Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 18, Number 3

#### Publication Date: September 1951

Correction to “A property of Hausdorff measure”

H. G. Eggleston; 593

Compositions involving ternary cubics

A. R. Richardson; 595-598

Properties of linear transformations preserved under addition of a completely continuous transformation

Bertram Yood; 599-612

The Euler-Fermat theorem for matrices

Alex S. Davis; 613-617

The order of a matrix under multiplication ${\rm modulo} m$

Margaret Waugh Maxfield; 619-621

Separation in non-separable spaces

Mary Ellen Estill; 623-629

Topologies defined by bounded sets

B. H. Arnold; 631-642

Some extensions of Piranian’s theorem

R. Wilson; 643-651

Snake-like continua

R. H. Bing; 653-663

Contractions in a hyperbolic space

W. Gustin and J. A. Sullivan; 665-671

A class of spirals

S. B. Jackson; 673-682

Local theory of residues

George Whaples; 683-688

A new approach to the study of contact in the projective differential geometry of surfaces

P. O. Bell; 689-695

Projective differential invariants of a curve of a surface

P. O. Bell; 697-705

The essential multiplicity function

W. R. Scott; 707-717

Addendum to “A simplified proof of the expansion theorem for singular second order linear differential equations”

Norman Levinson; 719-722

An estimate of the error in Tauberian theorems for power series

Jacob Korevaar; 723-734

A note on basic sets of polynomials

W. F. Newns; 735-739

Non-existence of odd perfect numbers of the form $3^{2\beta}\cdot p^\alpha\cdot s_1^{2\beta_{1}}S_2^{2\beta_{2}}S_3^{2\beta_{3}}$

G. Cuthbert Webber; 741-749

Hankel determinants whose elements are sections of a Taylor series. Part I

J. L. Ullman; 751-756

Tests for primality

B. W. Brewer; 757-763