

Bibliography for
Complex Roots of
Polynomials
unabridged
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Niell, A. M.
Comput. Math. Appl. 41 (2001), no. 1-2, 1--14,
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Mignotte, Maurice; Stefanescu, Doru
Applicable Algebra in Engineering, Communications and Computing, v
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the fundamental theorem of algebra
Sudhir Kumar Goel, Denise T. Reid.
Mathematics Teacher Dec 2001 v94 i9 p749(1), Expanded
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- Fundamental theorem of albegra - yet
another proof
Anindya Sen
The American Mathematical Monthly Nov 2000 v107 i9 p842(2),
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Hoteit, Leila
ICASSP, IEEE International Conference on Acoustics, Speech and
Signal Processing - Proceedings, v 6, 2000, p 3315-3318,
Engineering Village.
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memory and O(n^2) time.
Uhlig, Frank
Linear and Multilinear Algebra 46 (1999), no. 4, 327--359,
MathSciNet.
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real and complex roots
Petitjean, S.
Journal of Mathematical Imaging and Vision, v 10, n 3, 1999, p
191-220, Engineering Village.
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Ramponi, A.
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Yau, Lily; Ben-Israel, Adi
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Farahmand, K.; Jahangiri, Jay M.
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- The Fundamental Theorem of
Algebra
Michael D. Hirschhorn
College Math Journal: Volume 29, Number 4, (1998), Pages:
276-277.
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the Roots of Polynomials (in Classroom
Capsules)
Holly P. Hirst; Wade T. Macey
The College Mathematics Journal, Vol. 28, No. 4. (Sep., 1997), pp.
292-295, Jstor.
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a Polynomial Equation: Some History and Recent
Progress
Victor Y. Pan
SIAM Review, Vol. 39, No. 2. (Jun., 1997), pp. 187-220,
Jstor.
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Roots
Uwe F. Mayer
College Math Journal: Volume 28, Number 1, (1997), Pages:
58.
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finding and its characterizations.
Kalantari, Bahman; Kalantari, Iraj; Zaare-Nahandi, Rahim
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Gemignani, Luca
BIT 37 (1997), no. 2, 333--345, MathSciNet.
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roots of polynomials.
Petkovi'c, Ljiljana D.; Trickovi'c, Slobodan; Petkovi'c, Miodrag
S.
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Moussa, Ousmane
Applicable Algebra in Engineering, Communications and Computing, v
8, n 6, dec, 1997, p 497-504, Engineering Village.
- Complex roots of a random algebraic polynomial
Farahmand, K.
Journal of Mathematical Analysis and Applications, v 210, n 2, Jun
15, 1997, p 724-730, Engineering Village.
- Why
Polynomials Have Roots
Javier Gomez-Calderon; David M. Wells
The College Mathematics Journal, Vol. 27, No. 2. (Mar., 1996), pp.
90-94, Jstor.
- A
Geometric Interpretation of the Solution of the General Quartic
Polynomial
William M. Faucette
American Mathematical Monthly, Vol. 103, No. 1. (Jan., 1996), pp.
51-57, Jstor.
- Tangent-secant method for polynomial complex root
calculation
Collins, George E.; Krandick, Werner
Proceedings of the International Symposium on Symbolic and
Algebraic Computation, ISSAC, 1996, p 137-141, Engineering
Village.
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Brugnano, L.; Trigiante, D.
Linear Algebra Appl. 225 (1995), 207--219,
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Equations, or Where Did the Examination Question Come
From
H. B. Griffiths; A. E. Hirst
American Mathematical Monthly, Vol. 101, No. 2. (Feb., 1994), pp.
151-161, Jstor.
- Two sufficient conditions for a polynomial of degree n with
real coefficients to have a complex root. (Chinese)
Xiao, Gong Fu
J. Yiyang Teachers College 11 (1994), no. 6, 70--71,
MathSciNet.
- Polynomial
Root Dragging (in Notes)
Bruce Anderson
American Mathematical Monthly, Vol. 100, No. 9. (Nov., 1993), pp.
864-866, Jstor.
- New tabular form for determining root distribution of a
complex polynomial with respect to the imaginary axis
Chen, Shyan S.; Tsai, Jason S.H.
IEEE Transactions on Automatic Control, v 38, n 10, Oct, 1993, p
1536-1541, Engineering Village.
- Fast adaptive polynomial root tracking using a homotopy
continuation method
Alexander, S.T.; Stonick, V.L.
Proceedings - ICASSP, IEEE International Conference on Acoustics,
Speech and Signal Processing, v 3, Digital Speech Processing,
1993, p 111.480-483, Engineering Village.
- Root distribution of a polynomial in subregions of the complex
plane
Tsai, Jason S.H.; Chen, Shyan S.
IEEE Transactions on Automatic Control, v 38, n 1, Jan, 1993, p
173-178, Engineering Village.
- The
pth Root of an Analytic Function (in
Notes)
Lawrence J. Wallen
Mathematics Magazine, Vol. 65, No. 4. (Oct., 1992), pp. 260-261,
Jstor.
- Infinitely
Many Different Quartic Polynomial
Curves
Nitsa Movshovitz-Hadar; Alla Shmukler
The College Mathematics Journal, Vol. 23, No. 3. (May, 1992), pp.
186-195, Jstor.
- Cubics
with a Rational Root (in Notes)
William C. Schulz
Mathematics Magazine, Vol. 64, No. 3. (Jun., 1991), pp. 172-175,
Jstor.
- Inclusion of multiple polynomial roots in complex rectangular
arithmetic.
Petkovi'c, M. S.; Herzberger, J.
Computer arithmetic, scientific computation and mathematical
modelling (Albena, 1990), 367--375, IMACS Ann. Comput. Appl.
Math., 12, Baltzer, Basel, 1991, MathSciNet.
- Determining Roots of Complex Functions
with Computer Graphics
Kowalski, Robert; Helen Skala
Coll. Micro., (1990), V. VIII, No.1, pp. 51-54.
- Finding
Rational Roots of Polynomials (in Classroom
Capsules)
Don Redmond
The College Mathematics Journal, Vol. 20, No. 2. (Mar., 1989), pp.
139-141, Jstor.
- Graphing
the Complex Zeros of Polynomials Using Modulus
Surfaces
Cliff Long; Thomas Hern
The College Mathematics Journal, Vol. 20, No. 2. (Mar., 1989), pp.
98-105, Jstor.
- Graphical Representation of Complex
Function
Renka, Robert J. and Floyd Vest
Math. and Comp. Ed., (1988), V. 22, No. 1, pp.
33-45.
- A method of isolating complex roots of polynomials---an
application of Wu-Ritt principle.
Liu, Zhuo Jun
Chinese Quart. J. Math. 3 (1988), no. 4, 101--108,
MathSciNet.
- Graphing
the Complex Roots of a Quadratic
Equation
Floyd Vest
The College Mathematics Journal, Vol. 16, No. 4. (Sep., 1985), pp.
257-261, Jstor.
- Picturing
Functions of a Complex Variable (in Computer
Corner)
Bart Braden
The College Mathematics Journal, Vol. 16, No. 1. (Jan., 1985), pp.
63-72, Jstor.
- Roots of unity
revisited
Denton, Brian
The Math. Gazette, (1985), V. 69, No. 447, pp. 17-20.
- Complex
Roots Made Visible (in Classroom
Capsules)
Alec Norton; Benjamin Lotto
The College Mathematics Journal, Vol. 15, No. 3. (Jun., 1984), pp.
248-249, Jstor.
- Using an Interactive Computer Program in
the Calculus Classroom to Find Complex Roots of Polynomial
Equations
Sorkin, Sylvia
Math. and Comp. Ed., (1984), V. 18, No. 2, pp. 93-99.
- Roots
of Polynomials and Loci
Ali R. Amir-Moez
The Two-Year College Mathematics Journal, Vol. 14, No. 4. (Sep.,
1983), pp. 313-317, Jstor.
- Measuring Complex
Roots
Farnsworth, David
Math. and Comp. Ed., (1983), V. 17, No. 3, pp. 191-194.
- Those elusive imaginary
zeros
Kim, David; Robert Travers
The Math. Teach., (1982), V. 75, pp. 62-64.
- Computers
and the Multiplicity of Polynomial
Roots
John J. Wavrik
American Mathematical Monthly, Vol. 89, No. 1. (Jan., 1982), pp.
34-36+45-56, Jstor.
- An
Advanced Calculus Proof of the Fundamental Theorem of Algebra (in
Classroom Notes)
Frank Forelli
American Mathematical Monthly, Vol. 88, No. 5. (May, 1981), pp.
347-348, Jstor.
- Proof
of the Fundamental Theorem of Algebra
J. L. Brenner; R. C. Lyndon
American Mathematical Monthly, Vol. 88, No. 4. (Apr., 1981), pp.
253-256, Jstor.
- Luddhar's
Method of Solving a Cubic Equation with a Rational
Root
R. S. Luthar
The Two-Year College Mathematics Journal, Vol. 11, No. 2. (Mar.,
1980), pp. 107-110, Jstor.
- A proof of the fundamental theorem of algebra (Spanish)
José Manuel Bayod
Gac. Mat. (Madrid) (1) 29 (1977), no. 5-6, 107--110,
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Fundamental Theorem of Algebra (in Classroom
Notes)
Frode Terkelsen
American Mathematical Monthly, Vol. 83, No. 8. (Oct., 1976), p.
647, Jstor.
- The
Influence of Practical Arithmetics on the Algebra of Rafael
Bombelli (in Documents &
Translations)
S. A. Jayawardene; Di Rafael Bombelli
Isis, Vol. 64, No. 4. (Dec., 1973), pp. 510-523,
Jstor.
- The
Solution of a Certain Quartic Equation
B. Fisher
Mathematics Magazine, Vol. 45, No. 2. (Mar., 1972), pp. 97-98,
Jstor.
- The
Quadratic Polynomial and Its Zeros (in First- or Second-Year
Transfer)
C. A. Long
The Two-Year College Mathematics Journal, Vol. 3, No. 1. (Spring,
1972), pp. 23-29, Jstor.
- A
Note on the Geometry of Zeros of
Polynomials
C. A. Long
Mathematics Magazine, Vol. 44, No. 3. (May, 1971), pp. 157-159,
Jstor.
- The Fundamental Theorem of
Algebra
Paul J. Campbell
Pi Mu Epsilon J., (1967), V. 4, No. 6, pp.
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- An
Easy Proof of the Fundamental Theorem of Algebra (in Classroom
Notes)
Charles Fefferman
American Mathematical Monthly, Vol. 74, No. 7. (Aug. - Sep.,
1967), pp. 854-855, Jstor.
- Proof
of the Fundamental Theorem of Algebra (in Classroom
Notes)
S. Wolfenstein
American Mathematical Monthly, Vol. 74, No. 7. (Aug. - Sep.,
1967), pp. 853-854, Jstor.
- On
the Fundamental Theorem of Algebra
Hans Zassenhaus
American Mathematical Monthly, Vol. 74, No. 5. (May, 1967), pp.
485-497, Jstor.
- A
Numerical Method for Locating the Zeros of an Analytic
Function
L. M. Delves; J. N. Lyness
Mathematics of Computation, Vol. 21, No. 100. (Oct., 1967), pp.
543-560, Jstor.
- What!
Another Note Just on the Fundamental Theorem of Algebra? (in
Classroom Notes)
R. M. Redheffer
American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), pp.
180-185, Jstor.
- Yet
Another Proof of the Fundamental Theorem of Algebra (in
Mathematical Notes)
R. P. Boas, Jr.
American Mathematical Monthly, Vol. 71, No. 2. (Feb., 1964), p.
180, Jstor.
- A
Method for the Real and Complex Roots of a
Polynomial
Van A. McAuley
Journal of the Society for Industrial and Applied Mathematics,
Vol. 10, No. 4. (Dec., 1962), pp. 657-667, Jstor.
- On
the Utility of Newton's Method for Computing Complex Roots of
Equations (in Technical Notes and Short
Papers)
I. M. Longman
Mathematics of Computation, Vol. 14, No. 70. (Apr., 1960), pp.
187-189, Jstor.
- The
Fundamental Theorem of Algebra (in Classroom
Notes)
J. E. Eaton
American Mathematical Monthly, Vol. 67, No. 6. (Jun. - Jul.,
1960), pp. 578-579, Jstor.
- Complex
Roots of Real Polynomials (in Classroom
Notes)
J. P. Ballantine
American Mathematical Monthly, Vol. 66, No. 5. (May, 1959), pp.
411-414, Jstor.
- The
Probability That the Roots of a Real Quadratic Equation Lie Inside
or on the Circumference of the Unit Circle in the Complex
Plane
Joseph W. Andrushkiw
Mathematics Magazine, Vol. 32, No. 3. (Jan. - Feb., 1959), pp.
123-128, Jstor.
- Routh's method for finding complex roots. (Chinese)
Chao F.
Acta Math. Sinica 9 1959 101--113, MathSciNet.
- A method of approximating the complex roots of equations.
Kulik, Stephen
Pacific J. Math. 8 1958 277--281, MathSciNet.
- The
Fundamental Theorem of Algebra (in Mathematical
Notes)
Raymond Redheffer
American Mathematical Monthly, Vol. 64, No. 8. (Oct., 1957), pp.
582-585, Jstor.
- Detection and evaluation of a certain type of complex roots by
Graeffe's root-squaring method.
Ghosh, P. K.
Bull. Calcutta Math. Soc. 49 1957 43--46,
MathSciNet.
- Polynomial
Root Solving on the Electronic Differential Analyser (A Technique
for Finding the Real and Complex Roots of a Polynomial Using an
Electronic Differential Analyser)
Cyril Atkinson
Mathematical Tables and Other Aids to Computation, Vol. 9, No. 52.
(Oct., 1955), pp. 139-143, Jstor.
- Newton's method for finding complex roots. (Chinese)
Chao, F. H.
Acta Math. Sinica 5 (1955), 137--147, MathSciNet.
- Complex
Roots of an Integral Rational Equation (in Classroom
Notes)
D. Trifan
American Mathematical Monthly, Vol. 61, No. 9. (Nov., 1954), pp.
640-641, Jstor.
- The
Fundamental Theorem of Algebra (in Mathematical
Notes)
S. Stein
American Mathematical Monthly, Vol. 61, No. 2. (Feb., 1954), p.
109, Jstor.
- A
Matric Proof of the Fundamental Theorem of Algebra for Real
Quaternions (in Mathematical Notes)
Mark Leum; M. F. Smiley
American Mathematical Monthly, Vol. 60, No. 2. (Feb., 1953), pp.
99-100, Jstor.
- Deduction
of Cardano's Formula by Conformal Mapping (in Mathematical
Notes)
C. F. Moppert
American Mathematical Monthly, Vol. 59, No. 5. (May, 1952), pp.
310-314.
- A
Topological Proof of the Fundamental Theorem of Algebra (in
Mathematical Notes)
B. H. Arnold
American Mathematical Monthly, Vol. 56, No. 7. (Aug. - Sep.,
1949), pp. 465-466, Jstor.
- Numerical solution of complex roots of quartic equations.
Lin, Shih-Nge
J. Math. Physics 26, (1948), MathSciNet.
- One
More Proof of the Fundamental Theorem of Algebra (in Mathematical
Notes)
N. C. Ankeny
American Mathematical Monthly, Vol. 54, No. 8. (Oct., 1947), p.
464, Jstor.
- The
Determination of the Complex Zeros of A
Polynomial
G. C. Best
American Mathematical Monthly, Vol. 54, No. 5. (May, 1947), pp.
269-273, Jstor.
- An
Elementary Constructive Proof of the Fundamental Theorem of
Algebra
P. C. Rosenbloom
American Mathematical Monthly, Vol. 52, No. 10. (Dec., 1945), pp.
562-570, Jstor.
- Graphical
Solutions for Complex Roots of Quadratics, Cubics and
Quartics
George A. Yanosik
National Mathematics Magazine, Vol. 17, No. 4. (Jan., 1943), pp.
147-150, Jstor.
- Graphical determination of real and complex roots of cubic
equations. (Spanish)
Babini, J.
An. Soc. Ci. Argentina 134, (1942), MathSciNet.
- Complex
Roots of a Polynomial Equation
H. M. Gehman
American Mathematical Monthly, Vol. 48, No. 4. (Apr., 1941), pp.
237-239, Jstor.
- A comparison of methods for evaluating the complex roots of
quartic equations.
Sharp, Henry S.
J. Math. Phys. Mass. Inst. Tech. 20, (1941). 243--258,
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- Sidelights
on the Cardan-Tartaglia Controversy (in Humanism and History of
Mathematics)
Martin A. Nordgaard
National Mathematics Magazine, Vol. 12, No. 7. (Apr., 1938), pp.
327-346, Jstor.
- A
Graphical Solution of the Cubic
H. B. Curtis
National Mathematics Magazine, Vol. 12, No. 7. (Apr., 1938), pp.
325-326, Jstor.
- Graphical
Representation of Complex Roots
James A. Ward
National Mathematics Magazine, Vol. 11, No. 7. (Apr., 1937), pp.
297-303, Jstor.
- Graeffe's
Method and Complex Roots (in Questions, Discussions, and
Notes)
B. A. Hausmann
American Mathematical Monthly, Vol. 43, No. 4. (Apr., 1936), pp.
225-229, Jstor.
- A
Graphical Solution for the Complex Roots of a
Cubic
George A. Yanosik
National Mathematics Magazine, Vol. 10, No. 4. (Jan., 1936), pp.
139-140, Jstor.
- The
Graphical Interpretation of the Complex Roots of Cubic Equations
(in Questions, Discussions, and Notes)
Garcia Henriquez
American Mathematical Monthly, Vol. 42, No. 6. (Jun. - Jul.,
1935), pp. 383-384, Jstor.
- A
Proof of the Fundamental Theorem of Algebra (in Questions,
Discussions, and Notes)
R. P. Boas, Jr.
American Mathematical Monthly, Vol. 42, No. 8. (Oct., 1935), pp.
501-502, Jstor.
- On
the Fundamental Theorem of Algebra
W. Paul Webber
Mathematics News Letter, Vol. 7, No. 5. (Feb., 1933), pp. 9-13,
Jstor.
- On
the Nature of the Roots of a Quartic
Equation
Raymond Garver
Mathematics News Letter, Vol. 7, No. 4. (Jan., 1933), pp. 6-8,
Jstor.
- Enrique
Cruchaga's Solution of the Quartic Equation (in Questions and
Discussions)
Raymond Garver
American Mathematical Monthly, Vol. 37, No. 6. (Jun. - Jul.,
1930), pp. 303-304, Jstor.
- A
Short Account of the History of Symmetric Functions of Roots of
Equations
H. Gray Funkhouser
American Mathematical Monthly, Vol. 37, No. 7. (Aug. - Sep.,
1930), pp. 357-365, Jstor.
- The
History of the Solution of the Cubic
Equation
Lucye Guilbeau
Mathematics News Letter, Vol. 5, No. 4. (Dec., 1930), pp. 8-12,
Jstor.
- On
the Numerical Solution of Equations with Complex
Roots
R. A. Frazer; W. J. Duncan
Proceedings of the Royal Society of London. Series A, Containing
Papers of a Mathematical and Physical Character, Vol. 125, No.
796. (Aug. 1, 1929), pp. 68-82, Jstor.
- Discussions:
A Solution of the Quartic Equation (in Questions and
Discussions)
Raymond Garver
American Mathematical Monthly, Vol. 35, No. 10. (Dec., 1928), pp.
558-560, Jstor.
- Discussions:
A Criterion that a Cubic Equation has an Integral Root (in
Questions and Discussions)
H. S. Vandiver
American Mathematical Monthly, Vol. 33, No. 2. (Feb., 1926), pp.
94-95, Jstor.
- A
Contribution of Leibniz to the History of Complex
Numbers
R. B. McClenon
American Mathematical Monthly, Vol. 30, No. 7. (Nov., 1923), pp.
369-374, Jstor.
- Graphical
Discussion of the Roots of a Quartic
Equation
E. L. Rees
American Mathematical Monthly, Vol. 29, No. 2. (Feb., 1922), pp.
51-55, Jstor.
- Discussions:
Resolution of a Certain Quintic Equation and a Geometrical
Construction for its Roots (in Questions and
Discussions)
C. B. Haldeman
American Mathematical Monthly, Vol. 27, No. 6. (Jun., 1920), pp.
257-258, Jstor.
- Discussions:
Relating to the Graph of a Cubic Equation Having Complex Roots (in
Questions and Discussions)
Edwin S. Crawley
American Mathematical Monthly, Vol. 25, No. 6. (Jun., 1918), pp.
268-269, Jstor.
- A
Simple Method for Graphically Obtaining the Complex Roots of a
Cubic Equation
Rutherford E. Gleason
The Annals of Mathematics, 2nd Ser., Vol. 11, No. 3. (Apr., 1910),
pp. 95-96, Jstor.
- On
the Reciprocal Quartic Equation
R. L. Berger
American Mathematical Monthly, Vol. 15, No. 4. (Apr., 1908), pp.
85-87, Jstor.
- Condition
in Terms of the Invariants of the Quartic that its Four Distinct
Root-Points be Concyclic
T. E. McKinney
American Mathematical Monthly, Vol. 14, No. 2. (Feb., 1907), p.
23, Jstor.
- Approximation
of the Greatest Root of a Cubic Equation with Three Real
Roots
Charles Gilpin, Jr.
American Mathematical Monthly, Vol. 13, No. 6/7. (Jun. - Jul.,
1906), pp. 140-141, Jstor.
- On
Certain Proofs of the Fundamental Theorem of
Algebra
Robert E. Moritz
American Mathematical Monthly, Vol. 10, No. 6/7. (Jun. - Jul.,
1903), pp. 159-161, Jstor.
- On
the Complex Roots of Numerical Equations of the Third and Fourth
Degree
A. C. Burnham
American Mathematical Monthly, Vol. 4, No. 8/9. (Aug. - Sep.,
1897), pp. 201-204, Jstor.
- On
the Solution of Cubic and Biquadratic
Equations
G. W. Hill
The Analyst, Vol. 2, No. 1. (Jan., 1875), pp. 4-8,
Jstor.
- Solution
of the Quartic Equation, x^4 + Ax + B =
0
A. M. Sawin
The Annals of Mathematics, Vol. 1, No. 1. (Mar., 1884), pp. 14-15,
Jstor.
- The
Deduction of Final Formulas for the Algebraic Solution of the
Quartic Equation
Mansfield Merriman
American Journal of Mathematics, Vol. 14, No. 3. (Jul., 1892), pp.
237-245, Jstor.
- On
a Soluble Quintic Equation
Prof. Cayley
American Journal of Mathematics, Vol. 13, No. 1. (Oct., 1890), pp.
53-58, Jstor.
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