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REVIEW QUESTIONS
5.1 Why do the results obtained through numerical methods differ from the exact
solutions solved analytically? What are some of the causes for this difference?
Analytical solutions are exact solutions based on mathematical principles. However, the
governing partial differential equations of fluid flow are complex and cannot be solved by
analytical means. The partial differential equations are therefore converted into a system of
algebraic equations that are subsequently solved through numerical methods to provide
approximate solutions to the governing equations. Some causes for the differences may arise
from the discretization methods, round-off errors and mesh resolution.
5.2 In the analysis of CFD results, what does consistency imply?
A formulation is consistency if the system of algebraic equations through the discretization
process provides the same (be consistent) solution with the original partial differential
equations as the finite quantities, such as the time step Δt and mesh spacing Δx, Δy and Δz,
tend to zero. The implication of consistency here is the recovery of the governing equations
by reversing the discretisation process through a Taylor series expansion.
5.3 What are the key aspects of consistency?
The discretized equations are an approximation of the real solution due to a truncation of the
Taylor series expansion. Essentially, the truncation error represents the difference between
the discretized equation and the exact one. As a result, the original partial differential
equation is recovered by the addition of a remainder, the truncation error. This error basically
measures the accuracy of the approximation and determines the rate at which the error
decreases as the time step and/or mesh spacing are reduced. Therefore the key aspects of
consistency require the truncation error to become zero when the time step Δt → 0 and/or
mesh spacing Δx, Δy and Δz → 0.
5.4 If a system of algebraic equations is equivalent to the partial differential equation
as the grid spacing tends to zero, does this also mean the solution of the system of
algebraic equations will approach the exact solution of the partial differential
equation? Why?
In situations when the finite quantities, such as the time step Δt and mesh spacing Δx, Δy and
Δz, tend to zero linearly with each other then the solution will be consistent. For example, the
discretization of the partial differential equation 0
=
∂
∂
+
∂
∂
y
x
u v
is found to be:
( ) 0
Δ
Δ
2Δ
2Δ
2
2
=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
−
+
−
P
error
Truncation
S
N
W
E
y
,
x
O
y
x
u
u

v
v
Here the original partial differential equation is recovered (satisfying consistency) from the
discretized equation that includes the truncation error, as the mesh spacing Δx and Δy → 0.
However if the finite quantities in the discretized equation are found linked to each other as
follows:
( )
2
2 2
2 2
2 2
, 0
i Truncation error i
Δt
O Δt Δx
t x Δx t
φ φ φ
α α
⎡ ⎤
⎡ ⎤
∂ ∂ ∂
⎛ ⎞ ⎢ ⎥
− + + =
⎢ ⎥
⎜ ⎟ ⎢ ⎥
∂ ∂ ∂
⎝ ⎠
⎢ ⎥
⎣ ⎦ ⎢ ⎥
⎣ ⎦

this may cause problems. Even though the discretized equations might be equivalent to the
partial differential equation as the finite quantities shrink to zero, it may not necessarily mean

that the solution of the discretized equations follows the exact solution of the partial
differential equation.
5.5 Explain why the following Taylor series expansion of the one-dimensional
transient diffusion equation:
2
2 2
0
2 2
Δt
t Δx
x t
i
φ φ φ
α α
∂ ∂ ∂
− + =
∂ ∂ ∂
⎡ ⎤
⎛ ⎞
⎢ ⎥
⎜ ⎟
⎝ ⎠
⎢ ⎥
⎣ ⎦
may not show
consistent properties.
The finite quantities Δt and Δx are found together in the form of
x
t
Δ
Δ
which must → 0 at the
same rate as Δt, Δx → 0 to achieve consistency. It is also required that Δt « Δx for consistency
or else the scheme becomes inaccurate (i.e. if (Δt / Δx)2
is large). For example if the time step
size Δt is fixed and we reduce the grid space size of Δx by half, then the solution will not be
consistent since (Δt / Δx)2
does not approach zero but instead it gets larger. If however we
decrease the time step size Δt then the term will (Δt / Δx)2
approach zero. It is clearly seen
that the solution for large (Δt / Δx) is inconsistent with the exact solution when compared
with a smaller (Δt / Δx).
5.6 Describe the concept of stability.
The concept of stability involves the growth or decay of errors that are introduced during any
stage of the computation. It is noted that the errors being referred here are not those produced
by incorrect logic but those that occur because of rounding-off at every step of computation
due to the finite number of significant figures the computer hardware can accommodate as
well as poor initial guess. A numerical solution method is therefore considered to be stable if
it does not magnify the errors that appear in the course of the numerical solution process.
5.7 What is the stability criteria produced by the von Neuman analysis?
The von Neumann analysis is based on predicting whether there will be a growth of error
between the true solution of the numerical method and the actual computed solution, which
also includes the round-off contamination for linear problems. In general, it is the easiest,
most dependable and straightforward method to apply. However it can only be used to
establish necessary and sufficient conditions for the stability of linear initial value problems
with constant coefficient.
The exact form of the stability criterion depends on the particular differencing approximation
applied to the equation. However the process is to analyze the stability of a discretization
where the errors introduced at every grid point is given as
n
i
n
i
n
i *φ
φ
ξ −
=
n
i
φ is the true solution of the numerical method and n
i
* φ is the actually computed solution.
For a linear computational algorithm, the error n
i
ξ in the majority of textbooks (Fletcher,
1991, Anderson, 1995) deals with just one term of the finite complex Fourier series, which is
given as
x
ik
at
n
i
m
e
e
=
ξ
where a is a constant, km is the wave number, t is the time step and x is the grid size.
5.8 What is the Courant number and what is its function?
The Courant number is a parameter that relates the velocity with the time step size and the
grid spacing size of a discretized formulation which is given as:
Formatted: Font: Italic
Formatted: Font: Italic

x
t
u
C
Δ
Δ
=
The Courant number is used in the Courant-Friedrichs-Lewy (CFL) condition where it
determines the stability criterion for convection-type equations (i.e. applied to advection
schemes). The von Neumann stability analysis produces the CFL condition of:
1
≤
Δ
Δ
=
x
t
u
C
This suggests that Δt ≤ Δx / u for the numerical solution to be stable.
5.9 Consider the following discretized equation, locate the Courant number and
discuss the Courant-Friedrichs-Lewy condition for stability in this case:
( )
1 2
1 1
2
Δt
n n n n n
i i i
i i
Δx
φ φ α φ φ φ
+ = + − +
+ − .
The CFL condition in this case is:
1
2
≤
Δ
Δ
=
x
t
C α .
This means that as long as ( )2
x
t Δ
≤
Δ is met then the CFL condition will apply.
5.10 Provide a definition on the concept of convergence?
If a numerical method can satisfy the two important properties of consistency and stability,
we generally find that the numerical procedure is convergent. Convergence of a numerical
process can therefore be defined as the solution of the system of algebraic equations
approaching the true solution of the partial differential equations having the same initial and
boundary conditions as the refined grid system (grid convergence).
5.11 State Lax’s equivalence theorem for convergence. Does it apply to non-linear
problems?
For initial value problems governed by the finite difference approximations of linear partial
differential equations, Lax’s equivalence theorem states that: “Given an initial valued
problem and a finite difference approximation consistency and stability are necessary and
sufficient conditions that need to be satisfied for convergence”, i.e. consistency + stability =
convergence. However it is must be noted that most computational work for non-linear
partial differential equations, as used in CFD, proceeds as though this theorem applies,
although it has not been proven directly for this general category of equations.
5.12 What are the three important rules when considering iterative convergence?
i. All the discretized equations (momentum, energy, etc.) are deemed to be converged
when they reach a user-specified tolerance level at every nodal location.
ii. The numerical solution no longer changes with additional iterations.
iii. Overall mass, momentum, energy and scalar balances throughout the system are
obtained. During the numerical procedure, the imbalances (errors) of the discretized
equations are monitored and these defects are commonly referred to as the residuals of
the system of algebraic equations, i.e. they measure the extent of imbalances arising
from these equations and terminate the numerical process when a user-specified
tolerance level is reached. For satisfactory convergence, the residuals should diminish
Deleted: Courant number is a
function of
( )
α
,
, x
t
f
C Δ
Δ
= .

as the numerical process progresses. In the likelihood that the imbalances grow, as
reflected by increasing residual values, the numerical solution is thus classified as being
unstable (divergent).
5.13 How is the concept of residual applied to describe the discretized equation of the
system of transport equations?
The residuals is a measure of the overall conservation of the flow properties. For any
transport variable φ, the discretised form of the partial differential equation can be
specifically written as:
P
nb
nb
p
P b
a
a +
= ∑ φ
φ
where the central coefficient aP should equal to the neighboring coefficients anb which
normally depend on the solution of other flow field variables including the time- and spatial-
varying fluid flow properties. At the start of the iteration process, the equality in the above
equation will not hold and there is a difference. The imbalance variable is called the residual
Rp and the above equation can be re-expressed as:
p
P
P
nb
nb
P a
b
a
R φ
φ −
+
= ∑
5.14 Differentiate between a local residual and a global residual.
The residual expression at a single nodal point P for one cell volume, which produces a local
residual is given as:
p
P
P
nb
nb
P a
b
a
R φ
φ −
+
= ∑
The global residual R, taken as the sum of each local residual Rp over all the grid nodal
points, is monitored:
∑
=
s
int
po
grid
P
R
R
5.15 What is implied when the residuals become negligible with increasing iterations?
When the residuals reduce with increasing iterations, the simulation is converging.
Convergence is deemed to be achieved when the global residual R satisfies a specified
tolerance, i.e. ε
≤
R or ε
≤
∑ s
int
po
grid
P
R .
5.16 What is the usual recommended residual tolerance level?
Small tolerance values will incur a large number of iteration steps in reaching convergence.
On the other hand, large tolerance values constitute an early termination of the iteration
process for which the numerical solution of the algebraic equations is considered to be rather
coarse or not sufficiently converged. Generally, a decrease of the residual by three orders of
magnitude during the iteration process indicates at least qualitative convergence. Here, the
major flow features are considered to be sufficiently established. Nevertheless, stricter
convergence consideration is required for transport variables like energy and scalar species. It
is recommended that the scaled energy residual decreases to a recommended convergence
tolerance of 10-6
while the scaled scalar species may need to only decrease to a convergence
tolerance of 10-5
to achieve energy and species balance respectively.
5.17 Define under-relaxation factor. State its advantages and disadvantages when
using a small value.

The under-relaxation is often introduced to stabilize the numerical calculations of the
governing equations that are generally non-linear and where the equation of one transport
variable is dependent on the others, for example, temperature affecting the velocities in
buoyancy flows. The under-relaxation factor α controls the advancement of the transport
variable φP during the iteration process.
i.e.
( )
old
P
new
P
old
P
new
P φ
φ
α
φ
φ −
+
= *
A smaller under-relaxation factor will assist in stability and convergence of the iterative
process; however it takes a longer time due to the smaller changes at each iteration step.
5.18 Is a converged solution also an accurate solution? Why?
A converged solution is not necessarily an accurate solution since accuracy is dependent on
the computational setup that can be affected by errors and uncertainties in the numerical
calculations. These errors and uncertainties can be generated in either the conceptual
modeling or during the computational design phase such as the truncation error occurring
during the discretization step.
5.19 Discuss some types of errors that can cause a solution to be inaccurate.
Some of the more common errors that can occur are:
o Discretisation error
These errors are due to the truncation errors introduced during the discretisation procedure.
o Round-off error
These errors exist due to the difference between the digital storage accuracy of a computer
and the true value of a variable. A single precision solution uses 7 significant figures while
a double precision solution uses 15 significant figures.
o Iteration or convergence error
These errors occur due to the difference between a fully converged solution of a finite
number of grid points and a solution that has not fully achieved convergence.
o Physical modeling error
These errors are those due to uncertainty in the formulation of the mathematical models
and deliberate simplifications of the models.
5.20 What are discretization errors? What is the difference between a global error
and a local error?
Discretization errors are due to the difference between the exact solution of the modeled
equations and a numerical solution with a limited time and space resolution. They arise
because an exact solution to the equation being solved is not obtained but numerically
approximated. There are two types of discretisation errors: local and global. The local error is
the formulation associated with a single step. For this error, the accuracy of the numerical
solution concerns mainly on the approximation of the spatial derivative. The solution
accuracy for a transient problem however, focuses on the advancement of the transport
variable φ through time usually characterized by the global error.
5.21 Which methods can be used to minimize discretization errors?
Discretization errors occur through the transformation of the partial differential equations into
algebraic equations where the full Taylor series expansion is truncated. One method to
minimize discretization errors is use a higher order discretization scheme such as central
differencing (second order) instead of the first order schemes of forward and backward
Formatted: Lowered by 5 pt
Deleted: u
Deleted: difference between the
exact solution of the modeled
equations and a numerical
solution with a limited time and
space resolution.
Deleted: machine

difference schemes. Another method is to reduce the grid or the time step size in order to
reduce the truncation error.
5.22 What are round-off errors and what kind of calculations are most affected by
them?
Round-off errors occur since there is a limit to a computer’s internal capacity to store digits.
This error is naturally random and in general it is difficult to predict. It depends on the
number of calculations, rounding off method, rounding-off type, and even sequence of
calculations. Typically however, round-off errors will occur when dealing with decimal
values that are limited by the precision. If computer round-off errors are suspected of being
significant, one test that can be performed is to employ double precision or on a computer
known to store floating point numbers at a higher precision.
5.23 Which method can be used to minimize round-off errors?
Round-off errors are due to the single precision setting during the numerical calculations.
Usually further refinement of the mesh may lead to an increase of the round-off error. One
possible way of significantly to reduce this round-off error is to extend the number of
significant figures during the iterative procedure to double precision. However the double
precision setting is more computationally demanding and hence a longer time is taken per
calculation. In practice, some trade-off of the solution accuracy is used to achieve a quicker
turnaround of the numerical solution.
5.24 What does it mean to perform a grid convergence (independency) test?
To determine that the discretization error is at an acceptable level a grid convergence test
may be performed. This involves decreasing the mesh sizes which leads to an increase in the
resolution of the total mesh. The computational results from the initial mesh are compared
with the results for the new refined mesh. If the results obtained do not differ significantly,
we can conclude that the discretization error is at an acceptable level. But if the values for the
transport variables are quite different for this second calculation, then the solution is a
function of the number of grid points. In all practical cases, the grid needs to be refined
further and the results compared again until a solution is achieved where no significant
changes in the results occur. This indicates that the discretization error is reduced to an
acceptable error and grid independence is reached.
5.25 What is the difference between verification and validation? Why are these two
steps important in analyzing results?
The verification primarily involves the input parameters used for geometry, initial conditions
and boundary conditions. This verification step assesses the numerical simulation uncertainty
and when conditions permit, estimating the sign and magnitude of the numerical simulation
error and the uncertainty in that estimated error.
The validation procedure involves validating the calculations by establishing a range of
physical conditions obtained from the calculations, and performing comparisons of the results
from the CFD code with experiments that span the range of conditions. These two procedures
represent the final phase of the CFD simulation to ensure quality of the results, the credibility
the numerical models applied and that the computational model shows an accurate
representation of the real physical flow problem.
5.26 Discuss briefly how multigrid methods are employed to increase the
computational efficiency of solving CFD problems.

For complex problems that require a large amount of grid points, the time taken to solve the
problem is usually a very long time. Multigrid methods can improve the solution time by
using a heirachy of where in the simplest case, the coarse ones are just subsets of the fine
ones. The main idea behind multigrid methods is the transferring of variables from one grid
to another. Usually the variables from a fine grid are transferred to a coarse grid which are
solved in quicker time and then the results are slowly refined going from a coarse grid back
to the original fine grid. More details on multigrid methods are discussed in Section 8.2.4.
5.27 Discuss briefly how parallel computing is used to achieve computational
efficiency.
Parallel computing makes use of multiple computer processors to increase the computational
time when compared with single processors. The idea behind parallel computing involves the
subdivision of the solution domain into subdomains where each subdomain is assigned to one
processor. Since each processor needs data that resides in other subdomains, exchange of data
between processors and storage overlap is necessary and specialized algorithms are required.
5.28 Consider the following algebraic equation: apΦp = ∑anbΦnb + b as described in
Chapter 4. In matrix form, ap represents the diagonal element while anb is the
neighboring element. The condition for convergence stipulates that P
nb a
a
∑ ≤
1, which simply means that the sum of the neighboring elements divided by the
diagonal elements must be less than unity, at all grid nodal points. Analyze the
condition for convergence given the system of equations below.
Case 1: Φ1 = 0.5Φ2 + 1.5 (1)
Φ2 = Φ1 + 2 (2)
by re-arranging the above equations, we have
Case 2: Φ1 = Φ2 – 2 (2)
Φ2 = 2Φ1 – 3 (1)
The convergence criteria is:
1
≤
∑
p
nb
a
a
Case 1:
5
.
1
5
.
0 2
1 +
= φ
φ
2
1
2 +
= φ
φ
∑ +
= b
a
a nb
nb
p
p φ
φ
Therefore 1
=
p
a and 5
.
0
=
nb
a for equation (1) which satisfies the stability criterion.
1
5
1
≤
Similarly 1
=
p
a and 1
=
nb
a for equation (2) which also satisfies the stability criterion.
1
1
1
≤
Deleted: ¶

This setup will produce a converged solution. Using the Gauss-Seidel method and setting the
variables arbitrarily to 1 we have the following iterations.
1
φ 2
φ 5
.
1
5
.
0 2
1 +
= φ
φ 2
1
2 +
= φ
φ
1 1 1 2 4
2 2 4 3.5 5.5
3 3.5 5.5 4.25 6.25
4 4.25 6.25 4.625 6.625
5 4.625 6.625 4.8125 6.8125
6 4.8125 6.8125 4.90625 6.90625
7 4.90625 6.90625 4.953125 6.953125
8 4.953125 6.953125 4.976563 6.976563
9 4.976563 6.976563 4.988281 6.988281
10 4.988281 6.988281 4.994141 6.994141
11 4.994141 6.994141 4.99707 6.99707
12 4.99707 6.99707 4.998535 6.998535
13 4.998535 6.998535 4.999268 6.999268
14 4.999268 6.999268 4.999634 6.999634
15 4.999634 6.999634 4.999817 6.999817
Case 2:
1
2
1 −
= φ
φ
3
2 1
2 −
= φ
φ
∑ +
= b
a
a nb
nb
p
p φ
φ
Therefore 1
=
p
a and 1
=
nb
a for equation (1) which satisfies the stability criterion.
1
1
1
≤
However 1
=
p
a and 2
=
nb
a for equation (2) which does not satisfy the stability criterion
because
2
1
2
=
This setup will produce a diverging solution. Using the Gauss-Seidel method and setting the
variables arbitrarily to 1 we have the following iterations.

1
φ 2
φ 1
2
1 −
= φ
φ 3
2 1
2 −
= φ
φ
1 1 1 0 -3
2 0 -3 -4 -11
3 -4 -11 -12 -27
4 -12 -27 -28 -59
5 -28 -59 -60 -123
6 -60 -123 -124 -251
7 -124 -251 -252 -507
8 -252 -507 -508 -1019
9 -508 -1019 -1020 -2043
10 -1020 -2043 -2044 -4091
11 -2044 -4091 -4092 -8187
12 -4092 -8187 -8188 -16379
13 -8188 -16379 -16380 -32763
14 -16380 -32763 -32764 -65531
15 -32764 -65531 -65532 -131067

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Language

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Title: A Dictionary of the First or Oldest Words in the English
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Author: Herbert Coleridge
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*** START OF THE PROJECT GUTENBERG EBOOK A DICTIONARY
OF THE FIRST OR OLDEST WORDS IN THE ENGLISH LANGUAGE
***

A DICTIONARY OF THE FIRST,
OR
OLDEST WORDS IN THE
ENGLISH LANGUAGE
A DICTIONARY
OF THE FIRST, OR
OLDEST WORDS IN THE ENGLISH
LANGUAGE:
FROM THE
SEMI-SAXON PERIOD OF a.d. 1250 to 1300.
CONSISTING OF
An Alphabetical Inventory of
EVERY WORD FOUND IN THE PRINTED ENGLISH
LITERATURE OF THE 13TH CENTURY.

BY THE LATE
HERBERT COLERIDGE,
SECRETARY TO THE PHILOLOGICAL SOCIETY.
LONDON:
JOHN CAMDEN HOTTEN, PICCADILLY.
M DCCC LXII.

PREFACE.
The present publication may be considered as the foundation-stone
of the Historical and Literary portion of the Philological Society’s
proposed English Dictionary. Its appearance in a separate form has
been necessitated by the nature of the scheme, on which that work
is being constructed. Without entering into details, which will be
found in the Society’s published Prospectus,[1] it will be sufficient for
the present purpose to mention, that the raw material of the
Dictionary, the words and authorities, are being brought together by
a number of independent collectors, for whom it is consequently
necessary to provide some common standard of comparison,
whereby each may ascertain what he is to extract, and what to
reject, from the author, or work, he has undertaken. This standard
for works of earlier date than 1526 is furnished by the following
pages, which contain an alphabetical inventory of every word found
in the printed English literature of the 13th century. As, however, a
mere index verborum would but inadequately fulfil its object, a
certain amount of explanatory and etymological matter has been
added, which it is hoped may render the work more generally
interesting and useful than could otherwise have been the case. It is
only proper to add that English literature, as distinguished from
Semi-Saxon, is assumed to commence about the middle of the 13th
century.
[1] London, Trübner and Co., Paternoster Row, price 6d.
All words are arranged under their modern forms, where such exist,
but the older forms, except where utterly unimportant, are always
noticed. The more remarkable of these older forms are also entered
in the Glossary in their alphabetical order, with cross references to
that under which the word is discussed. Thus under ‘Hymn’ and ‘Isle’
will be found the forms ‘ympne’ and ‘ydle;’ but ‘ympne’ and ‘ydle’

appear also in their proper places in the Glossary. Obsolete words
are of course entered as they are spelt in the passage whence they
are taken, a rule which applies as much to different forms of the
same word, as to different words. As to the etymological matter,
nothing further as a general rule has been attempted than to
indicate the nearest cognate, or cognates, of the particular word;
but it has not been thought necessary, or desirable, to load the
Glossary with illustrations of this nature in very simple cases. I have
to thank Hensleigh Wedgwood, Esq., for many kind and valuable
suggestions in this part of my work.
My best thanks are also due to the Rev. J. Eastwood, the Rev. W. H.
Herford, to my colleague Mr F. J. Furnivall, and to Messrs M’Ewan
and Harrison, for their valuable assistance in the formation of
separate indexes to several of the works comprised in this Glossary.
Their respective shares in the work are pointed out in the List of
Books and Editions, which will be found in page v.
And I cannot terminate this brief preface without expressing my
deep sense of the obligations I am under to Sir F. Madden, not
merely for the help of his invaluable editions of Laȝamon and
Havelok, without which this work would have been far less complete
than it now is, but also for much kind personal advice and
assistance, which probably few, if any, living philologists beside
himself would have been competent to bestow. It only remains for
me to add that, although no pains have been spared to render the
book as complete as possible, I cannot but expect that some
omissions and errors will be discovered, more especially as the
largest and most laborious portion of the work was carried on during
a long period of ill health. I shall feel very grateful to those who
discover any addenda, if they will kindly communicate them to me
for insertion hereafter in the Dictionary itself.
HERBERT COLERIDGE.
10, Chester Place, Regent’s Park,
June 13th, 1859

LIST OF BOOKS AND EDITIONS
REFERRED TO.
⁂ All the following pieces are cited by
the number of the verse, except where
the contrary is expressly mentioned.
Havelok the Dane. Edited by Sir F. Madden, for the Roxburgh Club.
(By Mr H. Coleridge.)
Geste of Kyng Horn. Edited by M. Michel, for the Bannatyne Club.
(N.B. The text of this poem in the second vol. of Ritson’s Metrical
Romances is taken from a later MS., and differs considerably from
the Bannatyne text.)
Kyng Alysaunder. In Weber’s Metrical Romances, vol. I. (By Mr H.
Coleridge.)
The Land of Cokaygne. In Hickes’s Thesaurus, vol. I. p. 231. (By Mr
Furnivall.)
The Life of St Margaret
(cited by stanzas),
}
in Hickes’s Thesaurus, vol. I. pp. 224,
233. (By Mr Furnivall.)
Metrical Version of the
Athanasian Creed,
The Owl and Nightingale. Edited by Mr Wright for the Percy Society.
(By Mr Furnivall and Mr H. Coleridge.)
Fragment on Popular Science, from the Early English Metrical Lives
of Saints, in Mr Wright’s ‘Popular Treatises on Science.’ (By Mr H.
Coleridge.)

Specimens of Lyric Poetry, temp. Edw. I. Edited by Mr Wright, for the
Percy Society. (By Mr M’Ewan.)
Various Pieces in the Reliquiæ Antiquæ (cited by volume and page).
Political Songs, temp. Hen. III. and Edw. I. Edited by Mr Wright, for
the Camden Society. (By the Rev. W. H. Herford.)
Ritson’s Ancient Songs, Class I. Most of these songs, however, are
contained in the Specimens of Lyric Poetry, temp. Ed. I., and are
quoted from that collection. (By Mr Harrison.)
Religious Songs, printed at the end of the Percy Society’s edition of
the Owl and Nightingale. (By Mr H. Coleridge.)
Dialogue between the Soul and Body. In the Appendix to Mapes’s
Poems, edited by Mr Wright, for the Camden Society, p. 334. (By the
Rev. J. Eastwood.)
The Early English Psalter. Edited by the Rev. J. Stevenson, for the
Surtees’ Society. Cited by the psalm and verse. (By Mr H. Coleridge.)
Robert of Gloucester’s Chronicle. Ed. Hearne (2nd ed., 1810). Cited
by the page. (By Mr. H. Coleridge.)
The Legend of St Brandan. Edited by Mr Wright, for the Percy
Society. (By the Rev. J. Eastwood.)
The Life and Martyrdom of Thomas Beket. Edited by Mr Black, for
the Percy Society. (By the Rev. J. Eastwood.)
(Owing to the gross inaccuracy of the marginal numbering in the
printed edition of this poem, it has been found necessary to go over
the whole afresh, and to cite according to the amended reckoning.
The following data will assist the reader:—The first error occurs in
page 64, where the line numbered 1280 should be 1282. The second
occurs in page 100, where ten lines are dropped, and 1961 is printed
for 1973, the true number. The third will be found in page 110,

where 2049 is made to succeed 2139, and after this, of course, the
confusion is hopeless. The exact number of lines in the poem is
2515, while the printed numbers give only 2398. Readers are
therefore requested to renumber their copies from page 64 onwards,
before attempting to verify the references in the Glossary.)
The following pieces will be printed in the second part of the
Philological Society’s Transactions for 1858, and are therefore
included in the Glossary. I am indebted to the kindness of my friend
and colleague, Mr Furnivall, for the loan of his transcripts.
A Moral Ode. MS. Egerton, 613. Cited by stanzas.
(Hickes printed Extracts from this Ode, in his Thesaurus, vol. I. p.
222, from one of the Digby MSS.; but his text is somewhat different
from that of the Egerton MS., and omits nine stanzas contained in
the latter.)
A Sermon (cited by stanzas),
}
MS. Harl.
913.
Signa Ante Judicium,
A Fragment on the Seven Sins,
The Ten Commandments,
Christ on the Cross,
A Poem on Miracles, containing a Tale of an Oxford
Student,
The Fall and Passion,
The Legends of
St Dunstan,
}from MS. Harl. 2277.
St Katherine,
St Andrew,
St Lucy,
St Swithin,
St Edward,
Pilate,
Judas Iscariot,

A few references will also be found to the Manuel des Pecches of
Robert Brunne, now being edited by Mr Furnivall, for the Roxburgh
Club, but the proof-sheets came into my hands too late to allow of
anything like a complete analysis of the language of the poem.
OTHER WORKS REFERRED TO IN THE GLOSSARY.
Burguy’s Grammaire de la Langue d’Oïl. 3 vols. 8vo. Berlin, 1856.
The third volume contains an excellent Glossary.
Cotgrave’s French and English Dictionary, by Howell. 1650.
Egilsson’s Lexicon Poeticum Antiquæ Linguæ Septemtrionalis.
Hafniæ, 1854-1859. One part is still wanting to complete the work.
Halliwell’s Provincial and Archaic Dictionary. 2 vols. 8vo. 1855.
Kilian’s Lexicon Teutonicum. Ed. Hasselt. 2 vols. 4to. 1777.
Laȝamon’s Brut. Ed. Sir F. Madden. 3 vols. 8vo. 1847. (Cited by
volume and page.)
The Ormulum. Ed. White. 2 vols. 8vo. 1852.
The Philological Society’s Transactions, from 1842-1856. 9 vols. 8vo.
Roquefort’s Glossaire de la Langue Romane. 2 vols. 8vo. 1808.
A Volume of Vocabularies, forming vol. I. of a Library of National
Antiquities. Edited by Wright. 1857. (Privately printed.)
Warton’s History of English Poetry. 3 vols. 8vo. Ed. 1840.

LIST OF ABBREVIATIONS MADE USE
OF IN THE GLOSSARY.
Alys. Kyng Alysaunder.
AS. Anglo-Saxon.
B. The Life of Beket.
β The Legend of St Brandan.
comp. comparative.
Cok. The Land of Cokaygne.
Cotgr. Cotgrave.
Dut. Dutch.
Fall and P. The Poem on the Fall and Passion.
Fr. Sci.
The Fragment on Popular Science in the Lives
of Saints.
Fr. French.
Hall. Halliwell.
HD. Havelok the Dane.
Kil. Kilian.
Laȝ. Laȝamon.
L. P. Specimens of Lyric Poetry, ed. Wright.
lit. literally.
Marg. The Life of St Margaret.
M. G. Mæso-Gothic.
M. Ode. The Moral Ode.
N. and Q. Notes and Queries.

O. and N. Owl and Nightingale.
ON. Old Norse.
O. H. G. Old High German.
Orm. Ormulum.
part. participle.
Pol. S. Political Songs.
pret. præterite.
Ps. Psalm.
Rel. S. Religious Songs.
RG. Robert of Gloucester.
Ritson’s AS. Ritson’s Ancient Songs.
Roq. Roquefort.
S. S. Semi-Saxon.
sb. substantive.
sup. superlative.
v. a. verb active.
v. n. verb neuter.
W. Welsh.
Warton, H. E.
P.
Warton’s History of English Poetry.

A
A, indef. art. RG. 367
—— == on. O. and N. 20
—— == he. Alys. 7809
—— == and. HD. 359
—— == one. Ps. liv. 14
Aback, adv. RG. 131
Abash, v. a. Alys. 224
Abate, v. a. == put an end to, make to cease. RG. 54. Fr. abattre
—— v. n. == cease from doing a thing. RG. 447
Abay, v. a. == drive to bay. Alys. 3882
Abbess, sb. RG. 370
Abbey, sb. RG. 369
Abbot, sb. RG. 376, 447
Abece, == ABC. RG. 266
Abed, adv. RG. 547
Abelde, v. n. == become bold. Alys. 2442
Abenche, == on a bench. St. Kath. 91
Abide, v. n. == remain, tarry. RG. 382. AS. bidan

—— v. a. == wait for, hence receive. RG. 265, and 302, pret.
‘abade.’ Ps. xxxix. 2
Abie, v. a. == pay for, pay the penalty for. [abigge] 1624. B. pret.
‘abouȝte.’ 58 B. ‘abid.’ O. and N. 1775. AS. a-bicgan. See Phil. Soc.
Proc. vol. v. p. 33
Abite, v. a. == bite. Alys. 7096
Ablende, v. a. == make blind. RG. 208
Aboht, part. == bought. Wright’s L. P. p. 103
About, adv. == round about (of locality). RG. 369; ‘ȝeode aboute’
76 B.
—— ‘about to,’ with a verb, as a future part. 1593 B.
—— == nearly. RG. 247
—— prep. == around, circum. RG. 467; [obout]. Ps. lxxvii. 28
—— == near (of time), ‘aboute noon.’ Wright’s L. P. p. 34
Above, adv. 266 B.
—— prep. O. and N. 1492
Abow, v. a. == make to bend. RG. 46. pret. ‘abuyde.’ RG. 476
—— v. n. == bow, 3s pres. ‘abueth.’ RG. 193. part. ‘abouynde.’ RG.
302
Abowes, sb. == patron saints. RG. 475. Fr. avoués
Abraid, v. a. == open. O. and N. 1042. AS. abredan
Abroad, adv. RG. 542
Abrode, adv. == breeding, lit. ‘on brood.’ O. and N. 518. Fragm. on
Seven Sins, v. 34

Abusse, v. a. == ambush, conceal. 1382 B.
Abuten, prep. == without (sine). M. Ode, st. 43
Ac, conj. == and, but. RG. 367
Acast, part. == disappointed. Pol. S. 149
Accord, v. a. == reconcile. RG. 388
—— v. n. == agree. RG. 388
—— sb. == agreement. RG. 388, 447
Account, v. n. == render an account or reckoning. Pilate 86
—— sb. == reckoning. 164 B. Sermon, st. 24
Accurse, v. a. RG. 296, 474
Accuse, v. a. RG. 523. part. ‘acoysing,’ == accusing or accusation.
Alys. 3973
Acele, v. a. == seal. RG. 510. See Asele
Ache, sb. == smallage or water-parsley. Wright’s L. P. p. 26. Fr.
ache
Ache, v. n. RG. 240 pret. ‘ok.’ RG. 208
Acoled, == cooled. O. and N. 215
Acomber, v. a. == encumber. Alys. 8025
Acopede, == accused. See Aculp
Acore, v. a. == make sorry, grieve. RG. 75. part. ‘acorye,’ ==
chastened, punished. RG. 390
Acost, adv. == at the side. Alys. 2443, 3547
Acquaint, v. a. RG. 15, 465

Acquit, v. a. RG. 565
Acton, sb. == a leathern jacket worn under the armour. Alys. 2153.
Fr. acoton. See Burguy s. v.
Acue, adv. == on his rump. Fr. au cul. Marg. 67
Aculp, v. a. == accuse. RG. 544. pret. ‘acopede.’ 773 B.
Adaunt, v. a. RG. 61, 372
Aday, adv. == by day. O. and N. 219
—— == of the day, ‘aȝen eve aday,’ ‘on the evening of the day.’ RG.
289
Adder, sb. Alys. 5262
Addle, adj. == rotten. O. and N. 133
Adiȝte, v. a. == adapt, prepare. O. and N. 326
Admiral, sb. [amyrayl.] RG. 409. [admirald.] K. Horn 95
Admonishment, sb. [amonestement]. Alys. 6974
Adown, prep. [adun]. O. and N. 1452
—— adv. RG. 376.
Adownward, adv. RG. 362. Fragm. Sci. 321
Adraw, v. a. == draw (as a sword). RG. 361, pret. ‘adrou.’ ==
drew. RG. 400
Adread, v. n. == fear, be in dread. O. and N. 1264
—— adj. == in fear. Rel. S. iv. 2. part. ‘adrad.’ 44 B.
Adrench, v. a. == to drown, pret. ‘adrentte.’ RG. 384
—— v. n. == be drowned, pret. ‘adrent.’ RG. 401. part. ‘adrencte.’
RG. 437. ‘adronke.’ RG. 430

Adriȝe, v. a. == endure. K. Horn, 1068. AS. a-dreogan
Adun, v. a. == stun. O. and N. 337
Adun, adv. == adown, q. v.
Advance, v. a. == set forward, promote. RG. 503; to advance a girl
in marriage. RG. 431
Advancement, sb. Alys. 2570
Advent, sb. == the season of Advent. 1849 B.
Advice, sb. 101 B.
Advowson, sb. [vowson]. RG. 471
Adwole, adv. == in error. O. and N. 177. AS. dwelian, dwola
Ae, adv. for ‘aȝe,’ == against. 1456 B.
Afaitment, sb. == address, skill. Alys. 661
Afare, part. == gone away. St Kath. 176
Afaytye, v. a. == manage, reduce to subjection. RG. 177
—— 3 s pret. ‘afighteth.’ Alys. 6583. Fr. afaiter
Afar, adv. 1226 B.
Afaunce, == affiance? Weber. Gl. ad Alys. 732
Afear, v. a. == frighten. RG. 504, 22
Afeard, adj. RG. 388
Afell, v. a. == fell, cut down. Alys. 5240
Afeng, v. a. == take up, receive, pret. afong. RG. 368
Aferd, part. == affaired, i.e. charged with an affair to be executed.
Alys. 1813

Affair, sb. Alys. 410
Affie, v. a. == give confidence to a person. Alys. 4753
Affirm, v. a. Alys. 7356
Afighteth. See Afaytye
Afiled, == defiled. Alys. 1064
Afind, v. a. == find. O. and N. 527
Afingred, part. == hungered. 416 β. Cf. ‘fyrst’ for ‘thirst,’ ‘frefownd’
for ‘greyhound;’ and see Wright’s Vocab. pp. 250, 259, note
Afire, adv. RG. 380, 541, 546
Afoled, part. == befooled, made a fool of. O. and N. 206
Afoot, adv. RG. 378
Aforce, v. a. == force, compel. RG. 121. Alys. 789
Aforeward, adv. == foremost, foreward. 492 B.; first of all. RG.
567
Aforth, adv. == forwards. O. and N. 822
Afretie, v. a. == devour. Pol. S. 237, 240. AS. fretan
Afte, sb. == folly? Pol. S. 210
After, prep. == in expectation of, ‘after betere wynde hii moste
þere at stonde.’ RG. 367
—— == of time, ‘after Mydsomer.’ RG. 407
—— == like. Alys. 5418
—— == in; ‘after eche strete.’ M. Ode, st. 117
—— == ‘behind,’ of place. RG. 398

Afterblismed, == pregnant. Ps. lxxvii. 70. AS. blósma == a bud
Afterward, adv. == in the after part (of a book). RG. 6
—— == next in order, afterwards. Wright’s L. P. p. 24
Aftertale, sb. == postscript. 627 B.
Afterwending, sb. == following. Alys. 7280
Again, adv. == iterum, a second time. RG. 36
—— == back again [aȝé]. 147 B.
Againbuy, v. a. == redeem, pret. ‘agaynboghte.’ Ps. lxxiii. 2
Againbuying, sb. == redemption. Ps. xlviii. 9
Againcall, v. a. Ps. ci. 25
Againlook, v. a. == look back upon. Ps. xxxiv. 3
Againres, sb. == meeting. Ps. lviii. 6. [ogain raas]. Ps. xviii. 7
Againsaw, sb. == contradiction. Ps. lxxx. 8
Againsaying, sb. == contradiction. Ps. cv. 32
Against, prep. == contra, [aȝe]. 54 B. [aȝen]. RG. 367. [ogaines]
Ps. lxxxii. 4
—— == opposite to, of place, [aȝeyn]. RG. 6
—— == by the time that. Wright’s L. P. p. 23
—— == in comparison with, [aȝeynes]. Wright’s L. P. p. 68
Againstand, v. n. Ps. lxxv. 8
Againturn, v. n. == return. Ps. lxxvii. 39
Againward, adv. Ps. lxxvii. 57

Againwend, v. n. == retreat, part, ‘aȝenwendand.’ Ps. lxxvii. 9
Agast, v. a. == frighten. RG. 387
—— adj. == frightened. RG. 402. Alys. 3912. MG. us-gaisjan.
Age, sb. == sæculum. RG. 9
Agesse, vb. == calculate on, expect. K. Horn, 1219
Agin, v. n. == begin. O. and N. 1287
Ago, v. n. == go. O. and N. 1451. part. ‘agonne.’ == proceeded.
RG. 561
Ago, == gone, neglected. Pol. S. 197
Agrame, v. a. == make angry. Alys. 3309
Agrief, v. a. Alys. 3785
Agrill, v. a. == annoy. [a-grulle]. O. and N. 1108. AS. grillan
Agrise, v. a. == terrify. RG. 463. pret. ‘agros.’ RG. 549. part.
‘agrise,’ == frightened. RG. 539. ‘To agrise him,’ == become furious.
K. Horn, 895. AS. agrýsan
Aground, or ‘alaground,’ == on the ground. RG. 378
Ahen, adj. == own. O. and N. 1284. AS. ágen
Aheve, v. a. == lit. lift up; hence, bring up, educate. Marg. 5. AS. a-
hefan
Ahte, sb. == property, goods. Wright’s L. P. p. 46. AS. æht
Ahwene, v. a. == vex, trouble. O. and N. 1562. AS. a-hwænan
Ainoȝe, adj. == anew. RG. 397
Air, sb. 697 β
—— == airs, pride, vaunting. RG. 51, 397

Aither, == either. 434 β
Aiware—Aihwar, == everywhere. O. and N. 216. Moral Ode, st.
42, ed. Hickes, but the Egerton MS. reads the verse “eiðer he mai
him finde”
Akelde, vb. a. pret. == cooled. The other reading is ‘acoled,’ q. v.
RG. 442
Aken, v. a. == reconnoitre. Alys. 3468
Aknee, adv. == on the knee’s. 993 B. [aknawe]. Alys. 3540
Alaboute, adv. 2258 B. Many other compounds of ‘all’ are thus
written as one word, where they are now generally disjoined, thus
—‘alaground.’ RG. 378
Alamed, part. == lamed. O. and N. 1602
Alas! interj. RG. 443
Alast, adv. == at last. Pol. S. 216
Alb, sb. == clothing, lit. a white robe. RG. 347. AS. albe
Albidene, adv. == by and by. HD. 730. Wright’s L. P. p. 61
Albysi, adv. == about, scarcely. RG. 81. The V. L. gives ‘unnethe’
Alday, adv. == all the day. RG. 197
—— == continually. RG. 92
Aldeman, sb. == elder. Ps. civ. 22
Aldest, == oldest. RG. 232
Alderelde, sb. == extreme old age. Ps. lxx. 18
Ale, sb. HD. 14

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