at her with wondering eyes; but this mystery
was too deep for him to solve. He had no insight into those deep matters
which occupied his father’s time, nor had he the least notion that Lucy’s
wealth depended upon that father’s death, though it had all been discussed
with so much detail day by day over his dreaming head.
“When you are rich, shall I be rich too, Lucy?” he said.
“I am afraid not, Jock; but if I am rich, it will not matter; you shall have
whatever you please. Won’t that do just as well?”
Jock paused and thought.
“Why shouldn’t I be rich too?” he remarked. It was not said as a
question; it was an observation. The fact did not trouble him, but en passant

he noticed it as a thing which might perhaps want explaining. It was not of
half so much importance, however, as the next thing that came into his
head.
“I say, Lucy, do you think that boy on the pony has to go to school?
What do you think he can be learning at school? I should like to go there
too.”
“When you go, it shall be to a much nicer place,” she said, with energy.
“There is one thing I should like to be rich for, and that is for you, little
Jock. You don’t know anything at all yet. You ought to be learning Greek
and Latin, and mathematics, and a great many other things. It makes me
quite unhappy when I think of it. I go to school, but it does not matter for
me; and you are living all your time, not learning anything, reading
nonsense on the hearth-rug. I could cry when I think of it,” Lucy said. She
said it very quietly, but this was vehemence in her.
Jock looked up at her with wondering eyes; for his own part he had no
enthusiasm for study, nor, except for the pleasure of being with the circus
boy, whom he vaguely apprehended as caracoling about the very vague
place which his imagination conceived of as “School,” on his pretty pony,
had he any desire to be sent there; but it did not occur to him to enter into
any controversy on the subject.
“Are you going up-town, Lucy?” he asked; “have you got to go to shops
again? I wish you would buy all your ribbons at one time, and not be
always, always buying more. Aunty Ford when she goes out goes to shops
too, and you have to stand and stare about, and there’s nothing to look at,
and nothing to do.”
“What would you like to do, Jock?”
“Oh, I don’t know—nothing,” said the boy; “if I had a pony I’d get on its
back and ride off a hundred miles before I stopped.”
“The horse couldn’t go a hundred miles, nor you either, dear.”
“Oh, yes, I could, or ten at least, and if I met any one on the road I’d run
races with him; and I’d call the horse Black Bess, or else Rozinante, or else
Chiron; but Chiron wasn’t only a horse, you know, he was a horseman.”
“Well, dear,” said Lucy, calmly, “I wish you were a horseman, too, if you
would like it so very much.”

“You don’t understand,” cried the child, “you don’t understand! I
couldn’t be like Chiron; he had four legs, he was a man-horse. He brought
up a little boy once, lots of little boys, and taught them. I say, Lucy, if
Chiron was living now I should like to go to school to him.”
“You are a silly little boy,” said Lucy. “Who ever heard of a school-
master that had four legs? I wonder papa lets you read so many silly
books.”
“They are not silly books at all; it is only because you don’t know,” said
Jock, reddening. “Suppose we were cast on a desert island, what would you
do? You don’t know any stories to tell round the fire; but I know heaps of
stories, I know more stories than any one. Aunty Ford is pretty good,” the
little fellow went on, reflectively: “she knows some; and she likes me to tell
her out of Shakespeare, and about the ‘Three Calenders’ and the ‘Genii in
the Bottle,’ and that improves her mind; but if you were in a desert island
what should you do? You don’t know one story to tell.”
“I should cook your suppers, and mend your clothes, and make the fire.”
“Ah!” said the boy with a little contempt; “bread and milk would do, you
know, or when we shot a deer we’d just put him before the fire and roast
him. We shouldn’t want much cooking; and the skin would do for clothes.”
“You would not be at all comfortable like that,” said Lucy gravely,
shocked by the savagery of the idea; “even Robinson Crusoe had to sew the
skins together and make them into a coat; and how could you have milk,”
she added, “without some one to milk the cow?”
“I will tell you something that is very strange,” said Jock: “Aunty Ford
never read ‘Robinson Crusoe;’ but she knows Christian off by heart, and all
about Mary and Christiana and the children. And she knows the history of
Joseph, and David, and Goliath; so you can not say she is quite ignorant;
and she makes me tell her quantities of things.”
“You should not mix up your stories,” said Lucy; “the Bible is not like
other books. About Joseph and David and those other—” (Lucy had almost
said gentlemen, which seemed the most respectful expression; but she
paused, reflecting with a little horror that this was too modern and common
a title for Bible personages). “They are for Sunday,” she went on, more
severely, to hide her own confusion; “they are not like ‘Robinson Crusoe’ or
the ‘Genii in the Bottle;’ you ought not to mix them up.”

“It is Christian that is the most Sunday,” said Jock; “she explains it to
me, and all what it means, about the House Beautiful and the ladies that
lived there. There is a Punch, Lucy! and there’s Cousin Philip; never mind
him, but run, run, and let us have a good look at the Punch.”
“I mustn’t run,” said Lucy, holding him back, “and I can not stand and
look at Punch. If Mrs. Stone were to see me she never would let me come
out with you any more.”
“Oh, run, run!” cried the little boy, straining at her hand like a hound in a
leash. He had dragged her half across the street when Cousin Philip came
up. This was the only other relative with whom Mr. Trevor had kept up any
intercourse. He was the young man to whom the old school-master had
made over his school, and he, too, like Lucy, was taking advantage of the
half holiday. In Farafield, where young men were scarce, Philip Rainy had
already made what his friends called a very good impression. He was not, it
was true (to his eternal confusion and regret) a University man; but neither
was he a certified school-master. He had greatly raised the numbers of old
John Trevor’s school, and he occupied a kind of debatable position on the
borders of gentility, partly because of his connection with the enriched
family perhaps, but partly because his appearance and manners were good,
and his aspirations were lofty from a social point of view. He had begun
with a determination, to resist steadily all claims upon him from below, and
to assert courageously a right to stand upon the dais of Farafield society;
and though there may be many discouragements in the path of a young man
thus situated, it is astonishing how soon a steady resolution of this kind
begins to tell. He had been five years in old John Trevor’s school, and
already many people accredited him with a B.A. to his name. Philip told no
fibs on that or any subject that concerned his position. “When it was
necessary,” as he said, he was perfectly frank on the subject; but there are so
few occasions on which it is necessary to be explanatory, a modest man
does not thrust himself before the notice of the world; and he was making
his way—he was making an impression. Though he had been brought up a
Dissenter like his uncle, he had soon seen the entire incompatibility of
Sectarianism with society, and he had now the gratification of hearing
himself described as a sound if moderate churchman. And he was now
permanently upon the list of men who were asked to the dinner-parties at
the rectory, when single men were wanted to balance a superabundance of

ladies, an emergency continually recurring in a country town. This of itself
speaks volumes. Philip Rainy was making his way.
He was a slim and a fair young man, bearing a family resemblance to his
cousin Lucy; and he had always been very “nice” to Lucy and to Jock. He
came up to them now to solve all their difficulties, taking Jock’s eager hand
out of his sister’s, and arresting their vehement career.
“Stop here, and I’ll put you on my shoulder, Jock; you’ll see a great deal
better than among the crowd, such a little fellow as you are; and Lucy will
talk to me.”
They made a very pretty group, as they stood thus at a respectful
distance from Punch and his noisy audience, Jock mounted on his cousin’s
shoulder, clapping his hands and crowing with laughter, while Lucy stood,
pleased and smiling, talking to Philip, who was always so “nice.” The
passers-by looked at them with an interest which was inevitable in the
circumstances. Wherever Lucy went people looked at her and pointed her
out as the heiress, and naturally the young man who was her relation was
the subject of many guesses and speculations. To see them standing together
was like the suggestion of a romance to all Farafield. Were they in love with
each other? Would she marry him? To suppose that Philip, having thus the
ball at his foot, should not be “after” the heiress, passed all belief.
But the talk that passed between them, and which suggested so many
things to the lookers-on, was of the most placid kind.
“How is my uncle?” Philip asked. Old John Trevor was not his uncle, but
the difference between age and youth made the cousinship resolvable into a
more filial bond, and it sounded much nearer, which pleased the young
man. “May I come and see him one of these evenings, Lucy? I am dining
out to-day and to-morrow; but Friday perhaps—”
“How many people you must know!” said Lucy, half admiring, half
amused; for young persons at school have a very keen eye for everything
that looks like “showing off.”
“Yes, I know a good many people—thanks chiefly to you and my uncle.”
“To me? I don’t know anybody,” said Lucy.
“But they know you; and to be a cousin to a great heiress is a feather in
my cap.”

Lucy only smiled; she was neither pleased nor annoyed by the reference,
her fortune was so familiar a subject to her. She said, “Papa will be glad to
see you. But I must not stand here on the street; Mrs. Stone will be angry;
and I think Jock must have seen enough.”
“Don’t knock my hat off, Jock. Have you seen enough? I will walk with
you to the Terrace,” said Philip, and the little family group as they went
along the street attracted a great deal of interest. What more natural than
that Philip should be “nice” to his young cousins, and turn with them when
he met them on a half holiday? and it is so good to be seen to have relations
who are heiresses for a young man who is making his way.

CHAPTER V.
AFTERNOON TALK.
The children, as they were called in the Terrace, came home just in time for
tea. Mr. Trevor had changed the course of his existence for some time past.
He who all his life had dined at two, and had tea at six, and “a little
something” in the shape of supper before he went to bed, had entirely
revolutionized his own existence by the troublesome invention of “late
dinner,” which Mrs. Ford thought was the suggestion of the Evil One
himself. His reason for it was the same as that of many other changes which
he had made at some cost to his own comfort, but he did not explain to any
one what this meant—at least, if he did explain it, it was to Lucy, and Lucy
was the most discreet of confidantes. When she came in with her little
brother the Fords were seating themselves at the table in their parlor, on
which were the tray and the tea-things, and a large plate of substantial bread
and butter. Here Jock took his place with the old people, while Lucy went
upstairs. She would have liked the bread and butter, too, but her father liked
her to spend this hour with him, and he despised the modern invention of
five o’clock tea, understanding that meal only, as the Fords did, who made
themselves thoroughly comfortable, and had muffins sometimes, and a
variety of pleasing adjuncts. Mr. Trevor was still sitting between the fire
and the window when Lucy went upstairs. She had taken off her hat and
out-door jacket, and went in to her father a spruce little gray maiden, with
hair as smooth and everything about her as neat as if she had just come out
of a bandbox. In Mr. Trevor’s rank of life there is no personal virtue in a
woman that tells like neatness. He looked at her with eyes full of fond
satisfaction and pleasure. He had put away the “Times” from his knees, and
now had a book, having finished his paper, which lasted him till about four
o’clock, and then went down-stairs to Mr. Ford. The books Mr. Trevor read
were chiefly travels. He did not think novels were improving to the mind;
and as for history and solid information at his age, what was the use of
them? they could serve very little purpose in his case: though Lucy ought to
read everything that was instructive. He put down his book open, on its

face, on his knee when his daughter came in. His eyes dwelt upon her with
genuine pleasure and pride as she took the chair in which Ford had been
sitting. She had some knitting in her hand, which she began to work at
placidly without looking at it. Lucy with her blue eyes, her fair smooth hair,
and her equally smooth gray dress without a crease in it, looked the very
impersonation of good order and calm. She looked at her father tranquilly
with a pleasant smile. She was no chattering girl with a necessity of talk
upon her. Even among the other girls at Mrs. Stone’s Lucy was never, as
Mrs. Ford said, “one to talk.” She waited for what should be said to her.
“Well,” said her father, rubbing his hands, “and where have you been,
Lucy, to-day?”
“Up into the High Street, papa.”
“I think you are fond of the High Street, Lucy?”
“I don’t know. The common is very wet, and Jock will run and jump. I
don’t like it in this weather. The High Street is dry and clean—at least it is
dry and clean in front of Ratcliffe’s shop.
“And there are all the pretty things in the windows.”
“I don’t look at the things in the windows—what is the good? You would
let me buy them all if I wanted them,” said Lucy, quietly.
“Every one!” said old Trevor, with a chuckle. “Every one! You might
have a new dress every day of the year, if you liked!”
Lucy smiled; she went on with her knitting. This delightful possibility
did not seem to affect her much—perhaps because it was a possibility.
“We met the little circus-boy on his pony,” she said. “Jock thinks so
much of him. Papa, you always let me have everything I want—might I
have a pony for Jock? It would make him so happy.”
“No,” said old Trevor, succinctly. “For yourself as many you like; but
that sort of thing is not for the child. No, nothing of that sort.”
“Why?” she said, with something which in Lucy was impatience and
vexation. It was too slight a ruffling of the calm surface to have told at all in
any one else.
“Because, my dear, Jock must not have anything that is above his own
rank in life. What should he do with a pony? He is not a gentleman’s son to
be bred up with foolish notions. It would be all the worse for him to find out
the difference afterward.”

“But he is my brother,” Lucy said, “and your son, papa. If he is not a
gentleman’s son neither am I— How is he different from me? And do you
think I can make such a difference when—when I am grown up—”
“You mean when I am dead? Say it out. Isn’t that what I’m always
thinking of? The little boy, my dear,” said old Trevor, gravely, yet with his
familiar chuckle breaking in, “is a mistake. He didn’t ought to have been at
all, Lucy. Now he’s here, we can’t help it—we’ve got to put up with it; and
we must make the best of him. We can’t send him out of the world because
it was a mistake his coming into it; but he must keep to his own rank in
life.”
“But, papa, if you would think a little why should there be such a
difference? I so rich—and if he is to have nothing—”
“He will be as well off as he has any right to be,” said old Trevor. “I’ve
laid by a little. Don’t trouble yourself about Jock. What have you been
doing to-day? That is the thing of the greatest importance. I want to know
all my little lady is about.”
“We had our French lesson,” said Lucy, a little disturbed under her
smooth surface; but the disturbance was so little that her father never found
it out, “and—all the rest just as usual, papa.”
“And can you understand what mounsheer says? Can you talk to him? I
used to know a few words myself, but never to talk it,” said the old man.
His acuteness seemed to have deserted him, and turned into the most
innocent simplicity—a little glow came upon his face. He was almost
childishly excited on this point.
“A few words were enough for me—what did I want with French?—
though things are altered now; and it’s taught, I’m told, in every
commercial academy, and the classics neglected. That wasn’t the way in my
time. If a boy learned anything besides reading and writing it was Latin;
and I was considered very successful with my Latin.”
“That is another thing, papa,” said Lucy; “don’t you think Jock should
go to school?”
Old Trevor’s face extended slightly. “Have you nothing to say to me,
Lucy, but about Jock?”
“Oh, yes, a great deal,” said the girl. She did not lose a single change in
his face, though she kept on steadily with her knitting, and she saw it was
not safe to go further. She changed the subject at once. “Monsieur says I get

on very well,” she said; “but not so well as Katie Russell. She is first in
almost everything. She is so clever. You should hear her chatter French—as
fast! It is like the birds in the trees, as pretty to listen to—and just as little
sense that you can make out.”
“Yes, yes, yes!” said the old man, with a little impatience, “There is no
occasion for you to learn like that, Lucy. She has to make her living by it,
that girl. I wonder now, you that are in so very different a position, why it’s
always this Russell girl you talk about, and never any of the real ladies, the
Honorable Miss Barringtons and Lady—what do you call her?—and the
better sort. It was for them I sent you to Mrs. Stone’s school, Lucy,” he said,
with a tone of reproach.
“Yes, papa. I like them very well—they are just like me. They do as little
work as they can, and get off everything they can. We had a famous ride—
but that was yesterday. I told you about it. Lily Barrington’s horse ran away,
or we thought it ran away; and mine set off at such a pace! I was dreadfully
frightened, but Lily liked it. She had done it on purpose, fancy! and thinks
there is nothing in the world so delightful as a gallop.”
“And you call her Lily?” said Mr. Trevor, with a glow of pleasure;
“that’s right, my dear. That’s what I like to hear. Not that I want you to
neglect the others, Lucy; but you can always get a hold on the poor; no fear
of them; I want you to secure the great ones, too. I want you to know all
sorts. You ought to with your prospects. I was saying to Ford to-day a girl
with your prospects belongs to England. The country has an interest in you,
Lucy. You ought to know all sorts, rich and poor. That is just what I have
been settling,” he said, laying his hand on the blotting-book now closed, in
which his papers were.
Lucy gave him a little smile nodding her head. She was evidently quite
in the secret of the document there. But she did not stop her knitting, nor
was she so much interested in that future which he was settling for her so
carefully as to ask any questions. Her little nod, her smile which had a kind
of indulgence in it, as for the vagaries of a child, her soft calm and
indifference bore the strangest contrast to his absorption in all that
concerned her. Perhaps the girl did not realize how entirely her future was
being mapped out; perhaps she did not realize that future at all. There was a
touch of the gentlest youthful contempt for that foolish wisdom of our
fathers to which we are all instinctively superior in our youth, in her perfect

composure. It amused him—though it was so odd that a man should be
amused in such a way—and it did not matter any further to her.
“Mrs. Stone sent her kind regards, papa, and she will gladly come over
and take a cup of tea any time you like.”
“Oh, she’ll come, will she? I want to tell her of something I’ve put in the
will,” said old Mr. Trevor.
This roused Lucy from her composure. She looked at him with a half-
startled glance.
“You will tell—her—of that paper?”
“Well, not much about it—only something that regards herself. You will
be much sought after when I am gone. All sorts of people will be after you
for your money; and I want to protect you, Lucy. It’s my business to protect
you. Besides, as I tell you, you’re too important to have just a couple of
guardians, like a little girl with ten thousand pounds. You belong to the
country, my dear. A fortune like yours,” said the old man, now launched
upon his favorite subject, “is a thing by itself; and I want to protect you, my
dear.”
This time Lucy, instead of the smile, breathed a little sigh. It was a sigh
of impatience, very momentary, very slight. This was the doctrine in which
she had been brought up, and she would as soon have thought of throwing
doubt upon the ten commandments as of denying that her own position
made her of almost national importance. She was aware of all that; it was
merely the reiteration of it which moved her to the faintest amount of
impatience; but this she very soon repressed.
“Is Mrs. Stone to protect me?” she said.
“She is to be one of them, my dear. You know I don’t wish to do
anything in secret, Lucy. I wish you to know all my arrangements. If you
came to think afterward that your father had taken you by surprise I—
should not like it; and now I have got as far as where you ought to live—
listen, Lucy,” said the old man. The big document in the writing-case was
evidently his one idea. His face brightened as he took it up and spread out
the large leaves. As for Lucy, she sighed again very softly. How the will
wearied her! But she was heroic, or stoical. She made no sort of stand
against it; and after that one soft little protest of nature, went on with her
knitting, and listened with great tranquillity. Her father read the paragraphs
that he had been consulting Ford about, one by one; and Lucy listened as if

he had been reading a newspaper. It awoke no warmer interest in her mind.
She had heard so much of it that it did not affect her in any practical way; it
seemed a harmless amusement for her father, and nothing more.
“Do you think you shall like going to Lady Randolph, Lucy?”
“How can I tell, papa? I don’t know Lady Randolph,” Lucy said.
“No; but that’s high life, my dear; and here’s humble life, Lucy. I want
you to know both; and as for your marriage, you know—”
“You do not want me to marry,” said the sensible girl, “and I don’t think
I wish it either, papa. But if I ever did, it would not be nice to have to go
and ask all these people; and they never would agree. We might be quite
sure of that.”
“Then you think I have been hard upon you? Always speak to me quite
openly, Lucy. I don’t want to be hard upon you, my child—quite the other
way.”
“Oh, it does not matter at all,” said Lucy, cheerfully, plying her knitting-
needles. “I don’t think it is the least likely that I shall ever want to marry. As
you have always told me, I shall have plenty to do, and there will be Jock,”
she added, after a momentary pause.
“You have a great many prejudices about Jock,” her father said, testily:
“what difference can he make? He has not so very much to do with you, and
he will be in quite a different sphere.”
“Do you want me to have nobody belonging to me?” Lucy cried, with a
sudden vivacity not without indignation in it, then subdued herself as
suddenly. “It doesn’t at all matter,” she said.
“And you remember,” said her father almost humbly, “this is only till
you are five-and-twenty. It is not for all eternity; you will have plenty of
time to marry, or do whatever you please, after that.”
Lucy nodded and smiled once more. “I don’t think I shall want to
marry,” she said; but while she spoke she was making a quiet calculation of
quite a different character. “Jock is eight and I am seventeen,” she was
saying within herself, “how old will Jock be when I am twenty-five?” It
does not seem a difficult question; but she was not great in arithmetic, and it
took her a moment or two to make it out. When she had succeeded her face
brightened up. “Still young enough to be educated,” she added, always
within herself, and this quite restored her patience and her cheerfulness.

“It will be very funny,” she said, “to see the rector and Mr. Williamson
consulting together. I wonder how they will begin; I am sure Mr.
Williamson will put on colored clothes to show how independent he is; and
the doctor—the doctor will smile and rub his hands.”
“You forget,” said old Trevor, with a slight sharpness of tone, though he
laughed, “that such things have been as that I should outlive the doctor.
He’s younger than I am, to be sure, but I would not have you to calculate on
my death before the doctor. It might be quite a different rector. It might be a
young man that would, perhaps, put in claims to the heiress himself. But I’ll
give you one piece of advice, Lucy, beforehand. Never marry a parson.
They’re always in the way. Other kinds of men have their occupations; but
a parson with a rich wife is always lounging about. Your mother used to say
so; and she was a very sensible woman. She had an offer from one of the
chapel ministers when she was young; but she would have nothing to say to
him. A man in slippers, always indoors, was what she never could abide.”
“I don’t think the rector would be like that, papa,” said Lucy; “he doesn’t
look as if he ever wore slippers at all—”
“Well, perhaps, it is the other kind I am thinking of,” said Mr. Trevor,
who had not much acquaintance with the class which he called “church
parsons,” though his liberality of mind was such that he had brought up
Lucy partially, at least, as a church woman. His conduct, in this respect, was
much the same as it was in reference to the distinctions of society. He
wanted her to have her share in all—to be familiar alike with poverty and
riches, and, as a kind of moral consequence, with church and chapel, too.
It was almost a disappointment to the old man that Lucy let the subject
drop, and showed no further interest in it. He was a great deal more excited
about her future life than she was. Lucy’s life was, indeed, to her father at
once his great object and his pet plaything. It was his determination that it
should be such a life as no one had ever lived before; a perfection of
beneficence, wisdom, well-doing, and general superiority. He wanted to
guard her against all perils, to hedge her round from every enemy.
Unfortunately, he knew very little of the world, the dangers of which he was
so intent on avoiding; but he was quite unaware of his own ignorance. He
foresaw the well-known danger of fortune-hunters; but he did not perceive
the impossibilities of the arrangement by which he had, he flattered himself,
so carefully and cleverly guarded against them. In this respect Lucy had

more insight than her father, in her gentle indifference. Her life was not a
matter of theory to Lucy. It was not a thing at all to be molded and formed
by any one, it was to-day and to-morrow. She listened to, without being
affected by, all her father’s plans for her. They seemed a dream—a story to
her, the future to which they referred was quite unreal in her eyes.
“We met Philip, papa,” she said, after a pause, with her usual tranquillity.
“He is always very nice to Jock. He put him upon his shoulder to see the
Punch. And he says he is coming to see you.”
“You met Philip,” said the old man, “and he is coming to see me? Well,
let him come, Lucy. He is a rising man, and a fine gentleman—too fine for
a homely old man like me. But we are not afraid of Philip. Let him come;
and let us hope he will find his match when he comes here.”
“You do not like Philip, papa? I think he is the only person you are—not
quite just to. What has he done? He is always very nice to Jock, and—”
Lucy added, hastily, in a tone of conciliation, “to me, too.”
“Done?” said the old man, with a snarl in place of his usual chuckle. “He
has done nothing but what is virtuous. He has doubled the school, and he
sets up for being a gentleman. Don’t you know that I have the highest
opinion of Philip? I always say so—the best of young men; and he calls me
uncle, though he is only my wife’s distant cousin, which is very
condescending of him. Not to approve of Philip would be to show myself a
prejudiced old fool, and—” Mr. Trevor added, after a pause, showing his
old teeth in yellow ferocity, not unmixed with humor, “that is exactly what I
am.”
Lucy looked at him with her peaceful blue eyes. She shook her head in
mild disapproval. “He is very nice to Jock—and to me, too,” she repeated,
softly. But she made no further defense of her cousin. This was all she said.

CHAPTER VI.
PHILIP.
Philip Rainy was, as his relation had been obliged to avow, an excellent
young man; there was nothing to be found fault with in his moral character,
and everything to be applauded in his manners and habits. He had acquired
his education in the most laborious way, at the cheapest possible rate, and
he had used it, since he was in a condition to do so, in the most admirable
manner. He was intelligent and amiable as well as prudent and ambitious,
and though he meant to establish a reputation for himself, and a position
among those who were considered best in Farafield, yet he never forgot his
family, whom he had left behind; nor, though he did not think it necessary
to brag that he had begun the world in the lowliest way, did he ever, when it
was called for, shrink from an avowal of his origin, humble as that was.
Why old Mr. Trevor should dislike him, it would be difficult to say, or
rather, though it might be easy enough to divine the causes, it would be
almost impossible to offer any justification of them. Old Trevor disliked the
young man because—he was so altogether unexceptionable a young man.
Every inducement that could have led an old man to patronize and
encourage a young one existed here, and yet these very reasons why he
should like Philip made his old relation dislike him. He was too good, and,
alas, too successful. He had doubled the school in Kent’s Lane, which the
old gentleman, distracted by other occupations, had brought down very low,
indeed; and this was something which it was rather hard to forgive, though
it was worthy of nothing but praise. And he was Lucy’s cousin, on the side
of the house from which the fortune came, and perfectly suitable to Lucy in
point of age, and in almost every way. How much trouble it would have
avoided, how much ease and security it would have given, if Philip had
been placed in Lucy’s way, and an attachment encouraged between them! It
would have been the most natural thing in the world; it would have restored
the fortune to the name, it would have enriched the family of the original
possessor, it would have saved all the trouble of the will which old Trevor
was elaborating with so much care. Therefore, it was that old Trevor

detested Philip Rainy, or, at least, was so near detesting him that only
Christian principle prevented that climax of feeling. As it was, with a
distinct effort because the sentiment was wrong, the old man restrained his
conscious dislike of the young one within the bounds of what he considered
permissible hostility. But all he could do could not entirely control that
fierce impulse of repugnance. He could not keep his voice from altering, his
expression from changing, when Philip Rainy’s name was mentioned.
Perhaps at the bottom of all his anxiety about Lucy’s fortune, and his desire
to shape and control her actions, was an underlying dread that Lucy’s fate
might be lying quite near, and might be decided at any moment before ever
his precautions could come into effect.
Philip himself had no conception how far the dislike of his uncle—as he
called old Trevor, without being in the least aware that this of itself was an
offense—went. He did not even know that it was only to himself that the
old man was so systematically ill-tempered. It was seldom he saw old
Trevor in the society of other people, and he took it for granted, with much
composure, that the sharpness of his gibes and the keenness of his criticisms
were natural, and employed against the world in general as well as against
himself. Being a young man determined to rise in the world, it was not to be
supposed that he had not taken the whole question of his family connections
into earnest consideration, or that he was entirely unmoved by the
consciousness that within his reach, and accessible to him in many ways not
possible for other men, was one of the greatest prizes imaginable, an
heiress, whose soft little hand could raise him at once above all the chance
of good or evil fortune, and confer upon him a position far beyond anything
that was within his possibilities in any other way. On this latter point,
however, he was not at all clear; for Philip was young, and had not learned
to know these inexorable limits which hem in possibility. He thought he
could do a great many things by his unaided powers which he would have
easily seen to be impossible for any one else. He believed in occasions
arising which would give scope to his talents, and show the world what
manner of man it was which the irony of fate confined to the humble
occupation of a school-master in a little country town; and he entertained no
doubt that when the occasion came he would show himself worthy of it.
Therefore, he was not sure that Lucy’s fortune could do much more for him
than he could do for himself; but he was too sensible to ignore the
difference it would make in his start, the great assistance it would be in his

career. It would give him an advantage of ten years, he said to himself, in
the musings of that self-confidence which was so determined and arrogant,
yet so simple; a difference of ten years—that stands for a great deal in a
man’s life. To attain that at thirty which in ordinary circumstances you
would only attain at forty, is an advantage which is worthy many sacrifices;
but yet, at the same time, if you are sure of attaining at forty, or by good
luck at thirty-nine, the good fortune on which your mind is set, it is not
perhaps worth your while to make a very serious sacrifice of your self-
esteem or pride merely for the sake of saving these ten years. This was why
Philip maintained with ease so dignified and worthy a position in respect to
his heiress-cousin. She would make a difference of ten years—but that was
all; and besides being a young man determined to get on in the world, he
was a young man who gave himself credit for fine feelings, and
independence of mind, and generosity of sentiment. He could not, at this
early stage of his existence, have come to a mercenary decision, and made
up his mind to marry for money. He did not see any necessity for it; he felt
quite able to encounter fate in his own person; therefore, though he did not
refuse to acknowledge that it would be a very good thing to marry an
heiress, and very pleasant if the woman with whom he fell in love should
belong to that class, he had not proposed to himself the idea either of trying
to fall in love with Lucy or attempting to secure her affections to himself.
The idea of her hovered before his mind as a possibility—but there were
many other possibilities hovering before Philip, and some more enticing,
more attractive, than any heiress. Therefore he did not spoil his own
prospects by perpetual visits, or by paying her anything that could be called
“attention” in the phraseology of the drawing-room. His relations with her
were no more than cousinly; he was very “nice;” but then he was even more
“nice” to little Jock, who was not his relation at all, than to Lucy. It was part
of his admirable character that he was fond of children, and always good to
them, so that no suspicion could possibly attach to the very moderate
amount of intercourse which was conducted on so reasonable a footing. But
the more it was reasonable, the more it was cousinly, the more did old
Trevor dislike his child’s relation; he had not the slightest ground for fault-
finding, therefore his secret wrath was nursed in secret, and grew and
increased. It was all he could do to receive Philip with civility when he
came. He came in after dinner in a costume carefully adapted to please, or
at least to disarm all objections, a compromise between morning and

evening dress; he made judicious inquiries after the old man’s health, not
too much, as if there was anything special in his solicitude, but as much as
mingled politeness and family affection required.
“I hope you are standing the cold pretty well, sir,” he said; “spring is
always so trying. I can bear the winter better myself; at all events, one does
not expect anything better in December, and one makes up one’s mind to
it.”
“At your age,” said old Trevor, “it was all the same to me, December or
July; I liked the one as much as the other. But I think we might find
something better to talk of than the weather; every idiot does that.”
“That is true,” said the young man, “it is always the first topic among
English people. With our uncertain climate—”
“I never was out, of England, for my part,” the old man interrupted him
sharply. “English climate is the only climate I know anything about. I don’t
pretend to be superior to it, like you folks that talk of Italy and so forth.
What have I got to do with Italy? It may be warmer, but warm weather
never agreed with me.”
“I have never been out of England, either,” said the young man, with that
persistence in the soft word that turns away wrath, which is of all things in
the world the most provoking to irritable people; and then he changed the
subject gently, but not to his own advantage. “I thought you would like to
hear, uncle, how well everything is going on in Kent’s Lane. I am thinking
of an assistant, the boys are getting beyond my management; indeed, if
things go on as they are doing, I shall soon have enough to do managing,
without teaching at all. I have heard of a very nice fellow, a University man.
Don’t you think that, on the whole, would be an advantage? people think so
much more nowadays—for the mere teaching, you know, only for the
teaching—of a man with a degree.”
“A man with a fiddlestick!” said old Trevor. “The question is, are you
going into competition with Eton and Harrow, Mr. Philip Rainy, or are you
the master of a commercial academy, that’s the question. The man that
founded that establishment hadn’t got a degree, no, nor would have
accepted one if they had gone on their knees to him. He knew his place, and
the sort of thing that was expected from him. Oh, surely, get your man with
a degree! or go and buy a degree for yourself (it’s a matter of fees more
than anything else, I have always heard), and starve when you have got it.

But I’d like you to hand over Kent’s Lane first to somebody that will carry
it on as it used to be.”
“I beg your pardon with all my heart, uncle,” cried the young man. “I
have not the least intention of abandoning Kent’s Lane. It’s my sheet-
anchor, all I have in the world; and I would not alter the character you
stamped upon it for any inducement. The only thing is, that so much more
attention is paid to the classics nowadays—”
“Curse nowadays, sir!” cried old Trevor, his countenance glowing with
anger. Then he pulled himself up, and recollected that such language was
far from becoming to his age and dignity, not to speak of his Christian
principles. “I shouldn’t have said that,” he added, in a subdued tone; “I
don’t want to curse anything. Still I don’t know what the times are coming
to with all these absurd novelties. The classics” (he had been boasting of his
Latin an hour before) “for a set of shop-keepers’ sons that want to know
how to add up their fathers’ books! It’s folly and nonsense, that’s what it is.
Even if you could do it, what’s the advantage of snipping all classes out on
the same pattern? It’s a great deal better to have a little difference. Women,
too—you’d clip them all out like images in paper, the same shape as men.
It’s a pity,” he added, grimly, “that your classics and your degrees don’t do
more for those that have got them. Many an M. A. I’ve seen in my time
tacked to the names of the biggest fools I’ve ever known.”
“Still it is not necessary to be a big fool, sir, because you are an M. A.,”
said Philip, always mildly, but with a sigh. “It is a great advantage to a man;
I wish I had it. I know what you will say, better men than I have not had it;
but just because I am not a better man—”
For the first time old Trevor broke into his habitual chuckle.
“Give him some tea, Lucy,” he said. “I suppose you’re one of the
fashionable kind, and have your dinner when I used to have my supper.
That’s not the way to thrive, my lad.”
“What does it matter whether you call it dinner or supper, sir?” said
Philip; “and, pardon me, don’t you do the same?”
“It makes a deal of difference,” said the old man. “Parents like to hear
that you have your tea at six o’clock, and your supper at nine, like
themselves. They don’t like you to give yourself airs, as if you were better
than they are. You’re a clever fellow, Philip Rainy, and you think you are
getting on like a house on fire. But you’re a fool all the same.”

“Papa, I wish you would not be so uncivil,” said Lucy, who had yet
taken no part in their talk.
“I tell you he’s a fool all the same. I kept Kent’s Lane a-going for thirty
years, and I ought to know. I’ve taught the best men in the town. Oxford
fellows, and Cambridge fellows, and all sorts, have come to me for their
mathematics, though I never had a degree; and I eat my dinner at two, and
my tea at six as regular as clock-work all the time. That’s the way to do, if
you mean to keep it up all your life, and lay by a little money, and leave the
place to your son after you. If Jock had been older that’s what I should have
made him do; that is the way to succeed in Kent’s Lane.”
There was a little pause after this, for Philip was a little angry too, and
had not command for the moment of that soft word of which he made so
determined a use; and at the same time he was resolved not to quarrel with
Lucy’s father. He said, after a while, in as easy a tone as he could assume:
“I wish you would let me have Jock. He is old enough for school now,
and whatever you want to do with him I could always begin his education;
of course, you will give him every advantage—”
“I will give him as good as I had myself, Philip, and as you had. Do you
think I am going to take Lucy’s money for that child? Not a penny! He shall
be bred up according to his own rank in life; and by the time he’s a man,
you’ll have grown too grand for the old place, and you can hand it over to
him.”
Philip opened his eyes in spite of himself.
“Then Lucy will be a great lady,” he said, half laughing, “and her brother
a little school-master in Kent’s Lane.”
Lucy, who was standing behind her father at the moment, began to make
the most energetic signs of dissent. She made her mouth into a puckered
circle of inarticulate “No-os,” and shook her head with vehement
contradiction. Just below, and all unconscious of this pantomime, the old
man grinned upon his visitor, delighted with the opportunity at once of
declaring his intentions, and of inflicting a salutary snub.
“That is exactly what I intend,” he said, “you have hit it. Even if it hadn’t
been just, it would have been a fine thing to do as an example; but it is just
as well. Is a fine lady any better than a poor school-master? Not a bit! Each
one in the rank of life that is appointed, and one as good as another; that’s
always been my principle. I wouldn’t have stepped out of my rank of life, or

the habits of my rank of life, not if you had given me thousands for it; not, I
promise you,” cried old Trevor, with a snarl, “for the sake of being asked to
dinner here and there, as some folks are; but being in my own rank of life I
thought myself as good as the king; and that’s why Lucy shall be a great
lady, and her brother a little school-master, whether or not he’s in Kent’s
Lane.”
“But he shall not be so, papa, if I can help it,” Lucy said.
“You won’t be able to help it, my pet,” said her father, relapsing Into a
chuckle, “not you, nor any one else; that’s one thing of which I can make
sure.”
The two young people looked at each other over his old head. They
made no telegraphic signs this time. Philip was for the moment overawed
by the old man’s determination, while Lucy, the most dutiful of daughters,
was mute, in a womanly confidence of somehow or other finding a way to
balk him. She had not in the least realized how life was to be bound and
limited by the imperious will of the father who grudged her nothing. But
Lucy accepted it all quite tranquilly, whatever it might be—except this.
When she went with her cousin to the door, she confided to him the one
exception to her purposes of obedience.
“Papa does not think what he is saying; I never believe him when he
talks like that. I to be rich and Jock poor! He only says it for fun, Philip,
don’t you think?”
“It does not look much like fun,” Philip said, with a rueful shake of his
head.
“Well! but old people—old people are very strange; they think a thing is
a joke that does not seem to us at all like a joke. I will do all that papa
wishes, but not about Jock.”
“And I hope you won’t let him persuade you to think,” said Philip,
lingering with her hand in his to say good-night, “that I am neglecting my
work, or giving myself airs, or—”
“Oh, that is only his fun,” said Lucy, nodding her head to him with a
pleasant smile as he went out into the night.
She was not pretty, he thought, as he walked away, but her face was very
soft and round and pleasant; her blue eyes very steady and peaceful, with a
calmness in them, which, in its way, represented power. Philip, who was,
though so steady, somewhat excitable, and apt to be fretted and worried, felt

that the repose in her was consolatory and soothing. She would be good to
come home to after a man had been baited and bullied in the world. He had
thought her an insignificant little girl, but to-night he was not so sure that
she was insignificant, and Philip did not know anything, at all about the will
and its iron rod.

CHAPTER VII.
THE WHITE HOUSE.
The life of Lucy Trevor, at this period, was divided between two worlds,
very dissimilar in constitution. The odd household over which her father’s
will and pleasure was paramount, though exercised through the medium of
Mrs. Ford, and in which so many out-of-the-way subjects were continually
being discussed, all with some personal reference to the old man and his
experiences and crotchety principles of action, occupied one part of her
time and thoughts: but the rest of her belonged to another sphere—to the
orderly circle of studies and amusements of which the central figure was
Mrs. Stone, and the scene the White House, a large irregular low building
on the edge of the common, which was within sight of Mr. Trevor’s
windows in the Terrace, and had appeared, through all the mist and fog of
those wintery days, with a kind of halo round its whiteness like that of a
rainy and melancholy old moon, tumbled from its high place to the low
levels of a damp and flat country. Mrs. Stone’s was known far and wide as
the best school for a hundred miles round, the best as far as education was
concerned, and also the most exclusive and aristocratic. Lucy Trevor was
the only girl in Farafield who was received as a day-pupil. Efforts had been
made by people of the highest local standing to procure the admission of
other girls of well-known families in the town, but in vain. And why Mrs.
Stone had taken Lucy, who was nobody, who was only old John Trevor’s
daughter, was a mystery to her best friends. She had offended a great many
of the townspeople, but she had flattered the local aristocracy, the county
people, by her exclusiveness; and she offended both by the sudden
relaxation of her rule on behalf of Lucy. The rector’s daughter would have
been a thousand times more eligible, or even Emmy Rushton, whose mother
had knocked at those jealous doors in vain for years together; and why
should she have taken Lucy Trevor, old John’s daughter, who was nobody,
who had not the faintest pretension to gentility? Lady Langton drove in, as
a kind of lofty deputation and representative of the other parents who had
daughters at Mrs. Stone’s school, to remonstrate with her, and procure the

expulsion of the intruder; but Mrs. Stone was equal to the occasion. She did
not hesitate to say to the countess, “Your ladyship is at liberty to remove
Lady Maud whenever you please. I dispense with the three months’ notice.”
It was this speech which established Mrs. Stone’s position far more than
her excellence in professional ways. A woman who dared to look a countess
in the face, and make such a suggestion, was too wonderful a person to be
contemplated save with respect and awe. Lady Langton herself withdrew,
abashed and confounded, protesting that to take Maud a way was the last
idea in her mind. And Mrs. Stone’s empire was thus established. The
incident made a great impression on the county generally; and it nearly
threw into a nervous fever the other mistress, conjointly with Mrs. Stone, of
the White House, her sister Miss Southwood, called, as a matter of course,
Southernwood by the girls, who stood by aghast, and heard her say, “I
dispense with the three months’ notice:” and expected nothing less than that
the sky should fall, and the walls crumble in round them. Miss Southwood
liked to think afterward that it was her own deprecating glances, her look of
horror and dismay, and, above all, the cup of exquisite tea which she offered
Lady Langton as she waited for her carriage, which put everything straight;
but all her civilities would never have established that moral ascendency
which her sister’s uncompromising defiance secured.
Miss Southwood was the elder of the two. She was forty-five or
thereabouts, and she was old-fashioned. Whether it was by calculation, to
make a claim of originality for herself, such as it was, or simply because
she thought that style becoming to her, nobody knew; but she dressed in the
fashions which had been current in her youth, and never changed. She wore
her hair in a knot fastened by a high comb behind, and with little ringlets
drooping on either cheek; and amid the long and sweeping garments of the
present era, wore a full plain skirt which did not touch the ground, and gigot
sleeves. In this dress she went about the house softly and briskly, without
the whistling and rustling of people in long trains. She was a very mild
person in comparison with her high-spirited and despotic sister; but yet was
gifted with a gentle obstinacy, and seldom permitted any argument to
beguile her from her own way. She had, nominally, the same power in the
house as Mrs. Stone, and it was partly her money which was put in peril by
her sister’s audacity; but the elder had always been faithful to the younger,
and though she might grumble, never failed to make common cause with
her, even in her most heroic measures. As for Lucy Trevor, though she

shook her head, she submitted, feeling that to suffer on behalf of an heiress
was a pain from which the worst sting was taken out; for it was not to be
supposed that a girl so rich could allow her school-mistress to come to harm
on her account. Mrs. Stone was far more imposing in appearance. She was
full five years younger, and she was not old-fashioned. She was tall, with a
commanding figure, and her dresses were handsome as herself, made by an
artiste in town, not by the bungling hands of the trade in Farafield, of rich
texture and the most fashionable cut. She was a woman of speculative and
theoretical mind, believing strongly in “influence,” and very anxious to
exercise it when an opportunity occurred. She had her ideas, as Mr. Trevor
had, of what might be made of an heiress; and it seemed to Mrs. Stone that
there was no class in the world upon which “influence” might tell more, or
be more beneficially exercised. Her ideas on this subject laid her open to
various injurious suppositions. Thus, when she took Lady Maud Langton
into her bosom, as it were—moved by a brilliant hope of influence to be
exercised on society itself by means of a very pretty and popular young
woman of fashion—vulgar by-standers accused Mrs. Stone of tuft-hunting,
and of paying special honor to the girl who was the daughter of an earl out
of mere love of a title, an altogether unworthy representation of her real
motive. And her sudden stand on behalf of Lucy took the world by surprise.
They could not fathom her meaning; that she should have defied the
countess, whom up to this time she had been supposed to worship with a
servile adulation, on account of a little bit of a girl of no particular
importance, was incomprehensible. It was known in Farafield that Lucy had
a fortune, but it was not known how great that fortune was, and after much
groping among the motives possible to Mrs. Stone in the circumstances, the
country-town gossips had come to the conclusion that she aspired to a
marriage with old John Trevor, and an appropriation to herself of all his
wealth. This supplied a sufficient reason even for a breach with the
countess. To be asked to Langdale, which was the finest thing that could
happen to her in connection with Lady Maud, was, though gratifying, not to
be compared with the possibility of marrying a rich man in her own person,
and becoming one of the chief ladies of Farafield. This was how it was
accounted for by that chorus of spectators who call themselves society, and
Miss Southwood herself entertained, against her will, the same opinion.
This suggestion seemed to make everything clear.

A few days after that on which Mr. Trevor read to Ford the last
paragraph which he had added to his will, Lucy tapped at the door of Mrs.
Stone’s private parlor with her father’s message. The ladies were seated
together in their private sanctuary, resting from their labors. It was a
seclusion never invaded by the pupils except on account of some important
commission from a parent, or to ask advice, or by order of its sovereigns.
Lucy came in with the little old-fashioned courtesy which Mrs. Stone
insisted upon, and made her request.
“If you would come to tea to-morrow night. Papa is very sorry, but he
bids me say he thinks you know that he can not come to you.”
“How is Mr. Trevor, Lucy?”
Miss Southwood, who was looking at her sister anxiously, thought she
asked this question by way of gaining time. Could he have sent for her in
order to propose to her, the anxious sister thought. What a very curious way
of proceeding! But a rich old man, with one foot in the grave, could not be
expected to act like other men.
“He is—just as he always is; very busy, always writing; but he can not
go out, and if you would be so kind—”
“Oh, yes, I will be so kind,” said Mrs. Stone, with a smile; “it is not the
first time, Lucy. Is he going to complain of you, or to tell me of something
he wants for you?”
“I think,” said Lucy, “it is about the will.”
“Dear me!” Miss Southwood cried. “What can you have to do, Maria,
with Mr. Trevor’s will?”
Mrs. Stone smiled again.
“He goes on with it, then, as much as ever?” she said.
“Oh, yes, almost more than ever; it gives him a great deal of
occupation,” said Lucy, with a grave face. There were some things that she
had it in her heart to say on this subject; she looked at the school-mistress
anxiously, not knowing if she might trust her, and then was silent, fearing to
open her mind to any one on the subject of Jock.
“Poor child! he is putting a great burden upon you at your age; the
management of a fortune is too much for a girl; but, Lucy, you will always
know where to find advice and help so far as I can give it. You must never
hesitate to come to me, whatever happens,” Mrs. Stone said.

Welcome to our website – the ideal destination for book lovers and
knowledge seekers. With a mission to inspire endlessly, we offer a
vast collection of books, ranging from classic literary works to
specialized publications, self-development books, and children's
literature. Each book is a new journey of discovery, expanding
knowledge and enriching the soul of the reade
Our website is not just a platform for buying books, but a bridge
connecting readers to the timeless values of culture and wisdom. With
an elegant, user-friendly interface and an intelligent search system,
we are committed to providing a quick and convenient shopping
experience. Additionally, our special promotions and home delivery
services ensure that you save time and fully enjoy the joy of reading.
Let us accompany you on the journey of exploring knowledge and
personal growth!
ebookfinal.com

Asymptotic Methods in Resonance Analytical Dynamics 1st Edition Eugeniu Grebenikov

More Related Content

Similar to Asymptotic Methods in Resonance Analytical Dynamics 1st Edition Eugeniu Grebenikov (20)

Recently uploaded (20)

Asymptotic Methods in Resonance Analytical Dynamics 1st Edition Eugeniu Grebenikov