American Mathematical Society · TRANSACTIONS OF THE American Mathematical Society Volumes 1-10 1900 - 1909 Indices PUBLISHED BY THE SOCIETT Lancaster, Pa., and Nbw York

TRANSACTIONS

OF THE

American Mathematical Society

Volumes 1-10

1900 - 1909

Indices

PUBLISHED BY THE SOCIETT

Lancaster, Pa., and Nbw York

1909

CONTENTS.PAGE.

Index by Authors ........... 5

Index by Subject Matter . . . . . . . . .19

Arrangement of the Index by Subject Matter.

A. Logical Analysis of Mathematical Disciplines. 19

B. Algebra.

B1. Eational Functions. Theory of Equations. Determinants. Sym-

metric Functions. 20

B2. Algebraic Forms. Invariants. (Cf.F2.). 20

B 3. Linear Associative Algebra. Hypercomplex Number Systems. Fields.

(Cf.Fl.). 21

B4. Algebra of Logic. 21

C. Theory of Numbers. 21

(Cf. El, E2.)D. Analysis.

D 1. Functions of Eeal Variables. Point Sets. 22

D2. Functions of Complex Variables. 23

D3. Particular Functions. 24

D 4. Ordinary Differential Equations. (Cf. D 3, F 4. ). 24

D5. Partial Differential Equations. 25

D6. Differential Forms. 25

D 7. Calculus of Variations . 26

D 8. Difference Equations. 27

E. Groups.

El. Discrete Groups in General. (Cf. E2.). 27

E2. Linear Groups in Arbitrary or Special Fields. 29

E3. Continuous Groups. (Cf. E 2, F 1, F 3, G 3.). 30

F. Geometry.

F 1. Synthetic Geometry. Non-Euclidian Geometry. Geometry of n Di-

mensions. Analysis Situs. (Cf. Dl, D2.). 30

F 2. Algebraic Geometry. Algebraic Curves and Surfaces. (Cf. B2, D3,

E2, FI, F 4, F 5.). 31

F3. Geometry of Special Space-Elements. 32

F4. Differential Geometry. (Cf.D6.). 32

F 5. Geometric Transformations. Geometry of Motion. (Cf. E2.). 33

3

4 CONTENTS.

PAGE.

G. Applied Mathematics.

G 1. General Mechanics. .. ... 34

G2. Celestial Mechanics. 34

G 3. Elasticity, Hydromechanics and Sound. 35

G4. Electricity, Light and Heat. 35

INDEX BY AUTHORS.Vol.* Pages.

Allen, R. B., On hypercomplex number systems belonging to an

arbitrary domain of rationality. 92

Allardice, R. E., On the envelope of the axes of a system of

conies passing through three fixed points. 4,

Birkhoff, George D., General mean value and remainder the-

orems with applications to mechanical differentiation and

quadrature . 7,-On the asymptotic character of the solutions of certain dif-

ferential equations containing a parameter. 92-Boundary value and expansion problems of ordinary linear

differential equations. 94-Existence and oscillation theorems for a certain boundary

value problem. 10,-Singular

points of ordinary linear differential equations... 104

Blake, E. M., Two plane movements generating quartic scrolls 14

Blichfeldt, H. F., Note on the functions of the form

f(x) = <p(x) + axxn_1 + a2z"-2 + - - - + an, which in a given in-

terval differ the least possible from zero. 2,-A new determination of the primitive continuous groups in

two variables. 23-On the determination of the distance between two points in

space of n dimensions. 34-On the order of linear homogeneous groups. . 44-On the order of linear homogeneous groups (second paper) 5,-A theorem concerning the invariants of linear homogeneous f 54

groups, with some applications to substitution groups.1 64-On imprimitive linear homogeneous groups. 62-On the order of linear homogeneous groups (supplement). 74-On modular groups isomorphic with a given linear group... 8,

Bliss, Gilbert Ames, The second variation of a definite integral

when on e end-point is variable. 3,-An existence theorem for a differential equation of the sec-

ond order, with an application to the calculus of variations 5a

203-218

103-106

107-136

219-231

373-395

259-270

436-470

421-429

100-102

249-258

467-481

387-397

310-325

461-466

546

230-236

523-529

30- 32

132-141

113-125

*The numbers in this column indicate for every paper the volume and part oí volume of

publication, and thus the date of publication, e. g., the first paper in the list was published in

April, 1908, and the second in January, 1903.

In this column references are made also to the Notes and errata published in the concluding

numbers of various volumes, e. g., a note to the thirteenth paper appears in the Notes and errata

of volume 6.

ß INDEX BY AUTHORS. [October

■-Sufficient condition for a minimum with respect to one-

sided variations. 54 477-492-A generalization of the notion of angle. 7S 184-196-

(and M. Mason), A problem in the calculus of variations

in which the integrand is discontinuous. 72 325-336-A new form of the simplest problem of the calculus of vari- f 83 405-414

ations. (84 536-

(and M. Mason), The properties of curves in space which

minimize a definite integral . 94 440-466

Bûcher, Maxime, On regular singular points of linear differen-

tial equations of the second order whose coefficients are not j 1, 40- 52

necessarily analytic. ( 14 507

-■ Application of a method of D'Alembert to the proof of

Sturm's theorems of comparison. 14 414-420

-Certain cases in which the vanishing of the Wronskian is a

sufficient condition for linear dependence. 22 139-14Í/

-An elementary proof of a theorem of Sturm. 22 150-151

-On certain pairs of transcendental functions whose roots

separate each other. 24 428-436

-On the real solutions of systems of two homogeneous linear

differential equations of the first order. 32 196-215

-On the regions of convergence of power-series which repre-

sent two-dimensional harmonic functions. 10, 271-278

Bolza, Oskar, The elliptic <r-functions considered asa special] 1, 53- 65

case of the hyperelliptic «--functions. 1 24 484

-New proof of a theorem of Osgood's in the calculus of vari-

ations. 24 422-427

-Proof of the sufficiency of Jacobi's condition for a perma-nent sign of the second variation in the so-called isoperi-

metric problems. 33 305-311

-A fifth necessary condition for a strong extremum of the

integral Ç*"F(x, y, y')dx. 72 314-324

-Weierstrass's theorem and Kneser's theorem on trans-

versals for the most general case of an extremum of a

simple definite integral. 74 459-488

■-Existence proof for a field of extremals tangent to a given

curve. 8, 399-404

Bromwich, T. J. I'a., Similar conies through three points. 44 489^92

-The classification of quadrics. 63 275-285

Brown, Ernest William, On the small divisors in the lunar

theory. 32 159-185

-On the formation of the derivatives of the lunar coordi-

nates with respect to the elements. 43 234-248

1909] INDEX BY AUTHORS. 7

-On the variation of the arbitrary and given constants in

dynamical equations. . 4S 333-350

( 5 279—287-On the smaller perturbations of the lunar arguments.\ 3

t 04 ool

-On a general method for treating transmitted motions and

its application to indirect perturbations. 63 332-343

Bussey, W. H. (and O. Veblen), Finite protective geometries... 72 241-259

Cajori, Florian, Divergent and conditionally convergent series

whose product is absolutely convergent. 2, 25- 36

Campbell, J. E., On the types of linear partial differential

equations of the second order in three independent variables

which are unaltered by the transformations of a continu- ( 1, 243-258

ous group . ( 14 509

Carver, W. B., On the Cayley-Veronese class of configurations 64 534-545

Chessin, Alexander S., On relative motion. 12 116-169

Coble, A. B., The quartic curve as related to conies. 4, 65- 85-On the relation between the three-parameter groups of a

cubic space curve and a quadric surface. 7, 1-20

-An application of the form-problems associated with certain

Cremona groups to the solution of equations of higher degree 94 396-424

Cole, F. N., The groups of order p'ç". 52 214-219

Coolidge, Julian Lowell, A purely geometric representation

of all points in the protective plane. 12 182-192-Quadric surfaces in hyperbolic space. 42 161-170-The equilong transformations of space. 92 178-182

Curtiss, D. R., Theorems converse to Riemann's on linear dif-

ferential equations. 7, 99-106

Darwin, G. H., The approximate determination of the form of

Maclaurin's spheroid. 42 113-133

■-Further note on Maclaurin's spheroid. 9, 34- 38

Dentón, William Wells, On the osculating quartic of a plane

curve. 10s 297-308

Dickson, Leonard Eugene, Definition of the abelian, the two

hypoabelian, and related linear groups, as quotient groupsof the groups of isomorphisms of certain elementary groups 1, 30- 38

-A new definition of the general abelian linear group. 1, 91-96

-Determination of an abstract simple group of order 2' -36 ■

5 7 holoedrically isomorphic with a certain orthogonal group f 13 353-370

and with a certain hyperabelian group.1 14 509

-Canonical forms of quaternary abelian substitutions in an f 2, 103-138

arbitrary Galois field. I 34 499

,-, * ,* Í 24 363-394-Theory of linear groups in an arbitrary field.,

v o4 OUO

SO

on AK

8 index BY AUTHORS. [October

-On the group defined for any given field by the multiplica-

tion table of any given finite group. 33 285-301-The groups of Steiner in problems of contact (second paper). 33 377-382

-Definitions of a field by independent postulates.\ >J

F

r l54 549-550

-Definitions of a linear associative algebra by independent

postulates. 4, 21- 26-On the subgroups of order a power of p in the quater- ( 44 371-386

nary abelian group in the Galois field of order pn. ( 54 550-551-On the reducibility of linear groups. 44 434-436-The subgroups of order a power of 2 of the simple quinary j 5, 1- 38

orthogonal group in the Galois field of order p" = 81 ± 3... 1 54 551-Determination of all the subgroups of the known simple f 52 126-166

group of order 251)20.1 54 551-The minimum degree t of resolvents for the ^-section of

the periods of hyperelliptic functions of four periods. 6, 48- 57

-Definitions of a group and a field by independent postulates ■! * r.-

-On semi-groups and the general isomorphism between finite

groups . 62 205-208-On hypercomplex number systems . 63 344-348-On

quadratic, hermitian and bilinear forms. 72 275-292-■ Linear algebras in which division is always uniquely

possible . 73 370-390-On commutative linear algebras in which division is always

uniquely possible. 74 514-522.

(8 905—232-Invariants of binary forms under modular transformations \ fC 84 Ooo

——■ Modular theory of group-matrices. . 8S 389-398-Representations of the general symmetric group as linear

groups in finite and infinite fields. 92 121-148-Definite forms in a finite field. 10, 109-122-General theory of modular invariants. 102 123-158-Equivalence of pairs of bilinear or quadratic forms under

rational transformations. 103 347-360

Dresden, Arnold, The second derivatives of the extremal integral. 94 467-486

Eiesland, John, On a certain system of conjugate lines on a

surface connected with Euler's transformation . 64 450-471

Eisenhart, Luthek Pfahler, Conjugate rectilinear congruences. 33 354-371■-Congruences of curves. 44 470-488-Three

particular S3rstems of lines on a surface . 54 421-437-Surfaces of constant curvature and their transformations.. 64 472-485-Applicable surfaces with asymptotic lines of one surface

corresponding to a conjugate system of another.■] '


-Surfaces with isothermal representation of their lines of

curvature and their transformations.

Emch, Arnold, Algebraic transformations of a complex variable

realized by linkages.

Epsteen, Saul, On reducible groups.

-Semireducible hypercomplex number systems.-

9, 149-177

-On the definition of reducible hypercomplex number systems.■- (and J. H. Maclagan-Wedderburn), On the structure of

hypercomplex number systems .

Field, Peter, On the form of a plane quintic curve with five

cusps.

Fields, J. C., On the reduction of the general abelian integral.. -

Findlay, William, The Sylow subgroups of the symmetric

group.Fite, W. B., On metabelian groups. .-Groups whose orders are powers of a prime.-Irreducible linear homogeneous groups whose orders are

powers of aprime.- Irreducible homogeneous linear groups in an arbitrary

domain.

Ford, W. B., On the possibility of differentiating term by term

the developments for an arbitrary function of one real vari-

able in terms of Bessel functions.-On the analytic extension of functions defined by double

power series. .-On the integration of the homogeneous linear difference

equation of second order . .

Fréchet, M., Sur les opérations linéaires.

-Sur les opérations linéaires (deuxième note). ...-Sur l'écart de deux courbes et sur les courbes limites.

-Sur les opérations linéaires (troisième note).

Gale, Arthur Sullivan, On the rank, order and class of alge-

braic minimum curves.

Glenn, O. E., Determination of the abstract groups of order

p2qr ; p, q, r being distinct primes. .

Gordan, Paul, Formentheoretische Entwickelung der in Herrn

White's Abhandlung über Curven dritter Ordnung enthal-

ten en Sätze.-Die Hessische und die Cayley'sche Curve.

Goursat, E., Sur la définition générale des fonctions analy-

tiques, d'après Cauchy.-A simple proof of a theorem in the calculus of variations...

10,

42

72

10a

54

6,

64

84

3,

7,

493-498

249-250

437-444

551

105-109

6„ 172-178

26- 32

49- 86

486

263-278

331-353

61- 68

107-112

315-318

178-184

260-274

319-336

493-499

134-140

435-449

433-446

451-466

137-151

9- 13

402-413

14- 16

110-112

10 INDEX BY AUTHORS. [October

Greenhill, Alfred George, The elliptic integral in electro-

magnetic theory. 84 447-534

Griffin, Frank Loxley, Certain periodic orbits of k finite.

bodies revolving about a relatively large central mass. 9, 1- 33

Hadamard, J., La théorie des plaques élastiques planes. 34 401-422

Hartwell, George Wilbur, Plane fields of force whose trajec-

tories are invariant under a projective group.... 102 220-246

Haskell, M. W., The resolution of any collineation into per-spective reflections . . 73 361-369

Haskins, Charles Nelson, On the invariants of quadratic dif- ( 3, 71- 91

ferential forms.1 34 501-On the invariants of differential forms of degree higher

than two. 4, 38- 43-On the invariants of quadratic differential forms, II. 52 167-192-Note on the differential invariants of a surface in space.... 7 152-154-On the differential] invariants of a plane. 74 588-590

Hathaway, A. S., Quaternion space. 3, 46- 59

Hawkes, H. E., On hypercomplex number systems. 33 312-330

Hedrick, E. R., On derivatives over assemblages. 83 345-353

Heffter, L., Ueber Curvenintegrale im wi-dimensionalen Raum 42 142-148

Hilbert, David, Ueber Flächen von constan ter Gauss'scher

Krümmung. 2, 87- 99

Hill, G. W., On the extension of Delaunay's method in the} 12 205-242

lunar theory to the general problem of planetary motion... 114 508-509

Hun, John Gale, On certain invariants of two triangles. 5, 39- 55

Huntington, Edward V., A complete set of postulates for the ( 32 264-279

theory of absolute continuous magnitude.1 54 549-Complete sets of postulates for the theories of positive in-

tegral and of positive rational nu mbers. 3, 280-284-Two definitions of an abelian group by sets of independent

postulates. 4, 27- 30-Definitions of a field by sets of independent postulates. 4, 31- 37-Complete sets of postulates for the theory of real quantities 43 358-370

-Sets of independent postulates for the algebra of logic.j 3

-A set of postulates for real algebra, comprising postulatesfor a one-dimensional continuum and for the theory of (6, 17- 41

groups.. ( 64 546-Note on the definition of abstract groups by sets of inde- J 6, 181-197

pendent postulates.. ( 74 591-A set of postulates for ordinary complex algebra. 6 209-229

Hutchinson, J. I., On certain relations among the theta con-

stants. 14 391-394-On a class of automorphic functions. 3, 1- 11


-On the automorphic functions of the group (0, 3 ; 2, 6, 6) 54-On certain hyperabelian functions which are expressible by

theta series.... 7,-On automorphic groups whose coefficients are integers in a

quadratic field. . 74-A method for constructing the fundamental region of a dis-

continuous group of linear transformations. 82-The hypergeometric functions of N variables. 10,

Jackson, Dunham, Resolution into involutory substitutions of

the transformations of a non-singular bilinear form into

itself. 10.

Kasner, Edward, The invariant theory of the inversion group ;

geometry upon a quadric surface.,-The cogredient and digredient theories of multiple binary

forms. 4,-The generalized Beltrami problem concerning geodesic rep- f 42

resentation. 1 54-On the point-line as element of space : a study of the corre-

sponding bilinear connex.-Isothermal systems of geodesies. 5,-Surfaces whose geodesies may be represented in the plane

by parabolas. 62-The

problem of partial geodesic representation . 7,-The trajectories of dynamics . 73-Dynamical trajectories : the motion of a particle in an

arbitrary field of force. 82-Natural families of trajectories : conservative fields of Í 102

force. 1104

Kellogg, O. D., Potential functions on the boundary of their

regions of definition. 9,-Double distributions and the Dirichlet problem. 9,

Krause, Martin, Ueber Systeme von Differentialgleichungen

denen vierfach periodische Functionen Genüge leisten . 1,

Landry, Aubrey E., A geometrical application of binary

syzygies. 10,

Lehmer, D. N., Constructive theory of the unicursal cubic by

synthetic methods. 33

Leib, David D., On a complete system of invariants of two

triangles. 103

Lennes, N. J., Volumes and areas. 64

Levi, Beppo, Geometrie proiettive di congruenza é géométrie

proiettive finite. 83

Loewy, Alfred, Ueber die Reducibilität der Gruppen linearer

homogener Substitutionen.:. 4,

447-460

21- 25

530-536

261-269

61- 70

479-484

430-498

485

86-102

149-152

550

213-233

550

56- 60

141-158

200-206

401-424

135-158201-219

510

39- 50

51- 66

287-292

95-108

372-376

361-390486-490

354-365

44- 64


-Ueber die Reducibilität der reellen Gruppen linearer homo-

gener Substitutionen. 4S 171-177-Zur Gruppentheorie mit Anwendungen auf der Theorie der

linearen homogenen Differentialgleichungen. 5, 61- 80-Ueber die vollständig reduciblen Gruppen, die zu einer

Gruppe linearer homogener Substitutionen gehören. 64 504-533

Longley, William Raymond, A class of periodic orbits of an J 82 159-188

infinitesimal body subject to the attraction of n finite bodies i 84 535

Loud, Frank H., Sundry metric theorems concerning n lines in

aplane. 13 323-338

Lovett, E. O., On a problem including that of several bodies and

admitting of an additional integral. 64 491-495

Macaulay, F. S., On a method of dealing with the intersections

of plane curves. 54 385-410

Maclagan-Wedderburn, J. H. (and S. Epsteen), On the struc-

ture of hypercomplex number systems. 6 172-178-A theorem on finite algebras. 6 349-352- (and O. Veblen), Non-desarguesian and non-pascalian

geometries. 83 379-388

McClintock, E., On the nature and use of the functions employed

in the recognition of quadratric residues. 3, 92-109

McDonald, J. H., On the system of a binary cubic and quadraticand the reduction of hyperelliptic integrals of genus two to

elliptic integrals by a transformation of the fourth order. 24 437-458-A problem in the reduction of hyperelliptic integrals. 74 578-587

Manning, W. A., The primitive groups of class 2p which con-

tain a substitution of order p and degree 2p. 43 351-357-On the primitive groups of class Up. 6, 42- 47-Groups in which a large number of operators may corre-

spond to their inverses. 72 233-240-On multiply transitive groups. 74 499-508-On the order of primitive groups. 102 247-258

Maschke, Heinrich, Note on the unilateral surface of Moebius. 1, 39-A new method of determining the differential parameters ( 1, 197-204

and invariants of quadratic differential quantics. ( 14 508-On superosculating quadric surfaces. 34 482-484

-A symbolic treatment of the theory of invariants of quad-ratic differential quantics of n variables. 44 445-469

-Differential parameters of the first order.\ '

-The Kronecker-Gaussian curvature of hyperspace. 7 81- 93

Mason, Max, Green's theorem and Green's functions for certain

systems of differential equations. 52 220-225-The doubly periodic solutions of Poisson's equation in two

independent variables. 62 159-164


- (and G. A. Bliss), A problem in the calculus of variations

in which the integrand is discontinuous. 73

-On the boundary value problems of linear ordinary differ-

ential equations of second order. 7,

-The expansion of a function in terms of normal functions.. 84

-(and G. A. Bliss), The properties of curves in space

which minimize a definite integral. 94

Merrill, Helen A., On solutions of differential equations whichÍ4'

possess an oscillation theorem.

Mertens, F., Zur linearen Transformation der 0-Reihen. 23

Metzler, W. H., On certain aggregates of determinant minors.. 24

Miller, G. A., On the groups which are the direct products of

two subgroups. 1,-On the groups which have the same group of isomorphisms 14

-Determination of all the groups of order pm which contain ( 23

the abelian group of type (m — 2, 1), p being any prime_ I 34-On the groups of order pm which contain operators of order

P"'-2-:. 34

-On the holomorph of a cyclic group. 42

-(and H. C. Moreno), Non-abelian groups in which every

sub-group is abelian. 44-Determination of all the groups of order 2m which contain

an odd number of cyclic subgroups of composite order. 6,-On the invariant subgroups of prime index. 63-Groups containing only three operators which are squares.. 7,

-The groups of order pm which contain exactly p cyclic sub-

groups of order p". . 72

Generalization of the groups of genus zero. Í 8l

lio4-The

groups in which every subgroup is either abelian or

hamiltonian. . 8,-Groups defined by the orders of two generators and the

order of their commutator. 9,

-On the holomorph of the cyclic group of order p™. 92

-■ The central of a group. 10,-Automorphisms of order two. 104

Moore, Charles N., On the introduction of convergence factors f 8,

into summable series and summable integrals.1 84

-The summability of the developments in Bessel functions,

with applications. 104

Moore, Eliakim Hastings, On certain crinkly curves.\ '

-A simple proof of the fundamental Cauchy-Goursat theorem. j *

325-336

337-360

427-432

440-466

423-433

551

331-342

395-403

66- 71

395-401

259-272

499-500

383-387153-160

398-404

58- 62

326-331

94- 98

228-232

1- 13

510

25- 29

67- 78232-236

50- 60

471-478

299-330

535

391-435

72- 90

507499-506

486


Concerning Harnack's theory of improper definite integrals..

On the theory of improper definite integrals.

■ On the projective axioms of geometry.

- A definition of abstract groups.

On a definition of abstract groups.Moore, Robert L., Geometry in which the sum of the angles of

every triangle is two right angles.-Sets of metrical hypotheses for geometry.Moreno, H. C. (and G. A. Miller), Non-abelian groups in which

every sub-group is abelian.

Morley, Frank, On the metric geometry of the plane n-line....-■ Orthocentric properties of the plane n-line.-■ Projective coordinates.-On the geometry whose element is the 3-point of a plane...-On reflexive geometry.Morris, R., On the automorphic functions of the group (0, 3 ;

h, h, '»).

Moulton, Forest Ray, On a class of particular solutions of the

problem of four bodies.. ._ .

-A simple non-desarguesian plane geometry.-A class of periodic solutions of the problem of three bodies

with application to the lunar theory.

Neikirk, L. I., Groups of order pm, which contain cyclic sub-

groups of order p™-8 .

Osgood, W. F., On the existence of the Green's function for the

most general simply connected plane region.

-On the existence of a minimum of the integral

2S

24

24

3.34

A

»a

9.

1.

*,54

8,

73

1,-K5.

7<

1.2,

f ' F(x, y, y')dx

when x0 and xx are conjugated points, and the geodesies on

an ellipsoid of revolution : a revision of a theorem of

Kneser ' s..

-On a fundamental property of a minimum in the calculus

of variations and the proof of a theorem of Weierstrass's...

-A Jordan curve of positive area.-On Cantor's theorem concerning the coefficients of a con-

vergent trigonometric series, with generalizations.Peirce, J. M., On certain complete systems of quaternion ex-

pressions, and on the removal of metric limitations from the

calculus of quaternions .

296-330

487459-475

142-158

501485-492

549

179-180

369-378487-512

398-404

97-1151- 12

288-296

467-476

14- 24

425-148

17- 29

499

549

192-195

537-577

316-325

310-314484-485

166-182

273-295

486

500

107-112

10. 337-346

5, 411-420


Pell, Alexander, " D " lines on quadrics. ls 315-322

Pierpont, J., On multiple integrals. 63 416-434-On improper multiple integrals. 7, 155-174-Area of curved surfaces. 74 489-498

Poincare, Henri, Sur les lignes géodésiques des surfaces convexes 6 237-274

Porter, M. B., Sets of coincidence points on the non-singular

cubics of a syzygetic sheaf. 2, 37- 42

Pringsheim, A., Ueber die Anwendung der Cauchy'sehen Multi-

plicationsregel auf bedingt convergente oder divergente

Reihen . 24 404-412-Ueber den Goursat'schen Beweis des Cauchy'schen Inte-

gralsatzes. 24 413-421

Pupin, M. L, Wave propagation over non-uniform electrical] 13 259-286

conductors .1 14 509

Ranum, Arthur, The groups of classes of congruent matrices,

with application to the group of isomorphisms of any

abelian group. 8, 71- 91■-■ Concerning linear substitutions of finite period with rational

coefficients. 9, 183-202

Reed, Frank Walker, On singular points in the approximate

development of the perturbative function . 104 485-509

Richardson, R. G. D., Improper multiple integrals. 7, 449-458-The integration of a sequence of functions and its applica-

tion to iterated integrals. 9, 339-372

Rietz, H. L., On groups in which certain commutative opera-

tions are conjugate. 54 500-508

Roe, E. D., Jr., On the coefficients in the product of an alternant ( 5, 193-213

and a symmetric function. \ 64 564( A fi^_ 74.

-On the coefficients in the quotient of two alternants. j '

Roever, William H., Brilliant points of curves and surfaces... 93 245-279

Royce, J., The relations of the principles of logic to the founda-

tions of geometry. 6, 353—415

Schur, I., Beiträge zur Theorie der Gruppen linearer homogener

Substitutionen. 103 159-175

Schweitzer, Arthur Richard, Note on a system of axioms for

geometry. 103 309-314

Scott, C. A., On a recent method for dealing with the intersec-

tions of plane curves. 3, 216-263-On the circuits of plane curves. 34 388-398-Note on the real inflexions of plane curves. 34 399-400

Sharpe, F. R., On the stability of the motion of a viscous liquid.. 64 496-503

Shaw, James Byrnie, Theory of linear associative algebra. 43 251-287

-On nilpotent algebras. 44 405-422


-Algebras defined by finite groups.-j *

Smith, A. W., The symbolic treatment of differential geometry... 7, 33- 60

Smith, Clara E., A theorem of Abel and its application to the

development of a function in terms of Bessel's functions... 8, 92-106

Smith, Percey F., On surfaces enveloped by spheres belonging

toa linear spherical complex. 14 371-390-Geometry within a linear spherical complex. 23 234-248-On the linear transformations of a quadratic form into

itself. 6, 1- 16

Snyder, Virgil, Surfaces derived from the cubic variety having

nine double points in four-dimensional space. 10, 71- 78

Stäckel, P., Die kinematische Erzeugung von Minimalflächen... 7, 293-313

Stecker, Henry Freeman, On the determination of surfaces

capable of conformai representation upon the plane in

such a manner that geodetic lines are represented by alge- f 2, 152-165

braic curves.I 24 486-Concerning the existence of surfaces capable of conformai

representation upon the plane in such a manner that geodeticlines are represented by a prescribed system of curves. 3, 12-22

Stephens, R. P., On the pentadeltoid. 7, 207-227

Stickelberger, L., Zur Theorie der vollständig reduciblen

Gruppen, die zu einer Gruppe linearer homogener Substitu-

tionen gehören. 74 509-513

Stolz, O., Zur Erklärung der Bogenlänge und des Inhaltes einer ( 3, 23- 37

krummen Fläche. ( 34 500-Nachtrag zum Artikel : " Zur Erklärung der Bogenlänge,

u.s.w." (dieses Bandes, S. 23 f.). 33 302-304

Story, William Edward, Denumerants of double differentiants 8, 33- 70

Stringham, Irving, On the geometry of planes in a parabolicspace of four dimensions. 2, 183-214

Stromquist, C. E., On geometries in which circles are the short-

est lines. 72 175-183

Strong, Wendell M., Note on non-quaternion number systems. 2, 43- 48

Study, Eduard, Zur Differential-geometrie der analytischen

Curven. 10, 1- 49

Taber, H., On hypercomplex number systems (first paper). 54 509-548

Underhill, Anthony Lispenard, Invariants of the function

F(x, y, x', y') in the calculus of variations. 93 316-338

Van Vleck, Edward B., On linear criteria for the determina- f 13 293-309

tion of the radius of convergence of a power series. ( 14 509-On the convergence of continued fractions with complex ( 23 215-233

elements. I 24 486-On the convergence and character of the continued fraction


3,

axz a2z a3z

T +T + T+.-A determination of the number of real and imaginary roots

of the hypergeometric series.-On an extension of the 1894 memoir of Stieltjes. 43-On the convergence of algebraic continued fractions whose

coefficients have limiting values. 53-A proof of some theorems on pointwise discontinuous

functions . 8,-On non-measurable sets of points, with an example., 9,

Veblen, Oswald, A system of axioms for geometry. 53-Theory of plane curves in non-metrical analysis situs. 6,-Definition in terms of order alone in the linear continuum

and in well-ordered sets. 62-the square root and relations of order. 72- (and W. H. Bussey), Finite projective geometries. . 72-Collineations in a finite projective geometry. 83

- fand J. H. Maclagan-Wedderburn) , Non-desarguesian

and non-pascalian geometries. 83-Continuous increasing functions of finite and transfinite

ordinals. 93

Westlund J., On the class number of the cyclotomic number

field h(e2"i/i'n) . 42

White, Henry S., Conies and cubics connected with a planecubic by certain covariant relations. 1,

Plane cubics and irrational covariant cubics.it

-On twisted cu bic curves that have a directrix. 4,

Wilczynski, E. J., An application of group theory to hydro-

dynamics .,

Invariants of systems of linear differential equations.\ '

Ú- Geometry of a simultaneous system of two linear homo

geneous differential equations of the second order.- Reciprocal systems of linear differential equations. 3,- Covariants of systems of linear differential equations and

applications to the theory of ruled surfaces. 34- On a certain congruence associated with a given ruled sur- ( 4,

face. (54- Studies in the general theory of ruled surfaces. 5,- On ruled surfaces whose fiecnode curve intersects every

generator in two coincident points. 54- General theory of curves on ruled surfaces. 6,- General projective theory of space curves. 6,

476-483

110-131

501297-332

253-262

189-204

237-244

343-384

83- 98

165-171

197-199

241-259

366-368

379-388

280-292

201-212

1- 8170-181

508134-141

339-352

5091- 24

486343-362

50060- 70

423-450

185-200

550226-252

438-446

75- 82

99-133

18 INDEX BY AUTHORS.

-Projective differential geometry of curved surfaces (firstmemoir). 8, 233-260

-(second memoir). 9, 79-120-(third memoir). 9, 293-315-(fourth memor). 10, 176-200-(fifth memoir). 10, 279-296

Wilson, Edwin B., The decomposition of the general collinea-

tion of space into three skew reflections. 1, 193-196- Oblique reflections and unimodular strains. 8, 270-298-On the differential equations of the equilibrium of an inex-

tensible string. 94 425-439

Wright, J. E., On differential invariants. 6 286-315-Correspondences and the theory of groups. 73 391-400

Young, Archer Everett, On certain isothermic surfaces. 8, 415-426-On a certain class of isothermic surfaces. 10, 79- 94

Young, John Wesley, On the holomorphisms of a group. 32 186-191-On the group of sign (0, 3 ; 2, 4, oo ) and the functions

belonging toit. 5, 81-104-General theory of approximation by functions involving a

given number of arbitrary parameters. 8, 331-344

INDEX BY SUBJECT MATTER.

A. Logical Analysis of Mathematical Disciplines.

Vol. Pages.

Blichfeldt, H. F., On the determination of the distance be-

tween two points in space of n dimensions. 3 467—481

Dickson, Leonard Eugene, Definitions of a field by independent ( 4 13- 20

postulates.1 5 549-550-Definitions of a linear associative algebra by independent

postulates. 4 21- 26-Definitions of a group and a field by independent postu- f 6 198-204

lates . (.6 547

Huntington, Edward V., A complete set of postulates for the f 3 264-279

theory of absolute continuous magnitude.1 5 549-Complete sets of postulates for the theories of positive inte-

gral and of positive rational numbers. 3 280-284-Two definitions of an abelian group by sets of independent

postulates. . 4 27- 30-Definitions of a field by sets of independent postulates. 4 31- 37-Complete sets of postulates for the theory of real quantities. 4 358-370

f 5 288—309-Sets of independent postulates for the algebra of logic.j ' __

-■ A set of postulates for real algebra, comprising postulates r „ ^ _ ._

for a one-dimensional continuum and for the theory of < „

groups.C-Note on the definitions of abstract groups and fields by sets Í 6 181-197

of independent postulates.1 7 591-A set of postulates for ordinary complex algebra. 6 209-229

Lennes, N. J., Volumes and areas. 6 486-490

Maclagan-Wedderburn, J. H. (and O. Veblen), Non-desar-

guesian and non-pascalian geometries. 8 379-388

Moore, Eliakim Hastings, On the projective axioms of geom- ( 3 142-158

etry. (3 501

-■ A definition of abstract groups.\

-On a definition of abstract groups. 6 179-180

Moore, R. L., Geometry in which the sum of the angles of every

triangle is two right angles. 8 369-378-Sets of metrical hypotheses for geometry. 9 487-512

19

20 INDEX BY SUBJECT MATTER. [October

Moulton, Forest Ray, A simple non-desarguesian plane geom-etry. 3 192-195

Royce, Josiah, The relation of the principles of logic to the

foundations of geometry. 6 353^115

Schweitzer, A. R., Note on a system of axioms for geometry.. 10 309-314

Veblen, Oswald, A system of axioms for geometry. 5 343-384-The square root and the relations of order. 7 197-199

Veblen, O. (and J. H. Maclagan-Wedderburn). Non-desar-

guesian and non-pascalian geometries. 8 379-388

B. Algebra.

B 1. Rational functions. Theory of Equations. Determinants. Symmetric Functions.

Coble, A. B., An application of the form-problems associated

with certain Cremona groups to the solution of equations of

higher degree. 9 396-424

Metzler, W. H., On certain aggregates of determinant minors 2 395-403

Roe, Jr., E. D., On the coefficients in the product of an alter- j 5 193-213

nantand asymmetric function.1 6 546-547

( fi fí"?_ 74--On the coefficients in the quotient of two alternants.\ „ „,„

(6 546

B 2. Algebraic Forms.

(Cf. F 2.)

Dickson, L. E., On quadratic, hermitian, and bilinear forms. 7 275-292

-Invariants of binary forms under modular transformations., -j

-Definite forms in a finite field. 10 109-122-General theory of modular invariants. 10 123-158

-Equivalence of pairs of bilinear or quadratic forms under

rational transformations. 10 347-360

Gordan, Paul, Formentheoretische Entwickelung der in Herrn

White's Abhandlung über Curven dritter Ordnung enthalt-

enen Sätze. 1 9- 13-Die Hessische und die Cay ley'sehe Curve. 1 402-413

Kasner, Edward, The invariant theory of the inversion group ; f 1 430-498

geometry upon a quadric surface. ( 2 485-The cogredient and disgredient theories of multiple binary

forms. 4 86-102

Landry, A. E., A geometrical application of binary syzygies. 10 95-108

Leib, David D., On a complete system of invariants of two

triangles. 10 361-390

McDonald, J. H., On the system of a binary cubic and quadraticand the reduction of hyperelliptic integrals of genus two to

elliptic integrals by a transformation of the fourth order. 2 437-458

8 205-232

8 535

1909] INDEX BY SUBJECT MATTER. 21

Smith, Percey F., On the linear transformations of a quadraticform into itself. 6 1- 16

Story, William Edward, Denumerants of double differentiants. 8 33- 70

B 3. Linear Associative Algebra. Hypereomplex Number Systems.

Fields. (Cf. Fl.)

Allen, R. B., On hypereomplex number systems belonging to

an arbitrary domain of rationality. 9 203-218

Dickson, Leonard Eugene, Definition of a field by independent j

4 13- 20

postulates.1 5 549-550-Definitions of a linear associative algebra by independent

postulates. 4 21- 26-On hypereomplex number systems. 6 344-348-Linear algebras in which division is always uniquely pos-

sible. 7 370-390-On commutative linear algebras in which division is always

uniquely possible. 7 514-522

(4 437-444Epsteen, Saul, Semireducible hypereomplex number systems... jt o ool-On the definition of reducible hypereomplex number systems 5 105-109-

(and J. H. Maclagan-AVedderdurn), On the structure of

hypereomplex number systems. 6 172-178

Hawkes, H. E., On hypereomplex number systems. 3 312-330

Huntington. Edward V., Definitions of a field by sets of inde-

pendent postulates. 4 31- 37

Maclagan-Wedderburn, J. H. (and S. Epsteen), On the

structure of hypereomplex number systems. 6 172-178-A theorem on finite algebras. 6 349-352

Peirce, J. M., On certain complete systems of quaternion ex-

pressions, and on the removal of metric limitations from the

calculus of quaternions. 5 411-420

Shaw, James Byrnie, Theory of linear associative algebra. 4 251-287-On nilpotent algebras. 4 405-422

-Algebras defined by finite groups.j

Strong, Wendell M., Note on non-quaternion number systems 2 43- 48

Taber, H., On hypereomplex number systems (first paper). 5 509-548

B4. Algebra of Logic.

Huntington, Edward V., Sets of independent postulates for the f 5 288-309

algebra of logic. (.5 552

C. Theory of Numbers.

(Cf. El, E2.)

Huntington, Edward V., Complete sets of postulates for the

theories of positive integral and of positive rational numbers 3 280-284


McClintock, E., On the nature and use of the functions em-

ployed in the recognition of quadratic residues. 3 92-109

Westlund, J., On the class number of the cyclotomic number

field fc(e2"*"). 4 201-212

D. Analysis.

D 1. Functions of Real Variables. Point Sets.

Birkhoff, G. D., General mean value and remainder theorems

with applications to mechanical differentiation and quad-rature . 7 107-136

Blichfeldt, H. F., Note on the functions of the form

/(*) = <p(x) + a,*"-1 + a,«'-2 + ---

+ an,

which in a given interval differ the least possible from zero. 2 100-102

Bocher, Maxime, Certain cases in which the vanishing of the

Wronskian is a sufficient condition for linear dependence... 2 139-149-On the regions of convergence of power-series which repre-

sent two-dimensional harmonic functions. 10 271-278

Cajori, Florian, Divergent and conditionally convergent series

whose product is absolutely convergent . 2

Frèchet, Maurice, Sur les opérations linéaires. 5-Sur les opérations linéaires (deuxième note). 6-Sur l'écart de deux courbes et sur les courbes limites. 6

-Sur les opérations linéaires (troisième note). 8

Hedrick, E. R., On derivatives over assemblages. 8

Heffter, L., Ueber Curvenintegrale in m-dimensionalen Raum. 4

Huntington, Edward V., A complete set of postulates for the f 3

theory of absolute continuous magnitude.1 5-Complete sets of postulates for the theory of real quantities. 4

Moore, Eliakim Hastings, On certain crinkly curves.\

-Concerning Harnack's theory of improper definite inte. J 2

grals. 1 2-On the theory of improper definite integrals. 2

Osgood, W. F. A., A Jordan curve of positive area. 4-On Cantor's theorem concerning the coefficients of a con-

vergent trigon ometric series, with generalizations. 10

Pierpont, James, On multiple integrals... 6-On improper multiple integrals. 7-Area of curved surfaces. 7

Pringsheim, A., Ueber die Anwendung der Cauchy'schen Multi-

plicationsregel auf bedingt convergente oder divergente

Reihen. 2

Richardson, R. G. D., Improper multiple integrals. 7

25- 36

493^99

134-140

435-449

433-446

345-353

142-148

264-279

349

358-370

72- 90

507

296-330

487

459-475

107-112

337-346

416-434

155-174

489-498

404^12

449-458


-The integration of a sequence of functions and its applica-

tion to iterated integrals. 9 339-372

Smith, Clara E., A theorem of Abel and its application to the

development of a function in terms of Bessel's functions. 8 92-106

Stolz, 0., Zur Erklärung der Bogenlänge und des Inhaltes einer ( 3 23- 37

krummen Fläche.1 3 500-Nachtrag zum Artikel : " Zur Erklärung der Bogenlänge,

u.s.w." (dieses Bandes, S. 23 f.). 3 302-304

Van Vleck, E. B., A proof of some theorems on pointwise dis-

continuous functions. 8 189-204-On non-measurable sets of points, with an example. 9 237-244

Veblen, Oswald, Definition in terms of order alone in the

linear continuum and in well-ordered sets. 6 165-171-Continuous increasing functions of finite and transtinite

ordinals. 9 280-292

Young, J. W., General theory of approximation by functions

involving a given number of arbitrary parameters. 8 331-344

D 2. Functions of Complex Variables.


realized by linkages. 3 493-498

Ford, W. B., On the analytic extension of functions defined by

double power series. 7 260-274

Goursat, E., Sur la définition générale des fonctions analytiques,

d'après Cauchy. 1 14- 16

Moore, Charles N., On the introduction of convergence factors J 8 299-330

into summable series and summable integrals.1 8 535

Moore, Eliakim Hastings, A simple proof of the fundamental f 1 499-506

Cauchy-Goursat theorem. I 2 486

Osgood, W. F., On the existence of the Green's function for the f 1 310-314

most general simply connected plane region.1 2 484-485

Pringsheim, A., Ueber den Goursat'sehen Beweis des Cauchy'

sehen Integralsatzes. 2 413-421

Van Vleck, Edward B., On linear criteria for the determina- ( 1 293-309

tion of the radius of convergence of a power series. (.1 509- On the convergence of continued fractions with complex f 2 215-233

.dements. 12 486- On the convergence and character of the continued fraction

T + Ï+¥+•••. 2 476-483

- On an extension of the 1894 memoir of Stieltjes. 4 297-332- On the convergence of algebraic continued fractions whose

coefficients have limiting values. 5 253-262


D 3. Particular Functions.

Bolza, Oskar, The elliptic <r-functions considered as a special f 1 53- 65

case of the hyperelliptic a-I unctions.1 2 484

Dickson., L. E., The minimum degree t of resolvents for the p-sec-tion of the periods of hyperelliptic functions of two periods. 6 48- 57

Fields, J. O, On the reduction of the general abelian integral., i12 48o

Ford, W. B., On the possibility of differentiating term by term

the developments for an arbitrary function of one real vari-

able in terms of Bessel functions. 4 178-184

Greenhill, Alfred George, The elliptic integral in electromag-

netic theory. 8 447-534

Hutchinson, J. I., On certain relations among the theta con-

stants. 1 391-394-On a class of automorphic functions. 3 1- 11-On the automorphic functions of the group (0, 3 ; 2, 6, 6).. 5 447-460-On certain hyperabelian functions which are expressible by

theta series. 7 21- 25-The hypergeometric functions of n variables. 10 61- 70

Krause, Martin, Ueber Systeme von Differentialgleichungen

denen vierfach periodische Functionen Genüge leisten. 1 287-292

McDonald, J. H., On the system of a binary cubic and quad-ratic and the reduction of hyperelliptic integrals of genustwo to elliptic integrals by a transformation of the fourth

order . 2 437-458-A problem in the reduction of hyperelliptic integrals. 7 578-587

Mason, Max, the expansion of a function in terms of normal

functions. 8 427-432

Mertens, F., Zur linearen Transformation der 0-Reihen. 2 331-342

Moore, Charles N., The summability of the developments in

Bessel functions, with applications. 10 391-435

Morris, Richard, On the automorphic functions of the group

(0, 3-lvl2, ls). 7 425-448

Van Vleck, Edward B., A determination of the number off 3 110-131

real and imaginary roots of the hypergeometric series.1 3 501

Young, John Wesley, On the group of sign (0, 3 ; 2, 4, oo )and the functions belonging to it. 5 81-104

D 4. Ordinary Differential Equations.

(Cf. D3, F 4.)

Birkhoff, George D., On the asymptotic character of the solu-

tions of certain differential equations containing a parameter. 9 219-231-Boundary values and expansion problems of ordinary linear

differential equations. 9 373-395


-Existence and oscillation theorem for a certain boundary-

value problem. 10 259-270-Singular

points of ordinary linear differential equations_ 10 436-470

Bliss, Gilbert Ames, An existence theorem for a differential

equation of the second order, with an application to the cal-

culus of variations._ 5 113-125

Bocher, Maxime, On regular singular points of linear diffe ren-

tial equations of the second order whose coefficients an not J

1 40- 52

necessarily analytic. ( 1 507

-Application of a method of D'Alembert to the proof of

Sturm's theorems of comparison. 1 414-420

-An elementary proof of a theorem of Sturm. 2 150-151

-On certain pairs of transcendental functions whose roots

separate each other. 2 428-436-On the real solutions of systems of two homogeneous linear

differential equations of the first order. 3 196-215

Curtiss, D. R., Theorems converse to Riemann's on linear dif-

ferential equations. 7 99-106

Loewy, Alfred, Zur Gruppentheorie mit Anwendungen auf die

Theorie der linearen homogenen Differentialgleichungen. 5 61- 80

Mason, Max, On the boundary value problems of linear ordinary

differential equations of second order. 7 337-360

Merrill, Helen A, On solutions of differential equations which J 4 423-433

possess an oscillation theorem . (5 551

Wilczynski, E. J., Invariants of systems of linear differential j 2 1- 24

equations . (2 486

-Covariants of systems of linear differential equations and

applications to the theory of ruled surfaces. 3 423-450

D 5. Partial Differential Equations.

Campbell, J. E., On the types of linear partial differential equa-

tions of the second order in three independent variables

which are unaltered by the transformations of a continuous J 1 243-258

group.1 1 509

Kellogg, O. D., Potential functions on the boundary of their

regions of definition. 9 39- 50-Double distribution and the Dirichlet problem. 9 51- 66

Mason, Max, Green's theorem and Green's functions for certain

systems of differential equations. 5 220-225-The doubly periodic solutions of Poisson's equation in two

independent variables. 6 159-164

D 6. Differential Forms.

Haskins, Charles; Nelson, On the invariants of quadratic dif- f 3 71- 91

ferential forms.1 3 501

26 index by subject matter. [October

-On the invariants of differential forms of degree higher than

two.-On the invariants of quadratic differential forms, II.

-Note on the differential invariants of a surface and of space-On the differential invariants of a plane.Maschke, Heinrich, A new method of determining the differ-

ential parameters and invariants of quadratic differential

quantics.-A symbolic treatment of the theory of invariants of quad-

ratic differential quantics of n variables.

-Differential parameters of the first order.

Smith, A. W., The symbolic treatment of differential geometry

Wright, J. E., On differential invariants.

4

5

77

1

1

4

7.77

6

38- 43

167-192

152-154

588-590

197-204

508

445-469

69- 80

591

33- 60

286-315

D 7. Calculus of Variations.

Bliss, Gilbert Ames, The second variation of a definite integral

when one-end point is variable. 3

-An existence theorem for a differential equation of the sec-

ond order, with an application to the calculus of variations 5

-Sufficient condition for a minimum with respect to one-

sided variations. 5

-A generalization of the notion of angle. 7

- (and Max Mason), A problem of the calculus of varia-

tions in which the integrand is discontinuous . 7

-A new form of the simplest problem of the calculus of ( 8

variations. (.8-(and Max Mason), The properties of curves in space which

minimize a definite integral. 9

Bolza, O., New proof of a theorem of Osgood's in the calculus

of variations. 2

-Proof of the sufficiency of Jacobi's condition for a perma-nent sign of the second variation in the so-called isoperi-

metric problems. 3

-A fifth necessary condition for a strong extremum of the

integral I F(x, y, y')dx. 7

-Weierstrass's theorem and Kneser's theorem on transversals

for the most general case of an extremum of a simple definite

integral. 7

-Existence proof for a field of extremals tangent to a given

curve. 8

Dresden, Arnold, The second derivatives of the extremal-

integral . 9

132-141

113-125

477-492

184-196

325-336

405-414

536

440-466

422-427

305-311

314-324

459-488

399-404

467-


Goursat, E., A simple proof of a theorem in the calculus of

variations. 5 110-112

Mason, Max (and G. A. Bliss), The properties of curves in

space which minimize a definite integral. 9 440-466

Osgood, W. F., On the existence of a minimum of the integral

f F(x, y, y')dx

when a, and xx are conjugate points, and the geodesies on an

ellipsoid of revolution : a revision of theorem of Kneser's 2 166-182

c 2 273—295-On a fundamental property of a minimum in the calculus \ _

of variations and the proof of a theorem of Weierstrass's... ( „ .

Stromquist, O E., On geometries in which circles are the short-

est lines. 7 175-183

Underhill, A. L., Invariants of the function F(x.y,x',y') in the

calculus of variations. 9 316-338

D 8. Difference Equations.

Ford, W. B., On the integration of the homogeneous linear dif-

ference equation of second order. 10 319-336

E. Groups.

E 1. Diserete Groups in General.

(Cf. E2.)

Coble, A. B., An application of the form-problems associated

with certain Cremona groups to the solution of equations of

higher degree. 9 396-424

Cole, F. N., The groups of order pY. 5 214-219

Dickson, Leonard Eugene, Determination of all the subgroups f 5 126-166

of the known simple group of order 25920.1 5 551-The minimum degree t of resolvents for the p-section of the

periods of hyperelliptic functions of four periods. 6 48-57-On semi-groups and the general isomorphism between infi-

nite groups. 6 205-208-Modular theory of group-matrices. 8 389-398

Findlay, William, The Sylow subgroups of the symmetric

group. 5 263-278

Fite, W. B., On metabelian groups. 3 331-353-Groups whose orders are powers of a prime. 7 61- 68

Glenn, E. O., Determination of the abstract groups of order

p2qr ; p, q, r being distinct primes. 7 137-151

Huntington, Edward V-, Two definitions of an abelian groupby sets of independent postulates. 4 27- 30


Manning, W. A., The primitive groups of class 2p which con-

tain a substitution of orderp and degree 2p. 4 351-357-On the primitive groups of class 3p. 6 42- 47-Groups in which a large number of operators may corre-

spond to their inverses . 7 233-240-On multiply transitive groups. 7 499-508-On the order of primitive groups. 10 247-258

Miller, G. A., On the groups which are the direct products of

two subgroups. 1 66- 71-On the groups which have the same group of isomorphisms. 1 395-401

-Determination of all the groups of order pm which contain ( 2 259-272

the abelian groups of type (m — 2, 1), p being any prime.... ( 3 499-500-On the groups of order pm which contain operators of order

pm-2. 3 383-387-On the holomorph of a cyclic group. 4 153-160-(and H. C. Moreno), Non-abelian groups in which every

subgroup is abelian. 4 398-404-Determination of all the groups of order 2™ which contain

an odd number of cyclic subgroups of composite order. 6 58- 62

-On the invariant subgroups of prime index . 6 326-331-Groups containing only three operators which are squares... 7 94- 98

-The groups of order pm which contain exactly p cyclic sub-

groups of order p«. 7 228-232

-Generalization of the groups of genus zero.\ _ '

-The groups in which every subgroup is either abelian or

hamiltonian . 8 25- 29-Groups defined by the orders of two generators and the

order of their commutator. 9 67— 78-On the holomorph of the cyclic group of order p". 9 232-236-The central of a group. 10 50- 60-Automorphisms of order two . 10 471-478

Moore, Eliakim Hastings, A definition of abstract groups. -j

Moreno, H. C. (and G. A. Miller), Non-abelian groups in

which every subgroup is abelian. 4 398-404

Neikirk, L. I., Groups of order p", which contain cyclic sub-

groups of order p"'-3. 6 316-325

Rietz, B. L., On groups in which certain commutative opera-

tions are conjugate. 5 500-508

Shaw, James Byrnie, Algebras defined by finite groups. \

Young, John Wesley, On the holomorphisms of a group. 3 186-191


E 2. Linear Groups in Arbitrary or Special Fields.

Blichfeldt, H. F., On the order of linear homogeneous groups. 4 387-397-On the order of linear homogeneous groups (second paper). 5 310-325

-A theorem concerning the invariants of linear homogeneous f 5 461-466

groups, with some applications to substitution groups. I 6 546

-On imprimitive linear homogeneous groups. 6 230-236

-On the order of linear homogeneous groups (supplement).. 7 523-529

-On modular groups isomorphic with a given linear group.. 8 30- 32

Dickson, Leonard Eugene, Definition of the abelian, the two

hypoabelian, and related linear groups, as quotient-groups of

the groups of isomorphisms of certain elementary groups. 1 30- 38

-A new definition of the general abelian linear group. 1 91- 96-Determination of an abstract simple group of order 2'36'57

holoedrically isomorphic with a certain orthogonal group and J 1 353-370

with a certain hyperabelian group. 11 509-Canonical forms of quaternary abelian substitutions in an f 2 103-138

arbitrary Galois field.I 3 499

-Theory of linear groups in an arbitrary field.j

-The groups of Steiner in problems of contact.\t o oOO

-On the group defined for any given field by the multiplica-

tion table of any given finite group. 3 285-301-The groups of Steiner in problems of contact (second

papera. 3 377-382-On the subgroups of order a power of p in the quaternary j

4 371-386

abelian group in the Galois field of order p". ( 5 550-551-On the reducibility of linear groups. 4 434-436-The subgroups of order a power of 2 of the simple quinary j 5 1-38

orthogonal group in the Galois field of order p" = 81 ± 3.1 5 551-Representations of the general symmetric group as linear

groups in finite and infinite fields. 9 121-148

Epsteen, Saul, On reducible groups. 4 249-250

Fite, W. B., Irreducible linear homogeneous groups whose orders

are powers of a prime. 8 107-112-Irreducible homogeneous linear groups in an arbitrary do-

main. 10 315-318

Hutchinson, J. I., On automorphic groups whose coefficients

are integers in a quadratic field. 7 530-536-A method for constructing the fundamental region of a dis-

continuous group of linear transformations. 8 261-269

Loewy, Alfred, Ueber die Reducibilität der Gruppen linearer

homogener Substitutionen. 4 44- 64-Ueber die Reducibilität der reellen Gruppen linearer homo-

gener Substitutionen. 4 171-177


-Zur Gruppentheorie mit Anwendungen auf die Theorie der

linearen homogenen Differentialgleichungen. 5 61- 80

-Ueber die vollständig reducibleu Gruppen, die zu einer

Gruppe linearer homogener Substitutionen gehören. 6 504-533

Ranum, Arthur, The groups of classes of congruent matrices,

with applications to the group of isomorphisms of any

abeliangroup. 8 71-91-■ Concerning linear substitutions of a finite period with ra-

tional coefficients. 9 183-203

Schur, I., Beiträge zur Theorie der Gruppen linearer homogener

Substitutionen. 10 159-175

Stickelberger, Ludwig, Zur Theorie der vollständig reduciblen

Gruppen, die zu einer Gruppe linearer homogener Substitu-

tionen gehören. 7 509-513

E 3. Continuous Groups.

(Cf. E2, FI, F3, G3.)

Blichfeldt, H. F., A new determination of the primitive con-

tinuous groups in two variables. 2 249-258

Campbell, J. E., On the types of linear partial differential equa-

tionsof the second order inthree independent variables which < 1 243-258

are unaltered by the transformations of a continuous group ( 1 509

Coble, A. B., On the relation between the three-parameter groupsof a cubic space curve and a quadric surface.,. 7 1- 20

Hartwell, G. W-, Plane fields of force whose trajectories are

invariant under a projective group. 10 220-246

F. Geometry.

Fl. Synthetic Geometry. Non-Euelidian Geometry. Geometry of n dimensions.

Analysis Situs.

(Cf. Dl, D2.)

Blichfeldt, H. F., On the determination of the distance be-

tween two points in space of n-dimensions. 3 467-481

Bliss, G. A., A generalization of the notion of angle. 7 184-196

Bussey, W. H. and Veblen, O., Finite projective geometries.... 7 241-259

Carver, W. B., On the Cayley-Veronese class of configuration.. 6 534-545

Coolidge, Julian Lowell, A purely geometric representation

of all points in the projective plane. 1 182-192-Quadric surfaces in hyperbolic space. 4 161-170

Hathaway, A. S., Quaternion space. 3 46- 59

Lehmer, D. N., Constructive theory of the unicursal cubic by

synthetic methods. 3 372-376


Levi, Beppo, Geometrie proiettive di congruenza e géométrie

proiettive finite. 8 354-365

Maschke, Heinrich, Note on the unilateral surface of Moebius. 1 39

Moore, Eliakim Hastings, On the projective axioms of geom- ( 3 142-158

etry. (3 501

Morley, Frank, Projective coordinates. 4 288-296

Moulton, Forest Ray, A simple non-desarguesian plane geom-etry. 3 192-195

Peirce, J. M., On certain complete systems of quaternion expres-

sions, and on the removal of metric limitations from the

calculus of quaternions. 5 411-420

Snyder, Virgil, Surfaces derived from the cubic variety having

nine double points in four dimensional space. 10 71 - 78

Stringham, Irving, On the geometry of planes in a parabolicspace of four dimensions. 2 183-214

Veblen, Oswald, A system of axioms for geometry. 5 343-384-■ Theory of plane curves in non-metrical analysis situs. 6 83- 98

- (and W. H. Bussey), Finite projective geometries. 7 241-259-■ Collineations in a finite projective geometry. 8 366-368

F 2. Algebraic Geometry; Algebraic Curves and Surfaces.

(Cf. B 2, D 3, E 2, F 1, F 4, F 5.)

Allardice, R. E., On the envelope of the axes of a system of

conies passing through three fixed points. 4 103-106

Bromwich, T. J. t'a., Similar conies through three points. 4 489-492-The classification of quadrics. 6 275-285

Coble, A. B., The quartic curve as related to conies. 4 65- 85

Dentón, William Wells, On the osculating quartic of a planecurve. 10 297-308

Field, Peter, On the form of a plane quintic curve with five

cusps. 7 26- 32

Gale, Arthur Sullivan, On the rank, order and class of alge-

braic minimum curves. 3 451-466

Hun, John Gale, On certain invariants of two triangles. 5 39- 55

Loud, Frank H, Sundry metric theorems concerning w-lines in

aplane. 1 323-338

Macaulay, F. S., On a method of dealing with the intersections

of plane curves. 5 385-410

Morley, Frank, On the metric geometry of the plane n-line. 1 97-115-Orthocentric

properties of the plane n-line. 4 1- 12-On the geometry whose element is the 3-point of a plane.. 5 467-476

-On reflexive geometry. 8 14- 24

Porter, M. B., Sets of coincidence points on the non-singular

cubics of a syzygetic sheaf. 2 37- 42


Roever, W. H., Brilliant points of curves and surfaces. 9 245-279

Scott, C. A., On a recent method for dealing with the intersec-

tions of plane curves. 3 216-263-On the circuits of plane curves. 3 388-398-Note on the real inflexions of plane curves. 3 399-400

Stephens, R. P., On the pentadeltoid. 7 207-227

White, Henry S., Conies and cubics connected with a planecubic by certain covariant relations. 1 1-8

-Plane cubics and irrational covariant cubics.\\ X Ovo

-On twisted cubic curves that have a directrix. 4 134-141

F 3. Geometry of Special Space-Elements.

Kasner, E., On the point-line as element of space ; a study of ( 4 213-233

the corresponding bilinear connex. 15 550

Morley, Frank, On the geometry whose element is the 3-point

of aplane. 5 467-476

Smith, Percey F., On surfaces enveloped by spheres belonging

to a linear spherical complex. 1 371-390-Geometry within a linear spherical complex. 2 234-248

F 4. Differential Geometry.

(Cf. D6.)

Eisenhart, Luther Pfahler, Conjugate rectilinear congruences 3 354-371-Congruences of curves. 4 470-488-Three particular systems of lines on a surface. 5 421-437

-Surfaces of constant curvature and their transformations.. 6 472-485

-Applicable surfaces with asymptotic lines of one surface f 8 113-134

corresponding to a conjugate system of another. ( 8 535

-Surfaces with isothermal representation of their lines of

curvature and their transformations. 9 149-177


surface connected with Euler's transformation. 6 450-471

Hilbert, David, Ueber Flächen von constanter Gaussscher

Krümmung. 2 87- 99

Kasner, Edward, The generalized Beltrami problem concerning ( 4 149-152

geodesic representation. 15 550

-Isothermal systems of geodesies. 5 56- 60

-Surfaces whose geodesies may be represented in the planebyparabolas. 6 141-158

-The problem of partial geodesic representation. 7 200-206

Maschke, Heinrich, On superosculating quadric surfaces. 3 482-484

-The Kronecker-Gaussian curvature of hyperspace. 7 81-93

Pell, Alexander, "D" lines on quadrics. 1 315-322


Poincaré, Henri, Sur les lignes géodésiques des surf aces con vexes 6 237-274

Smith, A. W., The symbolic treatment of differential geometry 7 33- 60

Stäckel, Paul, Die kinematische Erzeugung von Minimalflächen 7 293-313

Stecker, Henry Freeman, On the determination of surfaces

capable of conformai representation upon the plane in such

a manner that geodetic lines are represented by algebraic (2 152-165

curves. (2 486-Concerning the existence of surfaces capable of conformai

representation upon the plane in such a manner that geodeticlines are represented by a prescribed system of curves. 3 12- 22

Stromquist, C. E., On geometries in which circles are the shortest

lines. 7 175-183

Study, Eduard, Zur Differentialgeometrie der analytischen

Curven. 10 1- 49

WiLCZYNSKi, E. J., Geometry of a simultaneous system of two

linear homogeneous differential equations of the second ( 2 343-362

order. (3 500-Reciprocal systems of linear differential equations. 3 60- 70-Covariants of systems of linear differential equations and

applications to the theory of ruled surfaces. 3 423-450-On a certain congruence associated with a given ruled ( 4 185-200

surface .1 5 550-Studies in the general theory of ruled surfaces. 5 226-252-On ruled surfaces whose flecnode curve intersects every

generator in two coincident points. 5 438-446-General theory of curves on ruled surfaces . . 6 75- 82-General projective theory of space curves. . 6 99-133-Projective differential geometry of curved surfaces (first

memoir). 8 233-260-(Second memoir) . 9 79-120-(Third memoir). 9 293-315-■- (Fourth memoir). 10 176-200-(Fifth memoir). 10 279-296

Young, Archer Everett, On certain isothermic surfaces. 8 415-426-On a certain class of isothermic surfaces. 10 79- 94

F 5. Geometric Transformation. Geometry of Motion.

(Cf. E2.)

Blake, E. M., Two plane movements generating quartic scrolls 1 421-429

Coolidge, Julian Lowell, The equilong transformations of

space. 9 178-182


surface connected with Euler's transformation. 6 450-471



realized by linkages . 3 493-498

Hartwell, George Wilbur, Plane fields of force whose tra-

jectories are invariant under a projective group. 10 220-246

Haskell, M. W., The resolution of any collineation into per-spective reflections. 7 361-369

Jackson, Dunham, Resolution into involutory substitutions of

the transformations of a non-singular bilinear form into

itself. 10 479-484

Wilson, Edwin B., The decomposition of the general collinea-

tion of space into three skew reflections. 1 193-196

-Oblique reflections and unimodular strains. 8 270-298

Wright, J. E., Correspondences and the theory of groups. 7 391-400

G. Applied Mathematics.

G 1. General Mechanics.

Brown, Ernest William, On the variation of the arbitrary and

given constants in dynamical equations.

-On a general method for treating transmitted motions and

its application to indirect perturbations. 6

Chessin, Alexander S., On relative motion. 1

Griffin, Frank Loxley, Certain periodic orbits of k finite

bodies revolving about a relatively large central mass. 9

Kasner, Edward, The trajectories of dynamics. 7

-Dynamical trajectories : the motion of a particle in an arbi-

trary field of force. 8

-Natural families of trajectories : conservative fields of f 10

force . (10

Longley, William Raymond, A class of periodic orbits of an J 8

infinitesimal body subject to the attraction of n finite bodies l 8

Lovett, E. O., On a problem including that of several bodies

and admitting of an additional integral. 6

Moulton, Forest Ray, A class of periodic solutions of the prob-

lem of three bodies with applications to the lunar theory ... 7

G 2. Celestial Mechanics.

Brown, Ernest William, On the small divisors in the lunar

theory. 3

-On the formation of the derivatives of the lunar coordinates

with respect to the elements. 4

-On tue variation of the arbitrary and given constants in

dynamical equations. 4

-On the smaller perturbations of the lunar arguments.\

333-350

332-343

116-169

1- 33

401-424

135-158

iOl-219

510

159-188

535

491-495

537-577

159-185

234-248

333-350

279-287

551


Hill, G. W., On the extension of Delaunay's method in the f 1 205-242

lunar theory to the general problem of planetary motion_11 508-509

C 1 17— 29Moulton, Forest Ray, On a class of particular solutions of the \

problem of four bodies. ) „ _.„V 5 549

Reed, Frank Walker, On singular points in the approximate

development of the perturbative function. 10 485-509

G 3. Elasticity, Hydromechanics and Sound.

Darwin, G. H., The approximate determination of the form of

Maclaurin's spheroid. . 4 113-133-Further note on Maclaurin's spheroid. 9 34- 38

Hadamard, J., La théorie des plaques élastiques planes. 3 401-422

Sharpe, F. R., On the stability of the motion of a viscous liquid 6 496-503

Wilczynski, E. J., An application of group theory to hydro-f 1 339-352

dynamics.1 1 509

Wilson, Edwin Bidwell, On the differential equations of the

equilibrium of an inextensible string. 9 425-439

G 4. Electricity, Light, and Heat.

Greenhill, Alfred George, The elliptic integral in electromag-

netic theory. 8 447-534

Pupin, M. I., Wave propagation over non-uniform electrical f 1 259-286

conductors. 1 1 509

Documents

American Mathematical Society · TRANSACTIONS OF THE American Mathematical Society Volumes 1-10 1900 - 1909 Indices PUBLISHED BY THE SOCIETT Lancaster, Pa., and Nbw York