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Hydraulic Conductivity Issues Determination and
Applications 2nd Edition Lakshmanan Elango Digital
Instant Download
Author(s): Lakshmanan Elango
ISBN(s): 9789533072883, 9533072881
Edition: 2nd
File Details: PDF, 43.17 MB
Year: 2016
Language: english

HYDRAULIC CONDUCTIVITY
AND APPLICATIONS
ISSUES, DETERMINATION
Edited by Lakshmanan Elango
Second Edition

HYDRAULIC CONDUCTIVITY
ISSUES, DETERMINATION
AND APPLICATIONS

Hydraulic Conductivity – Issues, Determination and Applications
Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia
Copyright © 2011 InTech
All chapters are Open Access distributed under the Creative Commons Attribution 3.0
license, which permits to copy, distribute, transmit, and adapt the work in any medium,
so long as the original work is properly cited. After this work has been published by
InTech, authors have the right to republish it, in whole or part, in any publication of
which they are the author, and to make other personal use of the work. Any republication,
referencing or personal use of the work must explicitly identify the original source.
As for readers, this license allows users to download, copy and build upon published
chapters even for commercial purposes, as long as the author and publisher are properly
credited, which ensures maximum dissemination and a wider impact of our publications.
Notice
Statements and opinions expressed in the chapters are these of the individual contributors
and not necessarily those of the editors or publisher. No responsibility is accepted for the
accuracy of information contained in the published chapters. The publisher assumes no
responsibility for any damage or injury to persons or property arising out of the use of any
materials, instructions, methods or ideas contained in the book.
Publishing Process Manager Mirna Cvijic
Technical Editor Teodora Smiljanic
Cover Designer Jan Hyrat
Image Copyright Arvind Balaraman, 2011. Used under license from Shutterstock.com
First published October, 2011
Printed in Croatia
A free online edition of this book is available at www.intechopen.com
Additional hard copies can be obtained from orders@intechweb.org
Hydraulic Conductivity – Issues, Determination and Applications,
p. cm.
ISBN 978-953-307-288-3

Contents
Preface IX
Part 1 Hydraulic Conductivity and Its Importance 1
Chapter 1 Role of Hydraulic Conductivity on Surface
and Groundwater Interaction in Wetlands 3
Cevza Melek Kazezyılmaz-Alhan
Chapter 2 Dynamics of Hydraulic Properties of Puddled Soils 29
K. B. Singh
Chapter 3 Variation in Hydraulic Conductivity by the Mobility of
Heavy Metals in a Compacted Residual Soil 49
Rejane Nascentes, Izabel Christina Duarte de Azevedo
and Ernani Lopes Possato
Chapter 4 Evaluation of Cover Systems for the
Remediation of Mineral Wastes 73
Francis D. Udoh
Part 2 Hydraulic Conductivity and Plant Systems 83
Chapter 5 Plant and Soil as Hydraulic Systems 85
Mirela Tulik and Katarzyna Marciszewska
Chapter 6 Plant Hydraulic Conductivity:
The Aquaporins Contribution 103
María del Carmen Martínez-Ballesta,
María del Carmen Rodríguez-Hernández,
Carlos Alcaraz-López, César Mota-Cadenas,
Beatriz Muries and Micaela Carvajal
Chapter 7 Impacts of Wildfire Severity on Hydraulic Conductivity
in Forest, Woodland, and Grassland Soils 123
Daniel G. Neary

VI Contents
Part 3 Determination by Mathematical
and Laboratory Methods 143
Chapter 8 Estimating Hydraulic Conductivity
Using Pedotransfer Functions 145
Ali Rasoulzadeh
Chapter 9 Determination of Hydraulic Conductivity Based on
(Soil) - Moisture Content of Fine Grained Soils 165
Rainer Schuhmann, Franz Königer, Katja Emmerich,
Eduard Stefanescu and Markus Stacheder
Chapter 10 Determining Hydraulic Conductivity from Soil
Characteristics with Applications for Modelling
Stream Discharge in Forest Catchments 189
Marie-France Jutras and Paul A. Arp
Chapter 11 Analytical and Numerical Solutions of Richards' Equation
with Discussions on Relative Hydraulic Conductivity 203
Fred T. Tracy
Part 4 Determination by Field Techniques 223
Chapter 12 Instrumentation for Measurement of Laboratory and
In-Situ Soil Hydraulic Conductivity Properties 225
Jose Antonio Gutierrez Gnecchi, Alberto Gómez-Tagle (Jr),
Philippe Lobit, Adriana Téllez Anguiano, Arturo Méndez Patiño,
Gerardo Marx Chávez Campos and Fernando Landeros Paramo
Chapter 13 Contribution of Tracers for Understanding
the Hydrodynamics of Karstic Aquifers
Crossed by Allogenic Rivers, Spain 247
Rafael Segovia Rosales, Eugenio Sanz Pérez
and Ignacio Menéndez Pidal
Chapter 14 Estimating Hydraulic Conductivity of Highly
Disturbed Clastic Rocks in Taiwan 267
Cheng-Yu Ku and Shih-Meng Hsu
Chapter 15 Field Measurement of Hydraulic Conductivity of Rocks 285
Maria Clementina Caputo and Lorenzo De Carlo
Chapter 16 Electrokinetic Techniques for the Determination
of Hydraulic Conductivity 307
Laurence Jouniaux
Chapter 17 Contribution of Seismic and Acoustic
Methods to Reservoir Model Building 329
Jean Luc Mari and Frederick Delay

Contents VII
Part 5 Modelling and Hydraulic Conductivity 355
Chapter 18 Effects of Model Layer Simplification Using
Composite Hydraulic Properties 357
Nicasio Sepúlveda and Eve L. Kuniansky
Chapter 19 The Role of Hydraulic Conductivity in Modeling
the Movement of Water and Solutes in Soil
Under Drip Irrigation 377
René Chipana Rivera
Chapter 20 Simulation of Water and Contaminant Transport
Through Vadose Zone - Redistribution System 395
Thidarat Bunsri, Muttucumaru Sivakumar and Dharmappa Hagare
Chapter 21 Measurement and Modeling of Unsaturated
Hydraulic Conductivity 419
Kim S. Perkins

Preface
Hydraulic conductivity is the most important property of geological formations as the
flow of fluids and movement of solutes depend on it. Among fluids, water and
contaminant migration beneath, the ground surface have become critical for water
resource development, agriculture, site restoration and waste disposal strategies.
Furthermore, planning of regional water supply schemes based on groundwater
pumping and numerical groundwater flow modelling depend on hydraulic
conductivity for accurate prediction of future groundwater availability, well
performance, predicting groundwater decline, effect of rainfall variability etc.,.
Although valuable, hydraulic conductivity measurements are expensive to run and
labor-intensive to compile and evaluate for larger spatial coverage. There are several
books on broad aspects of hydrogeology, groundwater hydrology and geohydrology,
which do not discuss in detail on the intrigues of hydraulic conductivity elaborately.
However, this book on Hydraulic Conductivity presents comprehensive reviews of
new measurements and numerical techniques for estimating hydraulic conductivity.
This is achieved by the chapters written by various experts in this field into a number
of clustered themes covering different aspects of hydraulic conductivity.
The sections in the book are: Hydraulic Conductivity and Its Importance, Hydraulic
Conductivity and Plant Systems, Determination by mathematical and Laboratory
Methods, Determination by Field Techniques and Modelling and Hydraulic
Conductivity.
Each of these sections of the book includes chapters highlighting the salient aspects
and explain the facts with the help of some case studies. Thus this book has a good
mix of chapters dealing with various and vital aspects of hydraulic conductivity from
various authors of different countries.
I am sure that these thought provoking chapters will benefit young researchers and
lead to better understanding of concepts, measurement techniques and applications of
hydraulic conductivity. I thank the authors of all the chapters from all over the world
for their cooperation and support during the editorial process. The efforts of Intech-
Open access publisher in bringing out this book needs a special appreciation as the
content of this book is available online and accessible to diverse researchers across the
world. This will benefit the young researchers and students to a large extent. Special

X Preface
thanks are due to Ms. Mirna Cvijic, Publishing Process Manager of InTech - Open
Access Publisher, for her continued assistance which helped in the publication of this
book. I thank Ms. S. Parimala Renganayaki and Ms. L. Kalpana, Research Fellows of
Anna University, Chennai, India, for assisting me in reviewing some chapters of this
book. I also thank Ms. K. Brindha, Research Fellow, Anna University for her support
in reviewing and editing this book. I hope that you will find this book interesting and
perhaps even adopt some of these methods for use in your own research activities.
Lakshmanan Elango
Professor
Department of Geology
Anna University
Chennai (Madras)
India

Part 1
Hydraulic Conductivity and Its Importance

1
Role of Hydraulic Conductivity on Surface
and Groundwater Interaction in Wetlands
Cevza Melek Kazezyılmaz-Alhan
Istanbul University, Civil Engineering Department
Turkey
1. Introduction
There has been a growing interest in understanding the mechanisms involved in surface and
groundwater interactions since these interactions play a crucial role in the behavior of
hydrology and contaminant transport in streams, lakes, wetlands, and groundwater
(Hakenkamp et al, 1993; Winter, 1995; Packman & Bencala, 2000; Bencala, 2000; Medina et al,
2002). Wetlands are an important part of water resources since they control peak flow of
surface runoff and clean polluted water as downstream receiving water bodies and
therefore have been recognized as one of the best management practices (Mitsch &
Gosselink, 2000; Moore et al., 2002; Mitchell et al., 2002). Wetlands are located in transitional
zones between uplands and downstream flooded systems. Surface and groundwater
interactions, which occur in these critical zones, result in a change in surface and
groundwater depth. Moreover, pollutants in either surface water or groundwater are mixed
and the quality of both sources is affected by each other. Therefore, it is important to
understand the role of surface and groundwater interactions on wetland sites and
incorporate them into the wetland models in order to obtain accurate solutions.
The definition of a wetland is difficult since there is no definite boundary for wetlands over
the landscape and wetland characteristics change. Different definitions have resulted from
government agencies that take either legal or ecological criteria as a basis for wetlands
within their jurisdiction. In Section 404 of the Clean Water Act of Environmental Protection
Agency (EPA), wetlands are defined as “areas that are inundated or saturated by surface or
groundwater at a frequency and duration sufficient to support a prevalence of vegetation
typically adapted for life in saturated soil conditions”. From a hydrologic point of view, the
change of surface water level or subsurface water table level through time is important.
Usually, areas where the depth of standing water is less than 2 m are considered as
wetlands. The amount of water present in wetlands is important to support water supply
and water quality. It also affects the type of animals and plants living in these areas.
Wetlands are classified according to their ecological and hydrological similarities (Mitsch &
Gosselink, 2000).
The type of interaction between groundwater and wetlands depends on the
geomorphological location of the wetland. Wetlands gain water if they are located on
seepage faces where there is an abrupt change in landscape slope (Figure 1A), or if there is a
stream near the wetland location (Figure 1B). Water level in wetlands is changed usually by
direct precipitation or runoff. Especially in riverine wetlands, water level changes

4
periodically and very often, since its source comes from rivers. Due to this fact, this type of
wetland has more complex interactions which affect its hydraulic/hydrologic
characteristics. The water and chemical balances determine the principal characteristics and
functions of wetlands. Wetlands are very sensitive to changing hydrological conditions.
Since interactions between wetland and groundwater affect the water and chemical
balances, it is important to include these interactions into the wetland models.
Fig. 1. Wetland and groundwater interactions: (A) Inflow from seepage faces and break in
slope of water table. (B) Inflow to streams. (modified after Winter et al., 1998)
There have been previous studies reported in the literature that investigate various aspects
of surface and groundwater interactions in wetlands. The importance of modeling
interactions between groundwater and wetlands and their effect on wetland functions are
discussed in detail by Winter et al. (1998), Winter (1999), and Price & Wadington (2000).
Experiments are conducted in order to observe the effect of surface and groundwater
interactions on wetland hydrology and contaminant transport at different wetland sites
(Winter & Rosenberry, 1995; Devito & Hill, 1997; Choi & Harvey, 2000; McHale et al 2004).
In addition to these studies, many researchers worked on developing numerical models of
wetland hydrology and wetland water quality incorporating surface and groundwater
interactions (Restrepo et al., 1998; Krasnostein & Oldham, 2004; Keefe et al., 2004; Crowe et
al., 2004; Kazezyılmaz-Alhan et al., 2007).
Examples of recent studies include Harvey et al (2006) who modeled interactions between
surface water and groundwater in the wetland area located in central Everglades, Florida,
USA in order to quantify recharge and discharge in the basin’s vast interior areas.
Kazezyılmaz-Alhan & Medina (2008) discussed the effect of surface and groundwater
interactions on wetland sites with different characteristics. He et al (2008) developed a
coupled finite volume model by using depth averaged two dimensional surface flow and
three dimensional subsurface flow for wetlands incorporating surface-subsurface
Water¯Resources Investigations, Book 6, Chap A1, U.S. Geological Survey.
McHale, M.R.; Cirmo, C.P.; Mitchell, M.J. & McDonnell, J.J. (2004). Wetland Nitrogen
Dynamics in an Adirondack Forested Watershed. Hydrological Processerical model of
subsurface vertical flow constructed wetlands called as FITOVERT. Min & Wise (2010)
developed a two-dimensional hydrodynamic and solute transport modeling of a large-
scaled, subtropical, free water surface constructed wetland in the Everglades of Florida,
USA.
In this chapter, the role of hydraulic conductivity on surface and groundwater interactions
in wetlands is discussed. Both wetland hydrology and wetland water quality are
Water Table
Wetland
Break in slope
Land Profile
A
Wetland
River
B
Seepage face

Role of Hydraulic Conductivity on Surface and Groundwater Interaction in Wetlands 5
investigated and particularly, the behavior of surface water and groundwater depths and
the flux between surface water and groundwater are observed. For this purpose, several
models are employed which incorporate surface and groundwater interactions and handle
the interactions from different points of view. Among these models are WETland Solute
TrANsport Dynamics (WETSAND), Visual MODular Finite-Difference FLOW model
(MODFLOW) and EPA Storm Water Management Model (SWMM). WETSAND is a wetland
model which has both surface flow and solute transport components, and accounts for
upstream contributions from urbanized areas. Visual MODFLOW is a three-dimensional
groundwater flow and contaminant transport simulation model. EPA SWMM is a dynamic
rainfall-runoff model and calculates surface runoff, channel flow, groundwater flow and
depth in aquifer underlying each subcatchment, and water quality. Applications are
presented by simulating a conceptual wetland-aquifer system with Visual MODFLOW, the
Duke University restored wetland site in the Sandy Creek watershed of Durham, North
Carolina in USA with WETSAND and Büyükçekmece wetland site located around
Büyükçekmece Lake in Istanbul, Turkey with EPA SWMM.
2. Numerical modelling
This section discusses three numerical models on surface water and groundwater hydrology
and contaminant transport. The common point of these models is incorporating surface and
groundwater interactions but each model approaches the mechanism and the consequence
of these interactions from a different point of view.
2.1 WETland Solute TrANsport Dynamics (WETSAND)
WETland Solute TrANsport Dynamics (WETSAND) is a general comprehensive dynamic
wetland model developed by Kazezyılmaz-Alhan et al (2007) which has both water quantity
and water quality components, and incorporates the effects of surface and groundwater
interactions. While the water quantity component computes water level and velocity
distribution as a function of time and space, the water quality component computes
Phosphorus and Nitrogen compounds also as a function of time and space. WETSAND also
takes into account the effect of flow generated from upstream areas. Figure 2 shows the
graphical representation of the conceptual wetland model. During a storm event, overland
flow develops on urbanized areas and flows into the wetland area and streams located
downstream of the watershed. Overland flow washes off the pollutants which build up on
the surface during dry days and these pollutants also reach the wetland site with the
overland flow. Besides the overland flow, rainfall and groundwater discharge also
contribute to the surface water of the wetland site. Evapotranspiration, infiltration, and
groundwater recharge are the water sink terms of the wetland site.
2.1.1 Wetland hydrology
The surface water depth, velocity, and flow through the wetland area are calculated by the
diffusion wave equation that applies to the milder slopes (% 0.1 to % 0.01) which is the case
in wetlands. The one-dimensional diffusion wave equation is given as follows:
2
1 2
y y y
c K q
t x x
∂ ∂ ∂
+ = +
∂ ∂ ∂
(1a)

6
Fig. 2. Schematic of the WETSAND model (Kazezyılmaz-Alhan et al, 2007).
inf
r et drch l
q q q q q q
= − − + + c mV
= 1
0
2
Vy
K
S
= (1b)
where y is the surface water depth (L), t is time (T), x is the distance (L), c is the wave celerity
(L/T), K1 is the hydraulic diffusivity (L2/T), q is the water source/sink term (L/T), V is the water
velocity (L/T), S0 is the bottom slope (L/L) and m is given according to the flow rate-friction
slope relationship (Ponce, 1989). While rainfall (qr), groundwater discharge (qdrch), and lateral
inflow (ql) occupy as water source terms; infiltration (qinf), evapotranspiration (qet), and
groundwater recharge (qdrch) occupy as water sink terms in the term q . Infiltration is calculated
by the modified version of the Green-Ampt method during unsteady rainfall (Chu, 1978) and
evapotranspiration is calculated by the Thornthwaite (1948) method. The groundwater
recharge and groundwater discharge terms represent surface and groundwater interaction at
the wetland site and are calculated by using the Darcy’s Law as follows:
0 groundwater recharge
0 groundwater discharge
drch x
H
q K
x
<

∂
= − 
>
∂ 
(2)
where H is total head (L), and Kx is the horizontal hydraulic conductivity (L/T). The
exchange between surface water and groundwater is calculated in the lateral direction at the
banks of the wetland. Overland flow generated over both upland and wetland sites becomes
the lateral inflow of the stream. The flow on the wetland site is calculated by the power law
for velocity in terms of depth and the friction slope (Kadlec, 1990). This law employs both
the effect of a vertical vegetation stem density gradient and a bottom-elevation distribution.
The flow rate on a wetland site is given by (Kadlec and Knight, 1996):

3
d 0
3
s 0
dense vegetation
sparse vegetation
K Wy S
Q
K Wy S


= 


(3)
where Q is the flow rate in (m3/day), W is the wetland width (L), and Kd and Ks are the
coefficients which reflect the vegetation density with Kd=1×107 m-1day-1 and Ks=5×107
m-1day-1. In diffusion wave theory, the term S0 is replaced by 0
( / )
S y x
− ∂ ∂ . Therefore, the
surface water velocity V on a wetland with a cross-sectional area A=Wy is calculated using
both the continuity Q=VA and Equation (3) as follows:
( )
( )
2
0
2
0
/
/
d
s
K y S y x
V
K y S y x
 − ∂ ∂

= 
− ∂ ∂


(4)
The upper boundary condition of the stream flowing through the wetland site is defined as
the upstream surface runoff flowing from urbanized areas and the flow rate in the stream is
calculated by using the diffusion wave equation as follows:
2
1 2
Q Q Q
c K
t x x
∂ ∂ ∂
+ =
∂ ∂ ∂
c mV
= 1
0
2
Q
K
BS
= (5)
where B is the channel width (L) and c and K1 are the wave celerity (L/T) and the hydraulic
diffusivity (L2/T) in stream, respectively.
2.1.2 Wetland water quality
The water quality component of the WETSAND model calculates the concentration
distribution of both total Nitrogen and total Phosphorus through the wetland and along the
stream. WETSAND has also the capability to calculate each compound of nitrogen, namely,
organic nitrogen, ammonium nitrogen, and nitrate nitrogen, individually. For each
constituent, one dimensional advection-dispersion-reaction equation is solved. The
equations for nitrogen compounds are coupled through the first order loss rate constants
KON and KAN, which represent ammonification of organic nitrogen into ammonium and
nitrification of ammonium into nitrate, respectively. The equations also take into account the
vegetation effect of a wetland site represented by plant uptake/release terms as sources and
sinks. Finally, the influence of surface and groundwater interactions on contaminant
transport is incorporated via the mass flux terms that represent the incoming/outgoing
mass due to groundwater recharge/discharge. The surface water velocity in the wetland
calculated by the hydrology component of WETSAND is used in the advection term of
concentration equations. The concentration formulations of WETSAND are given as follows:
Total Phosphorus (TP):
( ) ( )
1 gwd gw
L
Lin
TP TP TP
x x TP TP TP TP TP
TP
x x x
q
q
C C C
V A D C C C C K C
t x A x x A A
∂ ∂ ∂ ∂
 
= − + + − + − −
 
∂ ∂ ∂ ∂
 
(6)
Total Nitrogen (TN):
( ) ( )
1 gwd gw
L
Lin
TN TN TN
x x TN TN TN TN TN
TN
x x x
q
q
C C C
V A D C C C C K C
t x A x x A A
∂ ∂ ∂
∂  
= − + + − + − −
 
∂ ∂ ∂ ∂
 
(7)

8
Organic Nitrogen (ON):
( )
( )
1 L
Lin
ON ON ON
x x ON ON
x x
gwd gw
ON ON ON RON
ON
x
q
C C C
V A D C C
t x A x x A
q
C C K C J
A
∂ ∂ ∂
∂  
= − + + −
 
∂ ∂ ∂ ∂
 
+ − − +
(8)
Ammonium Nitrogen (AN):
( )
( )
1 L
Lin
AN AN AN
x x AN AN
x x
gwd gw
AN ON ON AN AN UAN
AN
x
q
C C C
V A D C C
t x A x x A
q
C C K C K C J
A
∂ ∂ ∂
∂  
= − + + −
 
∂ ∂ ∂ ∂
 
+ − + − −
(9)
Nitrate Nitrogen (NN):
( )
( )
1 L
Lin
NN NN NN
x x NN NN
x x
gwd gw
NN AN AN NN NN UNN
NN
x
q
C C C
V A D C C
t x A x x A
q
C C K C K C J
A
ψ
∂ ∂ ∂
∂  
= − + + −
 
∂ ∂ ∂ ∂
 
+ − + − −
(10)
where C is the concentration (M/L3), CL is the lateral concentration (M/L3), Cgw is the
concentration in groundwater (M/L3), K is the first order loss rate constant (1/T), Ax is the
cross-sectional area in x-direction (L2), Dx is the dispersion coefficient (L2/T), qLin is the lateral
inflow (L2/T), qgwd is the groundwater discharge (L2/T), JRON is the release flux of organic
nitrogen from biomass (M/T), JUAN is the uptake flux of ammonium nitrogen absorbed by
biomass (M/T), JUNN is the uptake flux of nitrate nitrogen absorbed by biomass (M/T), ψ is
the fraction of ammonium that is nitrified, and TP, TN, ON, AN, NN are the subscripts
denoting total phosphorus, total nitrogen, organic nitrogen, ammonium nitrogen, and
nitrate nitrogen, respectively.
2.2 Visual MODular Finite-Difference FLOW model (MODFLOW)
Visual MODFLOW is a three-dimensional groundwater flow and contaminant transport
model that integrates several packages such as MODFLOW-2000, SEAWAT, MODPATH,
MT3DMS, MT3D99, RT3D, VMOD 3D-Explorer, WinPEST, Stream Routing, Zone Budget,
MGO, SAMG, and PHT3D.
MODFLOW (Modular Three-Dimensional Finite-Difference Ground-Water Flow Model)
package solves the three-dimensional ground-water flow equation for a porous medium by
using a finite-difference method. MODFLOW is first developed by United States Geological
Survey (USGS) (McDonald & Harbaugh, 1988), then continuously improved and enhanced
(Harbaugh & McDonald, 1996a; Harbaugh & McDonald, 1996b; Harbaugh et al., 2000;
Harbaugh, 2005) and finally integrated into Visual MODFLOW. The three-dimensional
movement of groundwater of constant density through porous earth material may be
described by the following partial-differential equation (McDonald & Harbaugh, 1988):
xx yy zz s
h h h h
K K K W S
x x y y z z t
 
∂ ∂ ∂ ∂ ∂ ∂ ∂
 
   
+ + + =
     
∂ ∂ ∂ ∂ ∂ ∂ ∂
   
 
 
(11)

where Kxx, Kyy, and Kzz are the hydraulic conductivities along the x, y, and z coordinate axes,
respectively and are assumed to be parallel to the major axes of hydraulic conductivity (L/T), h
is the potentiometric head (L), W is a volumetric flux per unit volume and represents sources
and/or sinks of water (1/T), Ss is the specific storage of the porous material (1/L), and t is time (T).
MODFLOW takes into account the surface and groundwater interactions in wetlands
through the RIVER (RIV) boundary condition via a seepage layer separating the surface
water body from the groundwater system as shown in Figure 3. River boundary condition
simulates the influence of a surface water body such as rivers, streams, lakes, and wetlands
on the groundwater flow. The term, which represents the seepage to or from the surface, is
added to the groundwater flow equation in this boundary condition. The flow between the
surface water and the groundwater system is given by the following equation:
( )
riv
riv
KLW
Q
M H h
=
−
(12)
where Qriv is the flow between the surface water and the aquifer, taken as positive if it is
directed into the aquifer, Hriv is the head in the surface water, L and W are the X-Y
dimensions of the River boundary grid cells, M is the thickness of the bed of the surface
water body, K is the vertical hydraulic conductivity of the bed material of the surface water
body, and h is the groundwater head in the cell underlying the River boundary. The term
Criv=KLW/M may be defined as the hydraulic conductance of the surface water-aquifer
interconnection which represents the resistance to flow between the surface water body and
the groundwater caused by the seepage layer.
Fig. 3. Schematic of River boundary in MODFLOW (modified after Visual MODFLOW, 2009)
MT3DMS (Modular 3-Dimensional Transport Model, Multi-Species) package solves the
three-dimensional contaminant transport in groundwater. MT3D is first developed by
Zheng (1990) at S. S. Papadopulos & Associates, Inc.; subsequently documented for the
Robert S. Kerr Environmental Research Laboratory of the U.S. EPA, then continuously
W
M Seepage
layer
Impermeable
Walls
Qriv
Qriv
L
Hriv
h

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The Age of Gold — 1496- 1497 3^9 than usual, languidly
answered, from force of habit : ''Ah, madam, you can easily conceive
to what condition I am reduced. My mind is occupied but with one
subject, how soonest I may be laid to rest beside my dove. " ''Nay,
nay. Your Excellency must not speak so ! " said Cecilia, with
deprecating hands. * ' Think if Madonna Beatrice could hear you! All
sorrow comes from God, and must be accepted even with
thankfulness." "You speak well," replied II Moro, "I would not
murmur. Nay, then, God forbid! Blessed are they that mourn, for
they shall be comforted. " And he raised his eyes to heaven,
pressing closely the hands of the two ladies. "May the Lord reward
you, my dear ones, that you have not abandoned the poor widowed
one!" He wiped his eyes, and then drew two papers from the pocket,
of his mourning attire. One was a deed of gift by which he gave the
rich lands of the Villa Sforzesca to the Monastery delle Grazie. "But,"
said the Countess, astonished, "I had thought Your Highness adored
this villa." "My love for terrestrial things is dead. And, madam, what
need has one man with lands so large? Cecilia laid her rosy fingers
on his lips with sympathetic reproach. Then she asked curiously :

330 The Forerunner **And this other paper, what is it?" At
this his face cleared, and the old, gay, somewhat cunning smile
appeared on his lips. He read the second document aloud, also a
deed of gift, with recital of the lands, woods, hamlets, himting
rights, and other advantages which he, Ludovico, Duke of Milan, was
conferring on Madonna Lucrezia Crivelli and his natural son
Giampaolo. With the rest was included the villa of Cusnago,
Beatrice's favourite country house, renowned for its fisheries. The
last words of the docimient Ludovico read in trembling tones: "In the
wondrous and rare bonds of great love, this lady has showed unto
us entire devotion and displayed such loftiness of sentiment that
often in our intercourse with her we have experienced an entrancing
and exceptional delight, added to great Hghtening of our cares. "
Cecilia clapped her hands and fell on her friend's neck, her eyes wet
with maternal tenderness. "Did I not tell you, my sweet sister, that
he had a heart of gold? Now my little grandson, Giampaolo, has the
richest inheritance in Milan. " "What date have we?" asked II Moro. "
'T is the 28th of December," replied Cecilia. "The 28th!" he echoed
pensively. It was the day, the hour, when a year ago Beatrice had
surprised her husband with his mistress. The room was unchanged :
the same winter wind howled in the chimney, the b^ght fire burned

The Age of Gold — 1496-1497 331 on the hearth, and
above it danced the chain of. naked cupids or cherubs. On the round
table with the green covering stood the same crystal goblet of
Balnea aponitana; the same mandoline, the same sheets of music
littered the floor. The doors opened into the bedroom, and there was
the wardrobe in which he had taken refuge. What would he not give,
so he thought, if he might at this moment hear the rap of the
knocker on the great door, if the frightened maid should run in with
the cry, "Madonna Beatrice!" Yes, he would gladly once again
tremble in the wardrobe like a caught thief, hearing in the. distance
the indignant voice of the lady of his love. Alas! it could not be, that
time had gone by for ever ! His head sank and tears filled his
e^^es, '*0h, Santo IddioT* said Cecilia, turning to. her friend, "he
weeps anew. Rouse yourself! Coax, comfort him! Console him! How
can you. be so cold?" And gently she pushed her rival into the
Duke's arms. Lucrezia had long felt sickened by this unnatural
friendship. She would have liked to get. up and go away;
nevertheless she took the Duke's, hand. He smiled at her through
his tears and laid it upon his heart. Cecilia took the mandoline, and,
assuming the pose in which twelve years ago Leonardo had painted
her, sang one of Petrarch's lyrics for Laura:

332 The Forerunner "Levommi il mio pensiero in parte ov'
era Quella ch' io cerco e non ritrovo in terra." The Duke, much
moved, wiped his eyes, and, stretching out his hands as to a
dissolving vision, he repeated the last line: "E compie' mia giornata
innanzi sera." "Ah, yes, my dove, thou didst indeed finish thy day
before the evening! . . . Ladies, sometimes it seems to me as if she
smiled upon us three from heaven. Ah, Bice, Bice, mia adorata!'' He
drew Lucrezia to him, and presently Cecilia rose and left them
together. The ''Evening Glow" was not jealous of the "Dawn"; from
long experience she knew that soon again her turn would come. Her
mandoline sounded from the next room. And above the merry
firelight, the naked cupids of Caradosso's moulding prolonged their

Beatrice d'Este (Leonardo da Vinci, Milan). Photo by
Anderson.

BOOK IX THE SIMILITUDES — I498-I499 ^/ sensi sono
terrestri, la ragione sta fuor di qiielli, guando contempla.'' —
Leonardo da Vinci. (The Senses belong to earth: Reason, when she
contemplates, stands outside them.) " Ovpav6s &VU) ovpavSs
Kdru).^^ (Heaven above — heaven below.) Tabula Smaragdina.
*'QEE here! On the map of the Indian Ocean, O westward of the
island of Taprobane, we find a note — 'The Sirens: prodigies of the
sea.' Christopher Columbus told me that having come there and
found no sirens, he was greatly astonished. But you smile. Why?"
"Oh, nothing! Go on, Guido; I am listening. ** **I know very well,
Messer Leonardo, that you don't believe in sirens! Well, and what
would you say of the skiapodes, who use their feet as parasols; or
the pygmies, whose ears are so large that they make one a bolster,
the other a blanket ; or of the tree which bears eggs for its fruit,
from which come yellow downy chickens, so fishy-fla33.^

334 The Forerunner voured they may be eaten on fast-days
; or of that marine monster upon which certain mariners, beHeving it
an island, disembarked and Hghted a fire for the cooking of their
supper? This last is a very true tale, related by an aged mariner from
Lisbon, a man in nowise given to wine, and who swore and swore
again by the blood and the body of Christ, that he spoke what was
true. " This conversation took place six years after the discovery of
the New World, on Palm Sunday, at Florence, in a room above the
storehouse of Messer Pompeo Berardi, a shipbuilder, who had a
branch establishment at Seville, and superintended there the
building of ships for sailing to the New Continent. Messer Guido
Berardi, Pompeo's nephew, was an impassioned seaman; he had
prepared to take part in Vasco di Gama's expedition, when he was
stricken by the terrible disease called French by the Italians, and
Italian by the French; German by the Poles, Polish by the
Muscovites, Christian by the Turks. In vain he had consulted all
physicians, in vain he had made waxen offerings at every wonder-
working shrine; paralysed, condemned to eternal immobility, he
preserved an extraordinary activity of mind, and by listening to
sailors' stories, and sitting up all night over books and maps, he
sailed the oceans of imagination, and made discoveries by proxy. His
room, which sextants, compasses, astrolabes, made like a ship's
cabin, opened on to a balcony, a Florentine loggia. The clear skv

The Similitudes — 1 498- 1 499 335 of a spring evening
was already darkening; the flame of the lamp flickered in the wind;
from the store-house below were wafted odours of spices —
cinnamon, ginger, nutmeg, and cloves. "And so, Messer Leonardo,"
he concluded,, rubbing his unhappy legs under their coverlet,, " 't is
not meaningless the saying that faith removes mountains. Had
Columbus doubted like you, he had accomplished naught. Confess,.
I pray you, is it not worth grey hair at thirty to have found the
Earthly Paradise?" ' ' Paradise ? ' ' said Leonardo ; ' ' nay, how is that
? ' * "What? Have you not heard? Know you not that by observations
on the Pole Star, taken by Messer Cristoforo near the Azores, he has
proved that the world has not the shape of an apple, as is commonly
supposed. 'T is a pear, with a protuberance like the nipple of a
woman's breast. On this nipple, a mountain so high that its summit
leans against the lunar sphere, lies the Earthly Paradise." " But, caro
Guido, science . . ." "Science!" cried the other contemptuously.
"Know you, Messere, what Columbus says of science? I will quote
you his words in his Libra de las Profecias. He says: 'Not
mathematics^ nor the charts of geographers, nor the arguments of
reason, helped me to my deed, but solely the prophecy of Isaiah
touching a new heaven and a new earth.' " Here Guido fell silent, for
at this hour began

33^ The Forerunner the nightly racking of his joints. He
was carried to his bed; and Leonardo, left alone, entertained himself
verifying those observations upon the Pole Star which had led to so
singular a delusion; and, in truth, he found errors so gross that he
could not believe his eyes. ''What ignorance!" he said to himself
more than once; "it would seem he has discovered the New World
by chance, groping at random. He himself sees no more than a blind
man, nor doth he know what it is he has discovered; he thinks it is
China or Solomon's Ophir; or, by my faith, the Earthly Paradise!
Death will overtake him before he has learned the truth." He read
the first letter, dated April 29th, 1493, in which Columbus informed
Europe of his discovery: ''The letter of Christopher Columbus, to
whom our age oweth much touching the newlyfound islands beyond
the Ganges. " Leonardo spent the whole night over the calculations
and the maps. At times he went out upon the loggia and looked at
the stars, thinking of this finder of the new heaven and the new
earth — that strange dreamer with the mind, and the heart, of a
child. Involuntarily he compared this man's destiny with his own.
"How little he knew; how much he did! And I, with all my
knowledge, am helpless as the paralysed Berardi. I, too, have aimed
at unknown worlds, but have made no step towards them. Faith, say
they, faith ! But is not perfect

The Similitudes— 1 498- 1 499 337 faith the same as
perfect knowledge? Cannot these eyes of mine see farther than
those eyes of Columbus, the bHnd prophet? Or is it the caprice of
Fate that men must see to know; must be bHnd to act?" II Leonardo
did not notice that the night was passing. The stars went out one by
one; rosy Hght overspread the sky and shone upon the tiled roofs
and the wooden cross-beams of the old brick houses ; the street
became gay with the hum of the people going forth to their daily
toil. Presently a knock came to the door, and Giovanni Boltraffio
entered, to remind his master that this was the day for the "trial by
fire. " ''What trial?" asked Leonardo. *'Fra Domenico on behalf of Fra
Girolamo, and Fra Giuliano Rondinelli on behalf of his enemies, will
pass through the fire. That one who is unhurt will be proved by God
to be in the right." **Very good; you can go, Giovanni, and I wish
you good entertainment. " "Will you not come also, Master?" "No. I
am busy." Giovanni took a step towards the door; then, trying to
appear indifferent, he said: "I am sorry you are so occupied. As I
came hither I met Messer Paolo Somenzi, who promised

338 The Forerunner to bring us to a place where we could
see excellently. The trial is not till mid-day. If you could finish your
work by then, we might yet be in time." Leonardo smiled. "You want
me so much to see the prodigy? Very well, then; we '11 go together.
" At the appointed time Messer Paolo Somenzi arrived. He was a spy
in the pay of the Duke of Milan, and a bitter enemy of Savonarola's:
a restless, fussy little man, with brains of quicksilver. "How is this,
Messer Leonardo?" he began in a harsh disagreeable voice, with
much gesticulation. "You thought of refusing your presence? Has this
physical experiment no attraction for the devotee of natural science?
" "But will the magistrates really permit them to go into the fire?"
asked Leonardo. " Chi lo sa ? But one thing is certain, that Fra
Domenico will not shrink from the flames. Nor is he the only one.
More than two thousand of the citizens, rich and poor, wise and
simple, women and children, declared last night at the Convent of
San Marco that they were ready to follow Fra Domenico to this
singular test. I tell you there is such a frenzy abroad that the most
sensible feel their heads go round. The very philosophers are taking
fright, and asking themselves if there is not a chance of neither
champion being burned. But for my part, I am wondering

The Similitudes — 1498- 1499 339 how the Piagnoni will
look when, on the contrary, the two poor fools are slain before their
eyes!" ''Does Savonarola really believe?" exclaimed Leonardo, as if
thinking aloud. "I suspect he has his doubts and would fain draw
back. But 't is too late. To his own hurt he has so debauched the
imagination of this people that now they require a miracle at all
costs. See you, Messer, *t is a pure question of mathematics, and of
a kind no less interesting than yours : if God really exist, why should
he not do a miracle — why should he not cause two and two to
make five? as, verily, the faithful daily request, that the impious like
you and me, Messer Leonardo, may be put to eternal confusion."
"Well, let us set forth," said Leonardo, interrupting Messer Paolo with
ill-concealed aversion. "Soft, though," said the other; "one little
whisper more. You and I, Messer Leonardo, are of one mind in this
matter; and at the day's end we shall cry 'Victory!' whether God
exist or no. Two and two will always make four. Viva la Scienza ! and
long live logic!" The streets were crowded, and on all faces was that
air of curiosity and happy expectation which Leonardo had already
remarked in Giovanni. The press was greatest in the Via de' Calzaioli
before the Orsanmichele, where was a bronze statue by Andrea
Verrocchio: The apostle Thomas thrusting his fingers into the
wounds

34^ The Forerunner of his Lord. Here the eight theses, the
truth or falsity of which was to be demonstrated by the fire, were
appended to the wall, "writ large" in vermilion letters. Some of the
crowd were spelling them out, others listening and making their
comments. I. The Church of the Lord needs to be bom again. II.
God will chastise her. III. God will transform her. IV. After the
chastisement, Florence also shall be renewed and shall rise above all
peoples. V. The infidels shall be converted. VI. All this shall happen
forthwith. VII. The excommunication of Savonarola by Pope
Alexander VI. is invalid. VIII. He committeth no sin who holds this
excommunication invalid. Jostled by the crowd, Leonardo and his
companions stopped to listen to the remarks of the people. ''It is all
gospel truth," said an old artisan; ''nevertheless deadly sin may
come of it." "What sin is stinking in your old nostrils. Filippo?" asked
a lad, smiling contemptuously.. "There can be no sin in it," said
another. "It 's a trap of the Evil One," said Filippo, undaunted. " We
are demanding a miracle. But we may be unworthy of a miracle. Is it
not

The Similitudes — 1 498-1 499 341 written in Scripture,
*Thou shalt not tempt the Lord thy God'?" * ' Hold your tongue, old
man ! Is not a mustardseed of faith able to raise mountains? God
cannot avoid a miracle once we have faith. " ''No! He can't! He can't!
" cried many voices. ''But who is to go into the fire first? Fra
Domenico or Fra Girolamo?" "The two together." "No, Fra Girolamo
will only pray. He is not going in. " "You don't know what you are
talking about. 'T will be first Fra Domenico, then Fra Girolamo, and
then all of us who wrote ourselves down last night at the convent." "
Is it true that Fra Girolamo is going to raise a dead man? " "Of
course it is true! First the trial by fire, and then the resurrection of
the dead. I, myself, have seen his letter to the Pope. He challenges
him to send a man who shall descend into a tomb with Fra Girolamo,
and say to the dead, * Come forth ! ' He who shall resuscitate the
corpse shall be the true prophet; and the other the deceiver." "Have
faith, brothers, only have faith! Many miracles await you. Ye shall
see the Son of Man in his flesh and bones coming on the clouds, and
other wonders, of which ancient times had not ftven the
conception!"

342 The Forerunner At these words several cried ''Amen!"
and all faces grew pale, and all eyes burned with the wild fires of
fanaticism. The crowd moved on, carrying Messer Paolo and the
others with it. Giovanni threw one more look at Verrocchio's bronze
figure. In the good-humoured, half-contemptuous smile of the
incredulous apostle, he seemed to see the smile of Leonardo. Ill As
they approached the Piazza della Signoria, the press was so great
that Paolo requested one of the mounted guards to escort them as
far as the balcony, where places were reserved for the orators and
for the more important of the citizens. Never, thought Giovanni, had
he seen so great a multitude. Not only was the square packed with
spectators, but the loggias, the towers, windows, and roofs of the
houses. Like limpets, they clung to the iron lamp-brackets, gratings,
gutters, eaves, rain-pipes. They hustled each other and fought for
room, and some fell and were trampled out of life. All the
approaches to the piazza were rigorously barred with iron posts and
chains; at three places only, men of full age and unarmed were
permitted to pass singly. Messer Paolo explained to his companions
the manner in which the pyre was constructed. There were two long
narrow piles of wood smeared with tar and sprinkled with powder,
whirh

The Similitudes — 1498- 1499 343 extended from the
Ringhiera or rostrum, where stood the Marzocco (the ancient Hon of
Florence) , as far as to the Tettoia de' Pisani. Between the two piles
was a narrow lane, paved with stones, sand, and clay, along which
the two friars were to pass. At the appointed hour the Franciscans
appeared from one side, the Dominicans from the other; the
procession was closed by Fra Domenico, in a velvet habit of brilliant
red, and Fra Girolamo, dressed in white, and bearing the Ostensorio,
which glittered in the sunlight. The Dominicans intoned a Psalm:
*'Come and see the works of God; he is terrible in his doing toward
the children of men!" And the crowd responded, ''Hosanna,
Hosanna! Blessed is he who cometh in the name of the Lord ! '* The
enemies of Savonarola occupied half the Loggia dei Lanzi, his
followers the opposite half, a partition having been erected between
them. All was now ready; nothing remained but to light the fire and
call forth the champions. At last the judges of the trial came from
the Palazzo Vecchio, and every one held his breath and watched
what they would do; but after speaking a few words in a low voice
with Fra Domenico they retired again, and suspense reigned as
before. Fra Giuliano Rondinelli had gone out of sight. Then the
tension of spirit became almost insupportable, and the crowd stood
on tiptoe, and craned their necks, making

344 The Forerunner the sign of the cross and telHng their
beads, and murmuring childish prayers: "Lord, Lordl perform us a
miracle!" The air was sultry ; a thunderstorm was drawing nearer
and growls of thunder, which had been heard at intervals all day,
were becoming louder and more insistent. Certain members of the
council, in long robes of red cloth, like the togas of ancient Rome,
issued from the Palazzo Vecchio and took places on the Ringhiera ;
an old man with spectacles and a quill behind his ear, evidently the
clerk, tried to recall them with shouts of : "Messeri! Messeri! the
sitting is not ended I the voting is in progress!" "To the devil with the
voting," said one of the magistrates; "I have had my fill of this stupid
discussion. The noise has broken my ear-drum." "What is the use of
deliberation? " said another. "If they wish to bum themselves let
them, do it, and Good-night to them!" "By my troth, it were
homicide!" "And an excellent homicide too! Two fools less on earth."
"But they must be burned according to the rule and canon of the
Holy Church. It *s a delicate theological question." "Well, then,
propose the question to the Pope. '* "What ha.ve we to do with the
Pope? We are concerned with the people. If by such means one
could restore the people to sanity, there

The Similitudes — 1498- 1499 345 would be no great evil in
sending all the priests and friars in the worid, not only into the fire,
but into the water and under the ground likewise. " ''Water will
serve. Throw them both into a tub of water, and let him who comes
forth dry be the victor. 'T would be a thought less dangerous than
these pranks." "Have you heard, most honourable signiors," said
Messer Paolo, with deep reverences, *'that poor Fra Giuliano has
fallen sick in his stomach? 'T is a malady caused by fear, and he has
been bled for it." "Sir," exclaimed an old man of imposing aspect, his
face showing at once distress and intelligence, "you make a jest of
everything. But I, when I hear such talk from the men highest in the
state, I ask myself whether it were not better to die. Truly, if the
founders of this city could rise from the dead and see the folly and
the infamy of this day's proceedings, they would flee back into their
graves for shame." The judges, meanwhile, came and went
incessantly from the Loggia to the Palazzo, from the Palazzo to the
Loggia, and it seemed as if the deliberations were to have no end.
The Franciscans first accused Savonarola of having enchanted Fra
Domenico's habit; he therefore removed it, but it was alleged that
sorcery might have influenced his under garments. He retired into
the Palazzo Vecchio, stripped himself naked, and donned the vesture
of another.

34^ The Forerunner Then the Franciscans demanded that
he should hold aloof from Savonarola, lest his new garments should
be enchanted; and that he should give up the cross which he held.
To this Domenico consented, but protested that he would not enter
the flames without the Holy Sacrament in his hands. The Franciscans
at this swore that Savonarola's disciple wished sacrilegiously to bum
the body and blood of Christ. In vain Domenico and Girolamo replied
that the Holy Sacrament could not be reduced to ashes; the material
part {modus) might indeed be burned, but not the eternal and
incorruptible part {substantia). An interminable scholastic dispute
now began between the two parties. The crowd in the piazza was
beginning to murmur, and dense black clouds were spreading over
the sky. Suddenly from behind the Palazzo Vecchio and the Via de'
Leoni where the lions of Florence were kept in cages, a prolonged
and hungry roar was heard. The mob imagined that the bronze
Marzocco, indignant with his city, was roaring out his wrath. They
responded with a sound no less furious, no less hungry: ''Have done!
Have done! To the fire at once ! Fra Girolamo ! We will have the
miracle ! We will have the miracle!'* At this cry Savonarola, who had
been kneeling in prayer, rose, shook himself, approached the parapet
of the Loggia and with imposing gesture commanded silence. But
the people refused to

The Similitudes — 1498- 1499 347 be silent. And then
some one from under the Tettoia de' Pisani cried : "He's afraid!" And
this cry was taken up and passed along. A company of horsemen of
the Arrabbiati tried to push their way to the Loggia to fall upon
Savonarola and seize him, making their profit of the confusion. ''Kill
him! Kill him! Down with the cursed schismatic!" was the shout.
Boltraffio closed his eyes that he might not see those furious faces
which had now lost all look of humanity; nothing, he thought, could
save Savonarola from being torn to pieces. At this moment the storm
broke. Rain descended, the like of which had not been seen in
Florence. It endured but a short time, and when it was over the trial
by fire had become an impossibility. For between the twin piles of
faggots the water ran with the fury of a channel hemmed in
between dykes. Some laughed. "Well done, friars! They undertook to
tread the fire, but they Ve got to swim for it! That 's their miracle,
eh?" Cursed by the crowd, Savonarola on his return to his convent
was escorted by soldiers, and Giovanni's heart bled as he watched
the deposed prophet, kicked and buffeted, making his way with
faltering step, his eyes on the ground, his

34^ The Forerunner white garb splashed with the mire of
the streets. Leonardo saw his disciple's wan face, and, as before at
the ''Burning of Vanities," took his hand and led him away. IV Next
day in the Casa Berardi, sitting in the chamber which was so like a
ship's cabin, Leonardo tried to prove to Messer Guido that Columbus
had erred in locating Paradise on a swelling upon a pear-shaped
earth. At first Guido listened and argued, then mournful silence fell
on him. He was vexed with his friend for telling him the truth.
Presently he discovered pains in his legs, and had himself carried
away. *'Why have I hurt him?" thought Leonardo. *'He wants a
miracle too!" Turning over his note-book, his eyes fell on the words
he had written that night when the Milanese mob had attacked his
house for the seizure of the Holy Nail: ''O marvellous justice of Thee,
Thou Prime Mover, who hast denied to no force the order and the
qualities of its necessary effect ! " * ' There ! " he exclaimed, ' '
there is the miracle ! ' ' And his thoughts turned to his Cenacolo and
to the face of Christ, still sought for, not yet found; and he felt that
between this inviolable law of Necessity, and the perfect wisdom of
Him who said, ''One of you shall betray me.'* there existed a deep
correlation.

The Similitudes — 1498- 1499 349 In the evening Giovanni
came with the day's news. The Signoria had exiled Fra Girolamo and
Fra Domenico from the city; and the "Enraged,'* brooking no delay,
had besieged San Marco with a countless throng of armed persons,
and had broken into the church where the brothers, were at vespers.
They defended themselves,, fighting with burning tapers,
candlesticks, and crucifixes; in the cloud of smoke they seemed
ridiculous as angry doves. One climbed on the roof and hurled
stones down from it. Another fired an arquebus from the altar,
shouting at each discharge ''Viva Crista f' Presently the monastery
was taken by storm. The brethren entreated Savonarola to fiee^ but
he, together with Domenico, gave himself up, and they were haled
to prison. The guards were imable or unwilling to defend them from
the insults of the crowd, who struck Fra Girolamo from behind,
crying: "Prophesy unto us, thou man of God, who is he that smote
thee?" Others crawled at his feet as though seeking something, and
cried: "The key? The key? Where is Fra Girolamo 's key?" — in
allusion to the key often spoken of in his sermons, with which he
would unlock the secrets of the abominations of Rome. The very
children who had belonged to the Sacred Troop of inquisitors now
pelted him with apples and rotten eggs. Those who could not

35^ The Forerunner penetrate the crowd howled frdcn a
distance, reiterating their abuse till their throats weie hoarse: *'
Dastard! Coward! Judas! Sodomite! Sorcerer ! Antichrist ! ' ' Giovanni
followed him to the doors of the prison of the Palazzo Vecchio,
whence he was not to issue till the day of his execution. On the
following morning Leonardo and Boltraffio quitted Florence. At once,
on arrival in Milan, the painter set himself to the task which had
baffled him for eighteen years — the face of the Christ in the Last
Supper. On the very day of that trial by fire, which in Florence had
had such bad results — Charles VIII., King of France, died very
suddenly. The news was of sinister import to II Moro, for the Duke
of Orleans, who was now to ascend the throne as Louis XII., was
descended from Valentina Visconti, daughter of the first Duke of
Milan. He claimed to be the only legitimate heir of the dominion of
Lombardy, and now proposed to reconquer it, annihilating ''the
robber nest of the Sforzas. " Shortly before the change of sovereigns
in France, there had taken place at the Milanese Court what was
called a ''scientific duel," and

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Hydraulic Conductivity Issues Determination and Applications 2nd Edition Lakshmanan Elango

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