PDF Computer Science Cacic 2018 24Th Argentine Congress Tandil Argentina October 8 12 2018 Revised Selected Papers Patricia Pesado Ebook Full Chapter
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Patricia Pesado
Claudio Aciti (Eds.)
Computer Science –
CACIC 2018
24th Argentine Congress
Tandil, Argentina, October 8–12, 2018
Revised Selected Papers
123
Communications
in Computer and Information Science 995
Commenced Publication in 2007
Founding and Former Series Editors:
Phoebe Chen, Alfredo Cuzzocrea, Xiaoyong Du, Orhun Kara, Ting Liu,
Krishna M. Sivalingam, Dominik Ślęzak, Takashi Washio, and Xiaokang Yang
Computer Science –
CACIC 2018
24th Argentine Congress
Tandil, Argentina, October 8–12, 2018
Revised Selected Papers
123
Editors
Patricia Pesado Claudio Aciti
National University of La Plata National University of Buenos Aires Center
La Plata, Argentina Buenos Aires, Argentina
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The XXIV Argentine Congress of Computer Science (CACIC 2018) was organized by
the School of Computer Science of the National University of the Center (UNICEN) on
behalf of the Network of National Universities with Computer Science Degrees
(RedUNCI).
Editors
Patricia Pesado National University of La Plata, Argentina
(RedUNCI Chair)
Claudio Aciti National University of Buenos Aires Center, Argentina
Editorial Assistant
Pablo Thomas National University of La Plata, Argentina
General Chair
Claudio Aciti National University of Buenos Aires Center, Argentina
Program Committee
Maria Jose Abásolo National University of La Plata, Argentina
Claudio Aciti National University of Buenos Aires Center, Argentina
Hugo Alfonso National University of La Pampa, Argentina
Jorge Ardenghi National University of South, Argentina
Marcelo Arroyo National University of Río Cuarto, Argentina
Hernan Astudillo Technical University Federico Santa María, Chile
Sandra Baldasarri University of Zaragoza, Spain
Javier Balladini National University of Comahue, Argentina
Luis Soares Barbosa University of Minho, Portugal
Rodolfo Bertone National University of La Plata, Argentina
Oscar Bria National University of La Plata, Argentina
Nieves R. Brisaboa University of La Coruña, Spain
Carlos Buckle National University of Patagonia San Juan Bosco,
Argentina
Alberto Cañas University of West Florida, USA
Ana Casali National University of Rosario, Argentina
Silvia Castro National University of South, Argentina
Antonio Castro Lechtaler National University of Buenos Aires, Argentina
Alejandra Cechich National University of Comahue, Argentina
viii Organization
Software Engineering
Smart Assistance Spots for the Blind or Visually Impaired People. . . . . . . . . 277
Guillermo Arispe, Claudio Aciti, Matías Presso, and José Marone
Computer Security
1 Introduction
A water distribution network consists of thousands of nodes with nonlinear
hydraulic behaviour, linked by thousands of interconnecting links. The inherent
problem associated with cost optimisation in the design of water distribution net-
works is due to the nonlinear relationship between flow and head loss and the dis-
crete nature of pipe sizes. As a consequence, the solution concerning the layout,
design, and operation of the network of pipes should result from good planning and
management procedures. In this way, this problem known as Water Distribution
Network Design (WDND) requires to manage an important number of variables
(pipes, pipe diameters, demand nodes, water pressure, reservoirs, etc.), and con-
straints (water velocity, pressure, etc.). This problem, even for simple networks,
is very difficult to solve, in particular it is classified as NP-hard [1].
Early research works in the WDND optimization area were focused on
the single-period, single-objective, gravity-fed design optimization problem.
c Springer Nature Switzerland AG 2019
P. Pesado and C. Aciti (Eds.): CACIC 2018, CCIS 995, pp. 3–16, 2019.
https://doi.org/10.1007/978-3-030-20787-8_1
4 C. Bermudez et al.
The first research works applied linear programming [2,3], and non-linear pro-
gramming [4,5]. After that, the metaheuristics have been used to solve these
problems, such as the trajectory-based ones: Simulated Annealing [6,7] and Tabu
Search [8]. Also population-based metaheuristics were applied, for example, Ant
Colony Optimization [9], Ant Systems [10], Genetic Algorithms [11–13] Scatter
Search [14], and Differential Evolution [15].
Recently, the single-period problem was extended to a multi-period setting in
which time varying demand patterns occur. Farmani et al. [16] formulated the
design problem as a multi-objective optimization problem and apply a multi-
objective evolutionary algorithm. In [12], a Genetic Algorithm was used to solve
six small instances considering velocity constraint on the water flowing through
the distribution pipes. This constraint was also taken into account in [17], but the
authors used mathematical programming on bigger, closer-to-reality instances. A
Differential Evolution (DE) algorithm was proposed in [18] to minimize the cost
of the water distribution network. Another version of a DE algorithm to solve this
problem was presented in [19]. An Iterative Local Search [20] was specifically-
designed in order to consider that every demand node has 24 hrs water demand
pattern and a new constraint, which imposes a limit on the maximal velocity of
water through the pipes.
Based on the problem formulation given by De Corte and Sörensen [20],
we propose an optimization technique, based on Simulated Annealing (SA), in
order to improve and optimize the distribution network design. Thus, this SA
is designed to obtain the optimal type of pipe connecting the supply, demand,
and junction nodes in the distribution network. This proposal incorporates a
local search procedure in order to improve the layout of the network, arising
the Hybrid Simulated Annealing (HSA). The HSA’s performance is compared
with algorithms present in the literature. This work constitutes an extension of
a previous work [21] and includes new content regarding an study and analysis
of the main control parameter of the HSA, known as temperature. Moreover,
we introduce and statistically compare four HSA’s variants, taking into account
different schemes to schedule the cooling process. We test the performance of
our proposals with a set of networks with different sizes expressed by number
of pipes and characteristics. The evaluation considers relevant aspects such as
efficiency and internal behavior.
The rest of this article is organized as follows. In Sect. 2, we introduce the
problem definition. Section 3 explains our algorithmic proposal, HSA, to solve the
WDND optimization problem and the four HSA’s variants. Section 4 describes
the experimental analysis and the methodology used. Then, we analyze the
results obtained by the variants and compare with the obtained by the ILS [20]
in Sects. 5 and 6, respectively. Finally, we present our principal conclusions and
future research lines.
where ICt is the cost of a pipe p of type t, Lp is the length of the tube, and xp,t
is the binary decision variable that determines whether the tube p is of type t
or not. The objective function is limited by: physical laws of mass and energy
conservation, minimum pressure demand in the nodes, and the maximum speed
in the pipes, for each time τ ∈ T . These laws are explained in the following
paragraphs.
Mass Conservation Law: It must be satisfied for each node N in each period
of time τ . This law establishes that the volume of water flowing towards a node
in a unit of time must be equal to the flow that leaves it (see Eq. 2),
Q(n1 ,n),τ − Q(n,n2 ),τ = W Dn,τ − W Sn,τ ∀n ∈ N ∀τ ∈ T (2)
n1 ∈N/n n2 ∈N/n
where Q(n1 ,n),τ is the flow from node n1 to node n at time τ , W Sn,τ is the
external water supplied and W Dn,τ is the external water demanded.
Energy Conservation Law: It states that the sum of pressure drops in a closed
circuit in an instant of time τ is zero. These drops can be approximated using
the Hazen-Williams equations with the parameters used in EPANET 2.0 [22]
(the hydraulic solver used in this paper), as indicated in Eq. 3.
10.6668yp,τ Qp,τ 1.852
Lp
1.852 D 4.871 = 0 ∀l ∈ L ∀τ ∈ T (3)
p∈l t∈T (xp,t Ct t
In Eq. 3, yp,τ is the sign of Qp,τ that indicates changes in the water flow direc-
tion relative to the defined flow directions, Qp,τ is the amount of water flowing
through pipe p in time τ , Lp is the pipe length, Ct is the Hazen-Williams rough-
ness coefficient of pipe type t, and Dt is the diameter of pipe type t.
Minimum Pressure Head Requirements: for each node n in each period of
time τ , it must be satisfied (see Eq. 4),
Hn,τ
min
≤ Hn,τ ∀n ∈ N ∀τ ∈ T (4)
being H min the minimum node pressure and Hn,τ the node’s current pressure.
Maximum Water Velocity: The water velocity vp,τ can not exceed the max-
imum stipulated speed vp,τ
max
. Equation 5 shows this relationship.
vp,τ ≤ vp,τ
max
∀p ∈ P ∀τ ∈ T (5)
6 C. Bermudez et al.
(a) (b)
Fig. 1. Different solutions or network designs. (a) Solution 1; (b) solution 2; (c) pipe
lengths; (d) available pipe types with their corresponding costs.
solution (line 3), an iterative process starts (lines 4 to 19). As a first step in the
iteration, the hybridization is carried out in order to intensify the search into the
current region of the solution space. In this way a feasible solution, S1 , is obtained
by applying the MP-GRASP local search [20] to S0 (line 7), and then a greedy
selection mechanism is performed (lines 9–11). As a consequence, S0 can be
replaced by S1 if this is better than S0 . In the next step a perturbation operator
is used to obtain a feasible neighbor, S2 , from S0 (line 12), in order to explore
another areas of the search space. This perturbation randomly changes some
pipe diameters. If S2 is worse than S0 , S2 can be accepted under the Boltzmann
probability (line 14, second condition). In this way, at high temperatures (T ) the
exploration of the search space is strengthened. In contrast, at low temperatures
the algorithm only exploits a promising region of the solution space, intensifying
the search. In order to update T , a cooling schedule [23] is used (line 18) and
it is applied after a certain number of iterations (k) given by the Markov Chain
Length (M CL) (line 17). Finally, SA ends the search when the total evaluation
number is reached or the T = 0.
Most features in SA, such as search space, perturbation operator, and cost
(evaluation) function, are fixed by the problem definition. The only feature that
is variable during the process is the temperature. Therefore one of the most
important features in simulated annealing is the choice of the annealing schedule,
and many attempts have been made to derive or suggest good schedules [24].
In this work, we study the behavior of the most known cooling process in the
literature to solve the Multi-Period WDND optimization problem, arising three
new HSA variants as explained in the following.
– HSAP r op applies the proportional cooling scheme, also called geo-
metric schedule [23], in order to reduce the temperature, as the Eq. 6 shows:
Tk+1 = α ∗ Tk (6)
where α is a constant close to, but smaller than, 1. Particularly, we calculate
α as follows:
k
α= (7)
k+1
This scheme is the most popular cooling function because, the temperature
decay is not too slow neither too fast allowing to achieve an equilibrium
between exploitation and exploration.
– HSAE xp uses the exponential cooling scheme [23] to produce the tem-
perature decay. The Eq. 8 describes these process, where the constant αk < 1
is calculated in the Eq. 9. This schedule quickly cools the temperature reduc-
ing the required time and iterations to converge to a good solution. In big and
complex problems, this becomes in a disadvantage, given that the equilibrium
between the exploitation and exploration is broken.
Tk+1 = Tk ∗ αk (8)
ek
αk = (9)
e1+k
Solving the Multi-Period Water Distribution Network Design Problem 9
Network Meshedness Pipes Demand Water Network Meshedness Pipes Demand Water
coefficient nodes reservoirs coefficient nodes reservoirs
HG-MP-1 0.2 100 73 1 HG-MP-9 0.1 295 247 2
HG-MP-2 0.15 100 78 1 HG-MP-10 0.2 397 285 2
HG-MP-3 0.1 99 83 1 HG-MP-11 0.15 399 308 2
HG-MP-4 0.2 198 143 1 HG-MP-12 0.1 395 330 3
HG-MP-5 0.15 200 155 1 HG-MP-13 0.2 498 357 2
HG-MP-6 0.1 198 166 1 HG-MP-14 0.15 499 385 3
HG-MP-7 0.2 299 215 2 HG-MP-15 0.1 495 413 3
HG-MP-8 0.15 300 232 2
Tk+1 = C ∗ Tk (10)
ln(k)
C= (11)
ln(1 + k)
4 Experimental Design
In this section, we summarize and analyze the results of using the four proposed
HSA’s variants (HSAP rop , HSAExp , HSALog , and HSARand ) on all the problem
instances, following the next methodology. First, we analyze the behavior of
these variants considering the results shown in the Table 4. The columns 2–5
show the average of the best cost values found by these four variants for the
75 instances grouped by their corresponding distribution network. The minimal
cost values found by each group are boldfaced. In the last column, the results of
the Kruskall-Wallis test are summarized, where the symbol “+” indicates that
the behavior of the four HSA’s variants are statistically similar, while the symbol
“-” specifies that these behaviors are significantly different. Secondly, we analyze
the temperature decay for each proposed HSA taking into account the variation
of the temperature parameter during the search, as shown in the Fig. 2.
Regarding the quality point of view, HSAP rop finds the best cost in many
more instances than the rest of variants, i.e. HSAP rop achieves the best solu-
tions in eight instances, followed by HSAExp with three, HSARand with two,
and HSALog with only one instance (see the boldfaced values in the Table 4).
These differences between the behaviors are supported by the KW results, which
indicate that the cooling schemes drive the search in significant different ways,
Solving the Multi-Period Water Distribution Network Design Problem 11
Table 4. Averages of the best cost values found by each proposed variant, which are
grouped by network.
strengthening the search when the proportional scheme is used. This scheme pro-
duces a temperature decay that allow an adequate exploration at the beginning,
enabling a greater exploitation at the ending of the search.
If the Fig. 2 is analyzed, no quick temperature convergence to zero is observed
when HSAP rop and HSALog are executed, but the temperature decay is greater
in the first one. This last property is the reason of the HSAP rop ’s success to find
the minimal cost values in more than 50% of the instances. Conversely, regarding
12 C. Bermudez et al.
Table 5. Average of the best TIC values obtained by ILS and HSAP rop for all instances
grouped by the corresponding network. The best values are boldfaced.
HSAExp and HSARand , the temperature converges quickly to values close to zero
restricting the exploration at the beginning of the search, although HSAExp
outperforms HSARand when the solution quality is analysed. It is remarkable
that, the stop condition is achieved by all HSA’s variants when the number of
evaluations (EPANET calls) is equal to 1,500,000 but the temperature remains
greater than zero.
Summarizing, the proportional cooling scheme allows HSAP rop outperforms
the remaining HSA’s variants, by balancing the exploitation and exploration
during the search. As a consequence, HSAP rop obtains the best networks designs
doing the same computational effort than the others variants.
Regarding that HSAP rop obtained the best results, we select this variant to com-
pare its performance with the ILS proposed in [20]. This metaheuristic is chosen
from literature for this comparison, since its authors also used the HydroGen
instances to test it. In this way, our results can be compared with ones of the
state-of-the-art, allowing to know the level of quality reached by our proposal.
The methodology used to analyze the results is described in the following.
First, we study the HSA behavior comparing the best cost values found by
HSAP rop and ILS [20] for the 75 instances, grouped by their corresponding dis-
tribution network, as presented in the Table 5. Secondly, we analyze the HSAP rop
convergence, in comparison with ILS, taking into account the cost values found
at the 1e+05, 3e+05, 5e+05, 10e+05, and 15e+05 EPANET calls (evaluations),
as shown in the Fig. 3. Besides, the HSA’s execution times (in seconds) to carry
out the maximum number of evaluations for each test case, grouped by network,
are shown in the Fig. 4. Note that, we only present the HSA’s total execution
time for all test cases, because no data about this metric are reported by De
Corte and Sörensen in [20].
Solving the Multi-Period Water Distribution Network Design Problem 13
Analyzing the Table 5, we detect that HSAP rop finds solutions with less TIC
values than the ones of ILS in nine networks. As a consequence, in 60% of the
problem instances better cost values are found when they are solved by HSAP rop .
The HSA advantage arises out of the Boltzmann probability application to accept
high TIC values, which allows to diversify the search to escape from local optima.
From the convergence point of view, we observe that HSAP rop finds solutions
with TIC values near to the best ones in 80% of the instances, with only 1e+05
evaluations. Instead, ILS needs at least 3e+05 evaluations for that, besides this
is achieved in only 66% of the test cases.
393000
750000
310000
650000
310000
390000
Cost
Cost
Cost
Cost
Cost
720000
500000
300000
280000
690000
387000
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
Evaluations Evaluations Evaluations Evaluations Evaluations
960000
950000
950000
900000
770000
950000
Cost
Cost
Cost
Cost
Cost
850000
840000
800000
850000
740000
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1400000
1600000
900000 1000000
Cost
Cost
Cost
Cost
Cost
1200000
1050000
1100000
1200000
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
1.0e+05
3.0e+05
5.0e+05
1.0e+06
1.5e+06
Fig. 3. Evolution of the TIC values during the search for all instances.
14 C. Bermudez et al.
500
time (sec.)
300
100
0
HG−MP−1
HG−MP−2
HG−MP−3
HG−MP−4
HG−MP−5
HG−MP−6
HG−MP−7
HG−MP−8
HG−MP−9
HG−MP−10
HG−MP−11
HG−MP−12
HG−MP−13
HG−MP−14
HG−MP−15
Networks
Fig. 4. Average of the total HSAP rop execution times for all instances grouped by the
corresponding network.
Evaluating both the Fig. 4 and the Table 2 together, we notice that the HSA’s
execution time is affected by the number of pipes and demand nodes. In this way,
five groups of three networks can be formed exhibiting similar execution times.
These instances have consecutive numbers, e.g. the set of the HG-MP-1, 2, and 3
networks have similar number of pipes and demand nodes, and so on. Being the set
formed by the HG-MP-13, 14, and 15 networks the most expensive cases to solve.
Furthermore, analyzing what happened into each set of networks, the network with
more demand nodes consumes less execution time than the other two, since more
feasible solutions exist and HSA needs less time to find one of them.
Summarizing, HSAP rop outperforms ILS for the 60% of the problem instances
when the result quality is considered. Moreover, a quick convergence to good
solutions is also evidenced by our proposal in most of the problem instances.
Furthermore, the HSA’s runtime is affected by the growing and combination of
the number of pipes and demand nodes.
7 Conclusions
cooling scheme to reduce the temperature, found the best networks designs out-
performing the remaining proposals.
Moreover, HSAP rop ’s results were compared with the obtained by the ILS
proposed in [20] to solve this problem. As a consequence, we observed that this
HSA variant also outperformed the results obtained by ILS in more than half
(60%) of instances. Additionally, HSA achieved a better exploration than ILS,
because of the Boltzmann probability application to accept solutions that can
explore new areas of the search space. This advantage combined with the local
search allowed HSA to converge quickly on the best solutions.
For future works, we will improve the HSA to solve the multi-period WDND
optimization problem, by introducing changes in the initialization method of
the temperature. We are also interested in testing larger dimension instances, as
close as possible to real scenarios.
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A furious gust of wind now came tearing down the valley, bending the
trees and snapping the branches, and the lightning flashed incessantly on
every side. The scouting-party hastened to get out of the woods as
quickly as possible. It was evident, even to David, that nothing could be
done till the storm was over.
Jeduthun Cooke had been one of the most active of the scouters, and he
came home wearied and wet enough, to find that Keziah had provided
him with a hot supper, and laid out dry clothes all ready for him. He
changed his wet garments, drank a cup of coffee, and then threw himself
on the bed to catch a little sleep. He had not slept, as it seemed to him,
more than five minutes, when he was wakened by Keziah:
"The vault!" he exclaimed. "What's gone and put that in your head,
Kissy?"
"I dunno," replied Kissy. "I got up to see if the storm was over, and it
come to me all at once."
"But Osric says they did not go to the funeral, and I'm sure I didn't see
'em there. To be sure, David Parsons mistrusted all the time that Osric
didn't tell the truth, but then I should think somebody would have seen
them."
"I can't help that," said Kissy, positively. "I'm just as sure as I can be, that
that poor child is in General Dent's vault this very minute. I feel that for
sure and certain."
When Kissy felt things "for sure and certain," there was no use in arguing
with her, as Jeduthun knew from long experience. Moreover, he was struck
with the idea himself.
"It don't seem very likely, and yet it is just possible," said he. "If I had the
key, I'd go up there this minute. Come to think of it, I have got it, or
what's as good," he exclaimed, starting up again. "Our grainery key fits
the vault-lock. I know, because the old general said so one day when he
was down at the mill. He saw me have the key, and said it looked like
his'n, and he and Mr. Antis tried it, and it just fitted. Put on your rubbers,
Kissy, and we'll go and see, anyhow. The storm's over now."
Kissy lost no time in getting ready, but she detained her husband while
she put some wood in her stove and set on a kettleful of water.
"If he's been in that damp, cold place all night, he'll be about chilled
through," she explained to her husband. "The first thing to do, will be to
put him in a warm bed and give him hot tea."
Elsie felt very unhappy both on her own account and her brother's. She
was sorry to have Osric disgraced and punished, but she was grieved
above all that he had been so wicked. Elsie did not believe Osric's story
any more than David did. As she thought the matter over, she
remembered that Osric had come, not from the direction of the woods,
but exactly the other way, from the village. She did not believe that
Christopher would undertake to go home alone through the woods,
especially as the old story of the wild cat had been revived and talked
over only the day before. As she lay pondering over these matters, she
was started by a tremendous flash and roar coming, as it seemed, at the
same moment, and then she heard Osric, whose room was next her own,
burst into a loud fit of crying. Forgetful of all his unkindness, Elsie jumped
out of bed at once and went to her brother, whom she found burying his
head under the bedclothes and crying bitterly.
"What's the matter, Ozzy?" said she, sitting down on the bed. "Are you
afraid?"
"But, Ozzy, you know that God can take care of us, even if the house is
struck. Don't you know the pretty verse we learned last Sunday?—
"'Ye winds of heaven, your force combine;
Without His high behest
Ye cannot in the mountain-pine
Disturb the sparrow's nest!'
"He won't take care of me," sobbed Osric, "I have been so wicked. You
don't know how wicked I have been, Elsie. I am sorry I told such a lie
about you."
"Never mind me," said Elsie. "I am sorry you told the lie, because that
was wicked, but I don't mind about myself. But, Ozzy, if you have not told
the truth about Christopher, do tell it now!"
"Oh what a flash!" exclaimed Osric, shrinking once more. "It seemed to
come right into the window."
"There, again! Oh, the house will be struck, I know it will, and we shall all
be killed, and what will become of Christopher?"
"I am afraid father will punish me again," said Osric, shrinking. "Oh dear!
What shall I do?"
"We went to the funeral," said Osric, reluctantly, at last. "We watched till
Isaac went away, and then hid in the vault to see the coffin. Then Chris
was scared, and cried, and went and hid in the farther end of the vault,
and I slipped out with the bearers, and hid in a bush till the people went
away, and—and—"
"But didn't Christopher come out?" asked Elsie, struck with horror.
"I don't know whether he did or not. I never saw him. I did not think
anything about him, till you asked where he was. Oh, Elsie, where are you
going?" cried Osric as Elsie rose and went towards the door. "Don't go
away and leave me alone! Suppose the lightning should strike me!"
"I can't help it, Ozzy. I must tell father this minute, so that he can know
what to do. And if you are afraid, just think what poor Christopher must
be. How would you feel if you were shut up in the burial-vault, instead of
being safe at home? The best thing you can do is to get up and come and
tell father yourself."
"Oh, I can't! I durstn't!" cried Osric. "Elsie, do come back! Only wait till
morning, and I will tell him."
Osric cried and pleaded, but in vain. Elsie had had enough of
concealments, and she felt how much might depend on the little boy's
having timely assistance. She went down to her father's room and told
him the story. Mr. Dennison came up and questioned Osric himself, and
felt convinced that Elsie's suspicions were correct, and that Christopher
had been left in the vault.
As soon as the storm abated, he harnessed his horse, drove down to the
village as fast as possible, and seeing a light in Jeduthun's cottage, he
went straight to his door, and arrived there just as Jeduthun and Kissy
came out.
"There!" said Jeduthun, as soon as he heard the story. "Kissy, she waked
me up half an hour ago. She felt it for 'sure and certain' that Christopher
was in there, and started me out to see."
Jeduthun explained that he had a key which would unlock the vault.
"You'd better hitch the horse under the shed," said he. "That road always
washes badly with such a heavy rain, and we shall get on faster a-foot."
"Seeing you've got company, I'll stay at home and have everything
ready," said Kissy. "You had better bring him right here the first thing. I'm
as sure you will find him, as if I see him this minute."
Three or four minutes brought the two men to the door of the vault.
Jeduthun unlocked it without difficulty, and entered, holding up his
lantern. The next moment he uttered a suppressed exclamation:
"Here he is, sure enough! Softly, squire! 'Twon't do to wake him too
sudden. See how he lies, poor lamb! Tired himself out worrying and
crying, I suppose."
Jeduthun knelt down and took the child's hand, saying gently:
But the next moment, he looked up, pale as ashes, and said in a half
whisper, "Squire, we're too late. I'm dreadful afraid he's dead."
Mrs. Parsons would have taken her son home, but the doctor declared
that he must not be moved, since everything depended on the most
perfect quietness.
"Suppose I should bring my son over to see him?" said Mr. Dennison to
the doctor.
"It can do no harm, that is certain," said Doctor Henry, "and it may be
good for him, if not for Christopher."
Osric cried, and begged to be allowed to stay at home at first, but he
yielded when his father represented to him that he might perhaps save
Christopher's life by going to see him. He shrank back in the carriage as
they drove through the village, and burst out crying at the sight of Mrs.
Parsons's pale face and the sound of Christopher's voice from the room
beyond.
"Listen to me, Osric," said Mrs. Parsons, sitting down and drawing Osric
towards her. "I am not going to reproach you. I am sure your own
conscience does that. We want you to go in and speak gently to
Christopher, and try to quiet him and make him sleep. But to do this you
must be very quiet yourself—not cry or be afraid. Will you try?"
"Yes, ma'am," answered Osric, choking down his sobs. "Oh, Mrs. Parsons,
I am so sorry that I led Christopher off!"
"I hope you are, my poor boy! Now see what you can do to repair your
fault."
The moment Christopher's eyes fell on Osric, he stretched out his hand to
him.
"Oh, Ozzy, I knew you wouldn't leave me all alone to die. But what made
you stay so long?"
"Never mind that now, Christopher," said his mother. "You see he has
come back."
"And you won't leave me again, will you?" continued Christopher, holding
Osric's hand tightly in his own. "It was very wicked to tell a lie and run
away from school, but we will confess our sins and say our prayers, and
when the angels come to take Miss Lilla to heaven, perhaps they will let
us out if we ask them. Don't you believe they will, Ozzy?"
Osric could not bear these words, and he burst into tears, and hid his face
on the pillow. His tears seemed to have a quieting effect on Christopher,
who said, soothingly, "There! Don't cry. Maybe we shall get out, after all. I
wish you could sing, Ozzy. It would make the time pass quicker. I would,
but my voice seems all gone away."
"I don't know, my boy. I can tell better when he wakes. He has had a
great shock, and we cannot foresee the effects."
"Oh how mean I have been!" he said to himself. "I wonder if I ever could
be as good as Elsie, if I were to try? Perhaps I could if I were to pray and
read the Bible as she does. I will try, anyway;" and Osric made a good
beginning by laying his head down, confessing his sins to his heavenly
Father, and begging for forgiveness and help for his Redeemer's sake.
When Christopher awoke, he was perfectly sensible, but so weak that the
doctor thought he would hardly live through the night. He rallied a little
towards morning, but for many days, he hovered between life and death,
sometimes insensible, at other times deranged and thinking himself again
in the burial-vault.
At these times, no one could quiet him like Osric. Osric stayed at
Jeduthun's cottage day and night, always at the sick boy's call, never
seeming to care for rest or amusement, or anything else, but waiting on
Christopher. These days, dreary and anxious as they were, proved the
turning-point in Osric Dennison's life. He had many long and profitable
talks with Jeduthun and Mrs. Parsons, and learned a great deal. His
devotion to his friend was of service to him in another way. Even David,
who had thought at first that he never would forgive Osric, felt his heart
soften towards him as he saw how thin and pale Ozzy grew day by day,
and how careful he was never to go out of calling distance from the
cottage, lest Christopher should want him.
David told the story to the other boys, and they all agreed that when
Osric came among them once more, they would never reproach him with
his faults, but would try and help him to be a good boy.
At last, Christopher was so much better, that the doctor said that he could
be taken home. He begged hard that Osric might go with him, and Mr.
Dennison consented, thinking justly that the lesson his son was learning
was worth more to him than any he would lose in school. Osric stayed all
summer at Mrs. Parsons's, who became much attached to him. He on his
part, was never weary of waiting on her, and Mr. Ezra Parsons said one
day that his sister had lost one son to find two.
The society of the Parsons boys was of great benefit to Osric. They were
brave, truthful, manly lads, good both at work and play, and they did their
best to make a man of him. Every one noticed the improvement when
Osric went back to school in the winter, and no one rejoiced in it more
than Elsie.
THE END.
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