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OF THE

AMERICAN M1ATHEM:ATICAL SOCIETY

EDITED) BY

ELIAK1D1 HASTINGS MOORE

ERNEST WILLIAM1 BROWN THOMIAS SCOTT FISKE

WITH THE COOPERATION OF

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

PUBLISHED QUARTERLY BY THE SOCIETY WITH THE SUPPORT OF

HARVARD UNIVERSITY NORTHWESTERN UNIVERSITY YALE UNIVERSITY CORNELL UNIVERSITY COLUMBIA UNIVERSITY THE UNIVERSITY OF CALIFORNIA WESLEYAN UNIVERSITY BRYN MAVwR COLLEGE HAVERFORD COLLEGE THE UNIVERSITY OF C IJICAGO

VOLUME 'a" 1904

LANCASTER, PA., AND NEW YORK THE MACMILLAN COMPANY AGENTS FOR THE SOCIETY 1 904 PRESS OF THE NEW ERA PRINTING COMPANY, LANCASTER. PA, TABLE OF CONTENTS

VOLUME 5 1904 PAGES BLICHFELDT, H. F., of Stanford University,Cal. On the orderof linear homogeneQusg'oupS (secondpaper) .310-325 A theoremconcerning the inivariantsof linear homo- geneous groups,with some applications to substitutiongroups 461-466 BLISs, G. A., of Columbia,Mo. An existencetheorem for a differ- ential equationlof the second order,with an applicationto the calculus of variations.113-125

___ _ Sufficientcondition for a minimumwith respect to one-sidedvariations. 477-492 BROWN, E. W., of Haverford,Pa. On the smallerperturbations of the lunar arguments.279-287 COLE, F. N., of New York, N. Y. The groupsof orderp'q . . 214-219 DICKSON, L. E., of Chicago, Ill. The subgroupsof ordera power of 2 of the simplequinary orthogonal groups in the Galois field of orderpn 81i 3 ..1- 38 Determinationof all the subgroupsof the knownsim- ple group of order25920 .126-166 EISENHART, L. P., of Princeton,N. J. Three particularsystems of lines on a surface.421-437 EPSTEEN, S., of Chicago, Ill. On the definitionof reduciblehyper- comiplexnumber systems .105-109 FINDLAY, W., of New York, N. Y. The Sylow subgroups of the symmetricgroup. 263-278 FRECHET, M., of Paris, France. Sur les operationslineaires . 493-499 GOURSAT, E., of Paris, France. A simpleproof of a theoremin the calculus of variations. (Extract from a letter to Mlr.W. F. Osgood.). 110-112 HASKINS, C. N., of Ithaca, N. Y. Oni the invariantsof quadratic differentialformis, TI. 167-192 HUN, J. G., of Princeton,N. J. On certain invarianitsof two tri- angles.39- 55 HUNTINGTON, E. V., of Cainbridge,Mass. Sets of inidependenit postulatesfor the algebra of logic.288-309 HUTCHINSON, J. I., of Ithaca, N. Y. On the automorphicfunctions of the grouip(0, 3; 2, 6, 6) 447-460 iv TABLE OF CONTENTS

PAGES KASNER,E., of New York, N. Y. Isothermalsystems of geodesics. 56- 60 LOEWY A., of Freiburg,i. B., Germany. Zur Gruppentheoriemit Anwendungenauf die Theorieder linearenhomogenen Differen- tialgleichungen.61-80 MACAULAY, F. S., of London, England. On a miethodof dealing withthe inltersectionsof plane curves. 385-410 MASON, MAX, of New Haven, Conn. Green's theoremalnd Green's functiolnsfor certainsystems of differentialequations . . 220-225 MORLEY,F., of Baltimore,Md. On the geometrywhose element is the 3-pointof a plane. 467-476 PEIRCE,J. M., of Cambridge,Mass. On certain completesystems of quaternionexpressions, and on the removalof metriclimita- tionsfrom the calculus of quaternions.411-420 RIETZ, H. L., of Urbana, Ill. On groups in whichcertain coinmu- tativeoperations are conjugate.500-508 IROE, E. D., Jr.,of Syracuse,N. Y. Onl the coefficienltsin the prod- uct of an alternantand a symmetricfunction .193-213 SHAW, J. B., of Decatur, Ill. Algebras definedby finitegroups 326-342 TABER, H., of Worcester,Mass. On hypercomplexnumnber systems (firstpaper). 509-548 VAN VLECK, E. B., of Middletown,Conn. The convergenceof alge- braic continuedfractions whose coefficients have limitingvalues. 253-262 VEBLEN, O., of Chicago, Ill. A systemof axioms forgeometry 343-384 WILCZYNSKI, E. J., of Berkeley,Cal. Studies in the generaltheory of ruled surfaces ..226-252 On ruled surfaceswhose fleenode curve intersectsevery generatorin two coincidentpoints . .438-446 YOUNG, J. W., of Evanstoni,Ill. On the group of the sign (0, 3; 2, 4, xo) and the functionsbelonging to it. .81-104 Notes and errata: volumes1, 3, 4, 5 .. 549-552