TRANSACTIONS

OF THE American Mathematical Society

EDITED BY

EEIAKIM HASTINGS MOORE

EBNEST WILLIAM BROWN THOMAS SCOTT FISKE

WITH THE COOPERATION OF

EDWARD BURR VAN VLECK HENRY SEELY WHITE CHARLES LEONARD BOUTON JOHN IRWIN HUTCH1NSON EDWARD KASNER EDWIN BIDWELL WILSON

Published quarterly hy the Society with the support of

Harvard University Northwestern University Yale University Cornell University Columbia University The Universität of California Wesleyan University Bryn Mawr College Haverford College The University' of Chicago

Volume 5 1904

Lancaster, Pa., and New York THE MACMILEAN COMPANY Agents for the Society 1901

Reprinted with the permission of The American Mathematical Society Johnson Reprint Corporation 111 Fifth Avenue, New York 3, N. Y.

Johnson Reprint Company Limited Berkeley Square House, London, W. 1 First Reprinting, 1963, Johnson Reprint Corporation TAELE OF CONTENTS

VOLUME 5 1904. PAGES Blichfeldt, H. F., of Stanford University, Cal. On the order of linear homogeneous groups (second paper).310-325 _ A theorem concerning the invariants of linear homo- geneous groups, with some applications to substitution groups 461-466 Bliss, G. A., of Columbia, Mo. An existence theorem for a differ- ential equation of the second order, with an application to the calculus of variations.113-125 _Sufficient condition for a minimum with respect to one-sided variations.477-492 Brown, E. W., of Haverford, Pa. On the smaller perturbations of the lunar arguments.279-287 Cole, F. N., of New York, N. Y. The groups of order fq» . . 214-219 Dickson, L. E., of Chicago, 111. The subgroups of order a power of 2 of the simple quinary orthogonal groups in the Galois field of ordery = 8Z±3. 1-38 _ Determination of all the subgroups of the known sim- ple group of order 25920.126-166 Eisenhart, L. P., of Princeton, N. J. Three particular systems of lines on a surface.421*437 Epsteen, S., of Chicago, 111. On the definition of reducible hyper- complex number systems.105-109 Findlay, W., of New York, N. Y. The Sylow subgroups of the symmetric group.263-278 Fréchet, M., of Paris, France. Sur les opérations linéaires . . 493-499 Goursat, E., of Paris, France. A simple proof of a theorem in the calculus of variations. (Extract from a letter to Mr. W. F. Osgood.).110-112 Haskins, C. N., of Ithaca, N. Y. On the invariants of quadratic differential forms, II.167-192 Hun, J. G., of Princeton, N. J. On certain invariants of two tri-

angleso . 39- 55 Huntington, E. V., of Cambridge, Mass. Sets of independent postulates for the algebra of logic.288-309 Hutchinson, J. I., of Ithaca, N. Y. On the automorphic functions of the group (0, 3; 2, 6, 6).447-460 iv TABLE OF CONTENTS

PAGES Kasner, E., of New York, N. Y. Isothermal systems of geodesies. 56- 60 Loewy, A., of Freiburg, i. B., . Zur Gruppentheorie mit Anwendungen auf die Theorie der linearen homogenen Differen- tialgleichungen .,. 61-80 Macaulay, F. S., of London, England. On a method of dealing with the intersections of plane curves.385—410 Mason, Max, of New Haven, Conn. Green's theorem and Green's functions for certain systems of differential equations . . . 220—225 Morley, F., of Baltimore, Md. On the geometry whose element is the 3-point of a plane.467-476 Peirce, J. M., of Cambridge, Mass. On certain complete systems of quaternion dxpressions, and on the removal of metric limita- tions from the calculus of quaternions.411-420 Rietz, H. L., of Urbana, 111. On groups in which certain commu- tative operations are conjugate.500—508 Boe, E. D., Jr., of Syracuse, N. Y. On the coefficients in the prod- uct of an alternant and a symmetric function.193-213 Shaw, J. B., of Decatur, 111. Algebras denned by finite groups . 326-342 Taber, H., of Worcester, Mass. On hypercomplex number systems (first paper).509-548 Van Vleck, E. B., of Middletown, Conn. The convergence of alge- braic continued fractions whose coefficients have limiting values. 253-262 Veblen, O., of Chicago, 111. A system of axioms for geometry . 343-384 Wilczynski, E. J., of Berkeley, Cal. Studies in the general theory of ruled surfaces.226-252 _ On ruled surfaces whose flecnode curve intersects every generator in two coincident points.438-446 Young, J. W., of Evanston, 111. On the group of the sign (0,3; 2,4, oo) and the functions belonging to it.81-104 Notes and errata : volumes 1, 3, 4, 5.549-552 INDEX BY AUTHOKS.

Vol.* Pages. Class.! Allardice, K. E., On the envelope of the axes of a sys- tem of conies passing through three fixed points. 4, 103-106 F 2 Blake, E. M., Two plane movements generating quartic scrolls. 14 421-429 F5 Blichfeldt, H. F., Note on the functions of the form f(x) =

-On certain pairs of transcendental functions whose roots separate each other. 2. 428-436 D4 -On the real solutions of systems of two homogeneous linear differential equations of the first order. 196-215 D4 Bolza, Oskar, The elliptic «--functions considered as a 53- 65 D3 special case of the hyperelliptic «--functions_. 484 -New proof of a theorem of Osgood's in the calculus of variations. 2, 422-427 D 7 -Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so- called isoperimetric problems. 33 305-311 D7 Bromwich, T. J. I'a., Similar conies through three points 489-492 F 2 Brown, Ernest AVilliam, On the small divisors in the 1unar theory. 159-185 G 2 -On the formation of the derivatives of the lunar co- ordinates with respect to the elements. . 4. 234-248 G 2 -On the variation of the arbitrary and constants Gl given 333-350 in dynamical equations. G2 279-287 G 2 -On the smaller of the lunar arguments perturbations 551 Cajori, Florian, Divergent and conditionally convergent series whose product is absolutely convergent. 25- 36 Dl Campbell, J. E., On the types of linear partial differen- tial equations of the second order in three inde- variables which are unaltered by the trans- 243-258 D 5 pendent j formations of a continuous group. 509 1 E 3 Chessin, Alexanders., On relative motion. 116-169 G1 Coble, A. B., The quartic curve as related to conies. 65- 85 F 2 Cole, F. N., The groups of order ps

• 363-394 E2 -Theorymi of«it linear in an arbitraryu*~ *field.i m í2< groups (. o. 000 C Ql S8— 45 F 2 -The groups of Steiner in problems of contact.\ -On the group defined for any given field by the multi- plication table of any given finite group. 33 285-301 E 2 -The groups of Steiner in problems of contact (second paper). 33 377-382 E2 -Definitions field independent ' of a by postulates.j _ _ j_„ -Definitions of a linear associative algebra by inde- A ' j pendent postulates. I B3 -On the subgroups of order a power of p in the qua- f 44 371-386 E 2 ternary abelian group in the Galois field of order p"... ( 54 550-551 -On the reducibility of linear groups. 44 434-436 E2 -The subgroups of order a power of 2 of the simple quinary orthogonal group in the Galois field of order f 5, 1-38 E 2 p"=8Z±3 . (54 551 -Determination of all the subgroups of the known f 52 126-166 E1 simple group of order 25920. I 54 551 Eisenhart, L. P., Conjugate rectilinear congruences. 3S 354-371 F4 -Congruences of curves. 44 4/0-488 F4 -Three particular systems of lines on a surface. 54 421-437 F4 Emch, Arnold, Algebraic transformations of a complex f F 5 variable realized by linkages. * 1 D2 Epsteen, Saul, On reducible groups. . 43 249-250 E2 137 111 B 3 {4 -On the definition of reducible hypercomplex number systems . 5, 105-109 B3 Fields, J. C., On the reduction of the general abelian J 2, 49- 86 D 3 integral.t 24 486 Findlay, William, The Sylow subgroups of the sym- metric group. 5S 263-278 El Fite, AV. B., On metabelian groups. 33 331-353 El Ford, AV. B., On the possibility of differentiating term by term the developments for an arbitrary function of one real variable in terms of Bessel functions. 42 178-184 D3 Fréchet, M., Sur les opérations linéaires. 54 493-499 Dl Gale, Arthur Sullivan, On the rank, order and class of algebraic minimum curves. 34 451-466 F 2 Gordan, Paul, Formentheoretische Entwickelung der in Herrn AVhite's Abhandlung über Curven dritter Ord- nung enthaltenen Sätze. lx 9- 13 B2 8 INDEX BY AUTHORS [October

-Die Hessische und die Cayley'sche Curve. 14 402-413 B2 Goursat, E., Sur la définition générale des fonctions analytiques, d'après Cauchy. 1, 14-16 D2 -A simple proof of a theorem in the calculus of varia- tions. 5, 110-112 D7 Hadamard, J., La théorie des plaques élastiques planes.. 34 401-422 G3 Haskins, Charles Nelson, On the invariants of quad- ( 3, 71- 91 D6 ratic differential forms. ( 34 501 -On the invariants of differential forms of degree higher than two. 4, 38-43 DO -On the invariants of quadratic differential forms, IL, 5, 167-192 D6 Hathaway, A. S., Quaternion space. 3, 46- 5S) FI Hawkes, H. E., On hypercomplex number systems . 3, 312-330 .153 Heffter, L., TJeber Curvenintegrale im m-dimensionalen Kaum. 4, 142-148 l'i Hilbert, David, Ueber Flächen von constan ter Gauss- scher Krümmung. 2, 87-99 F4 Hill, G. W., On the extension of Delaunay's method in the lunar theory to the general problem of planetary ( 1, 205-242 ( ; 2 motion.(14 508-509 Hun, John Gale, On certain invariants of two triangles. 5, 39- 55 F2 Huntington, Edward V., A complete set of postulates for j 32 264-279 ( A the theory of absolute continuous magnitude. U4I 54 549 ( Dl Complete sets of postulates for the theories of posi- (A o„2 2o0—2o4 tive integral and of positive rational numbers. I C - Two definitions of an abelian group by sets of inde- A | A ' pendent postulates . (El -Definitions of a field by sets of independent f A postu- 4' dl_d7lB3 lates. -Complete sets of postulates for the theory of real { A 3 quantities. (Dl "'' -Sets independent for logic :l of postulates the algebra of j r-o] r>¿ Hutchinson, J. I., On certain relations among the theta constants. 14 391-394 D3 -On a class of automorphic functions. 3, 1-11 D3 -On the automorphic functions of the group (0. 3 ; 2,6,6). 54 447-460 D3 Kasner, Edward, The invariant theory of the inversion f 14 480-498 B2 group : geometry upon a quadric surface. I 24 485 -The cogredient and digredient theories of multiple binary forms . 4, 86-102 B2 -The generalized Beltrami problem concerning geo- f 42 149-152 F 4 desic representation . ( 54 550 1904] INDEX BY AUTHORS 9

-On the point-line as element of space : a study of the f 43 213-233 F 3 corresponding bilinear connex. I 54 550 -Isothermal systems of geodesies. 5, 56-60 F4 Krause, Martin, Ueber Systeme von Differentialgleich- ungen denen vierfach periodische Functionen Genüge leisten . 13 287-292 D3 Lehmer, D. N., Constructive theory of the unicursal cubic by synthetic methods. 33 372-376 Fl Loewy, Alfred, Über die Beducibilität der Gruppen lin- earer homogener Substitutionen . 4, 44- 64 E2 -Über die Beducibilität der reellen Gruppen linearer homogener Substitutionen. 42 171-177 E2 -Zur Gruppentheorie mit Anwendungen auf die Theorie der linearen homogenen Differentialgleich- K J D 4 ungen. ' ( E2 Loud, Frank H., Sundry metric theorems concerning n- lines in a plane . 1, 323-338 F2 Macaulay, F. S., On a method of dealing with the intersec- tions of plane curves. 54 385-410 F2 Manning, AV. A., The primitive groups of class 2p which contain a substitution of order p and degree 2p . .. . 43 351-357 E 1 Maschke, Heinrich, Note on the unilateral surface of Moebius. 1, 39 Fl -A new method of determining the differential param- eters and invariants of quadratic differential quan- f 12 197-204 D 6 tics. ll4 508 -On superosculating quadric surfaces . 34 482-484 F 4 -A symbolic treatment of the theory, of invariants of quadratic differential quantics of n variables. 44 445-469 D6 Mason, Max, Green's theorem and Green's functions for certain systems of differential equations . 52 220-225 D5 McClintock, E., On the nature and use of the functions employed in the recognition of quadratic residues .... 3, 92-109 C McDonald, J. H,, On the system of a binary cubic and and the reduction of hyperelliptic integrals quadratic *"4 JB2 of genus two to elliptic integrals by a transformation 1 D 3 of the fourth order. Merrill, Helen A., On solutions of differential equa- J 44 423-433 D4 tions which possess an oscillation theorem.1 54 551 Mertens, F., Zur linearen Transformation der 0-Beihen 23 331-342 D3 Metzler, AV. H., On certain aggregates of determinant minors. 24 395-403 Bl Miller, G. A., On the groups which are the direct prod- ucts of two subgroups. 1, 66-71 El 10 INDEX BY AUTHORS [October

-On the groups which have the same group of isomor- phisms. 14 395-401 El -Determination of all the groups of order pm which contain the abelian group of type (m — 2,l),p being f 23 259-272 E1 any prime.1 34 499-500 -On the groups of order pm which contain operators of orderpm-2. 34 383-387 El -On the holomorph of a cyclic group. 42 153-160 El - (and H. C. Moreno), Non-abelian groups in which every subgroup is abelian. 44 398-404 E1 ( 1 72- 90 D1 Moore, Eliakim Hastings, On certain crinkly curves.i ' .„_ -A simple proof of the fundamental Cauchy-Goursat j 14 499-506 D2 theorem.t 24 486 -Concerning Harnack's theory of improper definite] 23 296-330 Dl integrals.j 24 487 -On the theory of improper definite integrals. 24 459-475 Dl n ...... - . (3, ' 142-158 (A -On the projective axioms of geometry.i i ( -A a i « •*• * k * * Í 3<' 485-492 A definition of abstract groups.-j j „1 Moreno, H. C. (and G. A. Miller), Non-abelian groups in which every sub-group is abelian. 44 398-404 El Morley, Frank, On the metric geometry of the plane »-line. . la 97-115 F2 -Orthocentric properties of the plane ra-line. 4, 1-12 F2 -Projective coordinates. 43 288-296 FI -■ On the geometry whose element is the 3-point of a ~~ F 2 4 j plane. (F3 ' Moulton, Forest Ray, On a class of particular solutions \ of the of four bodies. J ._ rproblem V/ o¿ 549, -j( A -A simple non-desarguesian plane geometry. 32 192-195 _ Osgood, W. F., On the existence of the Green's function ( 13 310-314 D2 for the most general simply connected plane region... ( 24 484-485 -On the existence of a minimum of the integral

\"F(x, y, y')dx n when x0 and xx are conjugate points, and the geodesies on an ellipsoid of revolution : a revision of a theorem of Kneser's. 22 166-182 D7 -On a fundamental property of a minimum in the cal. r 23 273-295 D7 culus of variations and the proof of a theorem of -j 24 486 Weierstrass's. (-34 500 1904] INDEX BY AUTHORS 11

-A Jordan curve of positive area. 4X 107-112 Dl Peirce, J. M., On certain complete systems of quaternion expressions, and on the removal of metric limitations 1^3 * i_¿on~" from the calculus of quaternions. (Fl "D" Pell, Alexander, lines on quadrics. 13 315-322 F4 Porter, M. B., Sets of coincidence points on the non- singular cubics of a syzygetic sheaf. 2X 37- 42 F2 Pringsheim, A., Ueber die Anwendung der Cauchy'schen Multiplicationsregel auf bedingt convergente oder divergente Keihen. 24 404^12 Dl -Ueber den Goursat'sehen Beweis des Cauchy'schen Integralsatzes. 24 413-421 D2 Püpin, M. I., AVave propagation over non-uniform elec- f 13 259-286 G 4 trical conductors. I 14 509 Bietz, H. L., On groups in which certain commutative operations are conjugate. 54 500-508 El Boe, E. D., Jr., On the coefficients in the product of an alternant and a symmetric function. 52 193-213 Bl Scott, C. A., On a recent method for dealing with the intersections of plane curves. 32 216-263 F 2 -On the circuits of plane curves.... 34 388-398 F2 -Note on the real inflexions of plane curves. 34 399-400 F 2 Shaw, James Byrnie, Theory of linear associative algebra. 43 251-287 B 3 -On nilpotent algebras. 44 405-422 B3 ai u a « a v. * •* , 53 326-342 ÍB3 -Algebras defined by finite groups.< 7 < t 04 002 (. xlj X Smith, Percey F., On surfaces enveloped by spheres be- longing to a linear spherical complex. 14 371-390 F 3 -Geometry within a linear spherical complex. 23 234-248 F 3 Stecker, Henry Freeman, On the determination of sur- faces capable of conformai representation upon the plane in such a manner that goedetic lines are repre- < 22 152-165 F 4 sented by algebraic curves . | 24 486 -Concerning the existence of surfaces capable of conformai representation upon the plane in such a manner that geodetic lines are represented by a pre- scribed system of curves. 3, 12-22 F 4 Stringham, Irving, On the geometry of planes in a para- bolic space of four dimensions. 22 183-214 Fl Stolz, O., Zur Erklärung der Bogenlänge und des In-j 3X 23- 37 Dl haltes einer krummen Fläche. . 1 34 500 -Nachtrag zum Artikel : ,, Zur Erklärung der Bogen- länge, u.s.w." (dieses Bandes, S. 23 f.) . 3, 302-304 Dl Strong, AA7endell M., Note on non-quaternion number systems. 2, 43-48 B3 12 INDEX BY AUTHORS

Taber, H, On hypercomplex number systems (first paper) 54 509-548 B3 Van Vleck, Edward B., On linear criteria for the deter- j 13 293-309 D2 mination of the radius of convergence of a power series 114 509 -On the convergence of continued fractions with f 23 215-233 D2 complex elements .I 24 486 -On the convergence and character of the continued "f fraction -£■ -, 3?. . 24 476-483 D2 1 +, 1 + 1 + -A determination of the number of real and imaginary | 3, 110-131 D3 roots of the hypergeometric series.1 34 501 -On an extension of the 1894 memoir of Stieltjes. 4., 297-332 D2 -On the convergence of algebraic continued fractions whose coefficients have limiting values. 53 253-262 D2

Veblen, Oswald, A system of axioms for geometry. 53 343-384 \ "Westlund, J., On the class number of the cyclotomic number field k(e-"i/pn). 42 201-212 C White, Henry S., Conies and cubics connected with a plane cubic by certain covariant relations. 1, 1- 8 F 2 -Plane cubics and irrational covariant cubics.\ A _.n (. 14 508 -On twisted cubic curves that have a directrix. 42 134-141 F 2 Wilczynski, E. J., An application of group theory to ( 13 339-352 G3 hydrodynamics. ( 14 509 -Invariants of systems of linear differential equa- (2, 1- 24 D 4 tions. 1 24 486 -Geometry of a simultaneous system of two linear homogeneous differential equations of the second ( 24 343-362 F 4 order.t 34 500 -Reciprocal systems of linear differential equations... 3, 60-70 F4 -Covariants of systems of linear differential equations j D 4 and applications to the theory of ruled surfaces. * ( F 4 -On a certain congruence associated with a given f 4a 185-200 F 4 ruled surface.1 54 500 -Studies in the general theory of ruled surfaces. 52 226-252 F 4 -On ruled surfaces whose flecnode curve intersects every generator in two coincident points. 54 438-446 F 4 Wilson, Edwin B., The decomposition of the general col- lineation of space into three skew reflections. 12 193-196 F 5 Young, John Wesley, On the holomorphisms of a group. 32 186-191 El -On the group of sign (0, 3 ; 2, 4, oc) and the func- tions belonging to it. 5, 81-104 D3 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. 34 467-481 Dickson, Leonard Eugene, Definitions of a field by independent Í 4, 13- 20 postulates.I 54 549-550 -Definitions of a linear associative algebra by independent postulates. 4, 21- 26 Huntington, Edward V., A complete set of postulates for the f 32 264-279 theory of absolute continuous magnitude. I 54 549 -Complete sets of postulates for the theories of positive inte- gral and of positive rational numbers ,. 32 280-284 --Two definitions of an abelian group by sets of independent postulates. 4t 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 i' K 9KK_^0Q Sets of independent for the algebra of logic. postulates 54 552 Moore, Eliakim Hastings, On the projective axioms of geo- ( 3, 142-158 metry.j 34 501 a a « -*i * x, * * f 344 485-492 -A definition of abstract groups.s Moulton, Forest Ray, A simple non-desarguesian plane geo- metry. 32 192-195 Veblen, Oswald, A system of axioms for geometry. 53 343-384 B. Algebra. Bl. Rational Functions. Determinants. Symmetric Functions. Metzler, AV. H., On certain aggregates of determinant minors.. 24 395-403 Roe, Jr. , E. D., On the coefficients in the product of an alter- nant and a symmetric function. 52 193-213

B 2. Algebraic Forms. Invariants. (Cf. F 2.) 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. 14 402-413 Kasner, Edward, The invariant theory of the inversion group ; ( 14 430-498 geometry upon a quadric surface.1 24 485 13 14 INDEX BY SUBJECT MATTER [October

-The cogredient and digredient theories of multiple binary forms. 4, 86-102 McDonald, J. H., On the system of a binary cubic and quadratic and the reduction of hyperelliptic integrals of genus two to elliptic integrals by a transformation of the fourth order_ 24 437-458

BS. Linear Associative Algebra. Hypercomplex Number Systems. Fields. (Cf. FI.) Dickson, Leonard Eugene, Definitions of a field by indepen- f 4, 13- 20 dent postulates.1 54 549-550 -Definitions of a linear associative algebra by independent postulates. 4, 21- 26 r 4 437_444 Epsteen, Saul, Semireducible hypercomplex number systems... i * (. 04 001 -On the definition of reducible hypercomplex number systems. 5, 105-109 Hawkes, H. E., On hypercomplex number systems. 33 312-330 Huntington, Edward V., Definitions of a field by sets of inde- pendent postulates. 4, 31- 37 Peirce, J. M., On certain complete systems of quaternion ex- pressions, and on the removal of metric limitations from the calculus of quaternions. 54 411-420 Shaw, James Byrnie, Theory of linear associative algebra. 43 251-287 -On nilpotent algebras. 44 405-422 a i u a « a i « -,- Í 5s' 326-342 -Algebras denned by finite groups.-j Strong, Wendell M., Note on non-quaternion number systems.. 2, 43- 48 Taber, H, On hypercomplex number system (first paper). 54 509-548 B 4. Algebra of Logic. Huntington, Edward V., Sets of independent postulates for the ( 53 288-309 algebra of logic. I 54 552 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. 32 280-284 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 k(e2"iP"). 42 201-212 D. Analysis. Dl. Functions of Heal Variables. Blichfeldt, H. F., Note on the functions of the form '/(.T) =

Bôcher, Maxime, Certain cases in which the vanishing of the AVronskian is a sufficient condition for linear dependence ... 22 139-149 Cajori, Florian, Divergent and conditionally convergent series whose product is absolutely convergent. 2, 25- 36 Fréchet, Maurice, Sur les opérations linéaires. 54 493-499 Heffter, L., Ueber Curvenintegrale in w-dimensionalen Raum. 42 142-148 Huntington, Edward V., A complete set of postulates for the ( 8, 264-279 theory of absolute continuous magnitude.1 54 549 -Complete sets of postulates for the theory of real quantities. 43 358-370 72- 90 Moore, Eliakim Hastings, On certain crinkly curves.\ l 507 -Concerning Harnack's theory of improper definite inte- j 23 296-330 grals.;. (24 487 -On the theory of improper definite integrals. 24 459-475 Osgood, AV. F., A Jordan curve of positive area. 4X 107-112 Pringsheim, A., Ueber die Anwendung der Cauchy'sehen Multi- plication sregel auf bedingt convergente oder divergente Reihen. 24 404-412 Stolz, O., Zur Erklärung der Bogenlänge und des Inhaltes einer ( 3X 23- 37 krummen Fläche. .1 34 500 -Nachtrag zum Artikel : ,, Zur Erklärung der Bogenlänge, u. s. w." (dieses Bandes, S. 23 f.). 33 302-304

D 2. Functions of Complex Variables. Emch, Arnold, Algebraic transformations of a complex variable realized by linkages. 34 493-498 Goursat, E., Sur la définition générale des fonctions analytiques, d'après Cauchy. lx 14- 16 Moore, Eliakim Hastings, A simple proof of the fundamental f 14 499-506 Cauchy-Goursat theorem. ( 24 486 Osgood, AV. F., On the existence of the Green's function for the f 13 310-314 most general simply connected plane region.I 24 484-485 Pringsheim, A., Ueber den Goursat'sehen Beweis des Cauchy' sehen Integralsatzes. 24 413-421 Van Vleck, Edward B., On linear criteria for the determina- j 13 293-309 tion of the radius of convergence of a power series. ( 14 509 -On the convergence of continued fractions with complex f 23 215-233 elements.1 24 486 -On the convergence and character of the continued fraction axz a2z a3z ' ". 476-483 T + T + T + -On an extension of the 1894 memoir of Stieltjes. 43 297-332 -On the convergence of algebraic continued fractions whose coefficients have, limiting values. 53 253-262 16 INDEX BY SUBJECT MATTER [October

D 3. Particular Functions. Bolza, Oskar, The elliptic ^--functions considered as a special f 1, 53- 65 case of the hyperelliptic »--functions... I 24 484 Fields, J. O, On the reduction of the general abelian inte- f 2, 49- 86 gral.I 24 486 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. 42 178-184 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) .. 54 447-460 Krause, Martin, Ueber Systeme von Differentialgleichungen denen vierfach periodische Functionen Genüge leisten. 13 287-292 McDonald, J. H., On the system of a binary cubic and quad- ratic and the reduction of hyperelliptic integrals of genus two to elliptic integrals by a transformation of the fourth order . 24 437-458 Mertens, F., Zur linearen Transformation der ö-Reihen. 2S 331-342 Van Vleck, Edward B., A determination of the number of real \ 3, 110-131 and imaginary roots of the hypergeometric series.) 34 501 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.) Bliss, Gilbert Ames, An existence theorem for a differential equation of the second order, with an application to the cal culus of variations. 52 113-125 Bôcher, Maxime, On regular singular points of linear differen- tial equations of the second order whose coefficients are not ) 1, 40- 52 necessarily analytic. i 14 507 -Application of a method of D'Alembert to the proof of Sturm's theorems of comparison. . 14 414-420 -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 Loewy, Alfred, Zur Gruppentheorie mit Anwendungen auf die Theorie der linearen homogenen Differentialgleichungen. 5, 61- 80 Merrill, Helen A., On solutions of differential equations which ( 44 423-433 possess an oscillation theorem .1 54 551 Wilczynski, E. J., Invariants of systems of linear differential ( 2, 1- 24 equations . 1 24 486 1904] INDEX BY SUBJECT MATTER 17

- Covariants of systems of linear differential equations and applications to the theory of ruled surfaces. 34 423-450 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 f 12 243-258 group.\li 509 Mason, Max, Green's theorem and Green's functions for certain systems of differential equations. 52 220-225 D 6. Differential Forms. Haskins, Charles Nelson, On the invariants of quadratic dif- f 3X 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 Maschke, Heinrich, A new method of determining the differ- ential parameters and invariants of quadratic differential j 1, 197-204 quantics .( 14 508 -■ A symbolic treatment of the theory of invariants of quad- ratic differential quantics of n variables. 44 445-469 D 7. Calculus of Variations. Bliss, Gilbert Ames, The second variation of a definite integ- ral when one end-point is variable. 3j 132-141 -An existence theorem for a differential equation of the sec- ond order, with an application to the calculus of variations 52 113-125 -Sufficient condition for a minimum with respect to one- sided variations. 54 447-492 Bolza, 0., New proof of a theorem of Osgood's in the calculus of variations. 24 422-427 -Proof of the sufficiency of Jacobi's condition for a perma- nent sign of the second variation in the so-tailed isoperi- metric problems . . 33 305-311 Goursat, E., A simple proof of a theorem in the calculus of variations. 5X 110-112 Osgood, AV. F., On the existence of a minimum of the integral f F(x> y> y')dx when x0 and xx are conjugate points, and the geodesies on an ellipsoid of revolution : a revison of a theorem of Kneser's 22 166-182 - On a fundamental property of a minimum in the calcu- r 23 273-295 lus of variations and the proof of a theorem of AVeier- -j 24 486 strass's. (34 500 18 INDEX BY SUBJECT MATTER [October

E. Groups. E1. Groups in General. Groups of Finite Order. (Cf. E2.) Cole, F. N., The groups of order p3qP. 5, 214-219 Dickson, Leonard Eugene, Determination of all the subgroups 126-166 of the known simple group of order 25920. A 551 Findlay, William, The Sylow subgroups of the symmetric group 263-278 Fite, W. B., On metabelian groups. 3. 331-353 Huntington, Edward V., Two definitions of an abelian group by sets of independent postulates. 27- 30 Manning, W. A., The primitive groups of class 2p which con- tain a substitution of order p and degree 2p. 351-357 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 395-401 o -Determination of all the groups of order pm which contain ~6 259-272 the abelian groups of type (in — 2, 1), p being any prime_ 499-500 -On the groups of order pm which contain operators of order V K 383-387 On the holomorph of a cyclic group. 153-160 Miller, G. A. (and Mokeno, H. C. ), Non-abelian groups in which every subgroup is abelian. 398-404 485-492 Moore, Eliakim Hastings, A definition of abstract groups. 5, 549 Moreno, H. C. (and Miller, G. A.), Non-abelian groups in which every subgroup is abelian. 4. 398-404 Rietz, H. L., On groups in which certain commutative opera- tions are conjugate. A 500-508 rA 326-342 Shaw, James Byrnie, Algebras defined by finite groups... A 552 Young, John Wesley, On the holomorphisms of a group. 3, 186-191

E2. Linear Groups in Arbitrary or Special Fields. Blichfeldt, H. F., On the order of linear homogeneous groups 44 387-397 -On the order of linear homogeneous groups (second paper. ) 53 310-325 -A theorem concerning the invariants of linear homogeneous groups, with some applications to substitution groups. 54 461-466 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 2136 5 7 holoedrically isomorphic with a certain orthogonal group and f 13 353 -370 with a certain hyperabelian group. ( 14 509 1904] INDEX BY SUBJECT MATTER 19

-Canonical forms of quaternary abelian substitutions in an ( 22 103-138 arbitrary Galois field. ( 34 499 4 -Theory of linear groups in an arbitrary field.-j

-The groups of Steiner i n problems of contact.\ f r nn -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 -On the subgroups of order a power of p in the quaternary J 44 371-386 abelian group in the Galois field of order p". 154 550-551 -On the reducibility of linear groups. 44 434-436 -The subgroups of order a power of 2 of the simple quinary ( 5X 1- 38 orthogonal group in the Galois field of order p" = 81 ± 3 .... 154 551 Epsteen, Saul, On reducible groups. 43 249-250 Loewy, Alfred, Über die Reducibilität der Gruppen linearer homogener Substitutionen. 4X 44- 64 - Über die Reducibilität der reellen Gruppen linearer homo- gener Substitutionen. 42 171-177 -Zur Gruppentheorie mit Anwendungen auf die Theorie der linearen homogenen Differentialgleichungen. 5X 61- 80

E3. Continuous Groups. (Cf. E2, FI, F3, G3.) Blichfeldt, H. F., A new determination of the primitive con- tinuous groups in two variables.,. 23 249-258 Campbell, J. E., On the types of linear partial differential equa- tions of the second order in three independent variables which j 12 243-258 are unaltered by the transformations of a continuous group. ( 14 509 F. Geometry. F 1. Synthetic Geometry. Non-Euclidian Geometry. Geometry of n dimensions. Analysis Situs. (Cf. Dl, D2.) Blichfeldt, H. F., On the determination of the distauce between two points in space of n-diniensions. 34 467-481 Coolidge, Julian Lowell, A purely geometric representation of all points in the projective plane. la 182-192 -Quadric surfaces in hyperbolic space. 42 161-170 Hathaway, A. S., Quaternion space. 3, 46- 59 Lehmer, D. N., Constructive theory of the unicursal cubic by synthetic methods. 8, 372-376 Maschke, Heinrich, Note on the unilateral surface of Moebius. lx 39 20 INDEX BY SUBJECT MATTER [October

Moore, Eliakim Hastings, On the projective axioms of geo- f 3X 142-158 metry .1 34 501 Morley, Frank, Projective coordinates. 43 288-296 Moulton, Forest Ray, A simple non-desarguesian plane geo- metry. 32 192-195 Peirce, J. M., On certain complete systems of quaternion expres- sions, and on the removal of metric limitations from the calculus of quaternions. 54 411-420 Stringham, Irving, On the geometry of planes in a parabolic space of four dimensions. 22 183-214 Veblen, Oswald, A system of axioms for geometry. 5, 343-384

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. I'a., Similar conies through three points. 44 489-492 Coble, A. B., The quartic curve as related to conies. 4, 65- 85 Gale, Arthur Sullivan, On the rank, order and class of alge- braic minimum curves. 34 451-466 Hun, John Gale, On certain invariants of two triangles. 5X 39- 55 Loud, Frank H., Sundry metric theorems concerning ?i-lines in a plane. 13 323-338 Macaulay, F. S., On a method of dealing with the intersections of plane curves. 54 385-410 Morley, Frank, On the metric geometry of the plane n-line_ 12 97-115 -Orthocentric properties of the plane n-line. 4, 1- 12 -On the geometry whose element is the 3-point of a plane... 54 467-476 Porter, M. B., Sets of coincidence points on the non-singular cubics of a syzygetic sheaf. 2, 37- 42 Scott, C. A., On a recent method for dealing with the inter- sections of plane curves. 32 216-263 -On the circuits of plane curves. 34 388-398 -Note on the real inflexions of plane curves. 34 399-400 White, Henry S., Conies and cubics connected with a plane cubic by certain covariant relations . 1X 1- 8 -Plane cubics and irrational covariant cubics.\ A _._ ( 14 508 -On twisted cubic curves that have a directrix. 42 134-141 F 3. Geometry of Special Space-Elements. Kasner. E., On the point-line as element of space; a study f 43 213-233 of the corresponding bilinear connex. . I 54 550 Morley, Frank, On the geometry whose element is the 3-point of a plane. 54 467-476 1904] INDEX BY SUBJECT MATTER 21

Smith, Percey F., On surfaces enveloped by spheres belonging to a linear spherical complex. 14 371-390 ■-Geometry within a linear spherical complex. 23 234-248 F 4. Differential Geometry. (Cf. D6.) Eisenhart, L. P., Conjugate rectilinear congruences. 33 354-371 -Congruences of curves . 44 470-488 ■-Three particular systems of lines on a surface. 54 421-437 Hilbert, David, Ueber Flächen von constanter Gaussscher Krümmung . 2, 87- 99 Kasner, Edward, The generalized Beltrami problem concerning f 42 149-152 geodesic representation . ( 54 550 -Isothermal systems of geodesies. 5, 56- 60 Maschke, Heinrich, On superosculating quadric surfaces. 34 482-484 " " Pell, Alexander, D lines on quadrics. 13 315-322 Stecker, Henry Freeman, On the determination of surfaces capable of conformai representation upon the plane in such a mauner that geodetic lines are represented by algebraic j 22 152-165 curves. I 24 486 - Concerning the existence of surfaces capable of conformai representation upon the plane in such a manner that geodetic lines are represented by a prescribed system of curves. 3t 12- 22 AVilczynski, E. J., Geometry of a simultaneous system of two linear homogeneous differential equations of the second ( 24 343-362 order. ( 34 500 -Reciprocal systems of linear differential equations. 3t 60- 70 -Covariants of systems of linear differential equations and applications to the theory of ruled surfaces. 34 423-450 -On a certain congruence associated with a given ruled f 42 185-200 surface . 1 54 550 ■-Studies in the general theory of ruled surfaces. 52 226-252 -On ruled surfaces whose flecnode curve intersects every generator in two coincident points. 54 438-446 F5. Geometric Transformations. Geometry of Motion. (Cf. E2.) Blake, E. M., Two plane movements generating quartic scrolls 14 421-429 Emch, Arnold, Algebraic transformations of a complex variable realized by linkages. 34 493-498 AVilson, Edwin B., The decomposition of the general collinea- tion of space into three skew reflections. 12 193-196 G. Applied Mathematics. G 1. General Mechanics. Brown, Ernest William, On the variation of the arbitrary and given constants in dynamical equations. 43 333-350 22 INDEX BY SUBJECT MATTER [October

Chessin, Alexander S., On relative motion. 12 116-169 G 2. Celestial Mechanics. Brown, Ernest William, On the small divisors in the lunar theory. 32 159-185 -On the formation of the derivatives of the lunar coordinates with respect to the elements. 43 234-248 -On the variation of the arbitrary and given constants in dynamical equations. 43 333-350 (5 s 279—287 -On the smaller perturbations of the lunar arguments.\ Hill, G. W., On the extension of Delaunay's method in the f 12 205-242 lunar theory to the general problem of planetary motion... 1 14 508-509 c 1' 17—29 Moulton, Forest Ray, On a class of particular solutions of the \ * problem of four bodies.1 G 3. Elasticity, Hydromechanics and Sound. Darwin, G. H., The approximate determination of the form of Maclaurin's spheroid. 42 113-133 Hadamard, J., La théorie des plaques élastiques planes. 34 401-422 Wilczynski, E. J., An application of group theory to hydro- j 13 339-352 dynamics. (. 14 509 G 4. Electricity, Light and Heat. Pupin, M. I., Wave propagation over non-uniform electrical ( 13 259-286 conductors.114 509 INDEX BY NUMBERS.

Volume 1, Number 1. January, 1900. Pages. Class. Conies and cubics connected with a plane cubic by certain covariant relations. By Henry S. AVhite, of Evans- ton, 111. 1- 8 F2 Formelltheoretische Entwickelung der in Herrn A\7hite's Abhandlung über Curven dritter Ordnung enthaltenen Sätze. By Paul Gordan, of Erlangen, Germany. 9-13 B2 Sur la définition générale des fonctions analytiques, d'après Cauchy. By E. Goursat, of Paris, France. 14-16 D2 On a class of particular solutions of the problem of four bodies. By Forest Ray Moulton, of Chicago, 111.... 17-29 G 2 Definition of the abelian, the two hypoabelian, and re- lated linear groups as quotient-groups of the groups of isomorphisms of certain elementary groups. By Leonard Eugene Dickson, of Austin, Tex. 30- 38 E2 Note on the unilateral surface of Moebius. By Heinrich Maschke, of Chicago, 111. 39 Fl On regular singular points of linear differential equations of the second order whose coefficients are not neces- sarily analytic. By Maxime Bôcher, of Cambridge, Mass. 40- 52 D4 The elliptic

Volume 1, Number 2. April, 1900.

On the metric geometry of the plane w-line. By F. Mor- ley, of Haverford, Pa. 97-115 F2 On relative motion. By Alexander S. Chessin, of New York, N. Y. 116-169 Gl Plane cubics and irrational covariant cubics. By Henry S. White, of Evanston, 111. 170-181 F2 23 24 INDEX BY NUMBERS [October

A purely geometric representation of all points in the pro- jective plane. By Julian Lowell Coolidge, of Cam- bridge, Mass. 182-192 Fl The decomposition of the general collineation of space into three skew reflections. By Edwin B. Wilson, of New Haven, Conn. 193-196 F5 A new method of determining the differential parameters and invariants of quadratic differential quantics. By Heinrich Maschke, of Chicago, 111. 197-204 D6 On the extension of Delaunay's method in the lunar theory to the general problem of planetary motion. By G. W. Hill, of West Nyack, N. Y. 205-242 G2 On the types of linear partial differential equations of the second order in three independent variables which are unaltered by the transformations of a continuous group. By J. E. Campbell, of Oxford, England. 243-258 D 5, E 3

Volume 1, Number 3. July, 1900. Wave propagation over non-uniform electrical conductors. By M. I. Pupin, of New York, N. Y. 259-286 G4 Ueber Systeme von Differentialgleichungen denen vierfach periodische Functionen Genüge leisten. By Martin Krause, of Dresden, Germany. 287-292 D3 On linear criteria for the determination of the radius of convergence of a power series. By Edward B. Van Vleck, of Middletown, Conn. 293-309 D2 On the existence of the Green's function for the most gen- eral simply connected plane region. By W. F. Osgood, of Cambridge, Mass. 310-314 D2 "D" lines on quadrics. By Alexander Pell, of Ver - million, S. D. 315-322 F4 Sundry metric theorems concerning w-lines in a plane. By Frank H. Loud, of Haverford, Pa. 323-338 F2 An application of group theory to hydrodynamics. By E. J. Wilczynski, of Berkeley, Cal. 339-352 G3 Determination of an abstract simple group of order 27 ■36 • 5 • 7 holoedrically isomorphic with a certain orthogonal group and with a certain hyperabelian group. By Leonard Eugene Dickson, Austin, Texas. 353-370 E 2

Volume 1, Number 4. October, 1900. On surfaces enveloped by spheres belonging to a linear spherical complex. By Percey F. Smith, of New Haven, Conn. 371-390 F3 1904] INDEX BY NUMBERS 25

On certain relations among the theta constants. By J. I. Hutchinson, of Ithaca, N. Y. 391-394 D3 On the groups which have the same group of isomorphisms. By G. A. Miller, of Ithaca, N. Y. 395^01 El Die Hessische und die Cayley'sche Curve. By Paul Gordan, of Erlangen, Germany. 402^13 B2 Application of a method of D'Alembert to the proof of Sturm's theorems of comparison. By Maxime Bôcher, of Cambridge, Mass. 414^20 D4 Two plane movements generating quartic scrolls. By E. M. Blake, of Ithaca, N. Y. 421-429 F5 The invariant theory of the inversion group : geometry upon a quadric surface. By Edward Kasner, of New York, N. Y. 430-498 B2 A simple proof of the fundamental Cauchy-Goursat theorem. By Eliakim Hastings Moore, of Chicago, 111. 499-506 D2 Notesand errata: volume 1. 507-509

Volume 2, Number 1. January, 1901. Invariants of systems of linear differential equations. By E. J. Wilczynski, of Berkeley, Cal. 1-24 D4 Divergent and conditionally convergent series whose prod- uct is absolutely convergent. By Florian Cajori, of Colorado Springs, Col. 25- 36 D 1 Sets of coincidence points on the non-singular cubics of a syzygetic sheaf. By M. B. Porter, of New Haven, Conn. 37- 42 F2 Note on non-quaternion number systems. By Wendell M. Strong, of New Haven, Conn. 43- 48 B3 On the reduction of the general abelian integral. By J. C. Fields, of Hamilton, Ont. 49- 86 D3 Ueber Flächen von constanter Gaussscher Krümmung. By David Hilbert, of Göttingen, Germany. 87- 99 F 4 Note on the functions of the form f(x) m

Volume 2, Number 2. April, 1901. Canonical forms of quaternary abelian substitutions in an arbitrary Galois field. By Leonard Eugene Dick- son, of Chicago, 111. 103-138 E2 26 INDEX BY NUMBERS [October

Certain cases in which the vanishing of the Wronskian is a sufficient condition for linear dependence. By Max- ime Bôcher, of Cambridge, Mass. 139-149 D 1 An elementary proof of a theorem of Sturm. By Maxime Bôcher, of Cambridge, Mass. 150-151 D4 On the determination of surfaces capable of conformai representation upon the plane in such a manner that geodetic lines are represented by algebraic curves. By Henry Freeman Stecker, of Göttingen, Germany... 152-165 F4 On the existence of a minimum of the integral

F(x, y, y')dx fJxq when x0 and xx are conjugate points, and the geodesies on an ellipsoid of revolution : a revision of a theorem of Kneser's. By W. F. Osgood, of Cambridge, Mass. 166-182 D 7 On the geometry of planes in a parabolic space of four dimensions. By Irving Stringham, of Berkeley, Cal. 183-214 F1 Volume 2, Number 3. July, 1901. On the convergence of continued fractions with complex elements. By E. B. Van Vleck, of Middletown, Conn. 215-233 D 2 Geometry within a linear spherical complex. By Percey F. Smith, of New Haven, Conn. 234-248 F3 A new determination of the primitive continuous groups in two variables. By H. F. Blichfeldt, of Stanford University, Cal..... 249-258 E3 Determination of all the groups of order pm which contain the abelian group of type (m — 2, 1), p being any prime. By G. A. Miller, of Ithaca, N. Y. 259-272 El On a fundamental property of a minimum in the calculus of variations and the proof of a theorem of Weier- strass's. By W. F. Osgood, of Cambridge, Mass. 273-295 D7 Concerning Harnack's theory of improper definite integrals. By Eliakim Hastings Moore, of Chicago, 111. 296-330 D1 Zur linearen Transformation der 0-Reihen. By F. Mer- tens, of Vienna, Austria. 331-342 D3 Volume 2, Number 4. October, 1901. Geometry of a simultaneous system of two linear homo- geneous differential equations of the second order. By E. J. Wilczynski, of Berkeley, Cal. 343-362 F4 Theory of linear groups in an arbitrary field. By Leonard Eugene Dickson, of Chicago, 111. 363-394 E2 On certain aggregates of determinant minors. By W. H. Metzler, of Syracuse, N. Y. 395-403 Bl 1904] INDEX BY NUMBERS

Ueber die Anwendung der Cauchy'schen Multiplications- regel auf bedingt convergente oder divergente Reihen. By A. Pringsheim, of Munich, Germany. 404-412 Dl Ueber den Goursat'schen Beweis des Cauchy'schen Inte- gralsatzes. By A. Pringsheim, of Munich, Germany. 413-421 D2 New proof of a theorem of Osgood's in the calculus of variations. By O. Bolza, of Chicago, 111. 422-427 D7 On certain pairs of transcendental functions whose roots separate each other. By Maxime Bôcher, of Cam- bridge, Mass. 428-436 D4 On the system of a binary cubic and quadratic and the reduction of hyperelliptic integrals of genus two to elliptic integrals by a transformation of the fourth order. By J. H. McDonald, of Lafayette, Ind. 437-458 D3. On the theory of improper definite integrals. By Eliakim Hastings Moore, of Chicago, 111. 459-475 Dl On the convergence and character of the continued frac-

tion Ä Ä Ä .... ByJ E. B. Van Vleck, 1 + 1 + 1 + of Middletown, Conn. 476-483 D2 Notes and errata : volumes 1 and 2. . 484-487

Volume 3, Number 1. January, 1902. On a class of automorphic functions. By J. I. Hutchin- son, of Ithaca, N. Y. 1- 11 D3 Concerning the existence of surfaces capable of conformai representation upon the plane in such a manner that geodetic lines are represented by a prescribed system of curves. By Henry Freeman Stecker, of Ithaca, N. Y. 12- 22 F4 Zur Erklärung der Bogenlänge und des Inhaltes einer krummen Fläche. By O. Stolz, of Innsbruck, Austria. 23- 37 Dl The groups of Steiner in problems of contact. By Leonard Eugene Dickson, of Chicago, 111. 38- 45 E2 Quaternion space. By A. .S. Hathaway, of Terre Haute, Ind. 46- 59 Fl Reciprocal systems of linear differential equations. By E. J. AVilczynski, of Berkeley, Cal. 60- 70 F4 On the invariants of quadratic differential forms. By Charles Nelson Haskins, of New Bedford, Mass.... 71-91 D6 On the nature and use of the functions employed in the recognition of quadratic residues. By E. McClin- tock, of New York, N. Y. 92-109 Cl 28 INDEX BY NUMBERS [October

A determination of the number of real and imaginary roots of the hypergeometric series. By Edward B. Van Vleck, of Middletown, Conn. 110-131 D3 The second variation of a definite integral when one end- point is variable. By G. A. Bliss, of Minneapolis, Minn. 132-141 D7 On the projective axioms of geometry. By Eliakim Hastings Moore, of Chicago, 111. 142-158 A, Fl

Volume 3, Number 2. April, 1902. On the small divisors in the lunar theory. By E. W. Brown, of Haverford, Pa. 159-185 G2 On the holomorphisms of a group. By J. W. Young, of Ithaca, N. Y. 186-191 El A simple non-desarguesian plane geometry. By Forest Ray Moulton, of Chicago, 111. 192-195 A, F 1 On the real solutions of systems of two homogeneous linear differential equations of the first order. By Maxime Bôcher, of Cambridge, Mass. 196-215 D4 On a recent method for dealing with the intersections of plane curves. By C. A. Scott, of Bryn Mawr, Pa.... 216-263 F2 A complete set of postulates for the theory of absolute con- tinuous magnitude. By E. V. Huntington, of Cam- bridge, Mass. 264-279 A, Dl Complete sets of postulates for the theories of positive integral and of positive rational numbers. By E. V. Huntington, of Cambridge, Mass. 280-284 A C

Volume 3, Number 3. July, 1902. On the group defined for any given field by the multipli- cation table of anjr given finite group. By Leonard Eugene Dickson, of Chicago, 111. 285-301 E2 Nachtrag zum Artikel : ,, Zur Erklärung der Bogenlänge, u. s. w." (dieses Bandes, S. 23 f.). By O. Stolz, of Innsbruck, Austria. 302-304 Dl Proof of the sufficiency of Jacobi's condition for a perma- nent sign of the second variation in the so-called iso- perimetric problems. By O. Bolza, of Chicago, 111... 305-311 D7 On hypercomplex number systems. By H. E. Hawkes, of New Haven, Conn. 312-330 B3 On metabelian groups. By W. B. Fite, of Ithaca, N. Y.. 331-353 El Conjugate rectilinear congruences. By L. P. Eisenhart, of Princeton, N. J. 354-371 F4 Constructive theory of the unicursal cubic by synthetic methods. By D. N. Lehmer, of Berkeley, Cal. 372-376 Fl 1904] INDEX BY NUMBERS 29

The groups of Steiner in problems of contact (second paper). By Leonard Eugene Dickson, of Chicago, 111. 377-382 E2 Volume 3, Number 4. October, 1902. On the groups of order pm which contain operators of order pm-\ By G. A. Miller, of Stanford University, Cal. 383-387 E1 On the circuits of plane curves. By C. A. Scott, of Bryn Mawr, Pa. 388-398 F2 Note on the real inflexions of plane curves. By C. A. Scott, of Bryn Mawr, Pa. 399-400 F2 La théorie des plaques élastiques planes. By J. Hada- mard, of Paris, France . 401-422 G3 Covariants of systems of linear differential equations and applications to the theory of ruled surfaces. By E. J. AVilczynski, of Berkeley, Cal. 423-450 D4, F4 On the rank, order and class of algebraic minimum curves. By Arthur Sullivan Gale, of New Haven, Conn... 451-466 F 2 On the determination of the distance between two points in space of n dimensions. By H. F. Blichfeldt, of Stanford University, Cal. 467-481 A, F 1 On superosculating quadric surfaces. By Heinrich Maschke, of Chicago, 111. 482-484 F4 A definition of abstract groups. By Eliakim Hastings Moore, of Chicago, 111. . 485-492 A, E 1 Algebraic transformations of a complex variable realized by linkages. By Arnold Emch, of Boulder, Col.... 493-498 D 2, F5 Notes and errata : volumes 1,2,3. 499-501 Volume 4, Number 1. January, 1903. Orthocentric properties of the plane 71-line. By , of Baltimore, Md.,. 1- 12 F2 Definitions of a field by independent postulates. By L. E. Dickson, of Chicago, 111. 13- 20 A, B3 Definitions of a linear associative algebra by independent postulates. By L. E. Dickson, of Chicago, 111. 21- 26 A, B3 Two definitions of an abelian group by sets of independent postulates. By E. V. Huntington, of Cambridge, Mass. 27- 30 A, El Definitions of a field by sets of independent postulates. By E. \. Huntington, of Cambridge, Mass. 31- 37 A, B3 On the invariants of differential forms of degree higher than two. By C. N. Haskins, of Boston, Mass. 38- 43 D6 Über die Reducibilität der Gruppen linearer homogener Substitutionen. By A. Loewy, of Freiburg, i. B., Germany . 44- 64 E2 30 INDEX BY NUMBERS [October

The quartic curve as related to conies. By A. B. Coble, of Columbia, Mo. 65- 85 F2 The cogredient and digredient theories of multiple binary forms. By E. Kasner, of New York, N. Y. 86-102 B2 On the envelope of the axes of a system of conies passing through three fixed points. By R. E. Allardice, of Stanford University, Cal. 103-106 F2 A Jordan curve of positive area. By W. F. Osgood, of Cambridge, Mass. 107-112 Dl Volume 4, Number 2. April, 1903. The approximate determination of the form of Maclaurin's spheroid. By G. H. Darwin, of Cambridge, England.. 113-133 G 3 On twisted cubic curves that have a directrix. By H. S. White, of Evanston, 111. 134-141 F2 Ueber Curvenintegrale im wi-dimensionalen Raum. By L. Heffter, of Bonn, Germany. 142-148 Dl The generalized Beltrami problem concerning geodesic representation. By E. Kasner, of New York, N. Y.. 149-152 F 4 On the holomorph of a cyclic group. By G. A. Miller, of Stanford University, Cal. 153-160 El Quadric surfaces in hyperbolic space. By J. L. Coolidge, of Cambridge, Mass. 161-170 Fl Über die Reducibilität der reellen Gruppen linearer homo- gener Substitutionen. By A. Loewy, of Freiburg, i. B., Germany. 171-177 E2 On the possibility of differentiating term by term the de- velopments for an arbitrary function of one real variable in terms of Bessel functions. By W. B. Ford, of Ann Arbor, Mich. 178-184 D3 On a certain congruence associated with a given ruled surface. By E. J. Wilczynski, of Berkeley, Cal. 185-200 F 4 On the class number of the cyclotomic number field k(e™lPn). By J. Westlund, of Lafayette, Ind. 201-212 Cl Volume 4, Number 3. July, 1903. On the point-line as element of space : a study of the cor- responding bilinear connex. By E. Kasner, of New York, N. Y.. 213-233 F3 On the formation of the derivatives of the lunar coordi- nates with respect to the elements. By E. W. Brown, of Haverford, Pa.,. 234-248 G2 On reducible groups. By S. Epsteen, of Chicago, 111. 249-250 E 2 Theory of linear associative algebra. By J. B. Shaw, of Gambier, Ohio. 251-287 B3 1904] INDEX BY NUMBERS 31

Projective coordinates. By Frank Morley, of Baltimore, Md. 288-296 Fl On an extension of the 1894 memoir of Stieltjes. By E. B. Van Vleck, of Middletown, Conn. 297-332 D2 On the variation of the arbitrary and given constants in dynamical equations. By E. W. Brown, of Haver- ford, Pa. 333-350 G1,G2 The primitive groups of class 2p which contain a substitu- tion of order p and degree 2p. By W. A. Manning, of Berkeley, Cal. 351-357 El Complete sets of postulates for the theory of real quanti- ties. By E. V. Huntington, of Cambridge, Mass... 358-370 A, Dl

Volume 4, Number 4. October, 1903. On the subgroups of order a power of p in the quaternary abelian group in the Galois field of order p". By L. E. Dickson, of Chicago, 111. 371-386 E2 On the order of linear homogeneous groups. By H. F. Blichfeldt, of Stanford University, Cal. 387-397 E2 Non-abelian groups in which every subgroup is abelian. by G. A. Miller and H. C. Moreno, of Stanford University, Cal. 398-404 El On nilpotent algebras. By J. B. Shaw, of Decatur, 111... 405-422 B3 On solutions of differential equations which possess an oscillation theorem. By Helen A. Merrill, of New Haven, Conn. 423-433 D4 On the reducibility of linear groups. By L. E. Dickson, of Chicago, 111. 434-436 E2 Semireducible hypercomplex number systems. By S. Ep- steen, of Chicago, 111.,. 437-444 B3 A symbolic treatment of the theory of invariants of quad- ratic differential quantics of n variables. By H. Maschke, of Chicago, 111. 445-469 D6 Congruences of curves. By L. P. Eisenhart, of Prince- ton, N. J.,. 470-488 F4 Similar conies through three points. By T. J. I'a. Brom- wich, of Galway, Ireland. 489-492 F2

Volume 5, Number 1. January, 1904. The subgroups of order a power of 2 of the simple quinary orthogonal group in the Galois field of order p" = 81 ± 3. - By Leonard Eugene Dickson, of Chi- cago, 111. 1- 38 E2 On certain invariants of two triangles. By John Gale Hun, of Princeton, N. J. 39- 55 F 2 32 INDEX BY NUMBERS [October,

Isothermal systems of geodesies. By Edward Kasner, of New York, N. Y. 56-60 F4 Zur Gruppentheorie mit Anwendungen auf die Theorie der linearen homogenen Differentialgleichungen. By Alfred Loewy, of Freiburg i. B., Germany. 61- 80 E2, D4 On the group of sign (0, 3 ; 2,4, oo ) and the functions belonging to it. By John Wesley Young, of Ithaca, N. Y. 81-104 D3 On the definition of reducible hypercomplex number sys- tems. By Saul Epsteen, of Chicago, 111. 105-109 B3 A simple proof of a theorem in the calculus of variations. By E. Goursat, óf Paris, France. 110-112 D7 Volume 5, Number 2. April, 1904. An existence theorem for a differential equation of the second order, with an application to the calculus of variations. By , of Chicago, 111. 113-125 D4, D7 Determination of all the subgroups of the known simple group of order 25920. By Leonard Eugene Dick- son, Chicago, 111. 126-166 El On the invariants of quadratic differential forms, II. By Charles Nelson Haskins, of New Bedford, Mass. 167-192 D6 On the coefficients in the product of an alternant and a symmetric function. By E. D. Roe, Jr., of Syracuse, N. Y. 193-213 Bl The groups of order p"q?.. By F. N. Cole, of New York, N. Y. 214-219 El Green's theorem and Green's functions for certain systems of differential equations. By Max Mason, of Boston, Mass. 220-225 D5 Studies in the general theory of ruled surfaces. By E. J. Wilczynski, of Berkeley, Cal. 226-252 F4 Volume 5, Number 3. July, 1904. On the convergence of algebraic continued fractions whose coefficients have limiting values. By Edward B. Van Vleck, of Middleto-vn, Conn. 253-262 D2 The Sylow subgroups of ie symmetric group. By Wil- liam Findlay, of New York, N. Y. 263-278 El On the smaller perturbations of the lunar arguments. By Ernest William Brown, of Haverford, Pa. 279-287 G 2 Sets of independent postulates for the algebra of logic. By Edward V. Huntington, of Cambridge, Mass. 288-309 A, B3 On the order of linear homogenous group (second paper.) By H. F. Blichfeldt, of Standford Uni- versity, Cal. 310-325 E2 1904] INDEX BY NUMBERS 33

Algebras defined by finite groups. By James Byrnie Shaw, of Decatur, 111. 326-342 B3. El A system of axioms for geometry. By , of Chicago, 111. 343-384 A, Fl Volume 5, Number 4. October, 1904. On a method of dealing with the intersections of plane curves. By F. S. Macaulay, of London, England... 385-410 F2 On certain complete systems of quaternion expressions, and on the removal of metric limitations from the calculus of quaternions. By J. M. Peirce, of Cambridge, Mass. 411-420 B3, Fl Three particular systems of lines on a surface. By L. P. Eisenhart, of Princeton, N. J. 421-437 F4 On ruled surfaces whose fiecnode curve intersects every generator in two coincident points. By E. J. AVil- czynski, of Berkeley, Cal. 438-446 F4 On the automorphic functions of the group (0, 3 ; 2,6, 6). By J. I. Hutchinson, of Ithaca, N. Y...... 447-460 D3 A theorem concerning the invariants of linear homogene- ous groups, with some applications to substitution groups. By H. F. Blichfeldt, of Berkeley, Cal. 461-466 E2 On the geometry whose element is the 3 point of a plane. By F. Morley, of Baltimore, Md. 467-476 F2, F3 Sufficient conditions for a minimum with respect to one- sided variations. By G. A. Bliss, of Columbia, Mo.. 477-492 D7 Sur les opérations linéaires. By M. Frechet, of Paris, France. 493-499 Dl On groups in which certain commutative operations are conjugate. By H. L. Rietz, of Urbana, 111 . 500-508 El On hypercomplex number systems (first paper). By H. Taber, of Worcester, Mass. 509-548 B3 Notes and Errata : Arolumes 1, 3, 4, 5.. . 549-552