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Multiprocessor scheduling Theory and applications
Levner E. (Ed.) Digital Instant Download
Author(s): Levner E. (ed.)
ISBN(s): 9783902613028, 3902613025
Edition: I-Tech
File Details: PDF, 4.94 MB
Year: 2007
Language: english

Multiprocessor Scheduling
Theory and Applications
Edited by
Eugene Levner
I-TECH Education and Publishing

Published by the I-Tech Education and Publishing, Vienna, Austria
Abstracting and non-profit use of the material is permitted with credit to the source. 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 articles. Publisher assumes no responsibility liability for any damage or injury to persons or
property arising out of the use of any materials, instructions, methods or ideas contained inside. After
this work has been published by the I-Tech Education and Publishing, authors have the right to
republish it, in whole or part, in any publication of which they are an author or editor, and the make
other personal use of the work.
© 2007 I-Tech Education and Publishing
www.i-techonline.com
Additional copies can be obtained from:
publication@ars-journal.com
First published December 2007
Printed in Croatia
A catalogue record for this book is available from the Austrian Library.
Multiprocessor Scheduling: Theory and Applications, Edited by Eugene Levner
p. cm.
ISBN 978-3-902613-02-8
1. Scheduling. 2. Theory and Applications. 3. Levner.

V
Preface
Scheduling theory is concerned with the optimal allocation of scarce resources (for instance,
machines, processors, robots, operators, etc.) to activities over time, with the objective of
optimizing one or several performance measures. The study of scheduling started about
fifty years ago, being initiated by seminal papers by Johnson (1954) and Bellman (1956).
Since then machine scheduling theory have received considerable development. As a result,
a great diversity of scheduling models and optimization techniques have been developed
that found wide applications in industry, transport and communications. Today, scheduling
theory is an integral, generally recognized and rapidly evolving branch of operations
research, fruitfully contributing to computer science, artificial intelligence, and industrial
engineering and management. The interested reader can find many nice pearls of
scheduling theory in textbooks, monographs and handbooks by Tanaev et al. (1994a,b),
Pinedo (2001), Leung (2001), Brucker (2007), and Blazewicz et al. (2007).
This book is the result of an initiative launched by Prof. Vedran Kordic, a major goal of
which is to continue a good tradition - to bring together reputable researchers from different
countries in order to provide a comprehensive coverage of advanced and modern topics in
scheduling not yet reflected by other books. The virtual consortium of the authors has been
created by using electronic exchanges; it comprises 50 authors from 18 different countries
who have submitted 23 contributions to this collective product. In this sense, the volume in
your hands can be added to a bookshelf with similar collective publications in scheduling,
started by Coffman (1976) and successfully continued by Chretienne et al. (1995), Gutin and
Punnen (2002), and Leung (2004).
This volume contains four major parts that cover the following directions: the state of the art
in theory and algorithms for classical and non-standard scheduling problems; new exact
optimization algorithms, approximation algorithms with performance guarantees, heuristics
and metaheuristics; novel models and approaches to scheduling; and, last but least, several
real-life applications and case studies.
The brief outline of the volume is as follows.
Part I presents tutorials, surveys and comparative studies of several new trends and modern
tools in scheduling theory. Chapter 1 is a tutorial on theory of cyclic scheduling. It is
included for those readers who are unfamiliar with this area of scheduling theory. Cyclic
scheduling models are traditionally used to control repetitive industrial processes and
enhance the performance of robotic lines in many industries. A brief overview of cyclic
scheduling models arising in manufacturing systems served by robots is presented, started
with a discussion of early works appeared in the 1960s. Although the considered
scheduling problems are, in general, NP-hard, a graph approach presented in this chapter
permits to reduce some special cases to the parametric critical path problem in a graph and
solve them in polynomial time.
Chapter 2 describes the so-called multi-agent scheduling models applied to the situations in
which the resource allocation process involves different stakeholders (“agents”), each
having his/her own set of jobs and interests, and there is no central authority which can

VI
solve possible conflicts in resource usage over time. In this case, standard scheduling models
become invalid, since rather than computing "optimal solutions”, the model is asked to
provide useful elements for the negotiation process, which eventually should lead to a
stable and acceptable resource allocation. The chapter does not review the whole scope in
detail, but rather concentrates on combinatorial models and their applications. Two major
mechanisms for generating schedules, auctions and bargaining models, corresponding to
different information exchange scenarios, are considered. Known results are reviewed and
venues for future research are pointed out.
Chapter 3 considers a class of scheduling problems under unavailability constraints
associated, for example, with breakdown periods, maintenance durations and/or setup
times. Such problems can be met in different industrial environments in numerous real-life
applications. Recent algorithmic approaches proposed to solve these problems are
presented, and their complexity and worst-case performance characteristics are discussed.
The main attention is devoted to the flow-time minimization in the weighted and
unweighted cases, for single-machine and parallel machine scheduling problems.
Chapter 4 is devoted to the analysis of scheduling problems with communication delays.
With the increasing importance of parallel computing, the question of how to schedule a set
of precedence-constrained tasks on a given computer architecture, with communication
delays taken into account, becomes critical. The chapter presents the principal results related
to complexity, approximability and non-approximability of scheduling problems in
presence of communication delays.
Part II comprising eight chapters is devoted to the design of scheduling algorithms. Here the
reader can find a wide variety of algorithms: exact, approximate with performance
guarantees, heuristics and meta-heuristics; most algorithms are supplied by the complexity
analysis and/or tested computationally.
Chapter 5 deals with a batch version of the single-processor scheduling problem with batch
setup times and batch delivery costs, the objective being to find a schedule which minimizes
the sum of the weighted number of late jobs and the delivery costs. A new dynamic
programming (DP) algorithm which runs in pseudo-polynomial time is proposed. By
combining the techniques of binary range search and static interval partitioning, the DP
algorithm is converted into a fully polynomial time approximation scheme for the general
case. The DP algorithm becomes polynomial for the special cases when jobs have equal
weights or equal processing times.
Chapter 6 studies on-line approximation algorithms with performance guarantees for an
important class of scheduling problems defined on identical machines, for jobs with
arbitrary release times.
Chapter 7 presents a new hybrid metaheuristic for solving the jobshop scheduling problem
that combines augmented-neural-networks with genetic algorithm based search.
In Chapter 8 heuristics based on a combination of the guided search and tabu search are
considered to minimize the maximum completion time and maximum tardiness in the
parallel-machine scheduling problems. Computational characteristics of the proposed
heuristics are evaluated through extensive experiments.
Chapter 9 presents a hybrid meta-heuristics based on a combination of the genetic algorithm
and the local search aimed to solve the re-entrant flowshop scheduling problems. The
hybrid method is compared with the optimal solutions generated by the integer
programming technique, and the near optimal solutions generated by a pure genetic
algorithm. Computational experiments are performed to illustrate the effectiveness and
efficiency of the proposed algorithm.

VII
Chapter 10 is devoted to the design of different hybrid heuristics to schedule a bottleneck
machine in a flexible manufacturing system problems with the objective to minimize the
total weighted tardiness. Search algorithms based on heuristic improvement and local
evolutionary procedures are formulated and computationally compared.
Chapter 11 deals with a multi-objective no-wait flow shop scheduling problem in which the
weighted mean completion time and the weighted mean tardiness are to be optimized
simultaneously. To tackle this problem, a novel computational technique, inspired by
immunology, has emerged, known as artificial immune systems. An effective multi-
objective immune algorithm is designed for searching the Pareto-optimal frontier. In order
to validate the proposed algorithm, various test problems are designed and the algorithm is
compared with a conventional multi-objective genetic algorithm. Comparison metrics, such
as the number of Pareto optimal solutions found by the algorithm, error ratio, generational
distance, spacing metric, and diversity metric, are applied to validate the algorithm
efficiency. The experimental results indicated that the proposed algorithm outperforms the
conventional genetic algorithm, especially for the large-sized problems.
Chapter 12 considers a version of the open-shop problem called the concurrent open shop
with the objective of minimizing the weighted number of tardy jobs. A branch and bound
algorithm is developed. Then, in order to produce approximate solutions in a reasonable
time, a heuristic and a tabu search algorithm are proposed.. Computational experiments
support the validity and efficiency of the tabu search algorithm.
Part III comprises seven chapters and deals with new models and decision making
approaches to scheduling. Chapter 13 addresses an integrative view for the production
scheduling problem, namely resources integration, cost elements integration and solution
methodologies integration. Among methodologies considered and being integrated together
are mathematical programming, constraint programming and metaheuristics. Widely used
models and representations for production scheduling problems are reconsidered, and
optimization objectives are reviewed. An integration scheme is proposed and performance
of approaches is analyzed.
Chapter 14 examines scheduling problems confronted by planners in multi product
chemical plants that involve sequencing of jobs with sequence-dependent setup time. Two
mixed integer programming (MIP) formulations are suggested, the first one aimed to
minimize the total tardiness while the second minimizing the sum of total
earliness/tardiness for parallel machine problem.
Chapter 15 presents a novel mixed-integer programming model of the flexible flow line
problem that minimizes the makespan. The proposed model considers two main
constraints, namely blocking processors and sequence-dependent setup time between jobs.
Chapter 16 considers the so-called hybrid jobshop problem which is a combination of the
standard jobshop and parallel machine scheduling problems with the objective of
minimizing the total tardiness. The problem has real-life applications in the semiconductor
manufacturing or in the paper industries. Efficient heuristic methods to solve the problem,
namely, genetic algorithms and ant colony heuristics, are discussed.
Chapter 17 develops the methodology of dynamical gradient Artificial Neural Networks for
solving the identical parallel machine scheduling problem with the makespan criterion
(which is known to be NP-hard even for the case of two identical parallel machines). A
Hopfield-like network is proposed that uses time-varying penalty parameters. A novel time-
varying penalty method that guarantees feasible and near optimal solutions for solving the
problem is suggested and compared computationally with the known LPT heuristic.

VIII
In Chapter 18 a dynamic heuristic rule-based approach is proposed to solve the resource
constrained scheduling problem in an FMS, and to determine the best routes of the parts,
which have routing flexibility. The performance of the proposed rule-based system is
compared with single dispatching rules.
Chapter 19 develops a geometric approach to modeling a large class of multithreaded
programs sharing resources and to scheduling concurrent real-time processes. This chapter
demonstrates a non-trivial interplay between geometric approaches and real-time
programming. An experimental implementation allowed to validate the method and
provided encouraging results.
Part IV comprises four chapters and introduces real-life applications of scheduling theory
and case studies in the sheet metal shop (Chapter 20), baggage handling systems (Chapter
21), large-scale supply chains (Chapter 22), and semiconductor manufacturing and
photolithography systems (Chapter 23).
Summing up the wide range of issues presented in the book, it can be addressed to a quite
broad audience, including both academic researchers and practitioners in halls of industries
interested in scheduling theory and its applications. Also, it is heartily recommended to
graduate and PhD students in operations research, management science, business
administration, computer science/engineering, industrial engineering and management,
information systems, and applied mathematics.
This book is the result of many collaborating parties. I gratefully acknowledge the assistance
provided by Dr. Vedran Kordic, Editor-in-Chief of the book series, who initiated this project,
and thank all the authors who contributed to the volume.
References
Bellman, R., (1956). Mathematical aspects of scheduling theory. Journal of Society of Industrial
and Applied Mathematics 4, 168–205.
Blazewicz, J., Ecker, K.H., Pesch, E., Schmidt, G., and Weglarz (2007), Handbook on Scheduling,
From Theory to Applications, Springer. Berlin.
Brucker, P. (2007), Scheduling Algorithms, Springer, 5th edition, Berlin.
Chretienne, P., Coffman, E.G., Lenstra, J.K., Liu, Z. (eds.) (1995), Scheduling Theory and its
Applications, Wiley, New York.
Coffman, E.G., Jr. (ed.), (1976), Scheduling in Computer and Job Shop Systems, Wiley, New York.
Gutin, G. and Punnen, A.P. (eds.) (2002), The Traveling Salesman Problem and Its Variations,
Springer, Berlin, 848 p.
Johnson, S.M. (1954). Optimal two- and three-stage production schedules with setup times
included. Naval Research Logistics Quarterly 1, 61–68.
Lawler, E., Lenstra, J., Rinnooy Kan, A., and Shmoys, D. (1985) The Traveling Salesman Problem:
A Guided Tour of Combinatorial Optimization, Wiley, New York.
Leung, J.Y.-T. (ed.) (2004), Handbook of Scheduling: Algorithms, Models, and Performance
Analysis, Chapman & Hall/CRC, Boca Raton
Pinedo, M. (2001), Scheduling: Theory, Algorithms and Systems, Prentice Hall, Englewood Cliffs.
Tanaev, V.S., Gordon, V.S., and Shafransky, Ya.M. (1994), Scheduling Theory. Single-Stage
Systems, Kluwer, Dordrecht.
Tanaev, V.S., Sotskov,Y.N. and Strusevich, V.A.. (1994), Scheduling Theory. Multi-Stage Systems,
Kluwer, Dordrecht.
Eugene Levner
September 10,2007

IX
Contents
Preface ........................................................................................................................................V
Part I. New Trends and Tools in Scheduling: Surveys and Analysis
1. Cyclic Scheduling in Robotic Cells:
An Extension of Basic Models in Machine Scheduling Theory ....................................001
Eugene Levner, Vladimir Kats and David Alcaide Lopez De Pablo
2. Combinatorial Models for Multi-agent Scheduling Problems ...................................021
Alessandro Agnetis, Dario Pacciarelli and Andrea Pacifici
3. Scheduling under Unavailability Constraints to Minimize Flow-time Criteria ........047
Imed Kacem
4. Scheduling with Communication Delays ......................................................................063
R. Giroudeau and J.C. Kinig
Part II. Exact Algorithms, Heuristics and Complexity Analysis
5. Minimizing the Weighted Number of
Late Jobs with Batch Setup Times and Delivery Costs on a Single Machine ............085
George Steiner and Rui Zhang
6. On-line Scheduling on
Identical Machines for Jobs with Arbitrary Release Times ...........................................099
Li Rongheng and HuangHuei-Chuen
7. A NeuroGenetic Approach for Multiprocessor Scheduling .......................................121
Anurag Agarwal
8. Heuristics for Unrelated Parallel Machine
Scheduling with Secondary Resource Constraints ........................................................137
Jeng-Fung Chen

X
9. A hybrid Genetic Algorithm
for the Re-entrant Flow-shop Scheduling Problem .........................................................153
Jen-Shiang Chen, Jason Chao-Hsien Pan and Chien-Min Lin
10. Hybrid Search Heuristics
to Schedule Bottleneck Facility in Manufacturing Systems ..........................................167
Ponnambalam S.G., Jawahar.N and Maheswaran. R
11. Solving a Multi-Objective No-Wait Flow
Shop Problem by a Hybrid Multi-Objective Immune Algorithm ....................................195
R. Tavakkoli-Moghaddam, A. Rahimi-Vahed and A. Hossein Mirzaei
12. Concurrent Openshop Problem
to Minimize the Weighted Number of Late Jobs ..............................................................215
H.L. Huang and B.M.T. Lin
Part III. New Models and Decision Making Approaches
13. Integral Approaches to Integrated Scheduling .........................................................221
Ghada A. El Khayat
14. Scheduling with setup Considerations: An MIP Approach .....................................241
Mohamed. K. Omar, Siew C. Teo and Yasothei Suppiah
15. A New Mathematical Model for Flexible Flow
Lines with Blocking Processor and Sequence-Dependent Setup Time ......................255
R. Tavakkoli-Moghaddam and N. Safaei
16. Hybrid Job Shop and Parallel Machine
Scheduling Problems: Minimization of Total Tardiness Criterion ................................273
Frederic Dugardin, HichamChehade,
Lionel Amodeo, Farouk Yalaoui and Christian Prins
17. Identical Parallel Machine Scheduling with
Dynamical Networks using Time-Varying Penalty Parameters .....................................293
Derya Eren Akyol
18. A Heuristic Rule-Based Approach for
Dynamic Scheduling of Flexible Manufacturing Systems .............................................315
Gonca Tuncel
19. A Geometric Approach to Scheduling
of Concurrent Real-time Processes Sharing Resources ...............................................323
Thao Dang and Philippe Gerner

XI
Part IV. Real-Life Applications and Case Studies
20. Sequencing and Scheduling in the Sheet Metal Shop ..................................................345
B. Verlinden, D. Cattrysse, H. Crauwels, J. Duflou and D. Van Oudheusden
21. Decentralized Scheduling of
Baggage Handling using Multi Agent Technologies .......................................................381
Kasper Hallenborg
22. Synchronized Scheduling of Manufacturing and 3PL Transportation ...................405
Kunpeng Li and Appa Iyer Sivakumar
23. Scheduling for Dedicated Machine Constraint ..........................................................417
Arthur Shr, Peter P. Chen and Alan Liu

1
Cyclic Scheduling in Robotic Cells:
An Extension of Basic Models in Machine
Scheduling Theory
Eugene Levner1, Vladimir Kats2 and David Alcaide López De Pablo3
1Holon Institute of Technology, Holon, 2Institute of Industrial Mathematics, Beer-Sheva,
3University of La Laguna, La Laguna, Tenerife
1, 2 Israel, 3Spain
1. Introduction
There is a growing interest on cyclic scheduling problems both in the scheduling literature
and among practitioners in the industrial world. There are numerous examples of
applications of cyclic scheduling problems in different industries (see, e.g., Hall (1999),
Pinedo (2001)), automatic control (Romanovskii (1967), Cohen et al. (1985)), multi-processor
computations (Hanen and Munier (1995), Kats and Levner (2003)), robotics (Livshits et al.
(1974), Kats and Mikhailetskii (1980), Kats (1982), Sethi et al. (1992), Lei (1993), Kats and
Levner (1997a, 1997b), Hall (1999), Crama et al. (2000), Agnetis and Pacciarelli (2000),
Dawande et al. (2005, 2007)), and in communications and transport (Dauscha et al. (1985),
Sharma and Paradkar (1995), Kubiak (2005)). It is, perhaps, a surprising thing that many
facts in scheduling theory obtained as early as in the 1960s, are re-discovered and re-
rediscovered by the next generations of researchers. About two decades ago, this fact was
noticed by Serafini and Ukovich (1989).
The present survey uniformly addresses cyclic scheduling problems through the prism of
the classical machine scheduling theory focusing on their features that are common for all
aforementioned applications. Historically, the scheduling literature considered periodic
machine scheduling problems in two major classes – called flowshop and jobshop - in which
setup and transportation times were assumed insignificant. Indeed, many machining centers
can quickly switch tools, so the setup times for these situations may be small or negligible.
There are a lot of results about cyclic flowshop and jobshop problems with negligible
setup/transportation times. Advantages of cyclic scheduling policies over conventional
(non-cyclic) scheduling in flexible manufacturing are widely discussed in the literature, we
refer the interested reader to Karabati and Kouvelis (1996), Lee and Posner (1997), Hall et al.
(2002), Seo and Lee (2002), Timkovsky (2004), Dawande et al. (2007), and numerous
references therein.
At the same time, modern flexible manufacturing systems are supplied by computer-
controlled hoists, robots and other material handling devices such that the transportation
and setup operation times are significant and should not be ignored. Robots have become a
standard tool to serve cyclic transportation and assembling/disassembling processes in
manufacturing of airplanes, automobiles, semiconductors, printed circuit boards, food

Multiprocessor Scheduling: Theory and Applications
2
products, pharmaceutics and cosmetics. Robots have expanded production capabilities in
the manufacturing world making the assembly process faster, more efficient and precise
than ever before. Robots save workers from tedious and dull assembly line jobs, and
increase production and savings in the processes. As larger and more complex robotic cells
are implemented, more sophisticated planning and scheduling models and algorithms are
required to perform and optimize these processes.
The cyclic scheduling problems, in which setup operations are performed by automatic
transporting devices, constitute a vast subclass of cyclic problems. Robots or other automatic
devices are explicitly introduced into the models and treated as special purpose machines.
In this chapter, we will focus on three major classes of cyclic scheduling problems –
flowshop, jobshop, and parallel machine shop.
The chapter is structured as follows. Section 2 is a historical overview, with the main
attention being paid to the early works of the 1960s. Section 3 recalls three orthodox classes
of scheduling theory: flowshop, jobshop, and PERT-shop. Each of these classes can be
extended in two directions: (a) for describing periodic processes with negligible setups, and
(b) for describing periodic processes in robotic cells where setups and transportation times
are non-negligible. In Section 4 we consider an extension of the cyclic PERT-shop, called the
cyclic FMS-shop and demonstrate that its important special case can be solved efficiently by
using a graph approach. Section 5 concludes the chapter.
2. Brief Historical Overview
Cyclic scheduling problems have been introduced in the scheduling literature in the early
1960s, some of them assuming setup/transportation times negligible while other explicitly
treating material handling devices with non-negligible operation times.
Cyclic Flowshop. Cuninghame-Greene (1960, 1962) has described periodic industrial
processes, which in today’s terminology might be classified as a cyclic flowshop (without
setups and robots), and suggested an algebraic method for finding minimum cycle time
using matrix multiplication in which one writes “addition” in place of multiplication and
operation “max” instead of addition. This (max, +)–algebra has become popular in the 1980s
(see, e.g. Cuninghame-Greene (1979), Cohen et al. (1985), Baccelli et al. (1992)) and is
presently used for solving the cyclic flowshop without robots, see, e.g., Hanen (1994), Hanen
and Munier (1995), Lee (2000), and Seo and Lee (2002).
Independently of the latter research, Degtyarev and Timkovsky (1976) and Timkovsky
(1977) have studied so-called spyral cyclograms widely used in the Soviet electronic industry;
they introduced a generalized shop structure which they called a “cycle shop”. Using a more
standard terminology, we might say that these authors have been the first to study a
flowshop with reentrant machines which includes, as special cases, many variants of the basic
flowshop, for instance, the reentrant flowshop of Graves et al. (1983), V-shop of Lev and
Adiri (1984), cyclic robotic flowshop of Kats and Levner (1997, 1998, 2002). The interested
reader is referred to Middendorf and Timkovsky (2002) and Timkovsky (2004) for more
details.
Cyclic Robotic Flowshop. In the beginning of 1960s, a group of Byelorussian mathematicians
(Suprunenko et al. (1962), Aizenshtat (1963), Tanaev (1964), and others) investigated cyclic
processes in manufacturing lines served by transporting devices. The latters differ from
other machines in their physical characteristics and functioning. These authors have
introduced a cyclic robotic flowshop problem and suggested, in particular, a combinatorial

The Extension of Basic Models in Machine Scheduling Theory 3
method called the method of forbidden intervals which today is being developed further by
different authors for various cyclic robotic scheduling problems (see, for example, Livshits
et al. (1974), Levner et al. (1997), Kats et al. (1999), Che and Chu (2005a, 2005b), Chu (2006),
Che et al. (2002, 2003)). A thorough review in this area can be found in the surveys by Hall
(1999), Crama et al. (2000), Manier and Bloch (2003), and Dawande et al. (2005, 2007).
Cyclic PERT-shop. The following cyclic PERT-shop problem has originated in the work by
Romanovskii (1967). There is a set S of n partially ordered operations, called generic
operations, to be processed on machines. As in the classic (non-cyclic) PERT/CPM problem,
each operation is done by a dedicated machine and there is sufficiently many machines to
perform all operations; so the question of scheduling operations on machines vanishes. Each
operation i has processing time pi > 0 and must be performed periodically with the same
period T, infinitely many times.
For each operation i, let <i, k> denote the kth execution (or, repetition) of operation i in a
schedule (here k is any positive integer). Precedence relations are defined as follows (here we
use a slightly different notation than that given by Romanovskii). If a generic operation i
precedes a generic operation j, the corresponding edge (i, j) is introduced. Any edge (i,j) is
supplied by two given values, Lij called the length, or delay, and Hij called the height of the
corresponding edge (i, j). The former value is any rational number of any sign while the
latter is integer. Then, for a pair of operations i and j, and the given length Lij and height Hij,
the following relations are given: for all k •1, t(i,k) + Lij d t(j, k + Hij), where t(i,k) is the
starting time of operation <i, k>. An edge is called interior if its end-nodes belong to the same
iteration (or, one can say “to the same block, or pattern”) and backward (or, recycling) if its
end-nodes belong to two consecutive blocks.
A schedule is called periodic (or cyclic) with cycle time T if t(i, k) = t(i,1) + (k-1)T, for all
integer k •1, and for all iS (see Fig. 1). The problem is to find a periodic schedule (i.e., the
starting time t(i,1) of operations) providing a minimum cycle time T, in a graph with the
infinite number of edges representing an infinitely repeating process.
Figure 1. The cyclic PERT graph (from Romanovskii, (1967))
In the above seminal paper of 1967, Romanovskii proved the following claims which have
been rediscovered later by numerous authors.
x Claim 1. Let the heights of interior edges be 0 and the heights of backward edges 1. The
minimum cycle time in a periodic PERT graph with the infinite number of edges is
equal to the maximum circuit ratio in a corresponding double-weighted finite graph in
which the first weight of the arc is its length and the second is its height: Tmin = maxC
ƴLij/ƴHij, where maximum is taken over all circuits C; ƴLij denotes the total circuit
length, and ƴHij the total circuit height.

4
x Claim 2. The max circuit ratio problem and its version, called the max mean cycle
problem, can be reformulated as linear programming problems. The dual to these
problems is the parametric critical path problem.
x Claim 3. The above problems, namely, the max circuit ratio problem and the max mean
cycle problem, can be solved by using the iterative Howard-type dynamic
programming algorithm more efficiently than by linear programming. (The basic
Howard algorithm is published in Howard (1960)).
x Claim 4. Mean cycle time counted for n repetitions of the first block in an optimal
schedule differs from the optimal mean cycle time by O(1/n).
The interested reader can find these or similar claims discovered independently, for
example, in Reiter (1968), Ramchandani (1973), Karp (1978), Gondran and Minoux (1985),
Cohen et al. (1985), Hillion and Proth (1989), McCormick et al. (1989), Chretienne (1991), Lei
and Liu (2001), Roundy (1992), Ioachim and Soumis (1995), Lee and Posner (1997), Hanen
(1994), Hanen and Munier (1995), Levner and Kats (1998), Dasdan et al. (1999), Hall et al.
(2002). In recent years, the cyclic PERT-shop has been studied for more sophisticated
modifications, with the number of machines limited and resource constraints added (Lei
(1993), Hanen (1994), Hanen and Munier (1995), Kats and Levner (2002), Brucker et al.
(2002), Kampmeyer (2006)).
3. Basic Definitions and Illustrations
In this section, we recall several basic definitions from the scheduling theory. Machine
scheduling is the allocation of a set of machines and other well-defined resources to a set of
given jobs, consisting of operations, subject to some pre-determined constraints, in order to
satisfy a specific objective. A problem instance consists of a set of m machines, a set of n jobs
is to be processed sequentially on all machines, where each operation is performed on
exactly one machine; thus, each job is a set of operations each associated with a machine.
Depending on how the jobs are executed at the shop (i.e. what is the routing in which jobs
visit machines), the manufacturing systems are classified as:
x flow shops, where all jobs are performed sequentially, and have the same processing
sequence (routing ) on all machines, or
x job shops, where the jobs are performed sequentially but each job has its own
processing sequence through the machines,
x parallel machine shop, where sequence of operations is partially ordered and several
operations of any individual job can be performed simultaneously on several parallel
machines.
Formal descriptions of these problems can be found in Levner (1991, 1992), Tanaev et al.
(1994a, 1994b), Pinedo (2001), Leung (2004), Shtub et al. (1994), Gupta and Stafford (2006),
Brucker (2007), Blazewicz et al. (2007). We will consider their cyclic versions.
The cyclic shop problems are an extension of the classical shop problems. A problem
instance again consists of a set of m machines and a set of n jobs (usually called products, or
part types) which is to be processed sequentially on all machines. The machines are
requested to process repetitively a minimal part set, or MPS, where the MPS is defined as the
smallest integer multiple of the periodic production requirements for every product. In
other words, let r = (r1, r2,… , rn) be the production requirements vector defining how many
units of each product (j=1,…,n) are to be produced over the planning horizon. Then the MPS

is the vector rMPS = (r1/q, r2/q, … , rn/q) where q is the greatest common divisor of integers
r1, r2,… , rn. Identical products of different, periodically repeated, replicas of the MPS have
the same processing sequences and processing times, whereas different products within an
MPS may require different processing sequences of machines and the processing times. The
replicas of the MPS are processed through equal time intervals T called cycle time and in
each cycle, exactly one MPS’s replica is introduced into the process and exactly one MPS’s
replica is completed.
An important subclass of cyclic shop problems are the robotic scheduling problems, in
which one or several robots perform transportation operations in the production process.
The robot can be considered as an additional machine in the shop whose transportation
operations are added to the set of processing operations. However, this “machine” has
several specific properties: (i) it is re-entrant (that is, any product requires the utilization of
the same robot several times during each cycle) and (ii) its setup operations, that is, the
times of empty robots between the processing machines, are non-negligible.
3.1. Cyclic Robotic Flowshop
In the cyclic robotic flowshop problem it is assumed that a technological processing
sequence (route) for n products in an MPS is the same for all products and is repeated
infinitely many times. The transportation and feeding operations are done by robots, and
the sequences of the robotic operations and technological operations are repeated cyclically.
The objective is to find the cyclic schedule with the maximum productivity, that is, the
minimum cycle time. In the general case, the robot's route is not given and is to be found as
a decision variable.
A possible layout of the cyclic robotic flowshop is presented in Fig. 2.
Figure 2. Cyclic Robotic Flowshop
A corresponding Gantt chart depicting coordinated movement of parts and robot is given in
Fig. 3. Machines 0 and 6 stand for the loading and unloading stations, correspondingly.
Three identical parts are introduced into the system at time 0, 47 and 94, respectively. The
bold horizontal lines depict processing operations on the machines while a thin line depicts

6
the route of a single robot between the processing machines. More details can be found in
Kats and Levner (1998).
Figure 3. The Gantt chart for cyclic robotic flowshop (from Kats and Levner (1998))
3.2 Cyclic Robotic Jobshop
The cyclic robotic jobshop differs from cyclic robotic flowshop only in that each of n
products in MPS has its own route as depicted in Fig. 4.
5
4
3
2
1
Unloading
station ul
Loading
station
Fig. 4. An example of a simple technological network with two linear product routes and
five processing machines, depicted by the squares, where denotes the route for
product a, and denotes the route for product b (from Kats et al. (2007))
The corresponding graphs depicting the sequence of technological operations and robot
moves in a jobshop frame are presented in Fig. 5 and 6 .
The corresponding Gantt chart depicting coordinated movement of parts and robots in time
is in Fig. 7, where stations 1 to 5 stand for the processing machines and stations 0 and 6 are,
correspondingly, the loading and unloading ones. In what follows, we refer to the machines
and loading/unloading stations simply as the stations.

Figure 5. The sequence of robot operations in two consecutive cycles (from Kats et al. (2007))
Cycle 1
Cycle 2
o2,b
o2,b
0
,
b
25,b-
b3,a-
b3,a-
0
,
,
b
1,b-
1,b-
b5,a-
b5,a-
0 1,a
0 0,a 0 1,a
b4,b-
b4,b-
0 0,a
25,b-
Figure 6. Graph depicting the sequence of processing operations and robot moves for two
successive cycles (Kats et al. (2007)). The variables are presented as nodes and the constraints
as arcs, where denotes the robot operation sequence, the processing time window
constraints, o setup time constraints, and the cut-off line between two cycles
b3,a- 0,a b5,a- 1,a
b4,b- o2,b 25,b-
1,b-
1,b-
Figure 7. The Gantt chart of coordinated movement of parts and a robot in time (Kats et al.
(2007))
Figure 7. The Gantt chart of coordinated movement of parts and a robot in time (Kats et al.
(2007))
0
1
2
3
4
5
6
-90 -60 -30 0 30 60 90 120 150
Time
S
tation
Part a of MPS 0 Part b of MPS 0 Part a of MPS -1 Part b of MPS -1 Part a of MPS 1
Part b of MPS 1 Part a of MPS -2 Part b of MPS -2 Robot
Cycle 2
Cycle 1
0,b
0,b
o
b3,a- 0,a b5,a- 1,a
b4,b- 2,b
o 25,b-

8
3.3 Cyclic Robotic PERT Shop
This major class of cyclic scheduling problems which we will focus on in this sub-section,
has several other names in the literature, for example, ‘the basic cyclic scheduling problem’,
‘the multiprocessor cyclic scheduling problem’, ‘the general cyclic machine scheduling
problem’. We will call this class the cyclic PERT shop due to its evident closeness to project
scheduling, or PERT/CPM problems: when precedence relations between operations are
given, and there is a sufficient number of machines, the parallel machine scheduling
problem becomes the well-known PERT-time problem.
We define the cyclic PERT shop as follows: A set of n products in an MPS is given and the
technological process for each product is described by its own PERT graph. A product may be
considered as assembly consisting of several parts. There are three types of technological
operations: a) operations which can be done in parallel on several machines, i.e. the parts
consisting the assembly are processed separately; b) assembling operations; c) disassembling
operations. There are infinitely many replicas of the MPS and a new MPS’s replica is introduced
in each cycle. In the cyclic robotic PERT shop, one or several robots are introduced for performing
the transportation and feeding operations. The objective is to find the cyclic schedule and the
robot route providing the maximum productivity, that is, the minimum cycle time.
Classes of scheduling
problems
Subclasses of cyclic
scheduling problems
Representative references
Models with negligible
setups and no-robot
Cuninghame-Greene (1960, 1962),
Timkovsky (1977), Karabati and
Kouvelis (1996), Lee and Posner
(1997)
Cyclic Flowshop
Models
Robotic models
Suprunenko et al. (1962), Tanaev
(1964), Livshits et al. (1974),
Phillips and Unger (1976), Kats
and Mikhailetskii (1980), Kats
(1982), Kats and Levner (1997a,
1997b), Crama et al. (2000),
Dawande et al. (2005, 2007).
Models with negligible
setups and no-robot
Roundy (1992), Hanen and
Munier (1995), Hall et al. (2002)
Cyclic Jobshop Models
Robotic models Kampmeyer (2006), Kats et al.
(2007)
Models with setups
negligible, no-robot
Romanovskii (1967), Chretienne
(1991), Hanen and Munier (1995)
PERT-shop Models
Robotic models
Lei (1993), Chen et al. (1998),
Levner and Kats (1998), Alcaide
et al. (2007), Kats et al. (2007)
Remark. For completeness, we might mention three more groups of robotic (non-cyclic) scheduling
problems which might be looked at as “atomic elements” of the cyclic problems: Robotic Non-cyclic
Flowshop (Kise (1991), Levner et al. (1995a,1995b), Kogan and Levner 1998), Robotic Non-cyclic Jobshop
(Hurink and Knust (2002)), and Robotic Non-cyclic PERT-shop (Levner et al. (1995c)). However, these
problems lie out of the scope of the present survey.
Table 1. Classification of major cyclic scheduling problems

The cyclic robotic PERT shop problems differs from the cyclic robotic jobshop in two main
aspects: a) the operations are partially ordered, in contrast to the jobshop where operations are
linearly ordered; b) there are sufficiently many processing machines, due to which the
sequencing of operations on machines vanishes. This type of problems is overviewed in
more detail in surveys by Hall (1999) and Crama et al. (2000).
We conclude this section by the classification scheme for cyclic problems and the
representative references (see Table 1).
4. The Cyclic Robotic FMS-shop
4.1. An Informal Description of the Cyclic Robotic FMS Shop
The cyclic robotic FMS-shop can be looked at as an extension of the cyclic robotic jobshop in
which there given PERT-type (not-only-chain) precedence relations between
assembly/disassembly operations for each product. In other view, the robotic FMS-shop can
be looked at as a generalized cyclic robotic PERT-shop in which a finite set of machines
performing the operations are given. In what follows, we assume that K PERT projects
representing the technological processes for K products in an MPS are given and to be
repeated infinitely many times on m machines.
Example. (Levner et al. (2007)). MPS consists of two products MPS ={a, b} with sequence of
processing operations for products a and b given in the form of PERT graphs as shown in
Fig. 8.
Product b
Product a
2
6
6
0
5
3
4
1
5
3
4
2
1
0
Figure 8. Two fragments of a technological network in which partially ordered (PERT-type)
networks are given for two individual products in an FMS-shop
There are five processing machines and loading and unloading stations (stations 0 and 6
correspondingly). Infinite number of MPS replicas are waiting for processing and arrive
periodically in process as shown in Fig. 9.
0
1
2
3
4
5
6
-90 -60 -30 0 30 60 90 120 150
Time
Station
Figure 9. The Gantt chart of several MPS replicas arriving in the technological process
through equal time intervals

10
We give the problem description basing on the model developed in Kats et al. (2007). The
product (part type) processing time at any machine is not fixed, but defined by a pair of
minimum and maximum time limits, called the time window constraints. The movements of
parts between the machines and loading/unloading stations are performed by a robot,
which travels in a non-negligible time. To move a part, the robot first travels to the station
where the part is located, wait if the part is still in process, unload the part and then travels
to the next station specified by a given sequence of material handling operations for the
robot. The robot is supplied by multiple grippers in order to transport several parts
simultaneously to an assembling machine or from an disassembling machine. There is no
buffer available between the machines and each machine can process only one product at
time. If different types of products are processed at the same machine, then a non-negligible
setup time between the processing of these products may be required. The general problem
is to determine the product sequence at each machine, the robot route and the exact
processing time of each product at each machine so that the cycle time is minimized while
the time windows, the setup times, and the robot traveling time constraints are satisfied.
Scheduling of the material handling operations of robots to minimize the cycle time, even
with a single part per MPS and a single one-gripper robot, has been known to be NP-hard in
strong sense (Livshits et al. (1974); Lei and Wang (1989)).
In this chapter, we are interested in a special case of the cyclic scheduling problem
encountered in such a processing network. In particular, we solve the multiple-product
problem of minimizing the cycle time for a processing network with a single multi-gripper
robot, a fixed and known in advance sequence of material handling operations for the robot
to be performed in each cycle and the known product sequence at each machine.
Throughout the remaining analysis of this chapter, we shall denote this problem as Q.
Problem Q is a further extension of the scheduling problem P introduced and solved in Kats
et al. (2007). The problem P is the jobshop scheduling problem where technological
operations for each product are linked by simple chain-like precedence relations (see Fig. 5
above). Like in P, in problem Q the sequence of robot moves is assumed to be fixed and
known. With this special case, the sequencing issue for the robot moves vanishes, and the
problem reduces to finding the exact processing times from the given intervals. This case
has been shown to be polynomial solvable by several researchers independently via
different approaches. Representative work on this can be found in the work by Livshits et al.
(1974), Matsuo et al. (1991), Lei (1993), Ioachim and Soumis (1995), Chen et al. (1998), Van de
Klundert (1996), Levner et al. (1996, 1997), Levner and Kats (1998), Crama et al. (2000), Lee
(2000), Lei and Liu (2001), Alcaide at al. (2007), Kats et al. (2007).
In this section, we analyze the properties of Q and show that it can be solved by the
polynomial algorithm, originating from the parametric critical path method by Levner and Kats
(1998) for the single-product version of the problem. Our main observation is that the
technological processes for products presented by PERT-type graphs (see Fig. 8) can be
treated by the same mathematical tools as more primitive processes presented by linear
chains considered in Kats et al. (2007).
4.2. A formal analysis of problem Q
Each given instance of Q has a fixed sequence of material handling operations V, and an
associated MPS with K products and PERT-type precedence relations. The set of processing
operations of a product in the MPS is not in the form of a simple chain like in problem P, but

rather linked into a technological graph, containing assembling and disassembling operations.
Let G denote the associated integrated technological network which integrates K technological
graphs of all products in the MPS with the given sequence of processing operations on
machines. In network G, each node specifies a machine or the loading station 0/unloading
station ul, each arc specifies a particular precedence relationship between two consecutive
processing operations of a product, and each technological graph to be performed for each
product corresponds to a subgraph in network G.
Now, let : be the set of distinct stations/nodes in a given technological network G, j be the
index to enumerate stations, ,
:

j and k be the index for product, .
1 K
k d
d Each
product k requires a total of nk partially ordered processing operations with each operation
taking place at a respective workstation. In each material handling operation the robot
removes a product (or a ”semi-product”) from a station. Therefore,
is the total number of all operations to be performed by the robot
in a cycle, including a total of K operations at station 0 (i.e., one for each product in the MPS
to be introduced into the process in a cycle). The processing time for product k at station j,
is a deterministic decision variable that must be confined within a given interval
, for 1 ” k ” K, j=1,2,…,nk, and
¦
K
k k
n
K
n ,...,
2
,
1
,
,k
j
p
]
,
[ ,
, k
j
k
j b
a ,
0
z
j where parameters aj,k and bj,k are the
given constants and define the time window constraints on the part processing time at
workstation j. That is, after arriving at workstation j, a part of type k must immediately start
processing and be processed there for a time interval no less than aj,k and no more than bj,k.
In the practices of assembling shops, the violating of the time window constraints,
may deteriorate the product quality and cause a defect product.
,
,
,
, k
j
k
j
k
j b
p
a d
d
For any given instance of Q sequenceV , V = ([i], r[i], f(i)), i=1,2, …,n specifies a total of n
(material handling) operations to be performed by the robot in each cycle. The ith operation
in V, ([i], r[i], f(i)) where },
{

]
[
,
1 ul
i
n
i :

d
d },
,...,
2
,
1
{
]
[ K
i
r f(i){keep, load}
consists of the following sequential motions:
x Unload product ]
[i
r from station [i];
x If f(i) = load, then transport product ]
[i
r to the next station on its technological route, s[i],
,
]
[ :

i
s and load product ]
[i
r to station s[i] which include the loading of all parts of the
product kept by grippers.
x If f(i) = keep, then keep the unloaded product in gripper.
x Travel to station [i+1], where },
{

]
1
[ ul
i :

and wait if necessary. When i=n, [n+1] =
0.
In each cycle, the given sequence of operations, V, is performed exactly once, so that exactly
one MPS is introduced into the process and exactly one MPS is completed and sent to
station ul. In this infinite cyclic process, parts being moved and processed within a cycle
could belong to different MPS’s replicas introduced in different cycles and full processing
time (life cycle) of one MPS could be much longer than cycle time T.
Network G introduces two types of precedence relationships. The first type of relationships
ensures the processing time window constraints, and the second type refers to the setup time

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subjects, they would have been found really without sight and
feeling. For, in general character, persons in somnambulism exactly
resemble other entranced persons, who certainly feel nothing; for
they have borne the most painful surgical operations without the
smallest indication of suffering. So I have little doubt that the
insensibility, which the observers imputed to the somnambulists,
really existed, although they may have failed to establish the fact by
positive evidence.
The question as to the development of a new power of
perception, such as I conjecture the lad used in his walk from Tarbes
to Bagnères, will be found to be resolved, or, at any rate, to be
attended with no theoretical difficulties, when the performances of
full-waking in trance, which I propose to describe in the next letter,
shall have been laid before the reader.

LETTER VIII.
Trance-waking.—Instances of its spontaneous occurrence in the form
of catalepsy—Analysis of catalepsy—Its three elements: double
consciousness, or pure waking-trance; the spasmodic seizure;
the new mental powers displayed—Cases exemplifying catalepsy
—Other cases unattended with spasm, but of spontaneous
occurrence, in which new mental powers were manifested—
Oracles of antiquity—Animal instinct—Intuition.
Under this head are contained the most marvellous phenomena
which ever came as a group of facts in natural philosophy before the
world; and they are reaching that stage towards general reception
when their effect is most vivid and striking. Five-and-twenty years
ago no one in England dreamed of believing them, although the
same positive evidence of their genuineness then existed as now.
Five-and-twenty years hence the same facts will be matters of
familiar knowledge. It is just at the present moment (or am I
anticipating the march of opinion by half a century?) that their
difference, and distinctness, and abhorrence even, from our previous
conceptions are most intensely felt; and that the powers which they
promise eventually to place within human control excite our
irrepressible wonder.
I shall narrate the facts which loom so large in the dawning light,
very simply and briefly, as they are manifested in catalepsy.
An uninformed person being in the room with a cataleptic patient,
would at first suppose her, putting aside the spasmodic affection of
the body, to be simply awake in the ordinary way. By-and-by her
new powers might or might not catch his observation. But a third
point would certainly escape his notice. I refer to her mental state of

waking trance, which gives, as it were, the local colouring to the
whole performance.
To elucidate this element, I may avail myself of a sketch ready
prepared by nature, tinted with the local colour alone—the case of
simple trance-waking, unattended by fits or by any marvellous
powers, as far as it has been yet observed, which is known to
physicians under the name of double consciousness.
A single fit of the disorder presents the following features:—The
young person (for the patient is most frequently a girl) seems to lose
herself for a moment or longer, then she recovers, and seems to be
herself again. The intervening short period, longer at first, and by
use rendered briefer and briefer, is a period of common initiatory
trance. When, having lost, the patient thus finds herself again, there
is nothing in her behaviour which would lead a stranger to suppose
her other than naturally awake. But her friends observe that she
now does every thing with more spirit and better than before—sings
better, plays better, has more readiness, moves even more
gracefully, than in her usual state. She manifests an innocent
boldness and disregard of little conventionalisms, which impart a
peculiar charm to her behaviour. Her mode of speaking is perhaps
something altered; a supernumerary consonant making its undue
appearance, but upon a regular law, in certain syllables. But the
most striking thing is, that she has totally forgotten all that has
passed during the morning. Inquire what her last recollections are,
they leave off with the termination of her last fit of this kind; the
intervening period is for the present lost to her. She was in her
natural state of waking when I introduced her to your notice; she
lost herself for a few seconds, found herself again; but found herself
not in her natural train of recollections, but in those of the last fit.
These fits occur sometimes at irregular intervals, sometimes
periodically and daily. In her ordinary waking state, she has her
chain of waking recollections. In her trance-waking state, she has
her chain of trance-waking recollections. The two are kept strictly
apart. Hence the ill-chosen term, double-consciousness. So at the

occurrence of her first fit, her mental existence may be said to have
bifurcated into two separate routes, in either of which her being is
alternately passed. It is curious to study, at the commencement of
such a case, with how much knowledge derived from her past life
the patient embarks on her trance-existence. The number of
previously realized ideas retained by different patients at the first fit
is very various. It has happened that the memory of facts and
persons has been so defective that the patient has had to learn even
to know and to love her parents. To most of her acquaintances she
is observed to give new names, which she uses to them in the
trance-state alone. But her habits remain; her usual propriety of
conduct: the mind is singularly pure in trance. And she very quickly
picks up former ideas, and restores former intimacies, but on a
supposed new footing. To complete this curious history, if the fits of
trance recur frequently, and through some accidental circumstance
are more and more prolonged in duration, so that most of her
waking existence is passed in trance, it will follow that the trance-
development of her intellect and character may get ahead of their
development in her natural waking. Being told this, she may become
anxious to continue always in her entranced state, and to drop the
other: and I knew a case in which circumstances favoured this final
arrangement, and the patient at last retained her trance-
recollections alone, from long continuance in that state having made
it, as it were, her natural one. Her only fear was—for she had
gradually learned her own mental history, as she expressed it to me
—that some day she should of a sudden find herself a child again,
thrown back to the point at which she ceased her first order of
recollections. This is, indeed, a very extreme and monstrous case.
Ordinarily, the recurrence of fits of simple trance-waking does not
extend over a longer period than three or four months or half a year,
after which they never reappear; and her trance acquirements and
feelings are lost to the patient’s recollection for good. I will cite a
case, as it was communicated to me by Dr. G. Barlow, exemplifying
some of the points of the preceding statement.

“This young lady has two states of existence. During the time that
the fit is on her, which varies from a few hours to three days, she is
occasionally merry and in spirits; occasionally she appears in pain,
and rolls about in uneasiness; but in general she seems so much
herself, that a stranger entering the room would not remark any
thing extraordinary: she amuses herself with reading or working,
sometimes plays on the piano—and better than at other times—
knows every body, and converses rationally, and makes very
accurate observations on what she has seen and read. The fit leaves
her suddenly, and she then forgets every thing that has passed
during it, and imagines that she has been asleep, and sometimes
that she has dreamed of any circumstance that has made a vivid
impression upon her. During one of these fits she was reading Miss
Edgeworth’s Tales, and had in the morning been reading a part of
one of them to her mother, when she went for a few minutes to the
window, and suddenly exclaimed, “Mamma, I am quite well, my
headache is gone.” Returning to the table, she took up the open
volume, which she had been reading five minutes before, and said,
“What book is this?” She turned over the leaves, looked at the
frontispiece, and replaced it on the table. Seven or eight hours
afterwards, when the fit returned, she asked for the book, went on
at the very paragraph where she had left off, and remembered every
circumstance of the narrative. And so it always is; she reads one set
of books during one state, and another during the other. She seems
to be conscious of her state; for she said one day, “Mamma, this is a
novel, but I may safely read it; it will not hurt my morals, for, when I
am well, I shall not remember a word of it.””
To form a just idea of a case of catalepsy, the reader has to
imagine such a case as I have just instanced, with the physical
feature added, that the patient, when entranced, is motionless and
fixed as a statue; the spasmodic state, however, not confining itself
closely to one type, but running into catochus, or into partial rigid
spasm, or into convulsive seizures, (see Letter V.) capriciously.

The psychical phenomena exhibited by the patient when thus
entranced, are the following:—
1. The organs of sensation are deserted by their natural sensibility.
The patient neither feels with the skin, nor sees with the eyes, nor
hears with the ears, nor tastes with the mouth.
2. All these senses, however, are not lost. Sight and hearing, if not
smell and taste, reappear in some other part—at the pit of the
stomach, for instance, or the tips of the fingers.
3. The patient manifests new perceptive powers. She discerns
objects all around her, and through any obstructions, partitions,
walls or houses, and at an indefinite distance. She sees her own
inside, as it were, illuminated, and can tell what is wrong in the
health of others. She reads the thoughts of others, whether present
or at indefinite distances. The ordinary obstacles of space and
matter vanish to her. So likewise that of time; she foresees future
events.
Such and more are the capabilities of cataleptic patients, most of
whom exhibit them all—but there is some caprice in their
manifestation.
I first resigned myself to the belief that such statements as the
above might be true, upon being shown by the late Mr. Bulteel
letters from an eminent provincial physician in the year 1838,
describing phenomena of this description in a patient the latter was
attending. In the spring of 1839, Mr. Bulteel told me that he had
himself in the interim often seen the patient, who had allowed him
to test in any way he pleased the reality of the faculties she
possessed when entranced. As usual, in the hours which she passed
daily in her natural state, she had no recollection of her
extraordinary trance performances. The following are some of the
facts, which Mr. Bulteel told me he had himself verified.
When entranced, the patient’s expression of countenance was
slightly altered, and there was some peculiarity in her mode of

speaking. To each of her friends she had given a new name, which
she used only when in the state of trance. She could read with her
skin. If she pressed the palm of her hand against the whole surface
of a printed or written page deliberately, as it were, to take off an
impression, she became acquainted verbally with its contents, even
to the extent of criticising the type or the handwriting. One day,
after a remark made to put her off her guard, a line of a folded note
was pressed against the back of her neck; she had read it. She
called this sense-feeling—contact was necessary for its
manifestation. But she had a general perceptive power besides. She
used to tell that persons, whom she knew, were coming to the
house, when they were yet at some distance. Persons sitting in the
room with her playing chess, to whom her back was turned, if they
made intentionally false moves, she would ask them what they
possibly could do that for.
The next three cases which I shall describe are from a memoir on
catalepsy (1787) by Dr. Petetin, an eminent civil and military
physician at Lyons.
M. Petetin attended a young married lady in a sort of fit. She lay
seemingly unconscious; when he raised her arm, it remained in the
air where he placed it. Being put to bed, she commenced singing. To
stop her, the doctor placed her limbs each in a different position.
This embarrassed her considerably, but she went on singing. She
seemed perfectly insensible. Pinching the skin, shouting in her ear,
nothing aroused her attention. Then it happened that, in arranging
her, the doctor’s foot slipped; and, as he recovered himself, half
leaning over her, he said, “How provoking we can’t make her leave
off singing!” “Ah, doctor,” she cried, “don’t be angry! I won’t sing any
more,” and she stopped. But shortly she began again; and in vain
did the doctor implore her, by the loudest entreaties, addressed to
her ear, to keep her promise and desist. It then occurred to him to
place himself in the same position as when she heard him before. He
raised the bed-clothes, bent his head towards her stomach, and
said, in a loud voice, “Do you, then, mean to sing for ever?” “Oh,

what pain you have given me!” she exclaimed; “I implore you speak
lower.” At the same time she passed her hand over the pit of her
stomach. “In what way, then, do you hear?” said Dr. Petetin. “Like
any one else,” was the answer. “But I am speaking to your stomach.”
“Is it possible!” she said. He then tried again whether she could hear
with her ears, speaking even through a tube to aggravate his voice—
she heard nothing. On his asking her, at the pit of her stomach, if
she had not heard him,—“No,” said she, “I am indeed unfortunate.”
A cognate phenomenon to the above is the conversion of the
patient’s new sense of vision in a direction inwards. He looks into
himself, and sees his own inside as it were illuminated or
transfigured: that is to say, his visual power is turned inwards, and
he sees his organs possibly by the Od-light they give out.
A few days after the scenes just described, Dr. Petetin’s patient
had another attack of catalepsy. She still heard at the pit of her
stomach, but the manner of hearing was modified. In the mean time
her countenance expressed astonishment. Dr. Petetin inquired the
cause. “It is not difficult,” she answered, “to explain to you why I
look astonished. I am singing, doctor, to divert my attention from a
sight which appals me. I see my inside, and the strange forms of the
organs, surrounded with a network of light. My countenance must
express what I feel—astonishment and fear. A physician who should
have my complaint for a quarter of an hour would think himself
fortunate, as nature would reveal all her secrets to him. If he was
devoted to his profession, he would not, as I do, desire to be quickly
well.” “Do you see your heart?” asked Dr. Petetin. “Yes, there it is; it
beats at twice, the two sides in agreement; when the upper part
contracts, the lower part swells, and immediately after that
contracts. The blood rushes out all luminous, and issues by two
great vessels, which are but a little apart.”
One morning (to quote from the latter part of this case) the
access of the fit took place, according to custom, at eight o’clock.
Petetin arrived later than usual; he announced himself by speaking
to the fingers of the patient, (by which he was heard.) “You are a

very lazy person this morning, doctor,” said she. “It is true, madam;
but if you knew the reason, you would not reproach me.” “Ah,” said
she, “I perceive you have had a headache for the last four hours: it
will not leave you till six in the evening. You are right to take
nothing; no human means can prevent it running its course.” “Can
you tell me on which side is the pain?” said Petetin. “On the right
side; it occupies the temple, the eye, the teeth: I warn you that it
will invade the left eye, and that you will suffer considerably
between three and four o’clock; at six you will be free from pain.”
The prediction came out literally true. “If you wish me to believe
you, you must tell me what I hold in my hand.” “I see through your
hand an antique medal.”
Petetin inquired of his patient at what hour her own fit would
cease: “At eleven.” “And the evening accession—when will it come
on?” “At seven o’clock.” “In that case it will be later than usual.” “It is
true; the periods of its recurrence are going to change to so and so.”
During this conversation, the patient’s countenance expressed
annoyance. She then said to M. Petetin, “My uncle has just entered;
he is conversing with my husband behind the screen; his visit will
fatigue me; beg him to go away.” The uncle, leaving, took with him
by mistake her husband’s cloak, which she perceived, and sent her
sister-in-law to reclaim it.
In the evening there were assembled, in the lady’s apartment, a
good number of her relations and friends. Petetin had, intentionally,
placed a letter within his waistcoat, on his heart. He begged
permission, on arriving, to wear his cloak. Scarcely had the lady, the
access having come on, fallen into trance, when she said—“And how
long, doctor, has it come into fashion to wear letters next the heart?”
Petetin pretended to deny the fact: she insisted on her correctness;
and, raising her hands, designated the size, and indicated exactly
the place of the letter. Petetin drew forth the letter, and held it,
closed, to the fingers of the patient. “If I were not a discreet
person,” she said, “I should tell the contents; but to show you that I

know them, they form exactly two lines and a-half of writing;”
which, on opening the letter, was shown to be the fact.
A friend of the family, who was present, took out his purse, and
put it in Dr. Petetin’s bosom, and folded his cloak over his chest. As
soon as Petetin approached his patient, she told him that he had the
purse, and named its exact contents. She then gave an inventory of
the contents of the pockets of all present, adding some pointed
remark when the opportunity offered. She said to her sister-in-law
that the most interesting thing in her possession was a letter;—much
to her surprise, for she had received the letter the same evening,
and had mentioned it to no one.
The patient, in the mean time, lost strength daily, and could take
no food. The means employed failed of giving her relief, and it never
occurred to M. Petetin to inquire of her how he should treat her. At
length, with some vague idea that she suffered from too great
electric tension of the brain, he tried, fantastically enough, the effect
of making deep inspirations, standing close in front of the patient.
No effect followed from this absurd proceeding. Then he placed one
hand on the forehead, the other on the pit of the stomach of the
patient, and continued his inspirations. The patient now opened her
eyes; her features lost their fixed look; she rallied rapidly from the
fit, which lasted but a few minutes instead of the usual period of two
hours more. In eight days, under a pursuance of this treatment, she
entirely recovered from her fits, and with them ceased her
extraordinary powers. But, during these eight days, her powers
manifested a still greater extension; she foretold what was going to
happen to her; she discussed with astonishing subtlety, questions of
mental philosophy and physiology; she caught what those around
her meant to say before they expressed their wishes, and either did
what they desired, or begged that they would not ask her to do
what was beyond her strength.
A young lady, after much alarm during a revolutionary riot, fell into
catalepsy. In her fits she appeared to hear with the pit of the
stomach; and most of the phenomena described in the preceding

case were again manifested. She improved in health, under the care
of Dr. Petetin, up to the 29th of May, 1790, the memorable day when
the inhabitants of Lyons expelled the wretches who were making
sport of their fortunes, their liberties, and their lives. At the report of
the first cannon fired, Mdlle. —— fell into violent convulsions,
followed by catalepsy and tetanus. When in this state she discerned
Petetin distinguishing himself under the fire of a battery; and she
blamed him the following day for having so rashly exposed his life.
In the progress of the complaint, during the attacks of catalepsy, the
occurrences of which she exactly foresaw, she likewise predicted the
bloody day of the 29th of September, the surrender of the city on
the 7th of October, the entrance of the republican troops on the 8th,
and the cruel proscriptions issued by the Committee of Public Safety.
The third case given by Petetin is that of Madame de Saint Paul,
who was attacked with catalepsy a few days after her marriage, in
consequence of seeing her father fall down in a fit of apoplexy at
table. The general features of her lucidity are the same as in the
former cases. I shall, therefore, content myself with quoting some
observations made by Dr. Prost, author of La Médecine éclairée par
l’Observation et l’Anatomie pathologique, on the authority of Dr.
Foissac, to whom he communicated them. Dr. Prost had studied this
case assiduously during nine months. “Her intellectual faculties,”
observed Dr. Prost, “acquired a great activity, and the richness of her
fancy made itself remarked in the picturesque images which she
threw into her descriptions. As she was telling her friends of an
approaching attack of catalepsy, suddenly she exclaimed,—‘I no
longer see or hear objects in the same manner; every thing is
transparent round me, and my observation extends to incalculable
distances.’ She designated, without an error, the people who were on
the public promenade, whether near the house, or still a quarter of
an hour’s walk distant. She read the thoughts of every one who
came near her; she marked those who were false and vicious; and
repelled the approach of stupid people, who bored her with their
questions and aggravated her malady. ‘Just as much as their pates

excite my pity,’ said she, 'do the heads of men of information and
intelligence, all whose thoughts I look into, fill me with delight.’”
The following facts I cite corroboratively, from one of several cases
of hysteria communicated by Dr. Delpit, inspecting physician of the
waters at Barèges.—(Bibliotheque Médicale, t. lvi. p. 308.)
Mdlle. V——, aged thirteen, after seeing the curé administer
extreme unction, fainted away. There followed extreme disgust
towards food. During eighteen days she neither ate nor drank; there
was no secretion; her breathing remained tranquil and regular; the
patient preserved her embonpoint and complexion. During this
complete suspension of the functions of digestion, the organs of
sensation would be alternately paralyzed. One day the patient
became blind; on the next, she could see, but could not hear;
another day she lost her speech. The mutations were noticed
generally in the night, upon her waking out of sleep. “Nevertheless,”
says M. Delpit, “her intellect preserved all its vivacity and force, and,
during the palsy of the organs of sensation, nature supplied the loss
in another way; when, with her eyes, Mdlle. Caroline could not
distinguish light, she yet read, and read distinctly, by carrying her
fingers over the letters. I have made her thus read, in the daytime
and in the profoundest darkness, either printed pages out of the first
book that came to hand, or written passages that I had previously
prepared.” In this, the alternation of different states of recollections
is not described as having been observed. But I have little doubt that
double consciousness was really present. I believe that feature to be
essential to waking trance. I have little doubt, likewise, that double
consciousness is attended by more or less trance-perception. The
co-existence of spasm, necessary to constitute the case one of
catalepsy, is accidental.
Sensorial illusions occasionally occur in catalepsy, but not
frequently; they are commoner in the inferior grades of trance. The
daimon of Socrates was, no doubt, a hallucination of this kind.

The trance-daimon, or sensorial illusion mixing itself with trance, is
exemplified in the following case of catalepsy, which occurred in the
person of the adopted daughter of the Baron de Strombeck.
Besides the ordinary features, on which I will not again dwell, at
one time it was her custom to apply to an imaginary being for
directions as to the treatment of her own case. Subsequently, she
one day observed—“It is not a phantom; I was in error in thinking it
so; it is a voice which speaks within me, and which I think without
me. This apparition comes because my sleep is less perfect. In that
case, I seem to see a white cloud rise out of the earth, from which a
voice issues, the echo of which reverberates within me.”
This patient had quintuple consciousness, or four morbid states,
each of which kept its own recollections to itself.
A final case I will quote, the authority of which is the Baron de
Fortis. It was treated by Dr. Despine of Aix-les-Bains.
The patient had had epilepsy, for the cure of which she went to
Aix. There she had all sorts of fits and day-somnambulism, during
which she waited at table, with her eyes shut, perfectly. She likewise
saw alternately with her fingers, the palm of her hand, and her
elbow, and would write with precision with her right hand,
superintending the process with her left elbow. These details are
peculiarly gratifying to myself, for in the little I have seen, I yet have
seen a patient walk about with her eyes shut, and well blinded
besides, holding the knuckles of one hand before her as a seeing
lantern. However, the special interest of this case is, that the patient
was differently affected by different kinds of matter; glass appeared
to burn her, porcelain was pleasantly warm, earthenware felt cold.
What comment can I make on the preceding wondrous details?
Those to whom they are new must have time to become familiar
with them; in order, reversing the process by which the eye gets to
see in the dark, to learn to distinguish objects in this flood of
excessive light. Those who are already acquainted with them will, I

think, agree with me that the principle which I have assumed—the
possibility of an abnormal relation of the mind and body allowing the
former, either to shift the place of its manifestations in the nervous
system, or partially to energize as free spirit—is the only one which
at present offers any solution of the new powers displayed in
catalepsy. One regrets that more was not made of the opportunities
of observation which Petetin enjoyed. But there are means, which I
shall by-and-by have occasion to specify, through which, in the
practice of medicine, and in the proper treatment of various
disorders, like instances may be artificially multiplied and modified so
as to meet the exigencies of inductive science. In the mean time, let
me append one or two corollaries to the preceding demonstration.
I. It is evident that the performances of catalepsy reduce the
oracles of antiquity to natural phenomena. Let us examine the
tradition of that of Delphi.
Diodorus relates, that goats feeding near an opening in the
ground were observed to jump about in a singular manner, and that
a goatherd approaching to examine the spot was taken with a fit
and prophesied. Then the priests took possession of the spot and
built a temple. Plutarch tells us that the priestess was an uneducated
peasant-girl, of good character and conduct. Placed upon the tripod,
and affected by the exhalation, she struggled and became
convulsed, and foamed at the mouth; and in that state she delivered
the oracular answer. The convulsions were sometimes so violent that
the Pythia died. Plutarch adds, that the answers were never in error,
and that their established truth filled the temple with offerings from
the whole of Greece, and from barbarian nations. Without supposing
it to have been infallible, we must, I think, infer that the oracle was
too often right to have been wholly a trick. The state of the Pythia
was probably trance with convulsions, the same with that in which
cataleptic patients have foreseen future events. The priestess was of
blameless life, which suits the production of trance, the fine
susceptibility of which is spoilt by irregular living. Finally, from what
we know of the effects of the few gases and vapours of which the

inhalation has been tried, it is any thing but improbable that one or
other gaseous compound should directly induce trance in
predisposed subjects.
II. The performances of Zschokke are poor by the side of those of
a cataleptic. But then he was not entranced. Nevertheless, an
approach to that state manifested itself in his losing himself when
inspecting his visiter’s brains. So again, those who had the gift of
second-sight are represented to have been subject to fits of
abstraction, in which they stood rapt. The præternatural gifts of
Socrates were probably those of a Highland seer; in which character
he is reported to have foretold the death of an officer, if he pursued
a route he contemplated. The officer would not change his plans,
and was met by the enemy, and slain accordingly. In all these cases,
the mind seems to have gone out to seek its knowledge. Two of Mr.
Williamson’s lucid patients, of whom more afterwards, told him that
their minds went out at the backs of their heads, in starting on these
occasions. They pointed to the lower and back part of the head,
opposite to the medulla oblongata. In prophetic, and in true
retrospective dreams, one may imagine the phenomena taking the
same course; most likely the dreamers have slipt in their sleep into a
brief lucid somnambulism. In the cases of ghosts and of dreams,
coincident with the period of the death of an absent person, it
seems simpler to suppose the visit to have come from the other
side. So the Vampyr-ghost was probably a visit made by the free
part of the mind of the patient who lay buried in death-trance. The
visit was fatal to the party visited, because trance is contagious.
III. The wonderful performances attributed to instinct in animals
appear less incomprehensible when viewed in juxtaposition with
some of the feats of lucid cataleptics. The term instinct is a very
vague one. It is commonly used to denote the intelligence of animals
as opposed to human reason. Instinct is, therefore, a compound
phenomenon; and I must begin by resolving it into its elements.
They are three in number:—

1. Observation and reasoning of the same kind with that of man,
but limited in their scope. They are exercised only in immediate self-
preservation, and in the direct supply of the creature’s bodily wants
or simple impulses. A dog will whine to get admission into the
house, will open the latch of a gate; one rook will sit sentry for the
rest; a plover will fly low, and short distances, as if hurt, to wile
away a dog from her nest. But in this vein of intelligence, animals
make no further advance. Reflection, with the higher faculties and
sentiments which minister to it, and with it constitute reason, is
denied them. So they originate no objects of pursuit in the way that
man does, and have no source of self-improvement. But, in lack of
human reflection, some animals receive the help of—
2. Special conceptions, which are developed in their minds at
fitting seasons. Of this nature, to give an instance, is the notion of
nest-building in birds. It may be observed of these conceptions that
they appear to us arbitrary, though perfectly suited to the being of
each species: thus, in the example referred to, we may suppose that
the material and shape of the nest might be varied without its object
being the less perfectly attained,—at least, as far as we can see. The
conception spontaneously developed in the mind of the bird is then
carried out intelligently, through the same quick and just
observation, in a little way, which habitually ministers to its
appetites, as I explained in a preceding paragraph.
The special conception is sometimes characterized by the utmost
perfectness of mechanical design. Here, however, is nothing to
surprise us. The supreme wisdom which preordained the
development of an idea in an insect’s mind, might as easily as not
have given it absolute perfectness. But—
3. Some animals have the power of modifying the special
conception, when circumstances arise which prevent its being
carried out in the usual way; and of realizing it in a great many
different ways, on as many different occasions. And their work, on
each of these occasions, is as perfect as in their carrying out the
ordinary form of the conception. I beg leave to call the principle, by

which they see thus how to shape their course so perfectly under
new circumstances—intuition. To instance it, there is a beetle called
the rhynchites betulæ. Its habit is, towards the end of May, to cut
the leaves of the betula alba, or betula pubescens, into slips, which
it rolls up into funnel-shaped chambers, which form singularly
convenient cradles for its eggs. This is done after one pattern; and
one may suppose it the mechanical realization of an inborn idea, as
long as the leaf is perfect in shape. But if the leaf is imperfect,
intuition steps upon the scene to aid the insect to cut its coat after
its cloth. The sections made are then seen to vary with the varying
shape of the leaf. Many different sections made by the insect were
accurately drawn by a German naturalist, Dr. Debey. He submitted
them for examination to Professor Heis of Aix-la-Chapelle. Upon
carefully studying them, Dr. Heis found these cuttings of the leaves,
in suitableness to the end proposed, even to the minutest technical
detail, to be in accordance with calculations compassable only
through the higher mathematics, which, till modern times, were
unknown to human intelligence. Such is the marvellous power of
“intuition,” displayed by certain insects. I know not how to define it
but as a power of immediate reference to absolute truth, evinced by
the insect in carrying out its little plans. It is evident that the insect
uses the same power in realizing its ordinary special conception,
when the result displays equal perfectness. And the question even
crosses one’s mind, Are the seemingly arbitrary plans really
arbitrary?—may they not equally represent a highest type of design?
But, be that as it may, the intuition of insects, as we now apprehend
it, no longer stands an isolated phenomenon. The lucid cataleptic
cannot less directly communicate with the source of truth, as she
proves by foreseeing future events.
IV. The speculations of Berkeley and Boscovich on the non-
existence of matter; and of Kant and others on the arbitrariness of
all our notions, are interested in, for they appear to be refuted by,
the intuitions of cataleptics. The cataleptic apprehends or perceives
directly the objects around her; but they are the same as when
realized through her senses. She notices no difference; size, form,

colour, distance, are elements as real to her now as before. In
respect again to the future, she sees it, but not in the sense of the
annihilation of time; she foresees it; it is the future present to her;
time she measures, present and future, with strange precision,—
strange, yet an approximation, instead of this certainty, would have
been still more puzzling.
So that it appears that our notions of matter, force, and the like,
and of the conditions of space and time, apart from which we can
conceive nothing, are not figments to suit our human and temporary
being, but elements of eternal truth.

LETTER IX.
Religious Delusions—The seizures giving rise to them shown to have
been forms of trance brought on by fanatical excitement—The
Cevennes—Scenes at the tomb of the Abbé Paris—Revivals in
America—The Ecstatica of Caldaro—Three forms of imputed
demoniacal possession—Witchcraft; its marvels, and the
solution.
There have been occasions, when much excitement on the subject
of religion has prevailed, and when strange disorders of the nervous
system have developed themselves among the people, which have
been interpreted as immediate visitings of the Holy Spirit. The
interpretation was delusive, the belief in it superstition. The effects
displayed were neither more nor less than phenomena of trance, the
physiological consequences of the prevailing excitement. The reader
who has attentively perused the preceding letters will have no
difficulty in identifying forms of this affection in the varieties of
religious seizures, which, without further comment, I proceed to
exemplify.
Every one will have met with allusions to some extraordinary
scenes which took place in the Cevennes, at the close of the
seventeenth century.
It was towards the end of the year 1688 that a report was first
heard of a gift of prophecy which had shown itself among the
persecuted followers of the Reformation, who, in the south of
France, had betaken themselves to the mountains. The first instance
was said to have occurred in the family of a glass-dealer of the name
of Du Serre, well known as the most zealous Calvinist of the
neighbourhood, which was a solitary spot in Dauphiné, near Mount

Peyra. In the enlarging circle of enthusiasts, Gabriel Astier and
Isabella Vincent made themselves first conspicuous. Isabella, a girl
of sixteen years of age, from Dauphiné, who was in the service of a
peasant, and tended sheep, began in her sleep to preach and
prophesy, and the Reformers came from far and near to hear her. An
advocate of the name of Gerlan describes the following scene, which
he had witnessed. At his request, she had admitted him and a good
many others, after nightfall, to a meeting at a chateau in the
neighbourhood. She there disposed herself upon a bed, shut her
eyes, and went to sleep. In her sleep she chanted, in a low tone, the
Commandments and a psalm. After a short respite she began to
preach, in a louder voice—not in her own dialect, but in good
French, which hitherto she had not used. The theme was an
exhortation to obey God rather than man. Sometimes she spoke so
quickly as to be hardly intelligible. At certain of her pauses she
stopped to collect herself. She accompanied her words with
gesticulations. Gerlan found her pulse quiet, her arm not rigid, but
relaxed, as natural. After an interval, her countenance put on a
mocking expression, and she began anew her exhortation, which
was now mixed with ironical reflections upon the Church of Rome.
She then suddenly stopped, continuing asleep. It was in vain they
stirred her. When her arms were lifted and let go, they dropped
unconsciously. As several now went away, whom her silence
rendered impatient, she said in a low tone, but just as if she was
awake,—Why do you go away?—why do not you wait till I am
ready?” And then she delivered another ironical discourse against
the Catholic Church. She closed the scene with prayer.
When Bouchier, the intendant of the district, heard of the
performances of Isabella Vincent, he had her brought before him.
She replied to his interrogatories, that people had often told her that
she preached in her sleep, but that she did not herself believe a
word of it. As the slightness of her person made her appear younger
than she really was, the intendant merely sent her to an hospital at
Grenoble; where, notwithstanding that she was visited by persons of

the Reformed persuasion, there was an end of her preaching—she
became a Catholic!
Gabriel Astier, who had been a young labourer, likewise from
Dauphiné, went, in the capacity of a preacher and prophet, into the
valley of Bressac, in the Vivarais. He had infected his family: his
father, mother, elder brother, and sweetheart, followed his example,
and took to prophesying. Gabriel, before he preached, used to fall
into a kind of stupor in which he lay rigid. After delivering his
sermon, he would dismiss his auditors with a kiss, and the words
—“My brother, or my sister, I impart to you the Holy Ghost.” Many
believed that they had thus received the Holy Ghost from Astier,
being taken with the same seizure. During the period of the
discourse, first one, then another, would fall down: some described
themselves afterwards as having felt first a weakness and trembling
through the whole frame, and an impulse to yawn and stretch their
arms; then they fell, convulsed and foaming at the mouth. Others
carried the contagion home with them, and first experienced its
effects, days, weeks, or months afterwards. They believed—nor is it
wonderful they did so—that they had received the Holy Ghost.
Not less curious were the seizures of the Convulsionnaires at the
grave of the Abbé Paris, in the year 1727. These Jansenist
visionaries used to collect in the churchyard of St. Médard, round the
grave of the deposed and deceased deacon; and before long, the
reputation of the place for working miracles getting about, they fell
in troops into convulsions. They required, to gratify an internal
impulse or feeling, that the most violent blows should be inflicted
upon them at the pit of the stomach. Carré de Montgeron mentions
that, being himself an enthusiast in the matter, he had inflicted the
blows required with an iron instrument, weighing from twenty to
thirty pounds, with a round head. And as a convulsionary lady
complained that he struck too lightly to relieve the feeling of
depression at her stomach, he gave her sixty blows with all his force.
It would not do, and she begged to have the instrument used by a
tall, strong man, who stood by in the crowd. The spasmodic tension

of her muscles must have been enormous; for she received one
hundred blows, delivered with such force that the wall shook behind
her. She thanked the man for his benevolent aid, and
contemptuously censured De Montgeron for his weakness, or want
of faith, and timidity. It was, indeed, time for issuing the mandate,
which, as wit read it, ran—
“De par le roi—Défense à Dieu,
De faire miracle en ce lieu.”
In the revivals of modern times, scenes parallel to the above have
been renewed.
“I have seen,” says Mr. Le Roi Sunderland, himself a preacher,
(Zion’s Watchman, New York, Oct. 2, 1842,) “persons often ‘lose
their strength,’ as it is called, at camp-meetings and other places of
great religious excitement; and not pious people alone, but those,
also, who were not professors of religion. In the spring of 1824,
while performing pastoral labour in Dennis, Massachusetts, I saw
more than twenty affected in this way. Two young men, of the name
of Crowell, came one day to a prayer-meeting. They were quite
indifferent. I conversed with them freely, but they showed no signs
of penitence. From the meeting they went to their shop, (they were
shoemakers,) to finish some work before going to the meeting in the
evening. On seating themselves, they were both struck perfectly
stiff. I was immediately sent for, and found them sitting paralyzed”
(he means taken with the initiatory form of trance-sleep, and
possibly cataleptic) “on their benches, with their work in their hands,
unable to get up, or to move at all. I have seen scores of persons
affected the same way. I have seen persons lie in this state forty-
eight hours. At such times they are unable to converse, and are
sometimes unconscious of what is passing round them. At the same
time, they say they are in a happy state of mind.”
The following extract from the same journal portrays another kind
of nervous seizure, as it was manifested at the great revival some
forty years ago, at Kentucky and Tennessee.

“The convulsions were commonly called ‘the jerks.’ A writer,
(M’Neman) quoted by Mr. Power, (Essay on the Influence of the
Imagination over the Nervous System,) gives this account of their
course and progress:
“'At first appearance these meetings exhibited nothing to the
spectator but a scene of confusion that could scarcely be put into
language. They were generally opened with a sermon, near the
close of which there would be an unusual outcry, some bursting out
into loud ejaculations of prayer, c.
“'The rolling exercise consisted in being cast down in a violent
manner, doubled with the head and feet together, or stretched in a
prostrate manner, turning swiftly over like a dog. Nothing in nature
could better represent the jerks, than for one to goad another
alternately on every side with a piece of red-hot iron. The exercise
commonly began in the head, which would fly backwards and
forwards, and from side to side, with a quick jolt, which the person
would naturally labour to suppress, but in vain. He must necessarily
go on as he was stimulated, whether with a violent dash on the
ground, and bounce from place to place, like a foot-ball; or hopping
round, with head, limbs, and trunk twitching and jolting in every
direction, as if they must inevitably fly asunder,’” c.
The following sketch is from Dow’s journal. In the year 1805 he
preached at Knoxville, Tennessee, before the governor, when some
hundred and fifty persons, among whom were a number of Quakers,
had the jerks. “I have seen,” says the writer, “all denominations of
religion exercised by the jerks—gentleman and lady, black and white,
young and old, without exception. I passed a meeting-house, where
I observed the undergrowth had been cut down for camp-meetings,
and from fifty to a hundred saplings were left for the people who
were jerked to hold by. I observed where they had held on they had
kicked up the earth, as a horse stamping flies.”
A widely different picture to the above is given in a letter from the
Earl of Shrewsbury to A. M. Phillips, Esq., published in 1841, and

describing the state of two religieuses, (the Ecstatica of Caldaro, and
the Addolorata of Capriana,) who were visited by members of their
own communion, in the belief that they lay in a sort of heavenly
beatitude. To this idea their stillness, the devotional attitude of their
hands and expression of their countenances, together with their
manifestation of miraculous intuition, contributed. But I am afraid
that, to the eye of a physician, their condition would have been
simple trance. However, while the absence of reasonable
enlightenment in the display is to be regretted, one agreeably
recognises the influence of the humanity of modern times. Had
these young women lived two centuries ago, they would have been
the subjects of other discipline, and their history, had I possessed it
to quote, must have been transferred to the darker section which I
have next to enter on.
The belief in possession by devils, which existed in the middle
ages and subsequently, embraced several dissimilar cases. The first
of them which I will exemplify would have included individuals in the
state of the religieuses described by Lord Shrewsbury. Behaviour and
powers which the people could not understand, even if exhibited by
good and virtuous persons, and only expressive of or used for right
purposes, were construed into the operation of unholy influences.
The times were the reign of terror in religion. I give the following
instance:—Marie Bucaille, a native of Normandy, became, towards
the year 1700, the subject of fits, which ordinarily lasted three or
four hours. It appears, by the depositions of persons of character on
her trial, that Marie had effected many cures seemingly by her
prayers; that she comprehended and executed directions given to
her mentally; that she read the thoughts of others. When in the fit,
the Curé of Golleville placed in the hands of Marie a folded note.
Without opening the note, she replied to the questions which it
contained; and, without knowing the writer, she accurately described
her person. Although Marie only employed her powers to cure the
sick and in the service of religion, she was not the less condemned
to death by the parliament of Valogne. The parliament of Rouen
mitigated her punishment to whipping and public ignominy.

A second class, who came nearer to the exact idea of being
possessed by devils, were persons who were deranged, and
entertained something of that impression themselves, and avowed
it. I am not speaking of single instances, but of an extensive popular
delusion, or frenzy rather, which prevailed in the fifteenth and
sixteenth centuries in parts of Europe as an epidemic seizure. It was
called the wolf-sickness. Those affected betook themselves to the
forests as wild beasts. One of these, who was brought before De
Lancre, at Bordeaux, in the beginning of the sixteenth century, was a
young man of Besançon. He avowed himself to be huntsman of the
forest lord, his invisible master. He believed that, through the power
of his master, he had been transformed into a wolf; that he hunted
in the forest as such; and that he was often accompanied by a
bigger wolf, whom he suspected to be the master he served; with
more details of the same kind. The persons thus affected were called
Wehrwolves. Their common fate was the alternative of recovering
from their derangement, under the influence of exorcism and its
accessories, or of being executed.
The third and proper type of possession by devils presented more
complicated features. The patient’s state was not uniform. Often, or
for the most part, his appearance and behaviour were natural; then
paroxysms would supervene, in which he appeared fierce,
malignant, demoniacal, in which he believed himself to be
possessed, and acted up to the character, and in which powers,
seemingly superhuman, such as reading the thoughts of others,
were manifested by the possessed. The explanation of these
features is happily given by Dr. Fischer of Basle, author of an
excellent work on Somnambulism. He resolves them, with evident
justice, into recurrent fits of trance—the patient, when entranced,
being at the same time deranged; and he exemplifies his hypothesis
by the case of a German lady who had fits of trance, in which she
fancied herself a French emigrée: it would have been as easy for her,
had it been the mode, to have fancied herself, and to have played
the part of being, possessed by the fiend. The case is this:

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