Fatigue and Fracture of Weldments The IBESS Approach for the Determination of the Fatigue Life and Strength of Weldments by Fracture Mechanics Analysis Uwe Zerbst
This lively introduction to geologic fracture mechanics provides a consistent treatment of all common types of geologic structural discontinuities. It explores the formation, growth, and interpretation of fractures and deformation bands, from theoretical, field, and laboratory-based perspectives, bridging the gap between a general textbook treatment and the more advanced research literature. It allows the reader to acquire basic tools to interpret discontinuity origins, geometries, patterns, and implications using many of the leading and contemporary concepts known to specialists in the field. Exercises are provided at the end of each chapter, and worked examples are included within each chapter to illustrate topics and enable self-study. With all common geologic structures including joints, hydrofractures, faults, stylolites, and deformation bands being discussed from a fresh perspective, it will be a useful reference for advanced students, researchers, and industry practitioners interested in structural geology, neotectonics, rock mechanics, planetary geology, and reservoir geomechanics.
Dr. Richard A. Schultz is the owner and principal consultant of Orion Geomechanics LLC, Cypress, Texas. He is a geologist specializing in the geomechanics of faulted overburden and reservoir systems, and in underground natural gas storage. He was previously Senior Research Scientist at The University of Texas at Austin, Principal Geomechanicist with ConocoPhillips, and Foundation Professor of Geological Engineering and Geomechanics (now Emeritus) with the University of Nevada, Reno. He is a member of the Interstate Oil and Gas Compact Commission, a Fellow of the Geological Society of America, a licensed Professional Geologist in the State of Texas, and was an instructor of State oil and gas regulators with TopCorp.
Geologic Fracture Mechanics
Richard A. Schultz
Orion Geomechanics LLC
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To my Father, who taught me initiative;
To my Mother, who taught me compassion; And to my wife and family for their loving support.
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Preface
Structural discontinuities in rock, including all types of fractures, joints, faults, and deformation bands, along with stylolites and fluid-filled cracks such as hydrofractures, veins, and dikes, have been studied extensively using the tools and terminology of geology, geomorphology, geophysics, rock engineering, geomechanics, tectonophysics, hydrology, petroleum geology, mining engineering, quarrying, soil mechanics/geotechnical engineering, crystallography, experimental rock physics, and materials science. Most of what is known about fractures and deformation bands, collectively referred to as geologic structural discontinuities in this book, comes from a synthesis of concepts flowing from these traditionally separate disciplines. Many of the basics of what structural discontinuities are, and how to identify them, can be found in various degrees by using any of a number of good textbooks on particular topics. However, these sources must necessarily cover a wide range of material appropriate for semester-long, comprehensive courses in, for example, structural geology and tectonics. On the other hand, journal articles provide in-depth explorations of these topics for the experienced and knowledgeable reader.
The purpose of this book is to help bridge the gap between general treatments of geologic structural discontinuities found in textbooks or more advanced topical monographs and the published research literature. The book explores geologic fracture mechanics—the formation, growth, and interpretation of geologic structural discontinuities—primarily from field-based and theoretical perspectives, with laboratory-based research incorporated as appropriate. In many cases, some large amount (like 70%) of what can be interpreted from a discontinuity set can be gained with only simple tools and observations and without extensive mathematical analysis. Many scientists and engineers working in industry utilize this to balance rigor with deadlines and the limitations of applicable data. Specialists in fracture mechanics (sometimes referred to as “crack aficionados” by other structural geologists who don’t live and breathe fracture mechanics to the same extent) can use sophisticated mathematical, geodetic, and computer analysis techniques to
pull a greater amount of understanding from the rocks, but for many professional geologists and engineers working in industry, or who may be some years away from their formal academic training, this additional insight may not be necessary. This book will help the reader acquire some basic tools that can help to interpret discontinuity origins, geometries, patterns, and implications using many of the leading or contemporary concepts known to specialists in these areas.
This book is intended to be read and used by geologists and engineers who have had some exposure to the standard principles of structural geology, whether in college-level courses, graduate study, or continuing education. It is not designed as a stand-alone textbook for a class in structural geology or rock mechanics, but it may be used to supplement such a class. Nor should it be regarded as a substitute for formal training at the graduate level for researchgrade work in geologic fracture mechanics. Instead, this book is an attempt to translate many of the major findings of the specialized literature on geologic structural discontinuities for the less specialized geoscientist or engineer.
The main emphasis of the book is field interpretation of geologic structural discontinuities. It is hoped that the material will provide a useful template for conceptually matching discontinuity sets on the outcrop with the implied stress states, local conditions, or three-dimensional (3-D) structural geometry, insofar as these are known or can be reasonably inferred from inspection. Equations are introduced and included as needed both to illustrate key concepts and to provide simple yet powerful tools for going deeper than just a simple visual scanning of the outcrop.
The literature bearing on geologic structural discontinuities is vast. References to the literature are inserted as called for in the text. The interested reader will quickly find that the rather extensive references provided are but the tip of the iceberg, so that by studying this book an appreciation of the overall scope, tenor, and terminology of the field may be gained that can facilitate a manageable entry into the realms of geologic fracture mechanics.
In preparing this book I have had to make difficult choices as to depth and rigor of treatment. Many of these choices, made to more succinctly or convincingly access and present the material for the nonspecialist, may challenge the purest researchers in fracture mechanics. Specialists may find other topics and applications here beyond their usual focus, while nonspecialists will perhaps appreciate the level of sophistication available about geologic structural discontinuities and the engineering approaches used to understand them.
The book begins with an overview in Chapter 1 of the main concepts, definitions, and terminology that underlie the interpretation and analysis of fractures, deformation bands, and other structures as mechanical discontinuities in an otherwise effectively continuous rock (or rock mass). The astute reader will note that some liberties from a more traditional approach have been taken which could be said to be justifiable extensions and refinements.
Many of the key relationships between elastic stress and strain that are helpful in dealing with discontinuities in rock are touched on in Chapter 2. Here rheological terminology (such as brittle, ductile, elastic, and plastic) that is important in geologic fracture mechanics is also discussed. The important concept of stress concentration due to flaws, cavities, fractures, and other kinds of inhomogeneities is also covered in this chapter. Here lies the basis for fracture mechanics and the redistribution of remote stress states—by structural discontinuities—into spatially variable, inhomogeneous stress states that are so important in fractured rock masses.
Chapter 3 provides a non-traditional summary of stress analysis, peakstrength concepts, frictional sliding and the Coulomb criterion, tensile failure and the several Griffith criteria, and concepts of rock-mass classification systems and rock-mass strength criteria—including the important and versatile Hoek–Brown criterion—that provide an understanding of the mechanics of fracturing and associated rock-mass deformation.
Chapter 4 concentrates on dilatant cracks—one of the most common types of brittle geologic structure. Because mechanical and rock engineers deal extensively with these types of structural discontinuities, the understanding of the behavior and analysis of cracks is well advanced; additionally, laboratory simulations can reproduce many of the surface textures and discontinuity patterns that are encountered in geology. As a result, this chapter may bear some resemblance to other reviews and treatises on mode-I cracks that already exist. The chapter ends with an overview of anticracks, stylolites, and pure compaction bands. These structures have the opposite sense of displacement to cracks (dissolution and interpenetration of opposing walls across the surface) yet the same direction (normal to the surface). Pressure solution surfaces (in soluble rocks) and compaction bands (in porous rocks) form patterns suggestive of lateral propagation and interaction, making them a form of stress concentrator and discontinuous deformation mechanism in susceptible rock types.
Some of the common discontinuity patterns are examined in Chapter 5. Here we’ll start with two discovery patterns—echelon discontinuities and end cracks—that can be interpreted by using the basic principles of geologic fracture mechanics including near-tip stress concentration. Other patterns that reveal key principles will be explored including growth of discontinuities into sets, spacing, fault formation, and the Riedel shear patterns that are so commonly observed in soils and soft porous granular rocks.
The extensive topic of faults and faulting is explored in Chapter 6 from the perspective of geologic fracture mechanics. Rather than relying on traditional and well-known means for determining the sense of fault offsets, such as fault-surface textures or offset stratigraphic markers, the use of stepover and fault-tip kinematics is illustrated as an alternative and additional technique for interpreting fault offsets and fault patterns. The context and growth of faults in various systems including Anderson’s classification, three-dimensional (3-D)
strain and polygonal fault sets, crustal strength envelopes, the stress polygon, and critically stressed systems is also discussed.
Chapter 7 presents an introduction to the important class of structures known as deformation bands. These tabular structures occur preferentially in porous granular rocks such as sandstones and are critically important as a precursor to faults in many sedimentary rocks and sedimentary basins around the world. Certain types of deformation bands can form barriers to fluid flow, defining compartments against fluid migration (water or petroleum) in the subsurface. Deformation bands display a rich variety of kinematics including opening, shearing, closing, and various combinations of these. Because much of the current theoretical or conceptual framework for deformation bands draws from critical-state soil mechanics and Cam cap-type models of pre-peak yielding, an extended but largely non-mathematical synopsis of this approach and its application to bands in porous granular rocks is included in this chapter.
In Chapter 8 an overview of linear elastic fracture mechanics (LEFM) is developed. It includes the ideas that are most important and useful in dealing with geologic structural discontinuities, presented in an order that, as will be seen, differs from the traditional engineering sequence. For example, the displacements and stresses generated in the vicinity of geologic structural discontinuities are emphasized early, because these are what are mapped, measured, and worked with most often in the field. Only toward the end is focus placed on the discontinuity tip, since the LEFM characterization of discontinuity tips as bounded by a negligibly small plastic zone describes actual discontinuity tips in rock only under certain sets of conditions.
The final chapter, Chapter 9, introduces some topics of relevance to the rapidly developing field of geologic fracture mechanics. These include subcritical fracture growth, more realistic (linear and “end-zone”) models for discontinuity tips, models of discontinuity propagation, displacement–length scaling relations, discontinuity populations, and brittle strain. The issues chosen for inclusion are under active research in contemporary structural geology, and this chapter may provide a readable entry into these exciting topics.
A learning map is included at the end of each chapter. Patterned loosely after a dendrite, learning maps are graphical summaries, limited to a single page, that highlight not only the most important points and concepts covered, but also the logical flow and connections between them. They are an exceptionally useful method for synoptically visualizing and remembering an entire chapter and for helping to place the important details into their larger context.
All chapters have exercise sets that encourage the reader to work through the material themselves. Many worked examples within the chapters illustrate the topics being discussed, and answers or helpful hints to selected exercises are provided at the publisherʼs website, www.cambridge.org/schultz. Many of the chapters and the exercises have been tested by undergraduate and graduate students in courses taught by the author, with modifications made as called
for. A glossary collects definitions of many of the specialized terms used in the book while providing definitions of well-known terms from the perspective of geologic fracture mechanics. Although some of these definitions may challenge traditional ones, their development in the glossary provides an additional approach to exploring the field, assumptions, methods, and utility of geologic fracture mechanics.
I have enjoyed writing this book, and I hope that you will enjoy it too. Learning about geologic fracture mechanics is an odyssey that never ends. It always gets more interesting and more fun—it is never dull or boring. I hope that something in this book spurs you to learn some new material, make new field observations, apply some new concepts, and contribute to this exciting area.
Acknowledgements
In writing this book I am pleased to acknowledge those who have, knowingly and willingly or not, provided many of the philosophical and logical underpinnings for my approach. While a graduate student at Arizona State University, I was introduced to the methods of the “Stanford School of Fracture Mechanics” by Jon Fink, who used Arvid Johnson’s excellent book Physical Processes in Geology as his text. This innovative book (and Jon’s tutelage and encouragement) provided a powerful motivation for me to learn and apply mechanics to geologic problems through unusually clear writing and examples. The philosophy embodied in that book continues to be an inspiration, especially the reflexive maxim that “all good problems begin in the field, and any (kinematic, mathematical, or computer) solution must fit what is seen in the field.” Following completion of my MS degree there I moved on to study for my doctorate at Purdue University with Atilla Aydin, who (initially unappreciated by me at the time) was a colleague and classmate of Jon’s at Stanford. Atilla taught me that maxim in innumerable and inscrutable ways, and I am grateful to him for it. Many of the concepts in this book have grown from my late-night, classroom, and in-field discussions with Atilla and many others over the years, although the responsibility for anything within these pages remains mine. I also thank my former graduate students at the University of Nevada, Reno—Kathleen Ward, Qizhi Li, Paul Piscoran, Andrea Fori, Edward Wellman, Jason Moore, Will Roadarmel, Paul Caruso, Dr. Scott Wilkins, Dr. Chris Okubo, Clara Balasko, Dr. Cheryl Goudy, Daniel Neuffer, Anjani Polit, Wendy Key, Dr. Amanda Nahm, and Dr. Christian Klimczak, and former postdocs Dr. Daniel Mège and Dr. Roger Soliva—for letting me practise and refine my translations of geologic fracture mechanics. I have benefited enormously, both professionally and personally, from stimulating and pleasant associations with a number of individuals. At the risk of inadvertent omission, I’d especially like to acknowledge Mike Piburn, Steve Fox, and Roger Hewins (Rutgers University); Uel Clanton and Herb Zook (NASA Johnson Space Center); Pete Schultz (Brown University); Mike Ward (Independence Mining Company); Steve Self (University of
Hawaii); Ron Greeley and Don Ragan (Arizona State University); Mike Malin (Malin Space Science Systems, Inc.); Nick Christensen (University of Wisconsin, Madison), Tom Tharp, Bob Nowack, James Doyle, and C. T. Sun (Purdue University); Jim DeGraff (formerly with ExxonMobil Development Company); Greg Ohlmacher (Black and Veatch); Paul Morgan (Colorado Geological Survey); David Pollard (Stanford University); Steve Martel (University of Hawaii); Terry Engelder (Pennsylvania State University); Herb Frey, Dave Smith, Jim Garvin, and Dave Harding (NASA Goddard Space Flight Center); Cindy Ebinger (Tulane University), Maria Zuber (MIT); Jian Lin (Woods Hole Oceanographic Institution); Greg Hirth (Brown University); Sean Solomon (Lamont-Doherty Earth Observatory); Ken Tanaka and Baerbel Lucchitta (U.S. Geological Survey); Tom Watters, Bob Craddock, and Jim Zimbelman (National Air and Space Museum); Ron Bruhn (University of Utah); Dick Bradt (University of Alabama); John Kemeny (University of Arizona); George McGill and Michele Cooke (University of Massachusetts); Dan Schultz-Ela and Martin Jackson (Texas Bureau of Economic Geology); Daniel Mège (Polish Academy of Sciences); Jacques Angelier and Catherine Homberg (Université Pierre et Marie Curie, Paris VI); Bill Higgs, Chuck Kluth (Colorado School of Mines), and Chuck Sword (Chevron Petroleum Technology Company); Eric Grosfils and Linda Reinen (Pomona College); Philippe Masson, François Costard, Nicolas Mangold, Jean-Pierre Peulvast, and Antonio Benedicto (Université de Paris-Saclay, Orsay); Roger Soliva (Université Montpellier II); Zoe Shipton (University of Strathclyde); Karen Mair (University of Oslo); Teng-fong Wong (formerly with Stony Brook University, now with The Chinese University of Hong Kong); Jim Carr, Bob Watters, Jaak Daemen, Jane Long, John Bell, Steve Wesnousky, John Louie, Raj Siddharthan, and Dhanesh Chandra (University of Nevada, Reno); Peter Hennings, Pete D’Onfro, Bob Krantz, Dave Amendt, Seth Busetti, Pijush Paul, Anastasia Mironova, and Zijun Fang (ConocoPhillips); Jon Olson, Steve Laubach, Maša Prodanović, Matt Balhoff, Larry Lake, Nicolas Espinoza, Hilary Olson, Peter Eichhubl, and Julia Gale (The University of Texas at Austin); Donnie Vereide (Geostock Sandia); Nicolas Bonnier, Louis Londe, and Bruno Paul-Dauphin (Geostock); Russell Bentley (WSP); David Evans (British Geological Survey), Doug Hubbard (Hubbard Decision Research), and Sam Savage (ProbabilityManagement.org and Stanford University).
The material presented here was formulated and initiated while at the University of Nevada, Reno. Much of it was further developed while I was enjoying a productive sabbatical leave at the Woods Hole Oceanographic Institution and the Université Pierre et Marie Curie (Sorbonne University) in Paris; then refined and expanded at ConocoPhillips and at The University of Texas at Austin; the work was completed at Orion Geomechanics LLC in Cypress, Texas. I am grateful to several agencies that sponsored my research financially including the US National Academy of Sciences/National Research Council, NASA, NSF, the Department of Energy, CNRS (France),
Chevron Petroleum Technology Company, Shell International Exploration and Production Company, the American Chemical Society’s Petroleum Research Fund, the Norwegian Research Council, UT’s Fracture Research and Applications Consortium, and the Texas Center for Integrated Seismicity Research along with various industrial and proprietary contracts.
Early drafts of this book were graciously reviewed by Terry Engelder, Tom Blenkinsop, Chris Wibberley, and Jaak Daemen, who provided vigorous, detailed, and thoughtful critiques that significantly improved its scope, style, and balance. Hunjoo Lee kindly read through Chapter 8. Much of the material including the exercise sets was used in various undergraduate and graduate classes in structural geology and geomechanics, and has been improved through the detailed feedback of these wonderful students.
I’m also happy to acknowledge and thank my wife, Rosemary, for her encouragement and support during my addiction with The Book. Writing a book like this one is not a trivial undertaking, as it impacts both normal scientific productivity and family life. It is a creative exercise that builds for the future while solidifying the present. Her active support was instrumental in producing a quality product. Thank you! Our sons Sebastian and Rainier provided a wonderful counterpoint as this book moved to completion.
Introduction to Geologic Structural Discontinuities
1.1 Localized Deformation Structures in Rock
In This Chapter:
♦ Types and expression of structural discontinuities in geology
♦ Displacement modes for geologic structural discontinuities
Planar breaks in rock are one of the most spectacular, fascinating, and important features in structural geology. Joints control the course of river systems, the extrusion of lava flows and fire fountains, and modulate groundwater flow. Joints and faults are associated with bending of rock strata to form spectacular folds as seen in orogenic belts from British Columbia to Iran, as well as seismogenic deformation of continental and oceanic lithospheres. Anticracks akin to stylolites accommodate significant volumetric strain in the fluid-saturated crust. Deformation bands are pervasive in soft sediments and in porous rocks such as sandstones and carbonates, providing nuclei for fault formation on the continents. Faults also form the boundaries of the large tectonic plates that produce earthquakes—and related phenomena such as mudslides in densely populated regions such as San Francisco, California—in response to tectonic forces and heat transport deep within the Earth. Faults, joints, and deformation bands have been recognized on other planets, satellites, and/or asteroids within our Solar System, attesting to their continuing intrigue and importance to planetary structural geology and tectonics.
Fractures such as joints and faults have long been recognized and described by geologists and engineers as expressions of brittle deformation of rocks (e.g., Price, 1966; Priest and Hudson, 1976; Gudmundsson, 2011; Peacock et al., 2018). They are important geologic structural discontinuities as they reveal types and phases of deformation, and they can be used to constrain paleostrain and paleostress magnitudes. Furthermore, they affect fluid flow in petroleum and groundwater reservoirs in a variety of ways, ranging from highly permeable fracture zones in limestones or crystalline rocks to sealing fault structures in hydrocarbon reservoirs. As a result, they have important practical implications in such fields as structural geology, geo-engineering, landscape geomorphology, hydrogeology, and petroleum geology (e.g., Cook et al., 2007).
Introduction to Geologic Structural Discontinuities
On the other hand, deformation bands, identified as thin, tabular zones of cataclasis, pore collapse, and/or grain crushing (e.g., Engelder, 1974; Aydin, 1978), now encompass five kinematic varieties, from opening through shearing to closing senses of displacement that may or may not involve cataclasis (e.g., Aydin et al., 2006). Both classes of discontinuity—fractures and deformation bands—share common attributes, such as approximately planar or gently curved geometries, small displacements relative to their horizontal lengths, echelon or linked geometries, displacement transfer between adjacent segments, variable effect on fluid flow, and systematic variation in displacement magnitude accommodated along them (see Fossen et al., 2007, 2017, for a review and discussion of these attributes for deformation bands). Building on these commonalities, a consistent terminology that encompasses all the variations noted above is available (for example, see Aydin et al., 2006; Schultz and Fossen, 2008) and utilized here.
In this chapter, we review the main types of structural discontinuities in rock. Aspects of rock mechanics and lithology that influence the type of structural discontinuity that can form will be reviewed. The related concept of modes of displacement that has proven so useful in studies of joints, faults, and other types of geologic discontinuities will then be outlined in the context of this framework. Subsequent chapters will explore the development, expression, patterns, and geological significance of these fascinating elements of rock deformation.
1.2 What Is a Structural Discontinuity?
In rock engineering, a discontinuity is a general term meant to include a wide range of mechanical defects, flaws, or planes of weakness, in a rock mass without regard to consideration of their origins (e.g., Fookes and Parrish, 1969; Attewell and Woodman, 1971; Goodman, 1976, 1989; Priest and Hudson, 1976; International Society for Rock Mechanics, 1978; Bieniawski, 1989; Fig. 1.1). This term includes bedding planes, cracks, faults, schistosity, and other planar surfaces that are characterized by small shear strength, small tensile strength, reduced stiffness, strain softening, and large fluid conductivity relative to the surrounding rock mass (Bell, 1993, p. 37; Brady and Brown, 1993, pp. 52–53; Priest, 1993, p. 1; Hudson and Harrison, 1997, p. 20). By implication, cataclastic deformation bands and solidified igneous dikes or veins in sedimentary host rock, for example, that are stronger and/or stiffer than their surroundings might not be considered as a discontinuity by a rock engineer. Pollard and Segall (1987) defined a discontinuity as “two opposing surfaces that are bounded in extent, approximately planar compared to the longest dimension, and having a displacement of originally adjacent points on the opposing walls that is both discontinuous and small relative to the longest dimension.” According to this definition, cracks, faults,
1.1. Examples of discontinuities in a rock mass as seen through the eyes of a rock engineer. Several joint planes are visible, including vertical ones exhibiting plumose structure that define the vertical face of the exposure, another vertical set perpendicular to the plane of the exposure that is restricted to certain of the horizontal sandstone layers, and sub-horizontal joints that mark separation along the bedding planes. A few inclined cracks in the uppermost massive bed suggest bedding-plane slip of that layer (top to the right) along the subjacent interface. The section shown is part of the Permian Elephant Canyon Formation exposed in southern Devils Lane graben, Canyonlands National Park, Utah.
veins, igneous dikes, stylolites, pressure solution surfaces, and anticracks would be considered as discontinuities. The term “structural discontinuity” encompasses a wide range of localized geologic structures, over a broad range of scales, strain rates, rock types, formation mechanisms, and tectonic environments.
The most common types of geologic structural discontinuities are listed in Table 1.1. An explanation of the genesis and context of these terms can be found in Schultz and Fossen (2008), with deeper exploration of their utility and significance contained in subsequent chapters.
Structural discontinuities are defined by a pair of surfaces, or fracture walls, that have been displaced (by opening or by shearing) from their original positions. For example, a crack or joint is open between its two walls (Fig. 1.2); these walls join smoothly at a crack or joint tip, defining the maximum horizontal or vertical extent of this structure in the rock. Similarly, a fault (Figs. 1.3–1.4) must be considered to be a pair of planes that are in frictional contact; a single fault plane begs the question of what was sliding against it. These paired fault walls or planes may be separated by gouge or other deformed material, and like cracks, join at a tip (Fig. 1.3) where the displacement magnitude decreases to zero. In the case of deformation bands (Fig. 1.5), the walls can be identified by a comparatively rapid change in displacement gradient or porosity, although they can be more indistinct than the clean sharp breaks typical of joints and fault planes (e.g., Aydin, 1978).
Fig.
Introduction to Geologic Structural Discontinuities
Table 1.1 Geologic structural discontinuities
Discontinuity
Structural discontinuity
Sharp discontinuity
Tabular discontinuity
Fracture
Joint
Anticrack
Deformation band
Fault
Mechanical defect, flaw, or plane of weakness in a rock mass without regard to its origin or kinematics
A localized curviplanar change in strength or stiffness caused by deformation of a rock that is characterized by two opposing surfaces that are bounded in extent, approximately planar compared to the longest dimension, and having a displacement of originally adjacent points on the opposing walls that is small relative to the longest dimension
A structural discontinuity having a discontinuous change in displacement, strength, or stiffness that occurs between a pair of discrete planar surfaces
A structural discontinuity having a continuous change in displacement, strength, or stiffness that occurs across a relatively thin band
A sharp structural discontinuity having a local reduction in strength and/or stiffness and an associated increase in fluid conductivity between the opposing pair of surfaces
A sharp structural discontinuity having field evidence for discontinuous and predominantly opening displacements between the opposing walls
A sharp or tabular structural discontinuity having field evidence for predominantly closing displacements between the opposing walls
A tabular structural discontinuity having a continuous change in displacement, strength, or stiffness across a relatively narrow zone in porous rocks
A sharp structural discontinuity defined by slip planes (surfaces of discontinuous displacement) and related structures including fault core and damage zones that formed at any stage in the evolution of the structure
Fault zone
Shear zone
Damage zone
A set of relatively closely spaced faults having similar strikes
A tabular structural discontinuity having a continuous change in strength or stiffness across a relatively narrow zone of shearing; shear and volumetric strains are continuous across the zone, and large or continuous (linked) slip surfaces are rare or absent
A zone of increased deformation density that is located around a discontinuity that formed at any stage in the evolution of the structure
A brittle fracture implies creation of these surfaces under conditions of relatively small strain and with a decreasing resistance to continued deformation (i.e., a strain-softening response in the post-peak part of the stress–strain curve for the rock; Jaeger, 1969; see also Hudson and Harrison, 1997; Chapter 8). Brittle deformation additionally implies localization of strain into one or more discrete planar elements, whereas ductile deformation implies nonlocalized, spatially distributed deformation (e.g., Pollard and Fletcher, 2005, p. 334).
The term “fracture” thus implies a local reduction in strength and/or stiffness and an associated increase in fluid conductivity between the pair of surfaces.
Fig. 1.2. Several thin, parallel joints from a granitic pluton near Ward Lake, California, are visible to the naked eye. Closer examination reveals that these joints are filled with epidote and other hydrothermal minerals that were present in the fluid that circulated within the joints as they dilated and propagated at mid-crustal depths.
Cracks, joints, and faults are, as a consequence, various types of brittle fractures. A solidified igneous dike that cuts a weaker and/or less stiff sedimentary sequence, however, would not be considered to be a fracture according to this definition, although the contact between the igneous rock and the country rock may qualify if it is weaker, or less stiff, than the igneous or country rock.
Fractures are seen to be a pair of surfaces that separate their displaced surroundings from what is between them (e.g., Johnson, 1995). Joints in the subsurface are filled by a variety of liquids including groundwater (e.g., Engelder, 1985; National Academy of Sciences, 1996), natural gas (Lacazette and Engelder, 1992), and petroleum (Dholakia et al., 1998; Engelder et al., 2009). Joints filled by solidified hydrothermal, diagenetic, or magmatic minerals are called veins and igneous dikes (Figs. 1.6 and 1.7), respectively. Rubin (1995b) calls igneous dikes “magma-filled cracks” to emphasize the mechanical basis for dike dilation and propagation. In all of these examples, it becomes important to determine whether the filling material was there
Fig. 1.3. Normal faults exposed on this dip slope of Upper Cretaceous carbonate rock (Garumnian Formation, Collado de Fumanyá) from the Spanish Pyrenees demonstrate a consistent spacing and clear fault terminations. The shadowed indentations are dinosaur footprints that predate the faults.
Fig. 1.4. A prominent normal fault cuts through a precursory zone of deformation bands in this view of “Aydin’s Wall” that formed in Entrada Sandstone east of the San Rafael Swell in eastern Utah. The bright sunlit high-angle planes are large slip surfaces whose corrugations are inherited from the architecture of the deformation band network. A second normal fault at the upper right defines this area as a fault zone having two major subparallel strands.
Fig. 1.5. Deformation bands are an important deformation mechanism in porous rocks such as sandstone, and they define intricate and informative arrays as in this fine example in Navajo Sandstone from southern Utah. The subhorizontal bedding can be seen to be cut by two oppositely dipping sets of shear-enhanced compaction bands and a subvertical set of pure compaction bands. Stratigraphic restriction of these band sets can be observed.
Fig. 1.6. A pair of echelon igneous dikes is shown in granitic rock of the central Sierra Nevada near Donner Lake, California. Each dike segment beyond the overlap region, where the dikes are linked, exhibits a separation of host rock by ~10 cm, with the intervening void within the dike being filled by a sequence of hydrothermal (light-toned) and igneous (dark-toned) fluids that have since crystallized, preserving the extensional strain in the pluton. The later crack in the left-hand part of the image (that cuts the dike) also demonstrates that a fracture must be defined by a pair of subparallel walls or surfaces, rather than a single plane.
initially, inside the joint, as it dilated and propagated, or whether the filling material came afterwards and simply occupied the volume within the joint (e.g., Laubach et al., 2010).
Fault walls may be separated by gouge (e.g., Chambon et al., 2006); those of a stylolite, by insoluble residue such as clays (e.g., Fletcher and Pollard, 1981; Engelder and Marshak, 1985; Pollard and Fletcher, 2005, p. 17); shear
Fig. 1.7. The detailed shape of the dike tip is clearly revealed by this view of the stepover between a pair of closely spaced igneous dikes. The dike segment width, normal to its trace, is ~10 cm (camera lens cap for scale). Dike shapes such as these can be predicted very well by representing the dikes as dilatant cracks propagating through a continuous elastic medium.
zones contain a variety of interesting rocks and fabrics (e.g., Fossen and Cavalcante, 2017). Deformation bands typically have either increased or decreased porosity within them (e.g., Aydin et al., 2006); grain-size reduction may also characterize the interior of a deformation band (e.g., Aydin, 1978; Davis, 1999; Fossen et al., 2007). As a result, cracks, joints, faults, stylolites, and deformation bands all contain various materials between their walls that can differ significantly from the host rock that surrounds them.
Discontinuity, part 1: Finite Dimensions
Discontinuity, part 2: Displacement Gradient
The term “discontinuity” has two distinct meanings when applied to localized structures. First, joining of the paired crack or fault walls at the fracture tips defines the dimensions of the fracture, such as its length, width, or height. Fractures that have discrete lengths are called discontinuous (e.g., Pollard and Segall, 1987) and this is the basis for the field of engineering fracture mechanics (because discontinuous fractures end at the fracture tips). The second, and more recent, use of “discontinuity” refers to the rate of change of displacement across the structure (e.g., Johnson, 1995; Borja, 2002). Fractures having a discrete step-wise change in displacement across them, such as cracks and faults (or slip surfaces), are said to have, or be, a displacement discontinuity. In contrast, shear zones and deformation bands may exhibit a continuous displacement across them. The boundary element modeling approach developed by Crouch and Starfield (1983, pp. 208–210) and used by many researchers in geologic fracture mechanics clearly illustrates how these (strong and weak) discontinuities can both be easily represented in a fracture model by specifying the properties of the filling material along with the strengths of the enclosing walls. This computational approach parallels the geologic work summarized in this section that motivates the integration of terminology espoused in this book.
The scale of the structure relative to its surroundings is also important to consider. For example, the rock cut by a structure is commonly taken as an
“effective continuum” (e.g., Pollard and Segall, 1987, and references therein). A geologic unit is considered to be continuous when its properties at the scale of the structure are statistically constant, leading to homogeneous values and behavior (Priest and Hudson, 1981). Rock units with spatially variable properties, such as joint sets, at a given scale are called discontinuous. In mechanics, a continuous material is said to be simply-connected, whereas a discontinuous one is multiply-connected (e.g., Nehari, 1952).
An outcrop of columnar-jointed basaltic lava flows (e.g., Fig. 1.8) provides an informative example of relative scale (Schultz, 1996). For a scale of observation of millimeters to centimeters, the rock within a column is intact basaltic rock, and it can be idealized by those properties. At significantly smaller scales, grain size and microcracks become important enough that the assumption of a continuous material may not apply. For a scale of a few meters, however, the rock unit can be described as intact basalt partly separated into irregular blocks by numerous discontinuous fractures (i.e., the columnar joints). Because this scale of observation is comparable to the scale of the fracturing (or equivalently, the block size), the flow must be considered as a discontinuum within which the properties of the rock and fractures both must be considered to understand and represent the behavior of the flow, as in the example shown in Fig. 1.8. An approach called block theory (Goodman and Shi, 1985; Priest, 1993, pp. 246–250) would be the method of choice here. At dimensions for which the scale of observation greatly exceeds (e.g., by a factor of 5–10) the block size or fracture spacing, such as would be found on an aerial or satellite image, the lava flow can be described as an effective continuum (Priest, 1993) and a rock mass (see also Bieniawski, 1989; Schultz, 1993, 1995a,b, 1996; Fig. 1.1). Various methods for “upscaling” rock
Fig. 1.8. View of columnar joints in basalt near Donner Lake, California, looking down the column axes; rock hammer for scale.
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Title: Natural history of intellect, and other papers
Author: Ralph Waldo Emerson
Release date: September 4, 2023 [eBook #71558]
Language: English
Original publication: Boston: Houghton, Mifflin and Company, 1893
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NATURAL HISTORY OF INTELLECT
BY RALPH WALDO EMERSON
BOSTON AND NEW YORK
HOUGHTON, MIFFLIN AND COMPANY
The Riverside Press, Cambridge 1893
Copyright, 1893, B EDWARD W. EMERSON.
All rights reserved.
The Riverside Press, Cambridge, Mass., U. S. A. Electrotyped and Printed by H. O. Houghton & Company
PREFATORY NOTE.
The first two pieces in this volume are lectures from the “University Courses” on philosophy, given at Harvard College in 1870 and 1871, by persons not members of the Faculty. “The Natural History of the Intellect” was the subject which Emerson chose. He had from his early youth cherished the project of a new method in metaphysics, proceeding by observation of the mental facts, without attempting an analysis and coördination of them, which must, from the nature of the case, be premature. With this view, he had, at intervals from 1848 to 1866, announced courses on the “Natural History of Intellect,” “The Natural Method of Mental Philosophy,” and “Philosophy for the People.” He would, he said, give anecdotes of the spirit, a calendar of mental moods, without any pretense of system.
None of these attempts, however, disclosed any novelty of method, or, indeed, after the opening statement of his intention, any marked difference from his ordinary lectures. He had always been writing anecdotes of the spirit, and those which he wrote under this heading were used by him in subsequently published essays so largely that I find very little left for present publication. The lecture which gives its name to the volume was the first of the earliest course, and it seems to me to include all that distinctly belongs to the particular subject.
The lecture on “Memory” is from the same course; that on “Boston” from the course on “Life and Literature,” in 1861. The other pieces are reprints from the “North American Review” and the “Dial.”
J. E. C .
September 9, 1893.
NATURAL HISTORY OF INTELLECT.
NATURAL HISTORY OF INTELLECT.
I have used such opportunity as I have had, and lately[1] in London and Paris, to attend scientific lectures; and in listening to Richard Owen’s masterly enumeration of the parts and laws of the human body, or Michael Faraday’s explanation of magnetic powers, or the botanist’s descriptions, one could not help admiring the irresponsible security and happiness of the attitude of the naturalist; sure of admiration for his facts, sure of their sufficiency. They ought to interest you; if they do not, the fault lies with you.
Then I thought—could not a similar enumeration be made of the laws and powers of the Intellect, and possess the same claims on the student? Could we have, that is, the exhaustive accuracy of distribution which chemists use in their nomenclature and anatomists in their descriptions, applied to a higher class of facts; to those laws, namely, which are common to chemistry, anatomy, astronomy, geometry, intellect, morals, and social life;—laws of the world?
Why not? These powers and laws are also facts in a Natural History. They also are objects of science, and may be numbered and recorded, like stamens and vertebræ. At the same time they have a deeper interest, as in the order of nature they lie higher and are nearer to the mysterious seat of power and creation.
For at last, it is only that exceeding and universal part which interests us, when we shall read in a true history what befalls in that kingdom where a thousand years is as one day, and see that what is
set down is true through all the sciences; in the laws of thought as well as of chemistry.
In all sciences the student is discovering that nature, as he calls it, is always working, in wholes and in every detail, after the laws of the human mind. Every creation, in parts or in particles, is on the method and by the means which our mind approves as soon as it is thoroughly acquainted with the facts; hence the delight. No matter how far or how high science explores, it adopts the method of the universe as fast as it appears; and this discloses that the mind as it opens, the mind as it shall be, comprehends and works thus; that is to say, the Intellect builds the universe and is the key to all it contains. It is not then cities or mountains, or animals, or globes that any longer command us, but only man; not the fact, but so much of man as is in the fact.
In astronomy, vast distance, but we never go into a foreign system. In geology, vast duration, but we are never strangers. Our metaphysic should be able to follow the flying force through all transformations, and name the pair identical through all variety.
I believe in the existence of the material world as the expression of the spiritual or the real, and in the impenetrable mystery which hides (and hides through absolute transparency) the mental nature, I await the insight which our advancing knowledge of material laws shall furnish.
Every object in nature is a word to signify some fact in the mind. But when that fact is not yet put into English words, when I look at the tree or the river and have not yet definitely made out what they would say to me, they are by no means unimpressive. I wait for them, I enjoy them before they yet speak. I feel as if I stood by an ambassador charged with the message of his king, which he does not deliver because the hour when he should say it is not yet arrived.
Whilst we converse with truths as thoughts, they exist also as plastic forces; as the soul of a man, the soul of a plant, the genius or constitution of any part of nature, which makes it what it is. The thought which was in the world, part and parcel of the world, has disengaged itself and taken an independent existence.
My belief in the use of a course on philosophy is that the student shall learn to appreciate the miracle of the mind; shall learn its subtle but immense power, or shall begin to learn it; shall come to know that in seeing and in no tradition he must find what truth is; that he shall see in it the source of all traditions, and shall see each one of them as better or worse statement of its revelations; shall come to trust it entirely, as the only true; to cleave to God against the name of God. When he has once known the oracle he will need no priest. And if he finds at first with some alarm how impossible it is to accept many things which the hot or the mild sectarian may insist on his believing, he will be armed by his insight and brave to meet all inconvenience and all resistance it may cost him. He from whose hand it came will guide and direct it.
Yet these questions which really interest men, how few can answer. Here are learned faculties of law and divinity, but would questions like these come into mind when I see them? Here are learned academies and universities, yet they have not propounded these for any prize.
Seek the literary circles, the stars of fame, the men of splendor, of bon-mots, will they afford me satisfaction? I think you could not find a club of men acute and liberal enough in the world. Bring the best wits together, and they are so impatient of each other, so vulgar, there is so much more than their wit,—such follies, gluttonies, partialities, age, care, and sleep, that you shall have no academy.
There is really a grievous amount of unavailableness about men of wit. A plain man finds them so heavy, dull and oppressive, with bad jokes and conceit and stupefying individualism, that he comes to write in his tablets, Avoid the great man as one who is privileged to be an unprofitable companion. For the course of things makes the scholars either egotists or worldly and jocose. In so many hundreds of superior men hardly ten or five or two from whom one can hope for a reasonable word.
Go into the scientific club and hearken. Each savant proves in his admirable discourse that he and he only knows now or ever did know anything on the subject: “Does the gentleman speak of anatomy? Who peeped into a box at the Custom House and then published a drawing of my rat?” Or is it pretended discoveries of new strata that are before the meeting? This professor hastens to inform us that he knew it all twenty years ago, and is ready to prove that he knew so much then that all further investigation was quite superfluous;—and poor nature and the sublime law, which is all that our student cares to hear of, are quite omitted in this triumphant vindication.
Was it better when we came to the philosophers, who found everybody wrong; acute and ingenious to lampoon and degrade mankind? And then was there ever prophet burdened with a message to his people who did not cloud our gratitude by a strange confounding in his own mind of private folly with his public wisdom?
But if you like to run away from this besetting sin of sedentary men, you can escape all this insane egotism by running into society, where the manners and estimate of the world have corrected this folly, and effectually suppressed this overweening self-conceit. Here each is to make room for others, and the solidest merits must exist only for the entertainment of all. We are not in the smallest degree helped. Great is the dazzle, but the gain is small. Here they play the game of conversation, as they play billiards, for pastime and credit.
Yes, ’tis a great vice in all countries, the sacrifice of scholars to be courtiers and diners-out, to talk for the amusement of those who wish to be amused, though the stars of heaven must be plucked down and packed into rockets to this end. What with egotism on one side and levity on the other we shall have no Olympus.
But there is still another hindrance, namely, practicality. We must have a special talent, and bring something to pass. Ever since the Norse heaven made the stern terms of admission that a man must do something excellent with his hands or feet, or with his voice, eyes, ears, or with his whole body, the same demand has been made in Norse earth.
Yet what we really want is not a haste to act, but a certain piety toward the source of action and knowledge. In fact we have to say that there is a certain beatitude—I can call it nothing less—to which all men are entitled, tasted by them in different degrees, which is a perfection of their nature, and to which their entrance must be in every way forwarded. Practical men, though they could lift the globe, cannot arrive at this. Something very different has to be done,—the availing ourselves of every impulse of genius, an emanation of the heaven it tells of, and the resisting this conspiracy of men and material things against the sanitary and legitimate inspirations of the intellectual nature.
What is life but the angle of vision? A man is measured by the angle at which he looks at objects. What is life but what a man is thinking of all day? This is his fate and his employer. Knowing is the measure of the man. By how much we know, so much we are.
The laws and powers of the Intellect have, however, a stupendous peculiarity, of being at once observers and observed. So that it is difficult to hold them fast, as objects of examination, or hinder them from turning the professor out of his chair. The wonder of the science of Intellect is that the substance with which we deal is of that subtle and active quality that it intoxicates all who approach it. Gloves on the hands, glass guards over the eyes, wire-gauze masks over the face, volatile salts in the nostrils, are no defence against this virus, which comes in as secretly as gravitation into and through all barriers.
Let me have your attention to this dangerous subject, which we will cautiously approach on different sides of this dim and perilous lake, so attractive, so delusive. We have had so many guides and so many failures. And now the world is still uncertain whether the pool has been sounded or not.
My contribution will be simply historical. I write anecdotes of the intellect; a sort of Farmer’s Almanac of mental moods. I confine my
ambition to true reporting of its play in natural action, though I should get only one new fact in a year.
I cannot myself use that systematic form which is reckoned essential in treating the science of the mind. But if one can say so without arrogance, I might suggest that he who contents himself with dotting a fragmentary curve, recording only what facts he has observed, without attempting to arrange them within one outline, follows a system also,—a system as grand as any other, though he does not interfere with its vast curves by prematurely forcing them into a circle or ellipse, but only draws that arc which he clearly sees, or perhaps at a later observation a remote curve of the same orbit, and waits for a new opportunity, well-assured that these observed arcs will consist with each other.
I confess to a little distrust of that completeness of system which metaphysicians are apt to affect. ’Tis the gnat grasping the world. All these exhaustive theories appear indeed a false and vain attempt to introvert and analyze the Primal Thought. That is upstream, and what a stream! Can you swim up Niagara Falls?
We have invincible repugnance to introversion, to study of the eyes instead of that which the eyes see; and the belief of men is that the attempt is unnatural and is punished by loss of faculty I share the belief that the natural direction of the intellectual powers is from within outward, and that just in proportion to the activity of thoughts on the study of outward objects, as architecture, or farming, or natural history, ships, animals, chemistry,—in that proportion the faculties of the mind had a healthy growth; but a study in the opposite direction had a damaging effect on the mind.
Metaphysic is dangerous as a single pursuit. We should feel more confidence in the same results from the mouth of a man of the world. The inward analysis must be corrected by rough experience. Metaphysics must be perpetually reinforced by life; must be the observations of a working-man on working-men; must be biography, —the record of some law whose working was surprised by the observer in natural action.
I think metaphysics a grammar to which, once read, we seldom return. ’Tis a Manila full of pepper, and I want only a teaspoonful in a year. I admire the Dutch, who burned half the harvest to enhance the price of the remainder.
I want not the logic but the power, if any, which it brings into science and literature; the man who can humanize this logic, these syllogisms, and give me the results. The adepts value only the pure geometry, the aerial bridge ascending from earth to heaven with arches and abutments of pure reason. I am fully contented if you tell me where are the two termini.
My metaphysics are to the end of use. I wish to know the laws of this wonderful power, that I may domesticate it. I observe with curiosity its risings and settings, illumination and eclipse; its obstructions and its provocations, that I may learn to live with it wisely, court its aid, catch sight of its splendor, feel its approach, hear and save its oracles and obey them. But this watching of the mind, in season and out of season, to see the mechanics of the thing, is a little of the detective. The analytic process is cold and bereaving and, shall I say it? somewhat mean, as spying. There is something surgical in metaphysics as we treat it. Were not an ode a better form? The poet sees wholes and avoids analysis; the metaphysician, dealing as it were with the mathematics of the mind, puts himself out of the way of the inspiration; loses that which is the miracle and creates the worship.
I think that philosophy is still rude and elementary. It will one day be taught by poets. The poet is in the natural attitude; he is believing; the philosopher, after some struggle, having only reasons for believing.
What I am now to attempt is simply some sketches or studies for such a picture; Mémoires pour servir toward a Natural History of Intellect.
First I wish to speak of the excellence of that element, and the great auguries that come from it, notwithstanding the impediments which our sensual civilization puts in the way.
Next I treat of the identity of the thought with Nature; and I add a rude list of some by-laws of the mind.
Thirdly I proceed to the fountains of thought in Instinct and Inspiration, and I also attempt to show the relation of men of thought to the existing religion and civility of the present time.
I. We figure to ourselves Intellect as an ethereal sea, which ebbs and flows, which surges and washes hither and thither, carrying its whole virtue into every creek and inlet which it bathes. To this sea every human house has a water front. But this force, creating nature, visiting whom it will and withdrawing from whom it will, making day where it comes and leaving night when it departs, is no fee or property of man or angel. It is as the light, public and entire to each, and on the same terms.
What but thought deepens life, and makes us better than cow or cat? The grandeur of the impression the stars and heavenly bodies make on us is surely more valuable than our exact perception of a tub or a table on the ground.
To Be is the unsolved, unsolvable wonder To Be, in its two connections of inward and outward, the mind and nature. The wonder subsists, and age, though of eternity, could not approach a solution. But the suggestion is always returning, that hidden source publishing at once our being and that it is the source of outward nature. Who are we and what is Nature have one answer in the life that rushes into us.
In my thought I seem to stand on the bank of a river and watch the endless flow of the stream, floating objects of all shapes, colors and natures; nor can I much detain them as they pass, except by running beside them a little way along the bank. But whence they come or
whither they go is not told me. Only I have a suspicion that, as geologists say every river makes its own valley, so does this mystic stream. It makes its valley, makes its banks and makes perhaps the observer too. Who has found the boundaries of human intelligence? Who has made a chart of its channel or approached the fountain of this wonderful Nile?
I am of the oldest religion. Leaving aside the question which was prior, egg or bird, I believe the mind is the creator of the world, and is ever creating;—that at last Matter is dead Mind; that mind makes the senses it sees with; that the genius of man is a continuation of the power that made him and that has not done making him.
I dare not deal with this element in its pure essence. It is too rare for the wings of words. Yet I see that Intellect is a science of degrees, and that as man is conscious of the law of vegetable and animal nature, so he is aware of an Intellect which overhangs his consciousness like a sky, of degree above degree, of heaven within heaven.
Every just thinker has attempted to indicate these degrees, these steps on the heavenly stair, until he comes to light where language fails him. Above the thought is the higher truth,—truth as yet undomesticated and therefore unformulated.
It is a steep stair down from the essence of Intellect pure to thoughts and intellections. As the sun is conceived to have made our system by hurling out from itself the outer rings of diffuse ether which slowly condensed into earths and moons, by a higher force of the same law the mind detaches minds, and a mind detaches thoughts or intellections. These again all mimic in their sphericity the first mind, and share its power
Life is incessant parturition. There are viviparous and oviparous minds; minds that produce their thoughts complete men, like armed soldiers, ready and swift to go out to resist and conquer all the armies of error, and others that deposit their dangerous unripe
thoughts here and there to lie still for a time and be brooded in other minds, and the shell not be broken until the next age, for them to begin, as new individuals, their career.
The perceptions of a soul, its wondrous progeny, are born by the conversation, the marriage of souls; so nourished, so enlarged. They are detached from their parent, they pass into other minds; ripened and unfolded by many they hasten to incarnate themselves in action, to take body, only to carry forward the will which sent them out. They take to themselves wood and stone and iron; ships and cities and nations and armies of men and ages of duration; the pomps of religion, the armaments of war, the codes and heraldry of states; agriculture, trade, commerce;—these are the ponderous instrumentalities into which the nimble thoughts pass, and which they animate and alter, and presently, antagonized by other thoughts which they first aroused, or by thoughts which are sons and daughters of these, the thought buries itself in the new thought of larger scope, whilst the old instrumentalities and incarnations are decomposed and recomposed into new.
Our eating, trading, marrying, and learning are mistaken by us for ends and realities, whilst they are properly symbols only; when we have come, by a divine leading, into the inner firmament, we are apprised of the unreality or representative character of what we esteemed final.
So works the poor little blockhead manikin. He must arrange and dignify his shop or farm the best he can. At last he must be able to tell you it, or write it, translate it all clumsily enough into the new skylanguage he calls thought. He cannot help it, the irresistible meliorations bear him forward.
II. Whilst we consider this appetite of the mind to arrange its phenomena, there is another fact which makes this useful. There is in nature a parallel unity which corresponds to the unity in the mind and makes it available. This methodizing mind meets no resistance
