![1 Introduction and Motivation 5
this simple system have some hallmarks of essentially random phenomena: their
behavior is irregular and unpredictable.
The mechanisms underlying the random character of this system are reasonably
well understood (see, e.g., Collet and Eckmann 1980), the key notion being sensi-
tivity to initial conditions and its consequences. However, within this framework it
is difficult to approach questions of the type “what is the asymptotic behavior of
a typical trajectory of this system?” Indeed, the very nature of sensitivity to initial
conditions would seem to preclude any notion of “typical” behavior, since even very
similar initial conditions eventually lead to their own very particular, uncorrelated
evolutions.
However, different conclusions are reached if one takes a probabilistic point
of view. Suppose that instead of being precisely determined, the initial state x0
has associated with it some uncertainty. In particular, suppose we know the initial
probability density, f , giving the probabilities of all possible values that x0 can take.
Then it makes sense to ask, “what will be the probability density of x1, the new
state after one iteration of the map (1.1)?” A precise answer to this question can be
found using analytical methods described in Chap. 2. For an approximate answer,
it suffices to simulate a large ensemble of different initial states x0 distributed
according to f , evolve these states forward under the map (1.1), and approximate the
transformed density of the ensemble by constructing a histogram of the ensemble of
values x1. One can then proceed, in the same fashion, to determine the probability
densities of subsequent states x2, x3, etc. Thus, even if the initial state x0 is not
known precisely, it is at least possible to give a probabilistic description of the
system’s evolution in terms of the evolution of a probability density.
The graphs in Fig. 1.2 show a particular choice for the probability density f
of the initial state x0, together with the subsequent densities of states x1, x2,
x3, x4, obtained by numerical simulation of an ensemble of 106 initial values
distributed according to f , iterated forward under the map (1.1). The striking feature
of this figure is that the sequence of densities rapidly approaches an equilibrium
or invariant density that does not change under further iteration. Moreover, the
invariant density appears to be unique. This is supported by Fig. 1.3, which shows
how a different choice of initial density evolves toward the same equilibrium density
as before.
A different but related statistical approach to this system is to focus on the
statistics of a single trajectory. For a given initial state x0, by iterating xn+1 =
4xn(1 − xn) we obtain an arbitrarily long sequence {xn} like the one illustrated in
Fig. 1.1. A histogram of this sequence reveals the long-term frequency with which
the trajectory visits various parts of the interval [0, 1]. Figure 1.4 shows such a
histogram, for a trajectory of length 106. Remarkably, this histogram reproduces
the invariant density shown in Figs. 1.2 and 1.3, which arises in a different context.
Moreover, the same histogram is obtained for almost any choice of initial state.1
1There are exceptions, such as x0 = 0, that yield trajectories with different (periodic) asymptotic
behavior. These exceptions are very rare: in fact they constitute a set of Lebesgue measure 0.](https://image.slidesharecdn.com/11208692-250607105652-fc2292a9/85/Density-Evolution-Under-Delayed-Dynamics-An-Open-Problem-1st-Ed-Jrme-Losson-17-320.jpg)
Density Evolution Under Delayed Dynamics An Open Problem 1st Ed Jrme Losson
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- 5. The Fields Institute for Research in Mathematical Sciences Fields Institute Monographs 38 Jérôme Losson Michael C. Mackey Richard Taylor Marta Tyran-Kamińska Density Evolution Under Delayed Dynamics An Open Problem
- 6. Fields Institute Monographs VOLUME 38 The Fields Institute for Research in Mathematical Sciences Fields Institute Editorial Board: Kumar Murty, Director Deirdre Haskell, Deputy Director of the Institute James G. Arthur, University of Toronto Kenneth R. Davidson, University of Waterloo Lisa Jeffrey, University of Toronto Barbara Lee Keyfitz, Ohio State University Thomas S. Salisbury, York University Noriko Yui, Queen’s University Juris Steprans, York University The Fields Institute is a centre for research in the mathematical sciences, located in Toronto, Canada. The Institutes mission is to advance global mathematical activity in the areas of research, education and innovation. The Fields Institute is supported by the Ontario Ministry of Training, Colleges and Universities, the Natural Sciences and Engineering Research Council of Canada, and seven Principal Sponsoring Universities in Ontario (Carleton, McMaster, Ottawa, Queen’s, Toronto, Waterloo, Western and York), as well as by a growing list of Affiliate Universities in Canada, the U.S. and Europe, and several commercial and industrial partners. More information about this series at http://www.springer.com/series/10502
- 7. Jérôme Losson • Michael C. Mackey Richard Taylor • Marta Tyran-Kamińska Density Evolution Under Delayed Dynamics An Open Problem
- 8. Jérôme Losson BC Partners London, UK Michael C. Mackey Department of Physiology McGill University Montreal, QC, Canada Richard Taylor Department of Mathematics and Statistics Thompson Rivers University Kamloops, BC, Canada Marta Tyran-Kamińska Institute of Mathematics University of Silesia Katowice, Poland ISSN 1069-5273 ISSN 2194-3079 (electronic) Fields Institute Monographs ISBN 978-1-0716-1071-8 ISBN 978-1-0716-1072-5 (eBook) https://doi.org/10.1007/978-1-0716-1072-5 © Springer Science+Business Media, LLC, part of Springer Nature 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Science+Business Media, LLC, part of Springer Nature. The registered company address is: 1 New York Plaza, New York, NY 10004, U.S.A.
- 9. Preface This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though we have no definitive solution to the problem, we offer this contribution in an attempt to define the problem as we see it and to sketch out several obvious attempts that have been suggested to solve the problem and which seem to have failed. We hope that by being available to the general mathematical community, they will inspire others to consider—and hopefully solve—the problem. Serious attempts have been made by all of the authors over the years and we have made reference to these where appropriate. Much of the material in this contribution has been previously published, but not all of it. A serious attempt has been made by Taylor (2004) and should be consulted for a variety of issues, some of which are repeated here. Along the same lines, many of the topics we raise here are also highlighted in Mitkowski and Mitkowski (2012), and in Mitkowski (2021). The material is organized as follows: Chapter 1 offers motivating examples to show why we want to study density evolution in systems with delayed dynamics. In Chap. 2, we review briefly what is known about density evolution in systems with finite dimensional dynamics, starting with a description of the connection between dynamics and densities in Sect. 2.1. Section 2.3 reviews the situation for the commonly known situation in which the dynamics are described by ordinary differential equations. Section 2.4 briefly considers dynamics described by stochas- tic differential equations, while Sect. 2.5 does the same for finite-dimensional maps. Section 2.6 concludes with a description of the dynamic density evolution behaviors of ergodicity, mixing, exactness, and asymptotic periodicity. Chapter 3 motivates the study of the dynamics of ensembles of differential delay equations through some simple numerical examples. Section 3.1 relates the formal “density evolution” problem for differential delay equations to what is actually measured in an experimental setting. Section 3.2 gives numerical evidence for the existence of interesting ergodic properties of density evolution dynamics in the presence of delays. Chapter 4 considers the real mathematical problems involved v
- 10. vi Preface ranging from the proper nature of the underlying space to the problem of defining a density and highlights all of the problems attendant in doing so. Chapter 5 outlines an approach that has been tried based on the Hopf functional. Section 5.1 introduces the notion of Hopf functionals, and Sect. 5.2 applies this to the specific case of delay differential equations. Chapter 6 considers the problem reformulated as the method of steps. Finally, Chap. 7 considers the approximations to the delay problem, first examining a high- dimensional map approximation to the delay equation. Chapter 8 is devoted to developing approximate Liouville-like equations and an examination of invariant densities for differential delay equations. We conclude in Chap. 9. We are indebted to numerous colleagues with whom we have discussed this problem over the years. We would like, in particular, to thank Andrzej Lasota (1932–2006), André Longtin, and Helmut Schwegler. The impetus for writing this is in large part due to a month-long workshop “Short Thematic Program on Delay Differential Equations” held at the Fields Institute (Toronto, May, 2015) and organized by Prof. Jianhong Wu (York University). Many colleagues there offered comments and suggestions, and for that we thank them, while other colleagues have generously shared their work with us ahead of publication. This work was supported at various times by NATO, MITACS (Canada), the Humboldt Stiftung (Germany), the Natural Sciences and Engineering Research Council (NSERC, Canada), and the Polish NCN grant no. 2017/27/B/ST1/00100. London, UK Jérôme Losson Montreal, QC, Canada Michael C. Mackey Kamloops, BC, Canada Richard Taylor Katowice, Poland Marta Tyran-Kamińska June 2020
- 11. Contents Part I Introduction and Background to Density Evolution Problems 1 Introduction and Motivation ............................................... 3 1.1 Summary ................................................................ 8 2 Density Evolution in Systems with Finite-Dimensional Dynamics ..... 9 2.1 Dynamics and Densities ................................................ 9 2.2 Frobenius–Perron Operator............................................. 10 2.3 The Liouville Equation ................................................. 11 2.4 The Fokker–Planck Equation ........................................... 11 2.5 Density Evolution in Maps ............................................. 12 2.6 The Dynamics of Density Evolution ................................... 13 2.7 Summary ................................................................ 16 Part II Illustrating the Problem and Making It Precise for Differential Delay Equations 3 Dynamics in Ensembles of Differential Delay Equations ................ 19 3.1 What Do We Measure? ................................................. 19 3.2 Numerical Evidence for Interesting Density Dynamics in Differential Delay Equations ........................................ 21 3.3 Summary ................................................................ 26 4 The Problem .................................................................. 29 4.1 Introduction ............................................................. 29 4.2 Delay Differential Equations ........................................... 29 4.2.1 Definition of a Solution......................................... 30 4.2.2 Method of Steps................................................. 31 4.3 Delay Equation as a Dynamical System ............................... 31 4.4 Frobenius–Perron Operator............................................. 33 4.5 Probability in Infinite-Dimensional Spaces ............................ 34 4.5.1 Appropriate σ-Algebra ......................................... 35 vii
- 12. viii Contents 4.5.2 Densities......................................................... 36 4.5.3 Lack of a “Natural” Measure on C ............................ 37 4.5.4 Wiener Measure................................................. 38 4.6 Conclusions ............................................................. 40 Part III Possible Analytical Approaches 5 The Hopf Functional Approach ............................................ 45 5.1 Hopf Characteristic Functionals and Functional Differential Equations ................................................................ 45 5.1.1 Functionals and Functional Derivatives ....................... 46 5.1.2 Hopf Characteristic Functionals ............................... 48 5.1.3 Hopf Characteristic Functionals and Partial Differential Equations........................................................ 53 5.2 Characteristic Functionals for Delay Equations ....................... 60 5.2.1 A Functional Differential Equation for Zt .................... 63 5.2.2 The Moments of the Measure Wt ............................. 65 5.2.3 Taylor Series Expansion of the Functional Zt ................ 66 5.2.4 Partial Differential Equations for the Moments ............... 67 5.2.5 Invariant Measures.............................................. 73 5.2.6 The Hopf Equation and the Kramers–Moyal Expansion ..... 73 5.3 Discussion and Conclusions ............................................ 78 6 The Method of Steps ......................................................... 79 6.1 Ordinary Differential Equation System ................................ 80 6.1.1 Method of Steps................................................. 80 6.1.2 Modified Method of Steps...................................... 81 6.2 Continuity Equation..................................................... 83 6.3 Method of Characteristics .............................................. 83 6.3.1 Alternative Formulation ........................................ 86 6.4 Geometric Interpretation................................................ 87 6.5 Methods of Steps and Piecewise Deterministic Markov Processes... 88 6.6 Summary and Conclusions ............................................. 95 Part IV Possible Approximating Solutions 7 Turning a Differential Delay Equation into a High-Dimensional Map 99 7.1 From Differential Delay to Ordinary Differential Equations ......... 100 7.1.1 Functions of Bounded Variation ............................... 104 7.1.2 The Result of Ionescu Tulcea and Marinescu ................. 105 7.2 Applications to Differential Delay Equations ......................... 107 7.2.1 Oscillatory Solutions and Expansion Requirements .......... 107 7.2.2 The Result....................................................... 108 7.3 Summary and Conclusions ............................................. 114
- 13. Contents ix 8 Approximate “Liouville-Like” Equation and Invariant Densities for Delay Differential Equations ........................................... 115 8.1 Discretized Frobenius–Perron Operator ............................... 115 8.2 Liouville-Like Equation ................................................ 117 8.3 Invariant Densities ...................................................... 118 8.4 Copulas .................................................................. 119 8.5 Approximate Invariant Densities ....................................... 120 8.6 Examples ................................................................ 122 9 Summary and Conclusions ................................................. 131 References......................................................................... 133 Index............................................................................... 137
- 14. Part I Introduction and Background to Density Evolution Problems Chapter 1 is an introductory section in which we set the stage for defining the problems of density evolution under the action of differential delay equations and motivating why we want to look at it. Chapter 2 (page 9) talks briefly about density evolution in systems with finite- dimensional dynamics, starting with a description of the connection between dynamics and densities in Sect. 2.1. Section 2.3 reviews the situation for the commonly known situation in which the dynamics are described by ordinary dif- ferential equations. Section 2.4 briefly considers dynamics described by stochastic differential equations, while 2.5 does the same for finite-dimensional maps. This chapter concludes in Sect. 2.6 with a description of the dynamic density evolution behaviors of ergodicity, mixing, exactness, and asymptotic periodicity.
- 15. Chapter 1 Introduction and Motivation In examining the dynamical behavior of a system there are fundamentally two options available to the experimentalist. 1. In the first option s/he will examine the dynamical trajectories of individuals, be they fundamental particles in a cloud chamber or cells in a petri dish or animals in an ecological experiment. In this case the experimentalist may be interested in replicating the experiment many times, and building up a statistical description of the observed behavior under the assumption (among others) that the trajectory behavior will be replicated between trials given the same initial conditions. 2. In the second option this approach will be forsaken for one in which the evolving statistics of large populations are examined. This is, of course, most familiar in statistical mechanics, but is also important in many other areas. The advantage of this approach is that if one can understand the dynamics of density evolution, then many interesting statistical quantities can be computed, and the results compared with experimental results. Which approach is taken is sometimes a matter of choice, but often dictated by the nature of the individual units being studied as well as the types of experiments that are possible. To illustrate these two points of view, consider the following, much-studied, example of a simple deterministic system whose evolution exhibits a species of random behavior. For a given real number x0 (the “initial state” of the system) between 0 and 1, let x1, x2, x3, etc. be defined by repeated application of the formula xn+1 = 4xn(1 − xn), n = 0, 1, 2, . . . (1.1) One can view this formula as prescribing the evolution of the state of the system, xn, at discrete times n = 0, 1, 2, . . .. The evolution of this system is deterministic, in that once the initial state is specified equation (1.1) uniquely determines the © Springer Science+Business Media, LLC, part of Springer Nature 2020 J. Losson et al., Density Evolution Under Delayed Dynamics, Fields Institute Monographs 38, https://doi.org/10.1007/978-1-0716-1072-5_1 3
- 16. 4 1 Introduction and Motivation n x n 0 20 40 60 80 100 n 0 20 40 60 80 100 n 0 20 40 60 80 100 n 0 20 40 60 80 100 0.0 0.4 0.8 x n 0.0 0.4 0.8 x n 0.0 0.4 0.8 x n 0.0 0.4 0.8 Fig. 1.1 Numerical trajectories for the map x → 4x(1 − x). The initial conditions differ only slightly for each trajectory sequence of values {x0, x1, x2, . . .} (i.e., the trajectory of the system) for all time. Thus, for example if x0 = 0.51 we obtain x1 = .9996, x2 ≈ .0026, x3 ≈ .0064, x4 ≈ .025, x5 ≈ .099, etc. The qualitative behavior of this system is most easily appreciated graphically, as in Fig. 1.1 which plots xn vs. n for typical trajectories obtained for different choices of x0. Each of these trajectories is erratic, and random in the sense that no regularity is apparent. Furthermore, it can be seen by comparing the graphs in Fig. 1.1 that two nearly identical initial states yield radically different time evolutions. This phenomenon, termed “sensitive dependence on initial conditions” (Lorenz 1963), imposes strong limits on the predictability of this system over long periods of time: a small error in the determination of the initial condition rapidly becomes amplified to the extent that reliable prediction of the future states of the system eventually becomes impossible. Thus, despite being entirely deterministic, trajectories of
- 17. 1 Introduction and Motivation 5 this simple system have some hallmarks of essentially random phenomena: their behavior is irregular and unpredictable. The mechanisms underlying the random character of this system are reasonably well understood (see, e.g., Collet and Eckmann 1980), the key notion being sensi- tivity to initial conditions and its consequences. However, within this framework it is difficult to approach questions of the type “what is the asymptotic behavior of a typical trajectory of this system?” Indeed, the very nature of sensitivity to initial conditions would seem to preclude any notion of “typical” behavior, since even very similar initial conditions eventually lead to their own very particular, uncorrelated evolutions. However, different conclusions are reached if one takes a probabilistic point of view. Suppose that instead of being precisely determined, the initial state x0 has associated with it some uncertainty. In particular, suppose we know the initial probability density, f , giving the probabilities of all possible values that x0 can take. Then it makes sense to ask, “what will be the probability density of x1, the new state after one iteration of the map (1.1)?” A precise answer to this question can be found using analytical methods described in Chap. 2. For an approximate answer, it suffices to simulate a large ensemble of different initial states x0 distributed according to f , evolve these states forward under the map (1.1), and approximate the transformed density of the ensemble by constructing a histogram of the ensemble of values x1. One can then proceed, in the same fashion, to determine the probability densities of subsequent states x2, x3, etc. Thus, even if the initial state x0 is not known precisely, it is at least possible to give a probabilistic description of the system’s evolution in terms of the evolution of a probability density. The graphs in Fig. 1.2 show a particular choice for the probability density f of the initial state x0, together with the subsequent densities of states x1, x2, x3, x4, obtained by numerical simulation of an ensemble of 106 initial values distributed according to f , iterated forward under the map (1.1). The striking feature of this figure is that the sequence of densities rapidly approaches an equilibrium or invariant density that does not change under further iteration. Moreover, the invariant density appears to be unique. This is supported by Fig. 1.3, which shows how a different choice of initial density evolves toward the same equilibrium density as before. A different but related statistical approach to this system is to focus on the statistics of a single trajectory. For a given initial state x0, by iterating xn+1 = 4xn(1 − xn) we obtain an arbitrarily long sequence {xn} like the one illustrated in Fig. 1.1. A histogram of this sequence reveals the long-term frequency with which the trajectory visits various parts of the interval [0, 1]. Figure 1.4 shows such a histogram, for a trajectory of length 106. Remarkably, this histogram reproduces the invariant density shown in Figs. 1.2 and 1.3, which arises in a different context. Moreover, the same histogram is obtained for almost any choice of initial state.1 1There are exceptions, such as x0 = 0, that yield trajectories with different (periodic) asymptotic behavior. These exceptions are very rare: in fact they constitute a set of Lebesgue measure 0.
- 18. 6 1 Introduction and Motivation 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 x density f( x ) n = 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 x density f( x ) n = 1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 x density f( x ) n = 2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 x density f( x ) n = 3 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 x density f( x ) n = 4 Fig. 1.2 Simulated evolution of an ensemble density f under iterations of the map x → 4x(1−x) Thus, the invariant density describes the behavior of “typical” trajectories, i.e., those whose statistics are described by this particular probability density. A probabilistic or ensemble treatment of dynamical systems provides a point of view complementary to one given in terms of the evolution of individual trajectories. The iterated map (1.1) is just one example of a system that behaves erratically on the level of individual trajectories, but has very regular asymptotic properties when considered at the level of probability densities. This observation appears to hold for many other systems. Moreover, it turns out that the converse holds as well: various regularity properties at the level of probability densities imply various degrees of disorder in the evolution of individual trajectories. For a large class of systems in which the underlying dynamics are described by differential equations, or stochastic differential equations, or maps, there is a large corpus of methods that have been developed with which one can approach both of the types of data collection outlined above and the connection of that data to underlying dynamical systems theory. However, many problems in the physical, and especially the biological, sciences involve the dynamic behavior of individual entities whose dynamics involve signif-
- 19. Exploring the Variety of Random Documents with Different Content
- 20. with small aduisement enter into the same. Certes it passeth my cunning, either to name or to describe all these one hundreth fourtie seauen, according to their estate; neither haue I had anie information of them, more than I haue gathered by Leland, or gotten out of a map of their description, which I had sometime of Reginald Woolfe: wherfore omitting as it were all the rags, and such as are not worthie to haue anie time spent about their particular descriptions, I will onelie touch the greatest, and those that lie togither (as I said) in maner of a roundle. S. Maries Ile. The first and greatest of these therefore, called S. Maries Ile, is about fiue miles ouer, or nine miles in compasse. Therein also is a parish-church, and a poore towne belonging thereto, of threescore housholds, beside a castell, plentie of corne, conies, wild swans, puffens, gulles, cranes, other kinds of foule in great abundance. This fertile Iland being thus viewed, we sailed southwards by the Norman Agnus Ile. rocke, and S. Maries sound vnto Agnus Ile, which is six miles ouer, and hath in like sort one towne or parish within the same of fiue or six housholds, beside no small store of hogs conies of sundrie colours, verie profitable to their owners. It is not long since this Ile was left desolate, for when the inhabitants thereof returned from a feast holden in S. Maries Ile, they were all drowned, and not one person left aliue. Annot. There are also two other small Ilands, betwéene this and the Annot, whereof I find nothing worthie relation: for as both of them ioind togither are not comparable to the said Annot for greatnesse and circuit, so they want both hogs and conies, wherof Annot hath great Minwisand. Smithy sound. Suartigan. Rousuian. Rousuiar. Cregwin. plentie. There is moreouer the Minwisand, from whence we passe by the Smithy sound (leauing thrée little Ilands on the left hand, vnto the Suartigan Iland, then to Rousuian, Rousuiar, and the Cregwin, which seauen are (for the most part) replenished with conies onelie, and wild garlike, but void of wood other
- 21. commodities, sauing of a short kind of grasse, or here there some firzes wheron their conies doo féed. Leauing therefore these desert peeces, we incline a little toward the Moncarthat. Inis Welseck. Suethiall. Rat Iland. northwest, where we stumble or run vpon Moncarthat, Inis Welseck, Suethiall. We came in like sort vnto Rat Iland, wherein are so manie monstrous rats, that if anie horsses, or other beasts, happen to come thither, or be left there by negligence but one night, they are sure to be deuoured eaten vp, without all hope of recouerie. There is Anwall. Brier. moreouer the Anwall and the Brier, Ilands in like sort void of all good furniture, conies onelie excepted, and the Brier (wherein is a village, castell, and parish-church) bringeth foorth no lesse store of hogs, and wild foule, than Rat Iland doth of rats, whereof I greatlie maruell. Rusco. Inis widdō. By north of the Brier, lieth the Rusco, which hath a Labell or Byland stretching out toward the southwest, called Inis widdon. This Rusco is verie neere so great as that of S. Maries. It hath moreouer an hold, and a parish within it, beside great store of conies and wild foule, whereof they make much gaine in due time of the yeare. Next vnto this we come to Round Iland. S. Lides. the Round Iland, which is about a mile ouer, then to S. Lides Iland, (wherein is a parish-church dedicated to that Saint, beside conies, wood, and wild foule, of which two later there is some indifferent store) Notho. Auing. the Notho, the Auing, (one of them being situat by south of another, and the Auing halfe a mile ouer, which is a iust halfe lesse than the Notho) Tyan. and the Tyan, which later is a great Iland, furnished with a parish-church, and no small plentie of conies as I heare. After the Tyan S. Martines. we come to S. Martines Ile, wherein is a faire towne, the Ile it selfe being next vnto the Rusco for greatnesse, and verie well furnished with conies fresh springs. Also betwixt this and S. Maries, are ten other, smaller, which reach out Knolworth.
- 22. Sniuilliuer. Menwethā. Vollis. 1. Surwihe. Vollis. 2. Arthurs Ile. Guiniliuer. Nenech. Gothrois. of the northeast into the southwest, as Knolworth, Sniuilliuer, Menwetham, Vollis. 1. Surwihe, Vollis. 2. Arthurs Iland, Guiniliuer, Nenech and Gothrois, whose estates are diuers: howbeit as no one of these is to be accounted great in comparison of the other, so they all yéeld a short grasse méet for sheepe and conies, as doo also the rest. In the greater Iles likewise (whose names are commonlie such as those of the townes or churches standing in the same) there are (as I here) sundry lakes, and those neuer without great plentie of wild foule, so that the Iles of Sylley, are supposed to be no lesse beneficiall to their lords, than anie other whatsoeuer, within the compasse of our Ile, Wild swine in Sylley. or neere vnto our coasts. In some of them also are wild swine. And as these Iles are supposed to be a notable safegard to the coast of Cornewall, so in diuerse of them great store of tin is likewise to be found. There is in like maner such plentie of fish taken among these same, that beside the feeding of their swine withall, a man shall haue more there for a penie, than in London for ten grotes. Howbeit their cheefe commoditie is made by Keigh, which they drie, cut in peeces, and carie ouer into little Britaine, where they exchange it there, for salt, canuas, readie monie, or other merchandize which they doo stand in need of. A like trade haue some of them also, with Buckhorne or dried whiting, as I heare. But sith the author of this report did not flatlie auouch it, I passe ouer that fish as not in season at this time. Thus haue we viewed the richest and most wealthie Iles of Sylley, from whence we must direct our course eastwards, vnto the mouth of the Sauerne, and then go backe againe vnto the west point of Wales, continuing still our voiage along vpon the west coast of Britaine, till we come to the Soluey whereat the kingdomes part,
- 23. from which foorth on we must touch such Ilands as lie vpon the west and north shore, till we be come againe vnto the Scotish sea, and to our owne dominions. Helenus. Priamus. From the point of Cornewall therefore, or promontorie of Helenus (so called, as some thinke, bicause Helenus the son of Priamus who arriued here with Brute lieth buried there, except the sea haue washed awaie his sepulchre) vntill we come vnto the mouth of Sauerne, we haue none Ilands at all that I doo know or heare of, but one litle Byland, Cape or Peninsula, which is not to be counted of in this place. And yet sith I Pendinas. haue spoken of it, you shall vnderstand, that it is called Pendinas, and beside that the compasse thereof is not aboue a mile, this is to be remembered farder thereof, how there standeth a Pharos or light therein, for ships which saile by those coasts in the night. There is also at the verie point of the said Pendinas, a chappell of saint Nicholas, beside the church of saint Ia, an Irish woman saint. It belonged of late to the Lord Brooke, but now (as I gesse) the Lord Mountioy enioieth it. There is also a blockhouse, and a péere in the eastside thereof, but the péere is sore choked with sand, as is the whole shore furthermore from S. Ies vnto S. Carantokes, insomuch that the greatest part of this Byland is now couered with sands, which the sea casteth vp, and this calamitie hath indured little aboue fiftie yeares, as the inhabitants doo affirme. There are also two rocks neere vnto Tredwy, and another not farre from Tintagell, all which many of the common sort doo repute and take for Iles: wherefore as one desirous to note all, I thinke it not best that these should be omitted: but to proceed. When we be come further, I meane vnto the Sauerne mouth, we meet the two Holmes, of which one is called Stepholme, and the other Flatholme, of their formes béeing in déed parcels of ground and low soiles fit for little else than to beare grasse for cattell, whereof they take those names. For Holme is an old Saxon word, applied to all such places. Of these also Stepholme lieth south of the Flatholme, about foure or fiue miles; the first also a mile and an halfe, the other two
- 24. miles or thereabout in length; but neither of them a mile and an halfe in breadth, where they doo seeme to be the broadest. It should séeme by some that they are not worthie to be placed among Ilands: yet othersome are of opinion, that they are not altogither so base, as to be reputed amongst flats or rocks: but whatsoeuer they be, this is sure, that they oft annoie such passengers and merchants as passe and repasse vpon that riuer. Neither doo I read of any other Iles Barri. which lie by east of these, saue onelie the Barri, and Dunwen: the first Barri is a flight shot from the shore. of which is so called of one Barroc, a religious man (as Gyraldus saith) and is about a flight shot from the shore. Herin also is a rocke standing at the verie entrance of the cliffe, which hath a little rift or chine vpon the side, wherevnto if a man doo laie his eare, he shall heare a noise, as if smithes did worke at the forge, sometimes blowing with their bellowes, and sometimes striking and clinking with hammers, whereof manie men haue great wonder; and no maruell. It is about a mile in compasse, situat ouer against Aberbarry, and hath a chappell in it. Dunwen. Dunwen is so called of a church (dedicated to a Welsh woman saint, called Dunwen) that standeth there. It lieth more than two miles from Henrosser, right against Neuen, and hath within it two faire mils, great store of conies. Certes if the sand increase so fast hereafter as it hath done of late about it, it will be vnited to the maine within a short season. Beyond these and toward the coast of southwales lie two other Ilands, larger in quantitie than the Holmes, of which the one is Caldee. called Caldee or Inis Pyr. It hath a parish- church with a spire steeple, and a pretie towne belonging to the countie of Pembroke, and iurisdiction of one Dauid in Wales. Leland supposeth the ruines that are found therein to haue béene of an old priorie sometimes called Lille, which was a cell belonging to the monasterie of S. Dogmael, but of this Londy. I can saie nothing. The other hight Londy, wherein is also a village or towne, and of this Iland the parson of the said towne is not onelie the captaine, but hath thereto weife, distresse, and all other commodities belonging to
- 25. the same. It is little aboue sixteene miles from the coast of Wales, though it be thirtie from Caldée, and yet it serueth (as I am informed) lord and king in Deuonshire. Moreouer in this Iland is great plentie of sheepe, but more conies, and therewithall of verie fine and short grasse for their better food pasturage; likewise much Sampere vpon the shore, which is carried from thence in barrels. And albeit that there be not scarslie fourtie housholds in the whole, yet the inhabitants there with huge stones (alredie prouided) may kéepe off thousands of their enimies, bicause it is not possible for anie aduersaries to assaile them, but onelie at one place, and with a most dangerous entrance. In this voiage also we met with two other Ilands, one of them called Shepes Ile, the other Rat Ile; the first is but a little plot lieng at the point of the Baie, before we come at the Blockehouse which standeth north of the same, at the verie entrie into Milford hauen vpon the eastside. By north also of Shepes Ile, and betwéene it Stacke rocke, which lieth in the verie middest of the hauen, at another point is Rat Ile yet smaller than the former, but what Schalmey. commodities are to be found in them as yet I cannot tell. Schalmey the greater and the lesse lie northwest of Milford hauen a good waie. They belong both to the crowne, but are not inhabited, bicause they be so Schoncold. often spoiled with pirates. Schoncold Ile ioineth vnto great Schalmey, and is bigger than it, onlie a passage for ships parteth them, whereby they are supposed to be one: Leland noteth them to lie in Milford hauen. Beside these also we found the Bateholme, Stockeholme, Midland, and Gresholme Iles, and then doubling the Wellock point, we came into a Baie, where we saw saint Brides Iland, and another in the Sound betwéene Ramsey and the point, of all which Iles and such rocks as are offensiue to mariners that passe by them, it may be my hap to speake more at large hereafter. Limen or Ramsey. Limen (as Ptolomie calleth it) is situat ouer against S. Dauids in Wales (wherevnto we must néeds come, after we be past another little one, which some men doo call Gresholme) lieth directlie west of Schalmey. In a late map I find this Limen to be called in English Ramsey: Leland also confirmeth the same, and I
- 26. cannot learne more thereof, than that it is much greater than anie of the other last mentioned (sithens I described the Holmes) and for temporall iurisdiction a member of Penbrookeshire, as it is vnto S. Dauids for matters concerning the church. Leland in his commentaries of England lib. 8. saieth that it contained thrée Ilets, whereof the bishop of S. Dauids is owner of the greatest, but the chanter of S. Dauids claimeth the second, as the archdeacon of Cairmarden dooth the third. And in these is verie excellent pasture for sheepe and horses, but not for other horned beasts which lacke their vpper téeth by nature (whose substance is conuerted into the nourishment of their hornes) and therefore cannot bite so low. Mawr. Next vnto this Ile we came to Mawr, an Iland in the mouth of Mawr, scant a bow shoot ouer, and enuironed at the low water with fresh, but at the high with salt, and here also is excellent catching of herings. After this, procéeding on still with our course, we fetched a compasse, going out of the north toward the west, and then turning againe (as the coast of the countrie leadeth) vntill we sailed full south, leauing the shore still on our right hand, vntill we came vnto a couple of Iles, which doo lie vpon the mouth of the Soch, one of them being distant (as we gessed) a mile from the other, and neither of them of anie greatnesse almost worthie to be remembred. The first that we came vnto is called Tudfall. Tudfall, and therein is a church, but without anie parishioners, except they be shéepe and conies. The quantitie thereof also is not much aboue Penthlin. six acres of ground, measured by the pole. The next is Penthlin, Myrach, or Mererosse, situat in maner betwixt Tudfall or Tuidall and the shore, and herein is verie good pasture for horsses, wherof (as I take it) that Guelyn. name is giuen vnto it. Next vnto them, we come vnto Gwelyn, a little Ile which lieth southeast of the fall of Daron or Daren, a thing of small quantitie, and yet almost parted in the mids by water, and next of all vnto Bardsey an Iland lieng ouer against Periuincle the southwest point or promontorie of Northwales (where Merlin Syluestris lieth buried) and whither the rest of the monks of Bangor did flie to saue themselues, when 2100. of their fellowes
- 27. were slaine by the Saxon princes in the quarell of Augustine the monke, the citie of Caerleon or Chester raced to the ground, and not since reedified againe to anie purpose. Ptolomie calleth this Iland Lymnos, the Britons Enlhi, and therein also is a parish-church, as the report goeth. From hence we cast about, gathering still toward the northest, till we came to Caer Ierienrhod, a notable rocke situat ouer against the mouth of the Leuenni, wherein standeth a strong hold or fortresse, or else some towne or village. Certes we could not well discerne whether of both it was, bicause the wind blew hard at southwest, the morning was mistie, and our mariners doubting some flats to be couched not far from thence, hasted awaie vnto Anglesei, whither we went a pace with a readie wind euen at our owne desire. This Iland (which Tacitus mistaketh no doubt for Mona Cæsaris, and so dooth Ptolomie as appeareth by his latitudes) is situat about two miles from the shore of Northwales. Paulus Iouius gesseth that it was in time Anglesei cut from Wales by working of the sea. past ioined to the continent, or maine of our Ile, and onelie cut off by working of the Ocean, as Sicilia peraduenture was from Italie by the violence of the Leuant or practise of some king that reigned there. Thereby also (as he saith) the inhabitants were constreind at the first to make a bridge ouer into the same, till the breach waxed so great, that no such passage could anie longer be mainteined. But as these things doo either not touch my purpose at all, or make smallie with the Anglesei. present description of this Ile: so (in comming to my matter) Anglesei is found to be full so great as the Wight, and nothing inferiour, but rather surmounting it, as that also which Cæsar calleth Mona in fruitfulnesse of soile by manie an hundred fold. In old time it was reputed and taken for the common granarie to Wales, as Sicilia was to Rome and Italie for their prouision of corne. In like maner the Welshmen themselues called it the mother of their countrie, for giuing their minds wholie to pasturage, as the most easie and lesse chargeable trade, they vtterlie neglected tillage, as men that leaned onelie to the fertilitie of this Iland for their corne, from whence they neuer failed to receiue continuall abundance. Gyraldus saith that the Ile of Anglesei was no lesse sufficient to
- 28. minister graine for the sustentation of all the men of Wales, than the mountaines called Ereri or Snowdoni in Northwales were to yeeld plentie of pasture for all the cattell whatsoeuer within the aforesaid compasse, if they were brought togither and left vpon the same. It contained moreouer so manie townes welnéere, as there be daies in a yeare, which some conuerting into Cantreds haue accompted but for three, as Gyraldus saith. Howbeit as there haue beene I say 363. townes in Anglesei, so now a great part of that reckoning is vtterlie shroonke, and so far gone to decaie, that the verie ruines of them are vnneath to be séene discerned: and yet it séemeth to be méetlie well inhabited. Leland noting the smalnesse of our hundreds in comparison to that they were in time past, addeth (so far as I remember) that there are six of them in Anglesei, as Menay, Maltraith, Liuon, Talbellion, Torkalin, and Tindaithin: herevnto Lhoid saith also how it belonged in old time vnto the kingdome of Guinhed or Northwales, and that therein at a towne called Aberfraw, being on the southwestside of the Ile, the kings of Gwinhed held euermore their palaces, whereby it came to passe, that the kings of Northwales were for a long time called kings of Aberfraw, as the Welshmen named the kings of England kings of London, till better instruction did bring them farther knowledge. There are in Anglesei many townes and villages, whose names as yet I cannot orderlie atteine vnto: wherefore I will content my selfe with the rehearsall of so many as we viewed in sailing about the coasts, and otherwise heard report of by such as I haue talked withall. Beginning therefore at the mouth of the Gefni (which riseth at northeast aboue Gefni or Geuenni, 20. miles at the least into the land) we passed first by Hundwyn, then by Newborow, Port-Hayton, Beaumarrais, Penmon, Elian, Almwoch, Burric (whereby runneth a rill into a creeke) Cornew, Holihed (standing in the promontorie) Gwifen, Aberfraw, and Cair Cadwalader, of all which, the two latter stand as it were in a nuke betweene the Geuenni water, and the Fraw, wherevpon Aberfraw is situate. Within the Iland we heard onelie of Gefni afore mentioned, of Gristial standing vpon the same water, of Tefri, of Lanerchimedh, Lachtenfarwy and Bodedrin, but of
- 29. all these the cheefe is now Beaumarais, which was builded sometime by king Edward the first, and therewithall a strong castell about the yeare 1295. to kéepe that land in quiet. There are also as Leland saith 31. parish-churches beside 69. chappels, that is, a hundreth in all. But héerof I can saie little, for lacke of iust instruction. In time past, the people of this Ile vsed not to seuerall their grounds, but now they dig stonie hillocks, and with the stones thereof they make rude walles, much like to those of Deuonshire, sith they want hedge bote, fire bote, and house bote, or (to saie at one word) timber, bushes and trees. As for wine, it is so plentifull and good cheape there most commonlie as in London, through the great recourse of merchants from France, Spaine, and Italie vnto the aforesaid Iland. The flesh likewise of such cattell as is bred there, wherof we haue store yearelie brought vnto Cole faire in Essex is most delicate, by reason of their excellent pasture, and so much was it esteemed by the Romans in time past, that Columella did not onelie commend and preferre them before those of Liguria, but the emperours themselues being neere hand also caused their prouision to be made for nete out of Anglesei, to feed vpon at their owne tables as the most excellent beefe. It taketh now the name of Angles and Ei, which is to meane the Ile of Englismen, bicause they wan it in the Conquerors time, vnder the leading of Hugh earle of Chester, and Hugh of Shrewesburie. Howbeit they recouered it againe in the time of William Rufus, when they spoiled the citie of Glocester, ransacked Shrewesburie, and returned home with great bootie and pillage, in which voiage also they were holpen greatlie by the Irishmen, who after thrée yeares ioined with them againe, and slue the earle of Shrewesburie (which then liued) with great crueltie. The Welshmen call it Tiremone and Mon, and herein likewise is a promontorie Holie head, or Cair kiby. or Byland, called Holie head (which hath in time past beene named Cair kyby, of Kyby a monke that dwelled there) from whence the readiest passage is commonlie had out of Northwales to get ouer into Ireland, of which Ile I will not speake at this time, least I shuld bereaue another of that trauell. Yet Plinie saith, lib. 4. cap. 16. that it lieth not farre off from and ouer against the Silures, which then dwelled vpon the west coast of our Iland, and euen so farre as
- 30. Dunbritton, and beyond: Enilsnach, holie Ile. but to our Cair kybi. The Britons named it Enylsnach, or holie Ile, of the number of carcases of holie men, which they affirme to haue beene buried there. But herein I maruell not a little, wherein women had offended, that they might not come thither, or at the least wise returne from thence without some notable reproch or shame vnto their bodies. By south also of Hilarie point, somewhat inclining toward the east, lieth Inis Lygod, a small thing (God wot) and therefore not worthie great remembrance: neuertheles not to be omitted, though nothing else inforced the memoriall thereof, but onelie the number and certeine tale of such Iles as lie about our Iland. I might also speake of the Ile Mail Ronyad, which lieth north west of Anglesei by sixe miles; but bicause the true name hereof, as of manie riuers and streames are to me vnknowne, I am the more willing to passe them ouer in silence, least I should be noted to be farther corrupter of such words as I haue no skill to deliuer and exhibit in their kind. And now to conclude with the description of the whole Iland, this I will ad moreouer vnto hir commodities, that as there are the best milstones of white, red, blew, and gréene gréets, (especiallie in Tindaithin) so there is great gaines to be gotten by fishing round about this Ile, if the people there could vse the trade: but they want both cunning and diligence to take that matter in hand. And as for temporall regiment, it apperteineth to the countie of Cairnaruon, so in spirituall cases it belongeth to the bishoprike of Bangor. This is finallie to be noted of Anglesei, that sundrie earthen Ancient buriall. pots are often found there of dead mens bones conuerted into ashes, set with the mouthes downeward contrarie to the vse of other nations, which turned the brims vpwards, whereof let this suffice. Hauing thus described Anglesei, it resteth to report furthermore, how that in our circuit about the same, we met with other little Ilets, of which one lieth northwest thereof almost ouer against Butricke mouth, or the fall of the water, that passeth by Butricke. Adar. Moil. Rhomaid. Ysterisd.
- 31. Adros. Lygod. The Britons called it Ynis Ader, that is to say, the Ile of birds in old time, but now it hight Ynis Moil, or Ynis Rhomaid, that is the Ile of porpasses. It hath to name likewise Ysterisd, and Adros. Being past this, we came to the second lieng by north east, ouer against the Hilarie point, called Ynis Ligod, that is to saie, the Ile of Mise, and of these two this latter is the smallest, neither of them both being of Seriall. Prestholme. any greatnesse to speake of. Ynis Seriall or Prestholme, lieth ouer against Penmon, or the point called the head of Mon, where I found a towne (as I told you) of the same denomination. Ptolomie nameth not this Iland, whereof I maruell. It is parcell of Flintshire, and of the iurisdiction of S. Asaph, and in fertilitie of soile, and breed of cattell, nothing inferiour vnto Anglesei hir mother: although that for quantitie of ground it come infinitelie short thereof, and be nothing comparable vnto it. The last Iland vpon the cost of Wales, hauing now Credine. left Anglesei, is called Credine, and although it lie not properlie within the compasse of my description, yet I will not let to touch it by the waie, sith the causey thither from Denbighland, is commonlie ouerflowne. It is partlie made an Iland by the Conwey, and partlie by the sea. But to proceed, when we had viewed this place, we passed foorth to S. Antonies Ile, which is about two or thrée miles compasse or more, a sandie soile, but yet verie batable for sheepe and cattell, it is well replenished also with fresh wels, great plentie of wild foule, conies and quarries of hard ruddie stone, which is oft brought thence to Westchester, where they make the foundations of their buildings withall. There are also two parish churches in the same, dedicated to S. Antonie and S. Iohn, but the people are verie poore, bicause they be so oft spoiled by pirats, although the lord of the same be verie wealthie thorough the exchange made with them of his victuals, for their wares, whereof they make good peniworths, as théeues commonlie doo of such preies as they get by like escheat, notwithstanding their landing there is verie dangerous, and onelie at one place. Howbeit they are constreined to vse it, and there to make their marts. From hence we went Hilberie. on, vntill we came to the cape of Ile Brée, or Hilberie,
- 32. and point of Wyrale, from whence is a common passage into Ireland, of 18. or 20. houres sailing, if the wether be not tedious. This Iland at the full sea is a quarter of a mile from the land, and the streame betwéene foure fadams déepe, as ship-boies haue oft sounded, but at a lowe water a man may go ouer thither on the sand. The Ile of it selfe is verie sandie a mile in compasse, and well stored with conies, thither also went a sort of supersticious fooles in times past, in pilgrimage, to our ladie of Hilberie, by whose offerings a cell of monkes there, which belonged to Chester, was cherished and mainteined. The next Iland vpon the coast of England is Man or Mona Cæsaris, which some name Mana or Manim, but after Ptolomie, Monaoida, as some thinke, though other ascribe that name to Anglesei, which the Welshmen doo commonlie call Môn, as they doo this Manaw. It is supposed to be the first, as Hirtha is the last of the Hebrides. Hector Boetius noteth a difference betwéene them of 300. miles. But Plinie saith that Mona is 200000. miles from Camaldunum, lib. 2. cap. 75. It lieth also vnder 53. degrées of latitude, and 30. minuts, and hath in longitude 16. degrees and 40. minuts, abutting on the north side vpon S. Ninians in Scotland, Furnesfels on the east, Prestholme and Anglesei on the south, and Vlsther in Ireland on the west. It is greater than Anglesei by a third, and there are two riuers in the same, whose heads doo ioine so néere, that they doo seeme in maner to part the Ile in twaine. Some of the Eubonia. Meuania. ancient writers, as Ethicus, c: call it Eubonia, and other following Orosius, Meuana or Mæuania, howbeit after Beda and the Scotish histories, the Meuaniæ are all those Iles aforesaid called the Hebrides, Eubonides, or Hebudes (whereof William Malmesburie, lib. 1. de regibus (beside this our Mona) will haue Anglesei also to be one. Wherefore it séemeth hereby that a number of our late writers ascribing the said name vnto Mona onelie, haue not beene a little deceiued. Iornandes lib. de Getis speaketh of a second Meuania; Habet aliam Meuaniam (saith he) necnon Orchadas. But which should be prima, as yet I do not read, except it should be Anglesei; and then saith Malmesburie well. In like sort Propertius speaketh of
- 33. a Meuania, which he called Nebulosa, but he meaneth it euidentlie of a little towne in Vmbria where he was borne, lib. 4. eleg. De vrbe Rom. Wherfore there néedeth no vse of his authoritie. This in the meane time is euident out of Orosius, lib. 1. capite 2. that Scots dwelled somtime in this Ile, as also in Ireland, which Ethicus also affirmeth of his owne time, and finallie confirmeth that the Scots and Irish were sometime one people. It hath in length 24. miles, and 8. in bredth, and is in maner of like distance from Galloway in Scotland, Ireland and Cumberland in England, as Buchanan reporteth. In this Iland also were some time 1300. families, of which 960. were in the west halfe, and the rest in the other. But now through ioining house to house land to land (a common plague and canker, which will eat vp all, if prouision be not made in time to withstand this mischéefe) that number is halfe diminished, and yet many of the rich inhabiters want roome, and wote not how and where to bestowe themselues, to their quiet contentations. Certes this impediment groweth not by reason that men were greater in bodie, than they haue béene in time past, but onelie for that their insatiable desire of inlarging their priuate possessions increaseth still vpon them, and will doo more, except they be restrained: but to returne to our purpose. It was once spoiled by the Scots in the time of king Athelstane, chéeflie by Anlafus in his flight from the bloudie battell, wherein Constantine king of Scotland was ouercome: secondlie by the Scots 1388. after it came to the possession of the English, for in the beginning the kings of Scotland had this Iland vnder their dominion, almost from their first arriuall in this Iland, and as Beda saith till Edwine king of the Northumbers wan it from them, and vnited it to his kingdome. After the time of Edwine, the Scots gat the possession thereof againe, and held it till the Danes Norwaies wan it from them, who also kept it (but with much trouble) almost 370. yeares vnder the gouernance of their viceroies, whome the kings of Norwaie inuested vnto that honor, till Alexander the third king of that name in Scotland recouered it from them, with all the rest of those Iles that lie vpon the west coast, called also Sodorenses in the daies of Magnus king of Norwaie. And sithens that time the Scotish princes
- 34. haue not ceased to giue lawes to such as dwelled there, but also from time to time appointed such bishops as should exercise ecclesiasticall iurisdiction in the same, till it was won from them by our princes, and Chronica Tinemuthi. so vnited vnto the realme of England. Finallie, how after sundrie sales bargains and contracts of matrimonie (for I read that William Scroope the kings Vicechamberleine, did buy this Ile and crowne thereof of the lord William Montacute earle of Sarum) it came vnto the ancestours of the earles of Darbie, who haue béene commonlie said to be kings of Man, the discourse folowing shall more at large declare. Giraldus noteth a contention betwéene the kings of England Ireland for the right of this Iland, but in the end, when by a comprimise the triall of the matter was referred to the liues or deaths of such venemous wormes as should be brought into the same, and it was found that they died not at all, as the like doo in Ireland, sentence passed with the king of England, so he reteined the Iland. But howsoeuer this matter standeth, and whether anie such thing was done at all or not, sure it is that the people of the said Ile were much giuen to witchcraft and sorcerie (which they learned of the Scots a nation greatlie bent to that horrible practise) in somuch that their women would oftentimes sell wind to the mariners, inclosed vnder certeine knots of thred, with this iniunction, that they which bought the same, should for a great gale vndoo manie, and for the Tall men in Man. lesse a fewer or smaller number. The stature of the men and also fertilitie of this Iland are much commended, and for the latter supposed verie néere to be equall with that of Anglesei, in all commodities. There are also these townes therein, as they come now to my remembrance, Rushen, Dunglasse, Holme towne, S. Brids, Bala cury (the bishops house) S. Mich. S. Andrew, kirk Christ, kirk Louel, S. Mathees, kirk S. Anne, Pala sala, kirk S. Marie, kirk Concane, kirk Malu, and Home. But of all these Rushen with the castell is the strongest. It is also in recompense Riuers. of the common want of wood, indued with sundrie pretie waters, as first of al the Burne rising in the northside of Warehill botoms, and branching out by
- 35. southwest of kirk S. An, it séemeth to cut off a great part of the eastside thereof, from the residue of that Iland. From those hils also (but of the south halfe) commeth the Holme and Holmey, by a towne of the same name, in the verie mouth whereof lieth the Pile afore mentioned. They haue also the Bala passing by Bala cury, on the westside, and the Rame on the north, whose fall is named Ramesei hauen, as I doo read in Chronicles. Hilles. There are moreouer sundrie great hils therein, as that wherevpon S. Mathees standeth, in the northeast part of the Ile, a parcell whereof commeth flat south, betwéene kirk Louell, and kirk Marie, yéelding out of their botoms the water Bala, whereof I spake before. Beside these and well toward the south part of the Ile, I find the Warehils, which are extended almost from the west coast ouertwhart vnto the Burne streame. Hauens. It hath also sundrie hauens, as Ramsei hauen, by north Laxam hauen, by east Port Iris, by southwest Port Home, and Port Michell, by west. In Calfe of man. The pile. S. Michels Ile. like sort there are diuers Ilets annexed to the same, as the Calfe of man on the south, the Pile on the west, and finallie S. Michels Ile Sheepe. in the gulfe called Ranoths waie in the east. Moreouer the sheepe of this countrie are excéeding huge, well woolled, and their tailes of such Hogs. greatnesse as is almost incredible. In like sort their hogs are in maner Barnacles. monstrous. They haue furthermore great store of barnacles bréeding vpon their coasts, but yet not so great store as in Ireland, and those (as there also) of old ships, ores, masts, peeces of rotten timber as they saie, and such putrified pitched stuffe, as by wrecke hath happened to corrupt vpon that shore. Howbeit neither the inhabitants of this Ile, Barnacles neither fish nor flesh. nor yet of Ireland can readilie saie whether they be fish or flesh, for although the religious there vsed to eat them as fish, yet elsewhere, some haue beene troubled, for eating of them in times prohibited for heretikes and lollards.
- 36. For my part, I haue béene verie desirous to vnderstand the vttermost of the bréeding of barnacls, questioned with diuers persons about the same. I haue red also whatsoeuer is written by forren authors touching the generation of that foule, sought out some places where I haue béene assured to sée great numbers of them: but in vaine. Wherefore I vtterlie despaired to obteine my purpose, till this present yeare of Grace 1584. and moneth of Maie, wherein going to the court at Gréenewich from London by bote, I saw sundrie ships lieng in the Thames newlie come home, either from Barbarie or the Canarie Iles (for I doo not well remember now from which of these places) on whose sides I perceiued an infinit sort of shells to hang so thicke as could be one by another. Drawing néere also, I tooke off ten or twelue of the greatest of them, afterward hauing opened them, I saw the proportion of a foule in one of them more perfectlie than in all the rest, sauing that the head was not yet formed, bicause the fresh water had killed them all (as I take it) and thereby hindered their perfection. Certeinelie the feathers of the taile hoeng out of the shell at least two inches, the wings (almost perfect touching forme) were garded with two shels or shéeldes proportioned like the selfe wings, and likewise the brestbone had hir couerture also of like shellie substance, and altogither resembling the figure which Lobell and Pena doo giue foorth in their description of this foule: so that I am now fullie persuaded that it is either the barnacle that is ingendred after one maner in these shels, or some other sea-foule to vs as yet vnknowen. For by the feathers appearing and forme so apparant, it cannot be denied, but that some bird or other must proceed of this substance, which by falling from the sides of the ships in long voiages, may come to some perfection. But now it is time for me to returne againe vnto my former purpose. Bishop of Man. There hath sometime beene, and yet is a bishop of this Ile, who at the first was called Episcopus Sodorensis, when the iurisdiction of all the Hebrides belonged vnto him. Whereas now he that is bishop there, is but a bishops shadow, for albeit that he beare the name of bishop of Man, yet haue the earles of Darbie, as it is
- 37. supposed, the cheefe profit of his sée (sauing that they allow him a little somewhat for a flourish) Patrone of Man. notwithstanding that they be his patrons, and haue his nomination vnto that liuing. The first bishop of this Ile was called Wimundus or Raymundus, and surnamed Monachus Sauinensis, who by reason of his extreame and tyrannicall crueltie toward the Ilanders, had first his sight taken from him, then was sent into exile. After him succéeded another moonke in king Stephens daies called Iohn, and after him one Marcus, c: other after other in succession, the sée it selfe being now also subiect to the archbishop of Yorke for spirituall iurisdiction. King of Man. In time of Henrie the second, this Iland also had a king, whose name was Cuthred, vnto whome Vinianus the cardinall came as legate 1177. and wherin Houeden erreth not. In the yeare also 1228. one Reginald was viceroy or petie king of Man, afterward murthered by his subiects. Then Olauus, after him Hosbach the sonne of Osmond Hacon, 1290. who being slaine, Olauus and Gotredus parted this kingdome of Sodora, in such wise, that this had all the rest of the Iles, the other onelie the Ile of Man at the first; but after the slaughter of Gotredus, Olauus held all, after whom Olauus his sonne succeeded. Then Harald sonne to Olauus, who being entered in Maie, and drowned vpon the coastes of Ireland, his brother Reginald reigned twentie and seuen daies, and then was killed the first of June, whereby Olauus aliàs Harald sonne to Gotred ruled in the Ile one yeare. Next vnto him succéeded Magnus the second sonne of Olauus, and last of all Iuarus, who held it so long as the Norwaies were lords thereof. But being once come into the hands of the Scots, one Godred Mac Mares was made lieutenant, then Alane, thirdlie Maurice Okarefer, and fourthlie one of the kings chapleines, c. I would gladlie haue set downe the whole catalog of all the viceroyes and lieutenants: but sith I can neither come by their names nor successions, I surcesse to speake any more of them, and also of the Ile it selfe, whereof this may suffice. After we haue in this wise described the Ile of Man, with hir commodities, we returned eastwards backe againe unto the point of Ramshed, where we found to the number of six Ilets of one sort and
- 38. other, whereof the first greatest and most southwesterlie, is named Wauay. the Wauay. It runneth out in length, as we gessed, about fiue miles and more from the southeast into the northwest, betwéene which and the maine land lie two little ones, whose names are Oldborrow and Fowlney. The Fouldra. fourth is called the Fouldra, and being situate southeast of the first, it hath a prettie pile or blockhouse therin, which the inhabitants name Fola. Roa. the pile of Fouldra. By east thereof in like sort lie the Fola and the Roa, plots of no great compasse, and yet of all these six, the first and Fouldra are the fairest and most fruitfull. From hence we went by Rauenglasse. Rauenglasse point, where lieth an Iland of the same denomination, as Reginald Wolfe hath noted in his great card, not yet finished, nor likelie to be published. He noteth also two other Ilets, betwéene the same and the maine land; but Leland speaketh nothing of them (to my remembrance) neither any other card, as yet set foorth of England: and thus much of the Ilands that lie vpon our shore in this part of my voiage. Hauing so exactlie as to me is possible, set downe the names and positions of such Iles, as are to be found vpon the coast of the Quéenes Maiesties dominions, now it resteth that we procéed orderlie with those Iles in Scotland. that are séene to lie vpon the coast of Scotland, that is to saie, in the Irish, the Deucalidonian the Germans seas, which I will performe in such order as I may, sith I cannot do so much therin as I would. Some therefore doo comprehend and diuide all the Iles that lie about the north coast of this Ile now called Scotland into thrée parts, sauing that they are either occidentals, the west Iles, aliàs the Orchades Zelandine, or the Shetlands. They place the first betwéene Ireland and the Orchades, so that they are extended from Man and the point of Cantire almost vnto the Orchades in the Deucalidonian sea, and after some are called the Hebrides. In this part the old writers indéed placed Hemodes of some called Acmodes, sée Plinie, Mela, Martianus, Capella, Plutarch. de defect. orac.the Hebrides or Hemodes, which diuers call the Hebudes and the Acmodes; albeit the writers varie in their numbers, some speaking of 30 Hebudes and seuen Hemodes; some of fiue Ebudes,
- 39. as Solinus, and such as follow his authoritie. Howbeit the late Scottish writers doo product a summe of more than 300 of these Ilands in all, which sometime belonged to the Scots, sometime to the Norwegians, and sometime to the Danes. The first of these is our Manaw, of which I haue before intreated: next vnto this is Alisa a desert Ile, yet replenished with conies, soland foule, and a fit harbor for fishermen that in time of the yeare lie vpon the coast thereof for herings. Next vnto this is the Arran, a verie hillie and craggie soile, yet verie plentifull of fish all about the coast, and wherein is a verie good hauen: ouer against the mouth whereof lieth the Moll, which is also no small defence to such seafaring men as seeke harbor in that part. Then came we by the Fladwa or Pladwa, no lesse fruitfull and stored with conies than the Bota, Bura, or Botha, of eight miles long foure miles broad, a low ground but yet verie batable, and wherein is good store of short and indifferent pasture: it hath also a towne there called Rosse, and a castell named the Camps. There is also another called the Marnech, an Iland of a mile in length, and halfe a mile in breadth, low ground also but yet verie fertile. In the mouth likewise of the Glot, lieth the more Cumber and the lesse, not farre in sunder one from another, and both fruitfull inough the one for corne, and the other for Platyceraton. The Auon another Iland lieth about a mile from Cantire, and is verie commodious to ships, wherof it is called Auon, that is to saie, Portuosa, or full of harbor: and therefore the Danes had in time past great vse of it. Then haue we the Raclind, the Kyntar, the Cray, the Gegaw six miles in length and a mile and a halfe in breadth; the Dera full of déere, and not otherwise vnfruitfull: and therefore some thinke Scarba. that it was called the Ile of déere in old time. Scarba foure miles in length, and one in breadth, verie little inhabited, and thereinto the sea betwéene that and the Ile of déere is so swift and violent, that except it be at certeine times, it is not easilie nauigable. Being past these, we come to certeine Ilands of no great fame, which lie scattered here and there, as Bellach, Gyrastell, Longaie, both the Fiolas, the thrée Yarues, Culbrenin, Duncomell, Lupar, Belnaua, Wikerua, Calfile, Luing, Sele Ile, Sound, of which the last thrée are fruitfull, and Slate Ile. belong to the earle of Argile. Then
- 40. haue we the Slate, so called of the tiles that are made therin. The Nagsey, Isdalf, and the Sken (which later is also called Thian, of a wicked herbe growing there greatlie hurtfull, and in colour not much vnlike the lillie, sauing that it is of a more wan and féeble colour) Vderga, kings Ile, Duffa or blacke Ile, Kirke Ile and Triarach. There is also the Ile Ard, Humble Ile, Greene Ile, and Heth Ile, Arbor Ile, Gote Ile, Conies Ile aliàs idle Ile, Abrid Ile or bird Ile, and Lismor, wherein the bishop of Argill sometime held his palace, being eight miles in length and two miles in breadth, and not without some mines also of good mettall. There is also the Ile Ouilia, Siuna, Trect, Shepey, Fladaw, Stone Ile, Gresse, great Ile, Ardis, Musadell, Berner, sometime called the holie sanctuarie, Vghe Ile, Molochasgyr, and Drinacha, now ouergrowne with bushes, elders, and vtterlie spoiled by the ruines of such great houses as haue heretofore béene found therin. There is in like sort the Wijc, the Ranse, and the Caruer. Ila. In this tract also, there are yet thrée to intreat of, as Ila, Mula and Iona, of which the first is one of the most, that hath not béene least accounted of. It is not much aboue 24 miles in length, and in breadth 16 reaching from the south into the north, and yet it is an excéeding rich plot of ground verie plentious of corne, cattell, déere, and also lead, and other mettals, which were easie to be obteined, if either the people were industrious, or the soile yéeldable of wood to fine and trie out the same. In this Iland also there is a lake of swéet water called the Laie, and also a baie wherein are sundrie Ilands; and therevnto another lake of fresh water, wherein the Falangam Ile is situate, wherein the souereigne of all the Iles sometime dwelled. Néere vnto this is the Round Ile. round Ile, so called of the consultations there had: for there was a court sometime holden, wherein 14 of the principall inhabitants did minister iustice vnto the rest, and had the whole disposition of things committed vnto them, which might rule vnto the benefit of those Ilands. There is also the Stoneheape, an other Iland so called of the heape of stones that is therein. On the south side also of Ila, we find moreouer the Colurne, Mulmor, Osrin, Brigidan, Corkerke, Humble Ile, Imersga, Bethy, Texa,
- 41. Shepeie, Naosig, Rinard, Cane, Tharscher, Aknor, Gret Ile, Man Ile, S. Iohns Ile, and Stackbed. On the west side thereof also lieth Ouersey, whereby runneth a perilous sea, and not nauigable, but at certeine houres, Merchant Ile, Vsabrast, Tanask, Neff, Wauer Ile, Oruans, Hog Ile, and Colauanso. Mula. Mula is a right noble Ile, 24 miles in length and so manie in bredth, rough of soile, yet fruitfull enough: beside woods, déere, good harbrough for ships, replenished with diuers and sundrie townes and castels. Ouer against Columkill also, it hath two riuers, which yeld verie great store of salmons, and other riuellets now altogither vnfruitfull, beside two lakes, in each of which is an Iland: and likewise in euerie of these Ilands a castell. The sea beating vpon this Ile, maketh foure notable baies wherein great plentie and verie good herrings are taken. It hath also in the northwest side Columbria, or the Ile of doues; on the southeast, Era: both verie commodious for fishing, cattell, and corne. Moreouer, this is woorth the noting in this Ile aboue all the rest, that it hath a plesant spring, arising two miles in distance from the shore, wherein are certeine little egs found, much like vnto indifferent pearles, both for colour and brightnesse, and thereto full of thicke humour, which egs being carried by violence of the fresh water vnto the salt, are there within the space of twelue houres conuerted into great shels, which I take to be mother pearle; except I be deceiued. Iona. Iona was sometime called Columkill, in fame and estimation nothing inferiour to anie of the other, although in length it excéed little aboue two miles, and in breadth one. Certes it is verie fruitfull of all such commodities, as that climat wherein it standeth dooth yeeld, and beareth the name of Columbus the abbat, of whome I haue spoken more at large in my Chronologie. There were somtimes also two monasteries therein, one of moonks builded by Fergus, another of nuns: and a parish church, beside many chappels builded by the Scotish kings, and such princes as gouerned in the Iles. And when the English had once gotten possession of the Ile of Manaw, a bishops see was erected in the old monasterie of Columbus,
- 42. whereby the iurisdiction of those Iles was still mainteined and continued. Certes there remaine yet in this Iland the old burials apperteining to the most noble families that had dwelled in the west Iles; but thrée aboue other are accompted the most notable, which haue little houses builded vpon them. That in the middest hath a stone, Regum tumuli. whereon is written, Tumuli regum Scotiæ, The burials of the kings of Scotland: for (as they saie) fourtie eight of them were there interred. Another is intituled with these words, The burials of the kings of Ireland, bicause foure of them lie in that place. The third hath these words written thereon, The graues of the kings of Norwaie, for there eight of them were buried also, and all through a fond suspicion conceiued of the merits of Columbus. Howbeit in processe of time, when Malcolme Cammor had erected his abbeie at Donfermeling, he gaue occasion to manie of his successors to be interred there. About this Iland there lie six other Iles dispersed, small in quantitie, but not altogither barren, sometimes giuen by the kings of Scotland and lords of the Iles vnto the abbeie of saint Columbus, of which the Soa, albeit that it yeeld competent pasturage for shéepe, yet is it more commodious, by such egs as the great plentie of wildfoule there bréeding doo The Ile of Shrewes. laie within the same. Then is there the Ile of Shrewes or of women; as the more sober heads doo call it. Also Rudan, next vnto that, the Rering. There is also the Shen halfe a mile from Mula, whose bankes doo swarme with conies: it hath also a parish church, but most of the inhabitants doo liue and dwell in Mula. There is also the Eorse or the Arse, and all these belong vnto saint Columbus abbeie. Two miles from Arse is the Olue, an Iland fiue miles in length, and sufficientlie stored with corne and grasse, not without a good hauen for ships to lie and harbor in. There is also the Colfans, an iland fruitfull inough, and full of cornell trées. There is not far off Mosse Ile. also the Gomater, Stafa, the two Kerneburgs, and the Mosse Ile, in the old Brittish speech called Monad, that is to saie Mosse. The soile of it is verie blacke, bicause of the corruption putrefaction of such woods as haue rotted thereon: wherevpon also no small plentie of mosse is bred and
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