TRANSACTIONS
OF THE
American Mathematical Society
EDITED BY
DAVID RAYMOND CUKTISS
LUTHER PFAHLER EISENHART
PERCEY F. SMITH
WITH THE COOPERATION OF
GEORGE D. BIRKHOFF ARTHUR B. COBLE WALL1E A. HURWITZ DUNHAM JACKSON EDWARD KASNER WILLIAM R. LONGLEY CHARLES N. HOORE ROBERT L. MOORE FOREST R. MOULTON ARTHUR RANDH FRANCIS R. 8HARFE ERNEST J. WILCZYNSKI
VOLUME 20 1919
PUBLISHED BY THE SOCIETY Lancaster, Pa., awd New Tobk 1919
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 TABLE OF CONTENTS VOLUME 20, 1919 PAGES Alexander, J. W., of New York, N. Y. Note on two three-dimensional manifolds with the same group.339 Blumberg, H., of Urbana, 111. On convex functions.40 Carmichael, R. D., of Urbana, 111. On a general class of integrals of the form
- A general system of linear equations.343 Pitcher, A. D., of Cleveland, 0. (with E. W. Chittenden). On the theory of developments of an abstract class in relation to the calcul fonctionnel.213 Shaepe, F. R., of Ithaca, N. Y. (with V. Snyder). Certain types of involutorial space transformations.185 Snyder, V., of Ithaca, N. Y. (with F. R. Sharpe). Certain types of involutorial space transformations.185 Van Vleck, E. B., of Madison, Wis. On the combination of non-loxo- dromic substitutions.299 Wilczynski, E. J., of Chicago, 111. Line-geometric representations for functions of a complex variable.271 Errata, volume 20.356 TRANSACTIONS
OF THE
American Mathematical Society
Volumes 11-20 1910-1919
Indices CONTENTS PAGE Index by Authors. 5 Index by Subject Matter. 17
Arrangement of the Index by Subject Matter A. Logical Analysis of Mathematical Disciplines. 17 (Cf. F 1.)
B. Algebra B 1. Rational Functions. Theory of Equations. Determinants. Sym- metric Functions. 17 B 2. Algebraic Forms. Invariants. (Cf. F 2.). 18 B 3. Linear Associative Algebra. Hypèrcomplex Number Systems. Fields. (Cf. F 1.). 18 B 4. Algebra of Logic. —
C. Theory of Numbers. 19 (Cf. E 1, E 2.) D. Analysis D 1. Functions of Real Variables. Point Sets. 19 D 2. Functions of Complex Variables. 21 D 3. Particular Functions. 22 D4. Ordinary Differential Equations. (Cf. D 2, D 3, F 4.). 23 D 5. Partial Differential Equations. 24 D 6. Differential Forms. — D 7. Calculus of Variations. 24 D 8. Difference Equations. 24 D 9. Integral Equations. 25
E. Groups E 1. Discrete Groups in General. (Cf. E 2.). 25 E 2. Linear Groups in Arbitrary or Special Fields. 26 E 3. Continuous Groups. (Cf. E 2, F 1, F 3, G 3.). 26
F. Geometry F 1. Synthetic Geometry. Non-Euclidean Geometry. Geometry of n Dimensions. Analysis Situs. (Cf. D 1, D 2.). 26 3 4 CONTENTS PAGE F 2. Algebraic Geometry. Algebraic Curves and Surfaces. (Cf. B 2, D 3, E 2, F 1, F 4, F 5.). 27 F 3. Geometry of Special Space-Elements. 27 F 4. Differential Geometry. (Cf. D 6.). 27 F 5. Geometric Transformations. Geometry of Motion. (Cf. E 2.).. . . 29
G. Applied Mathematics G 1. General Mechanics. 30 G 2. Celestial Mechanics. 30 G 3. Elasticity, Hydromechanics, and Sound. 31 G 4. Electricity, Light, and Heat. —
i INDEX BY AUTHORS Vol.* pages Alexander, J. W., II, A proof of the invariance of certain constants of analysis situs. 162 148-154 -On the factorization of Cremona plane transformations. . 173 295-300 -Note on two three-dimensional manifolds with the same group. 204 339-342 Barrow, D. F., Oriented circles in space. 163 235-258 Bates, W. H., An application of symbolic methods to the treatment of mean curvatures in hyperspace. 12i 19-38 Beck, H. Ein Seitenstück zur Möbius'schen Geometrie der Kreisverwandtschaften. 114 414^148 Bernstein, B. A., A set of four independent postulates for boolean algebras. 17i 50- 52 BiANCHi, L., Concerning singular transformations Bk of surfaces applicable to quadrics. I83 379-401 Bill, E. G., An existence theorem for a problem of the calculus of variations in space. 13i 50- 58 BiRKHOFF, G. D., A simplified treatment of the regular singular' . point. 112 199-202 -General theory of linear difference equations. 122 243-284 -Proof of Poincaré's geometric theorem. 14i 14- 22 -On a simple type of irregular singular point. 144 462-476 -Infinite products of analytic matrices. 173 386-404 -Dynamical systems with two degrees of freedom. I82 199-300 Blichfeldt, H. F., Theorems on simple groups. Hi 1-14 -On the order of linear homogeneous groups (fourth paper) 12i 39- 42 -A new principle in the geometry of numbers, with some applications. 153 227-235 Bliss, G. A. (with M. Mason), Fields of extremals in space. . . 113 325-340 -A generalization of Weierstrass' preparation theorem for a power series in several variables. 132 133-145 -(with A. L. Underhill), The minimum of a definite integral for unilateral variations in space. 153 291-310
* The numbers in this column indicate for every paper the volume and part of volume of publication, and thus the date of publication, e. g., the first paper in the list was published in April, 1915. In this column references are made also to the Notes and errata published in the concluding numbers of various volumes, e. g., anote to the paper by B. H. Camp appears in the Notes and errata of volume 16. >> 6 INDEX BY AUTHORS [October
Vol. Pages -The Weierstrass E-Function for problems of the calculus of variations in space. 154 369-378 -Jacobi's condition for problems in the calculus of variations in parametric form. 172 195-206 -The problem of Mayer with variable end points. 193 305-314 Blumberg, H., On the factorization of expressions of various types. 174 517-544 -On convex functions. 20i 40- 44 Bôcher, M., Applications and generalizations of the concep- tion of adjoint systems. 144 403-420 -Note "On supplementary to the paper certain pairs of transcendental functions whose roots separate each other" 184 519-521 Brink, R. W., A new integral test for the convergence and divergence of infinite series. 192 186-204 Buchanan, D., A new isosceles triangle solution of the three body problem. 163 259-274 Camp, B. H., Singular multiple integrals, with applications to series. 14x 42- 64 -Lebesgue integrals containing a parameter, with applica- fl5i 87-106 tions.*[l64 532 Car Michael, R. D., Linear difference equations and their analytic solutions. 12i 99-134 -On transcendentally transcendental functions. 143 311-319 -On a general class of series of the form Y,cng{x + n). . . . 173 207-232 -On a general class of integrals of the form
Vol. Pages -Points sets and allied Cremona groups (Part II). 173 345-385 -Points sets and allied Cremona groups (Part III). 183 331-372 Cole, F. N., The triad systems of thirteen letters. 14i 1- 5 CooliDge, J. L., The metrical aspect of the line-sphere trans- formation . 12i 43-69 -A study of the circle cross. 142 149-174 -Congruences and complexes of circles. 15i 107-134 Conner, J. R., Multiple correspondences determined by the rational plane quintic curve. 13» 265-278 Craig, C. F., On a class of hyperfuchsian functions. llx 37- 54 -(with F. R. Sharpe), An application of Severi's theory of a basis to the Kummer and Weddle surfaces. 153 236-244 Cummings, L. D., On a method of comparison for triple-systems. 153 311-327 Curtiss, D. R., Extensions of Descartes' Rule of Signs con- nected with a problem suggested by Laguerre. 163 350-360 Daniell, P. J., Differentiation with respect to a function of limited variation. 194 353-362 Dederick, L. S., On the character of a transformation in the neighborhood of a point where its jacobian vanishes. 14i 143-148 Dentón, W. W., Projective differential geometry of develop- able surfaces. 142 175-208 Dickson, L. E., An invariantive investigation of irreducible binary modular forms. 12i 1-18 -A fundamental system of invariants of the general modular linear group with a solution of the form problem. 12i 75- 98 -Linear algebras. 13i 59- 73 -Proof of the finiteness of modular covariants. 143 299-310 -Linear associative algebras and abelian equations. 15i 31- 46 -Invariants in the theory of numbers. 15¿ 497-503 -Quartic curves modulo 2. I62 111-120 Dines, L. L., Projective transformations in function space.... 20i 45- 65 Dresden, A., On the second derivatives of an extremal-integral with an application to a problem with variable end points. 174 425-436 -On the second derivatives of the extremal-integral for the integral f F(y; y')dt. 183 373-378 Eisenhart, L. P., Congruences of the elliptic type. 113 351-370 -Surfaces with isothermal representation of their lines of curvature and their transformations (second memoir).... 114 475-486 -Certain continuous deformations of surfaces applicable to the quadrics. 143 365-402 -Transformations of surfaces of Voss. 153 245-265 -Transformations of conjugate systems with equal point invariants. 154 397-430 -Surfaces it and their transformations. 163 275-310 s INDEX BY AUTHORS [October
Vol. Pages -Transformations of surfaces 0 (second memoir). 17i 53- 99 -Deformable transformations of Ribaucour. 174 437-458 -Transformations T of conjugate systems of curves on a surface. 18i 97-124 -Transformations of applicable conjugate nets of curves on surfaces. 192 167-185 -Transformations of surfaces applicable to a quadric. 204 323-338 Eiesland, J., On minimal lines and congruences in four- dimensional space. 124 403-428 Ettlinger, H. J., Existence theorems for the general real self- adjoint linear system of the second order. 19i 79- 96 E-VANS,G. C, Volterra's integral equation of the second kind, with discontinuous kernel. 114 393^413 -Volterra's integral equation of the second kind, with discontinuous kernel (second paper). 124 429-472 -The Cauchy problem for integro-differential equations. . . 152 215-226 -On the reduction of integro-differential equations. 154 477-496 Fields, J. C, A method of proving certain theorems relating to rational functions which are adjoint to an algebraic equa- tion for a given value of the independent variable. 132 164-174 Fite, W. B., Some theorems concerning groups whose orders are powers of a prime. 15i 47- 50 -Prime power groups in which every commutator of prime order is invariant. 162 134-138 -Concerning the zeros of the solutions of certain differ- ential equations. 194 341-352 Ford, L. R., Rational approximations to irrational complex numbers. 19i 1-42 Fréchet, M., Sur les classes V normales. 143 320-324 -Sur la notion de différentielle d'une fonction de ligne. ... 152 135-161 -Sur les fonctionnelles bilinéaires. 163 215-234 -Relations entre les notions de limite et de distance. 19i 53- 65 Gaba, M. G., A set of postulates for general projective geometry 16i 51- 61 Glenn, O. E., On semi-discriminants of ternary forms. 123 367-374 -The symbolical theory of finite expansions. 15i 72- 86 -On the invariant system of a pair of connexes. 174 405-417 -The formal modular invariant theory of binary quanti es. 174 545-556 -A memoir on the doctrine of associated forms. 184 443-462 -A fundamental system of formal covariants, modulo 2, of the binary cubic. 19i 109-118 -Modular concomitant scales, with a fundamental system of formal covariants, modulo 3, of the binary quadratic... 202 154-168 -On ' a new treatment of theorems of finiteness.\ „„ Q,ft 1919] INDEX BY AUTHORS 9
Vol. Pages Graustein, W. C, The equivalence of complex points, planes, lines with respect to real motions and certain other groups of real transformations. 16i 33- 44 Green, G. M., One-parameter families of curves in the plane. . 153 277-290 -On the theory of curved surfaces and canonical systems in projective differential geometry. 16i 1-12 -The linear dependence of functions of several variables, and completely integrable systems of homogeneous linear partial differential equations. 174 483-516 -Some geometric characterizations of isothermal nets on a curved surface. 184 480^188 -Memoir on the general theory of surfaces and rectilinear congruences. 202 79-153 Gronwall, T. H., On a theorem of Fejér's and an analogon to Gibb's phenomenon. 134 445-468 -Some asymptotic expressions in the theory of numbers... 14i 113-122 -On the degree of convergence of Laplace's series.15i 1-30 -On the expressibility of a uniform function of several vari- ables as the quotient of two functions of entire character. . 18i 50- 64 -On the influence of keyways on the stress distribution in cylindrical shafts. 203 234-244 Hardy, G. H., Weierstrass's non-differentiable function. 173 301-325 Hart, W. L., Differential equations and implicit functions in infinitely many variables. 182 125-160 Haskins, C. N., On the zeros of the function, P(x), comple- mentary to the incomplete gamma function. 164 405-412 -On the measurable bounds and the distribution of func- tional values of summable functions. 172 181-194 Hazlett, O. C, On the theory of associative division algebras. 182 167-176 -On scalar and vector covariants of linear algebras. 194 408-420 H'Doubler, F., (with E. B. Van Vleck), A study of certain functional equations for the tf-functions. 17i 9-49 Hedrick, E. R., On properties of a domain for which any de- rived set is closed. 123 285-294 -(with L. Ingold), A set of axioms for line geometry. 152 205-214 Hildebrandt, T. H., On a theory of linear differential equations . . . 73- 96 in analysis.-j Jl8i general 1 „ r4f) -On boundary value problems in linear differential equa- tions in general analysis. 19i 97-108 Hodgson, J. E., Orthocentric properties of the plane directed n-line. 13? 199-231 Hoskins, L. M., The strain of a gravitating, compressible elastic sphere. 112 203-248 10 INDEX BY AUTHORS [October
Vol. Pages -The strain of a non-gravitating sphere of variable density 114 494-504 Hopkins, J. W., Some convergent developments associated with irregular boundary conditions. 203 245-259 Hu, M. F., Linear integro-differential equations with a boundary condition. 194 363-407 Huntington, E. V. (with J. R. Kline), Sets of independent postulates for betweenness. 183 301-325 Hurwitz, W. A., On the pseudo-resolvent to the kernel of an integral equation. 134 405-418 -Mixed linear integral equations of the first order. 162 121-133 -(with L. L. Silverman), On the consistency and equivalence of certain definitions of summability. 18i 1-20 Ingold, L., Vector interpretation of symbolic differential parameters. 114 449-474 -Functional differential geometry. 133 319-341 -(with E. R. Hedrick), A set of axioms for line geometry. . 152 205-214 Jackson, D., On the degree of convergence of the development of a continuous function according to Legendre's poly- nomials . 133 305-318 -On approximation by trigonometric sums and poly- nomials . 134 491-515 -On the approximate representation of an indefinite integral and the degree of convergence of related Fourier's series. . 143 343-364 -On the accuracy of trigonometric interpolation. 144 453-461 -On the degree of convergence of Sturm-Liouville series... 154 439-466 -Proof of a theorem of Haskins. 172 178-180 -Algebraic properties of self-adjoint systems. 174 418^24 Johnson, R. A., The conic as a space element. 154 335-368 Kasner, E., The theorem of Thomson and Tait and natural families of trajectories.-.. 112 121-140 -Natural systems of trajectories generating families of Lamé 12i 70- 74 -Conformai classification of analytic arcs or elements; Poincaré's local problem of conformai geometry.163 333-349 Kellogg, O. D., Harmonic functions and Green's integral. ... 13i 109-132 Kempner, A. J., On transcendental numbers. 174 476-482 Kircher, E., Group properties of the residue classes of certain Kronecker modular systems and some related generaliza- tions in number theory. 164 413-434 Kline, J. R., The converse of the theorem concerning the division of a plane by an open curve. 182 177-484 -(with E. V. Huntington), Sets of independent postulates for betweenness. 183 301-325 Lamond, J. K., Improper multiple integrals over iterable fields. 134 434-444 1919] INDEX BY AUTHORS 11
Vol. Pages -The reduction of multiple L-integrals of separated func- tions to iterated L-integrals. 164 387-398 Landau, E., Ueber eine idealtheoretische Funktion. 13i 1-21 Larew, G. A., Necessary conditions in the problems of Mayer in the calculus of variations. 20i 1-22 Lefschetz, S., On the existence of loci with given singularities. 14i 23- 41 Lennes, N. J., Note on Van Vleck's non-measurable set. 14i 109-112 Lipke, J., Natural families of curves in a general curved space of n dimensions. 13i 77- 95 Longley, W. R., An existence theorem for a certain differential equation of the nth order. 153 328-334 Love, C. E., Singular integral equations of the Volterra type.. 154 467-476 Lovitt, W. V., A type of singular points for a transformation of three variables. 164 371-386 Lytle, E. B., Proper multiple integrals over iterable fields. . . . -{ -1 __ . * t154, 504-505„_ MacMillan, W. D., Periodic orbits about an oblate spheroid. Hi 55-120 -An existence theorem for periodic solutions. 132 146-158 -A reduction of certain analytic differential equations to differential equations of an algebraic type. 173 245-258 -On the reduction of certain differential equations of the second order. 192 205-222 Manning, W. A., On the limit of the degree of primitive groups 124 375-386 -On the order of primitive groups, II. 162 139-147 -The degree and class of multiply transitive groups. 184 463-479 -The order of primitive groups (III). 192 127-142 -The order of primitive groups (IV). 20i 66- 78 Mason, M. (with G. A. Bliss), Fields of extremals in space. . . 113 325-340 Mathewson, L. C, On the group of isomorphisms of a certain extension of an abelian group. 194 331-340 McDonnell, J., On quadratic residues. 144 477-480 Miles, E. J., The absolute minimum of a definite integral in a special field. 13i 35- 49 Miller, B. I., A new canonical form of the elliptic integral. . . 173 259-283 Miller, G. A., Groups generated by two operators (si, s2) satisfying the equation Sisl = s2s2. 113 341-350 -On the use of the co-sets of a group. 123 326-334 -Isomorphisms of a group whose order is a power of a prime 124 387-402 -Infinite systems of indivisible groups. 134 419-433 -On the representation groups of given abstract groups... 144 444-452 -The ^-subgroup of a group. 16i 20- 26 -Independent generators of a group of finite order. 164 399-404 -Finite groups represented by special matrices. 173 326-332 -Sets of independent generators of a substitution group... 193 299-304 Trans. Am. Math. Soe, Hü 12 INDEX BY AUTHORS [October
Vol. Pages -Groups possessing a small number of sets of conjugate oper- ators. 203 260-270 Milne, W. E., On the degree of convergence of Birkhoff's series 192 143-156 MiseRj W. L., On multiform solutions of linear differential equations having elliptic function coefficients. 172 109-130 Mitchell, H. B., On the imaginary roots of a polynomial and the real roots of its derivative. 19i 43- 52 Mitchell, H. H., Determination of the ordinary and modular ternary linear groups. 122 207-242 -Determination of the finite quaternary linear groups. 14i 123-142 -The subgroups of the quaternary abelian linear group... . 154 379-396 -On the generalized Jacobi-Kummer cyclotomic function. . 172 165-177 -Proof that certain ideals in a cyclotomic realm are prin- cipal ideals. 192 119-126 Moore, C. N., On the uniform convergence of the develop- ments in Bessel's functions. 122 181-206 -On convergence factors in double series and the double Fourier's series. 14i 73-104 Moore, R. L., A note concerning Veblen's axioms for geometry 13i 74- 76 -On a set of postulates which suffice to define a number- plane . 16i 27-32 -On the foundations of plane analysis situs. 172 131-164 -Concerning a set of postulates for plane analysis situs. . . 202 169-178 Morgan, F. M. (with J. W. Young), The geometries associated with a certain system of Cremona groups. 173 233-244 Moulton, E. J., On figures of equilibrium, of a rotating com- pressible fluid mass; certain negative results. 17i 100-108 Moulton, F. R., A class of periodic orbits of superior planets. 13i 96-108 Neikirk, L. I., Groups of rational transformations in a general field. 11, 294-300 Osgood, W. F., A condition that a function in a projective space be rational. 132 159-163 -(with E. H. Taylor), Conformai transformations on the boundaries of their regions of definition. 142 277-298 -On functions of several complex variables. 17i 1- 8 -On infinite regions. 173 333-344 -Singular points of analytic transformations. 193 251-274 Owens, F. W., The introduction of ideal elements and a new definition of projective n-space. 112 141-171 Pell, A. J., Biorthogonal systems of functions. 122 135-164 -Applications of biorthogonal systems of functions to the theory of integral equations. 122 165-180 -Linear equations with unsymmetric systems of coefficients 20i 23- 39 ■-A general system of linear equations. 204 343-355 1919] INDEX BY AUTHORS 13
Vol. Pages Pfeiffer, G. A., On the conformai mapping of curvilinear angles. The functional equation
Vol. Pages Shaw, J. B., Quaternion developments with applications. 133 279-292 -On parastrophic algebras. 163 361-370 Sheffer, H. M., A set of five independent postulates for boolean algebras, with application to logical constants.... 144 481-488 Silverman, L. L., On the notion of summability for the limit of a function of a continuous variable. 173 284-294 -(with W. A. Hurwitz), On the consistenc}' and equivalence of certain definitions of summability. 18i 1-20 Simonds, E. F., Invariants of differential configurations in the plane. 192 223-250 Slepian, J., The functions of a complex variable defined by an ordinary differential equation of the first order and the first degree. 16i 71-88 Smith, D. M., Jacobi's condition for the problem of Lagrange in the calculus of variations. 174 459—475 Smith, P. F., On osculating element-bands associated with loci of surface-elements. 113 301-324 -A theorem for space analogous to Cesàro's theorem for plane isogonal systems. 184 522-540 Snyder, V., Infinite discontinuous groups of birational trans- formations which leave certain surfaces invariant. Hi 15- 24 -Conjugate line-congruences contained in a bundle of quadric surfaces. 114 371-387 -An application of a (1, 2) quaternary correspondence to the Kummer and Weddle surfaces. 123 354-366 -Algebraic surfaces invariant under an infinite discon- tinuous group of birational transformations (second paper) 14i 105-108 -(with F. R. Sharpe), Birational transformations of certain quartic surfaces. 153 266-276 -(with F. R. Sharpe), Certain quartic surfaces belonging to infinite discontinuous cremonian groups. 16i 62- 70 - (with F. R. Sharpe), Types of (2, 2) point correspondences between two planes. 183 402-414 -(with F. R. Sharpe), Space involutions defined by a web of quadrics. 193 275-290 -(with F. R. Sharpe), Certain types of involutorial space transformations. 203 185-202 Study, E., Die natürlichen Gleichungen der analytischen Curven im Euclidischen Räume. 1I3 249-279 Sullivan, C. T., Properties of surfaces whose asymptotic curves belong to linear complexes. 152 167-196 -Scroll directrix curves. 162 199-214 Taylor, E. H. (with W. F. Osgood), Conformai transforma- tions on the boundaries of their regions of definition. 142 277-298 1919] INDEX BY AUTHORS 15
Vol. Pages Underhill, A. L. (with G. A. Bliss), The minimum of a definite integral for unilateral variations in space. 153 291-310 Urner, S. E., Certain singularities of point transformations in space of three dimensions. 132 232-264 de la Vallée Poussin, O, Sur l'intégraje de Lebesgue. 164 435-501 Vandiver, H. S., Theory of finite algebras. 133 293-304 -Note on Fermat's last theorem. 152 202-204 Van Vleck, E. B., On the extension of a theorem of Poincaré í 133 342-352 for difference equations.| 134 517 -One-parameter projective groups and the classification I 133 353-386 of collineations.} 134 517 -(with F. H'Doubler), A study of certain functional equa- tions for the ^-functions. 17i 9-49 -Haskin's momental theorem and its connection with Stieltjes's problem of moments. 183 326-330 -On the combination of non-loxodromic substitutions. 204 299-312 x Veblen, O., Decomposition of an V-space by a polyhedron \ { lot 506 Wahlin, G. E., On the base of a relative number-field, with f 114 487-493 an application to the composition of fields.j 124 511-512 -A new development of the theory of algebraic numbers. . 164 502-508 Walsh, J. L., On the location of the roots of the jacobian of two binary forms, and of the derivative of a rational function. 193 291-298 Wedderburn, J. H. M., A type of primitive algebra. 152 162-166 -On matrices whose coefficients are functions of a single variable. 163 328-332 Westlund, J., On the fundamental number of the algebraic number field k{^m)_. 114 388-392 White, H. S., Triple-systems as transformations, and their paths among triads. 14i 6-13 -The multitude of triad systems on 31 letters. 16i 13- 19 White, M. B., The dependence of focal points upon curvature for problems of the calculus of variations in space. 132 175-198 Whittemore, J. K., Spiral minimal surfaces. 194 315-330 Wiener, N, Certain formal invariances in boolean algebras.. . 18i 65- 72 Wilczynski, E. J., One-parameter families and nets of plane curves. 124 473-510 -On a certain set of self-projective surfaces. 144 421-443 -The general theory of congruences. 163 311-327 -Line geometric representations for functions of a complex variable. 204 271-298 Wilder, C. E., Expansion problems of ordinary linear differ- ential equations with auxiliary conditions at more than two points. 184 415-442 16 INDEX BY AUTHORS
Vol. Pages -Problems in the theory of ordinary linear differential equa- tions with auxiliary conditions at more than two points... 192 157-166 Wiley, F. B., Proof of the finiteness of the modular covariants of a system of binary forms and cogredient points. 154 431-438 Williams, K. P., The solutions of non-homogeneous linear difference equations and their asymptotic form. 142 209-240 Young, J. W., Two-dimensional chains and the associated collineations. Ils 280-293 -(with F. M. Morgan), The geometries associated with a certain system of Cremona groups. 173 233-244 INDEX BY SUBJECT MATTER
A. Logical Analysis of Mathematical Disciplines Vol. Pages Bernstein, B. A., A set of four independent postulates for boolean algebras. 17 50- 52 Gaba, M. G., A set of postulates for general projective geometry 16 51- 61 Hedrick, E. R. (with L. Ingold), A set of axioms for line geometry. 15 205-214 Huntington, E. V. (with J. R. Kline), Sets of independent postulates for betweenness. 18 301-325 Ingold, L. (with E. R. Hedrick), A set of axioms for line geometry. 15 205-214 Kline, J. R. (with E. V. Huntington), Sets of independent postulates for betweenness. 18 301-325 Moore, R. L., A note concerning Veblen's axioms for geometry 13 74- 76 -On a set of postulates which suffice to determine a number plane. 16 27-32 -On the foundations of plane analysis situs. 17 131-164 -Concerning a set of postulates for plane analysis situs... 20 169-178 Root, R. E., Limits in terms of order, with example of limiting element not approachable by a sequence. 15 51-71 Sheffer, H. M., A set of five independent postulates for boolean algebras, with application to logical constants... 14 481^188
B. Algebra B 1. Rational Functions. Theory of Equations. Determinants. Symmetric Functions Birkhoff, G. D., Infinite products of analytic matrices. 17 386-404 Blumberg, H., On the factorization of expressions of various types. 17 517-544 Coble, A. B., An application of Moore's cross-ratio group to the solution of the sextic equation. 12 311-325 Cole, F. N., The triad systems of thirteen letters. 14 1- 5 Cummings, L. D., On a method of comparison for triple- systems. 15 311-327 Curtiss, D. R., Extensions of Descartes' Rule of Signs con- nected with a problem suggested by Laguerre. 16 350-360 Dickson, L. E., Linear associative algebras and abelian equa- tions . 15 31- 46 17 18 INDEX BY SUBJECT MATTER [October
Vol. Pages Fields, J. C, A method of proving certain theorems relating to rational functions which are adjoint to an algebraic equa- tion for a given value of the independent variable. 13 164-174 Mitchell, H. B., On the imaginary roots of a polynomial and the real roots of its derivative. 19 43- 52 Walsh, J. L., On the location of the roots of the jacobian of two binary forms, and of the derivative of a rational function. 19 291-298 White, H. S., Triple systems as transformations, and their paths among triads. 14 6- 13 -The multitude of triad systems on 31 letters. 16 13- 19
B 2. Algebraic Forms (Cf. F 2) Dickson, L. E., An invariantive investigation of irreducible binary modular forms. 12 1-18 -A fundamental system of invariants of the general modular linear group with a solution of the form problem. 12 75- 98 -Proof of the finiteness of modular covariants. 14 299-310 -Invariants in the theory of numbers. 15 497-503 Glenn, O. E., On semi-discriminants of ternary forms. 12 367-374 -The symbolical theory of finite expansions. 15 72- 86 -On the invariant system of a pair of connexes. 17 405^17 -The formal modular invariant theory of binary quantics.. 17 545-556 -A memoir on the doctrine of associated forms. 18 443-462 -A fundamental system of formal covariants, modulo 2, of the binary cubic. 19 109-118 -Modular concomitant scales, with a fundamental system of formal covariants, modulo 3, of the binary quadratic.. 20 154-168 203-212 On a new treatment of theorems of finiteness. [20 [20 356 Rowe, J. E., Important covariant curves and a complete system of invariants of a rational quartic curve. 12 295-310 -Bicombinants of the rational plane quartic and combinants of the rational plane quintic. 13 387-404 Sanderson, M., Formal modular invariants with application to binary modular covariants. 14 489-500 Wiley, F. B., Proof of the finiteness of the modular covariants of a system of binary forms and cogredient points. 15 431-438
B 3. Linear Associative Algebra. Hyper complex Number Systems. Fields (Cf. F 1) Dickson, L. E., Linear algebras. 13 59- 73 -Linear associative algebras and abelian equations. 15 31- 46 1919] INDEX BY SUBJECT MATTER 19
Vol. Pages Hazlett, O. C, On the theory of associative division algebras. 18 167-176 -On scalar and vector covariants of linear algebras. 19 408-420 Shaw, J. B., Quaternion developments with applications. 13 279-292 -On parastrophic algebras. 16 361-370 Sheffer, H. M., A set of five independent postulates for boolean algebras, with application to logical constants... 14 481-488 Vandiver, H. S., Theory of finite algebras. 13 293-304 Wedderburn, J. H. M., A type of primitive algebra. 15 162-166 Wiener, N., Certain formal invariances in boolean algebras... 18 65- 72
C. Theory of Numbers (Cf. E 1, E 2) Blichfeldt, H. F., A new principle in the geometry of numbers, with some applications. 15 227-235 Dickson, L. E., Invariants in the theory of numbers. 15 497-503 Gronwall, T. H., Some asymptotic expressions in the theory of numbers. 14 113-122 Kempner, A. J., On transcendental numbers. 17 476^182 Kircher, E., Group properties of the residue classes of certain Kronecker modular systems and some related general- izations in number theory. 16 413-434 McDonnell, J., On quadratic residues. 14 477-480 Mitchell, H. H., On the generalized Jacobi-Kummer cyclo- tomic function. 17 165-177 -Proof that certain ideals in a cyclotomic realm are prin- cipal ideals. 19 119-126 Ranum, A., The groups of classes of congruent quadratic integers with respect to a composite ideal modulus. 11 172-198 Vandiver, H. S., Note on Fermat's last theorem. 15 202-204 Wahlin, G. E., On the base of a relative number-field, with j 11 487-493 an application to the composition of fields.[12 511-512 -A new development of the theory of algebraic numbers. . 16 502-508 Westlund, J., On the fundamental number of the algebraic number field fc(^rä). 11 388-392
D. Analysis Dl. Functions of Real Variables. Point Sets Brink, R. W., A new integral test for the convergence and divergence of infinite series. 19 186-204 Camp, B. H., Singular multiple integrals, with applications to series. 14 42- 64 20 INDEX BY SUBJECT MATTER [October
Vol. Pages -Lebesgue integrals containing a parameter, with applica- tions . 15 87-106 Chittenden, 'E. W., Relatively uniform convergence of se- quences of functions. 15 197-201 -On the equivalence of écart and voisinage. 18 161-166 -(with A. D. Pitcher), On the foundations of the calcul fonctionnel of Fréchet. 19 66- 78 -On the limit functions of sequences of continuous func- tions, converging relatively uniformly. 20 179-184 -(with A. D. Pitcher), On the theory of developments of an abstract class in relation to the calcul fonctionnel. 20 213-233 16 155-198 Coble, A. B., Point sets and allied Cremona groups.t 17 345-385 .18 331-372 Daniell, P. J., Differentiation with respect to a function of limited variation. 19 353-362 Fréchet, M., Sur les classes V normales. 14 320-324 -Sur la notion de différentielle d'une fonction de ligne.... 15 135-161 -Sur les fonctionnelles bilinéaires. 16 215-234 -Relations entre les notions de limite et de distance. 19 53- 65 Gronwall, T. H., On a theorem of Féjer's and an analogon to Gibb's phenomenon. 13 445-468 -On the degree of convergence of Laplace's series.15 1- 30 Hardy, G. H., Weierstrass's non-differentiable function. 17 301-325 Haskins, C. N., On the zeros of the function, P{x), comple- mentary to the incomplete gamma function. 16 405-412 -On the measurable bounds and the distribution of func- tional values of summable functions. 17 181-194 Hedrick, E. R., On properties of a domain for which any de- rived set is closed. 12 285-294 Hopkins, J. W., Some convergent developments associated with irregular boundary conditions. 20 245-259 Hurwitz, W. A. (with L. L. Silverman), On the consistency and equivalence of certain definitions of summability. 18 1- 20 Jackson, D., On the degree of convergence of the development of a continuous function according to Legendre's poly- nomials . 13 305-318 -On approximation by trigonometric sums and polynomials 13 491-515 -On the approximate representation of an indefinite integral and the degree of convergence of related Fourier's series. 14 343-364 -On the accuracy of trigonometric interpolation. 14 453^61 -On the degree of convergence of Sturm-Liouville series... 15 439-466 -Proof of a theorem of Haskins. 17 178-180 1919] INDEX BY SUBJECT MATTER 21
Vol. Pages Kellogg, O. D., Harmonic functions and Green's integral. ... 13 109-132 Kline, J. R., The converse of the theorem concerning the division of a plane by an open curve. 18 177-184 Lamond, J. K., Improper multiple integrals over iterable fields 13 434-444 -The reduction of multiple L-integrals of separated func- tions to iterated L-integrals. 16 387-398 Lennes, N. J., Note on Van Vleck's non-measurable set. 14 109-112 Lovitt, W. V., A type of singular points for a transformation of three variables. 16 371-386 11 25- 36 Lytle, E. B., Proper multiple integrals over iterable fields. 15 504-505 Moore, C. N., On convergence factors in double series and the double Fourier's series. 14 73-104 Osgood, W. F., A condition that a function in a projective space be rational. 13 159-163 Pell, A. J., Biorthogonal systems of functions. 12 135-164 Pitcher, A. D. (with E. W. Chittenden), On the foundations of the calcul fonctionnel of Fréchet. 19 66- 78 -(with E. W. Chittenden), On the theory of developments of an abstract class in relation to the calcul fonctionnel.. 20 213-233 Silverman, L. L., On the notion of summability for the limit of a function of a continuous variable. 17 284-294 -(with W. A. Hurwitz), On the consistency and equivalence of certain definitions of summability. 18 1- 20 De la Vallée Poussin, Sur l'intégrale de Lebesgue. 16 435-501
D 2. Functions of Complex Variables Bliss, G. A., A generalization of Weierstrass' preparation the- orem for a power series in several variables. 13 133-145 Carmichael, R. D., On a general class of series of the form £ cngix A-n). 17 207-232 .-»oo -On a general class of integrals of the form J Vol. Pages -On functions of several complex variables. 17 1- 8 -On infinite regions. 17 333-344 -Singular points of analytic transformations. 19 251-274 Ritt, J. F., The resolution into partial fractions of the re- ciprocal of an entire function of genus zero. 18 21- 26 Slepian, J., The functions of a complex variaole defined by an ordinary differential equation of the first order and the first degree. 16 71-88 Taylor, E. H. (with W. F. Osgood), Conformai transformations on the boundaries of their regions of definition. 14 277-298 Van Vleck, E. B., Haskin's momental theorem and its con- nection with Stieltjes's problem of moments. 18 326-330 Wedderburn, J. H. M., On matrices whose coefficients are functions of a single variable. 16 328-332 D 3. Particular Functions Blumberg, H., On convex functions. 20 40- 44 Carmichael, R. D., On transcendentally transcendental func- tions . 14 311-319 Coble, A. B., An application of finite geometry to the charac- teristic theory of the odd and even theta functions. 14 241-276 Craig, C F., On a class of hyperfuchsian functions. 11 37- 54 Fréchet, M., Sur la notion de différentielle d'une fonction de ligne. 15 135-161 Gronwall, T. H., On the degree of convergence of Laplace's series. 15 1-30 H'Doubler, F. (with E. B. Van Vleck), A study of certain functional equations for the ^-functions. 17 9-49 Jackson, D., On the degree of convergence of the development of a continuous function according to Legendre's poly- nomials. 13 305-318 -On the approximate representation of an indefinite integral and the degree of convergence of related Fourier's series. . 14 343-364 -On the degree of convergence of Sturm-Liouville series... 15 439-466 Kellogg, O. D., Harmonic functions and Green's integral.... 13 109-132 Landau, E., Ueber eine idealtheoretische Funktion. 13 1-21 Moore, C. N., On the uniform convergence of the developments in Bessel's functions. 12 181-206 -On convergence factors in double series and the double Fourier's series. 14 73-104 Pell, A. J., Biorthogonal systems of functions. 12 135-164 Van Vleck, E. B. (with F. H'Doubler), A study of certain functional equations for the .-functions. 17 9-49 1919] INDEX BY SUBJECT MATTER 23 D 4. Ordinary Differential Equations (Cf. D 2, D 3, F 4) Vol. Pages Birkhoff, G. D., A simplified treatment of the regular singular point. 11 199-202 -On a simple type of irregular singular point. 14 462-476 Bôcher, M., Applications and generalizations of the concep- tion of adjoint systems. 14 403-420 ''On -Note supplementary to the paper certain pairs of transcendental functions whose roots separate each other " 18 519-521 Ettlinger, H. J., Existence theorems for the general real self- adjoint linear system of the second order. 19 79- 96 Fite, W. B., Concerning the zeros of the solutions of certain differential equations. 19 341-32 Hart, W. L., Differential equations and implicit functions in infinitely many variables. 18 125-160 Hildebrandt, T. H., On a theory of linear differential equations in general analysis.f 18 73- 96 -On boundary value problems in linear differential equa- \ 18 540 tions in general analysis. 19 97-108 Jackson, D., Algebraic properties of self-adjoint systems. 17 418-424 Longley, W. R., An existence theorem for a certain differential equation of the nth order. 15 328-334 MacMillan, W. D., An existence theorem for periodic solutions 13 146-158 -A reduction of certain analytic differential equations to differential equations of an algebraic type. 17 245-258 -On the reduction of certain differential equations of the second order. 19 205-222 Miser, W. L., On multiform solutions of linear differential equations having elliptic function coefficients. 17 109-130 Richardson, R. G. D., Theorems of oscillation for two linear differential equations of the second order with two param- eters . 13 22- 34 -A new method in boundary problems for differential equa- tions . 18 489-518 Ritt, J. F., On a general class of linear homogeneous differ- ential equations of infinite order with constant coefficients 18 27- 49 Slepian, J., The functions of a complex variable defined by an ordinary differential equation of the first order and the first degree. 16 71- 88 Wilder, C. E., Expansion problems of ordinary linear differ- ential equations with auxiliary conditions at more than two points. 18 41^442 24 INDEX BY SUBJECT MATTER [October Vol. Pages -Problems in the theory of ordinary linear differential equations with auxiliary conditions at more than two points. 19 157-166 D 5. Partial Differential Equations Green, G. M., The linear dependence of functions of several variables, and completely integrable systems of homo- geneous linear partial differential equations. 17 483-516 D 7. Calculus of Variations Bill, E. G., An existence theorem for a problem of the calculus of variations in space. 13 50- 58 Bliss, G. A. (with M. Mason), Fields of extremals in space. . . 11 325-340 -(with A. L. Underhill), The minimum of a definite integral for unilateral variations in space. 15 291-310 -The Weierstrass E-Function for problems of the calculus of variations in space. 15 369-378 -Jacobi's condition for problems in the calculus of variations in parametric form. 17 195-206 The problem of Mayer with variable end points. 19 305-314 Dresden, A., On the second derivatives of an extremal-integral with an application to a problem with variable end points. 17 425-436 -On the second derivatives of the extremal-integral for the integral /F{y; y')dt. 18 373-378 Larew, G. A., Necessary conditions in the problems of Mayer in the calculus of variations. 20 1- 22 Mason, M. (with G. A. Bliss), Fields of extremals in space.... 11 325-340 Miles, E. J., The absolute minimum of a definite integral in a special field. 13 35- 49 Smith, D. M., Jacobi's condition for the problem of Lagrange in the calculus of variations. 17 459^75 Underhill, A. L. (with G. A. Bliss), The minimum of a definite integral for unilateral variations in space. 15 291-310 White, M. B., The dependence of focal points upon curvature for problems of the calculus of variations in space. 13 175-198 D 8. Difference Equations Birkhoff, G. D., General theory of linear difference equations 12 243-284 Carmichael, R. D., Linear difference equations and their analytic solutions. 12 99-134 Van Vleck, E. B., On the extension of a theorem of Poincaré j 13 342-352 for difference equations.[13 517 Williams, K. P., The solutions of non-homogeneous linear difference equations and their asymptotic form. 14 209-240 1919] INDEX BY SUBJECT MATTER 25 D 9. Integral Equations Vol. Pages Evans, G. C, Volterra's integral equation of the second kind, with discontinuous kernel. 11 393—413 -Volterra's integral equation of the second kind, with dis- continuous kernel (second paper). 12 429—472 -The Cauchy problem for integro-differential equations. . . 15 215-226 -On the reduction of integro-differential equations. 15 477—496 Hu, M. F., Linear integro-differential equations with a boundary condition. 19 363-407 Hurwitz, W. A., On the pseudo-resolvent to the kernel of an integral equation. 13 405—118 -Mixed linear integral equations of the first order. 16 121-133 Love, C. E., Singular integral equations of the Volterra type.. 15 467^176 Pell, A. J., Applications of biorthogonal systems of functions to the theory of integral equations. 12 165-180 -Linear equations with unsymmetric systems of coefficients 20 23- 39 -A general system of linear equations. 20. 343-355 Groups. E 1. Discrete Groups in General (Cf. E 2) Blichfeldt, H. F., Theorems on simple groups. 11 1-14 Fite, W. B., Some theorems concerning groups whose orders are powers of a prime. 15 47- 50 -Prime power groups in which every commutator of prime order is invariant. 16 134-138 Manning, W. A., On the limit of the degree of primitive groups ' 12 375-386 16 139-147 -On the order of primitive groups.- 19 127-142 20 66- 78 —— The degree and class of multiply transitive groups. 18 463-479 Mathewson, L. C, On the group of isomorphisms of a certain extension of an abelian group. 19 331-340 Miller, G. A., Groups generated by two operators (si, s2) satisfying the equation Sisl = s2s\. 11 341-350 -On the use of the co-sets of a gioup. 12 326-334 -Isomorphisms of a group whose order is a power of a prime 12 387-402 -Infinite systems of indivisible groups. 13 419-433 -On the representation groups of given abstract groups... 14 444—452 -The yj-subgroup of a group. 16 20- 26 -Independent generators of a group of finite order. 16 399-404 '-Finite groups represented by special matrices. 17 326-332 26 INDEX BY SUBJECT MATTER [October Vol. Pages -Sets of independent generators of a substitution group... 19 299-304 -Groups possessing a small number of sets of conjugate oper- ators . 20 260-270 Neikirk, L. I., Groups of rational transformations in a general field. 11 294-300 Ranum, A., The groups of classes of congruent quadratic integers with respect to a composite ideal modulus. 11 172-198 E 2. Linear Groups in Arbitrary or Special Fields Blichfeldt, H. F., On the order of linear homogeneous groups (fourth paper). 12 39-42 Coble, A. B., An application of Moore's cross-ratio group to the solution of the sextic equation. 12 311-325 Dickson, L. E., A fundamental system of invariants of the general modular linear group with a solution of the form problem. 12 75-98 Dines, L. L., Projective transformations in function space.... 20 45- 65 Mitchell, H. H., Determination of the ordinary and modular ternary linear groups. 12 207-242 -Determination of the finite quaternary linear groups. 14 123-142 -The subgroups of the quaternary abelian linear group.... 15 379-396 E 3. Continuous Groups (Cf. E 2, F 1, F 3, G 3) SiMONDS, E. F., Invariants of differential configurations in the plane. 19 223-250 Van Vleck, E. B., One-parameter projective groups and the J 13 353-386 classification of collineations.[13 517 -On the combination of non-loxodromic substitutions. 20 299-312 F. Geometry F 1. Synthetic Geometry. Non-Euclidean Geometry. Geometry of n dimen- sions. Analysis Situs (Cf. D 1, D 2) Alexander, J. W., A proof of the invariance of certain con- stants of analysis situs. 16 148-154 -Note on two three-dimensional manifolds with the same group. 20 339-342 Moore, R. L., On the foundations of plane analysis situs. 17 131-164 Veblen, O., Decomposition of an N-space by a polyhedron •••,,- cnfi 1919] INDEX BY SUBJECT MATTER 27 F 2. Algebraic Geometry; Algebraic Curves and Surfaces (Cf. B 2, D 3, E 2, F 1, F 4, F 5) Vol. Pages Conner, J. R., Multiple correspondences determined by the rational plane quintic curve. 13 265-278 Craig, C. F. (with F. R. Sharpe), An application of Severi's theory of a basis to the Kummer and Weddle surfaces.... 15 236-244 Dickson, L. E., Quartic curves modulo 2. 16 111-120 Graustein, W. C, The equivalence of complex points, planes, lines with respect to real motions and certain other groups of real transformations. 16 33- 44 Lefschetz, S., On the existence of loci with given singularities 14 23- 41 Rowe, J. E., Important covariant curves and a complete system of invariants of a rational quartic curve. 12 295-310 -Invariants of the rational plane quintic curve and of any rational curve of odd order. 16 45- 50 Sharpe, F. R. (with C. F. Craig), An application of Severi's theory of a basis to the Kummer and Weddle surfaces.... 15 236-244 Snyder, V., Infinite discontinuous groups of birational trans- formations which leave certain surfaces invariant. 11 15-24 -Conjugate line-congruences contained in a bundle of quadric surfaces. 11 371-387 -An application of a (1, 2) quaternary correspondence to the Kummer and Weddle surfaces. 12 354-366 F 3. Geometry of Special Space-Elements Barrow, D. F., Oriented circles in space. 16 235-258 Coolidge, J. L., A study of the circle cross. 14 149-174 -Congruences and complexes of circles. 15 107-134 Johnson, R. A., The conic as a space element. 15 335-368 Owens, F. W., The introduction of ideal elements and a new definition of projective n-space. 11 141-171 F 4. Differential Geometry (Cf. D 6) Bates, W. H., An application of symbolic methods to" the treatment of mean curvatures in hyperspace. 12 19- 38 Bianchi, L., Concerning singular transformations Bk of surfaces applicable to quadrics. 18 379-401 Carpenter, A. F., Ruled surfaces whose flecnode curves have plane branches. 16 509-532 Coolidge, J. L., The metrical aspect of the line-sphere trans- formation. 12 43-69 28 INDEX BY SUBJECT MATTER [October Vol. Pages -A study of the circle cross. 14 149-174 -Congruences and complexes of circles. 15 107-134 Dentón, W. W., Projective differential geometry of developable surfaces. 14 175-208 Eisenhart, L. P., Congruences of the elliptic type. 11 351-370 -Surfaces with isothermal representation of their lines of curvature and their transformations (second memoir). ... 11 475-486 -Certain continuous deformations of surfaces applicable to the quadrics. 14 365-402 -Transformations of surfaces of Voss. 15 245-265 -Transformations of conjugate systems with equal point invariants. 15 397-430 16 275-310 Ü and their transformations. Surfaces 17 53- 99 - Deformable transformations of Ribaucour. 17 437^58 -Transformations T of conjugate systems of curves on a surface. 18 97-124 -Transformations of applicable conjugate nets of curves on surfaces. 19 167-185 -Transformations of surfaces applicable to a quadric.20 323-338 Eiesland, J., On minimal lines and congruences in four-dimen- sional space. 12 403-428 Green, G. M., One-parameter families of curves in the plane. . 15 277-290 -On the theory of curved surfaces, and canonical systems in projective differential geometry. 16 1- 12 -Some geometric characterizations of isothermal nets on a curved surface. 18 480^88 -Memoir on the general theory of surfaces and rectilinear congruences. 20 79-153 Hodgson, J. E., Orthocentric properties of the plane directed «-line. 13 199-231 Ingold, L., Vector interpretation of symbolic differential parameters. 11 449-474 -Functional differential geometry. 13 319-341 Kasner, E.,. The theorem of Thomson and Tait and natural families of trajectories. 11 121-140 -Natural systems of trajectories generating families of Lamé 12 70- 74 Lipke, J., Natural families of curves in a general curved space of n dimensions. 13 77- 95 Pfeiffer, G. A., On the conformai mapping of curvilinear angles. The functional equation Vol. Pages Smith, P. F., On osculating element-bands associated with loci of surface-elements. 11 301-324 -A theorem for space analogous to Cesàro's theorem for plane isogonal systems. 18 522-540 Snyder, V., Conjugate line-congruences contained in a bundle of quadric surfaces. 11 371-387 Study, E., Die natürlichen Gleichungen der analytischen Curven im Euclidischen Räume. 11 249-279 Sullivan, C. T., Properties of surfaces whose asymptotic curves belong to linear complexes. 15 167-196 -Scroll directrix curves. 16 199-214 Whittemore, J. K., Spiral minimal surfaces. 19 315-330 Wilczynski, E. J., One-parameter families and nets of plane curves. 12 473-510 -On a certain set of self-projective surfaces. 14 421—443 -The general theory of congruences. 16 311-327 -Line geometric representations for functions of a complex variable. 20 271-298 F 5. Geometric Transformations. Geometry of Motion (Cf. E 2) Alexander, J. W., On the factorization of Cremona plane transformations. 17 295-300 Beck, H., Ein Seitenstück zur Möbius'schen Geometrie der Kreisverwandtschaften. 11 414-448 Birkhoff, G. D., Proof of Poincaré's geometric theorem. 14 14- 22 Graustein, W. O, The equivalence of complex points, planes, lines with respect to real motions and certain other groups of real transformations. 16 33- 44 Kasner, E., Conformai classification of analytic arcs or ele- ments ; Poincaré's local problem of conformai geometry... 16 333-349 Morgan, F. M. (with J. W. Young), The geometries associated with a certain system of Cremona groups. 17 233-244 Sharpe, F. R. (with V. Snyder), Birational transformations of certain quartic surfaces. 15 266-276 -(with V. Snyder), Certain quartic surfaces belonging to infinite discontinuous cremonian groups. 16 62- 70 -(with V. Snyder), Types of (2, 2) point correspondences between two planes. 18 402—414 -(with V. Snyder), Space involutions defined by a web of quadrics. 19 275-290 -(with V. Snyder), Certain types of involutorial space ' transformations. 20 185-202 30 INDEX BY SUBJECT MATTER [October Vol. Pages Snyder, V., Infinite discontinuous groups of birational trans- formations which leave certain surfaces invariant. 11 15-24 -Algebraic surfaces invariant under an infinite discon- tinuous group of birational transformations (second paper) 14 105-108 -(with F. R. Sharpe), Birational transformations of certain quartic surfaces. 15 266-276 -(with F. R. Sharpe), Certain quartic surfaces belonging to infinite discontinuous cremonian groups. 16 62- 70 -(with F. R. Sharpe), Types of (2, 2) point correspondences between two planes. 18 402-414 -(with F. R. Sharpe), Space involutions defined by a web of quadrics. 19 275-290 -(with F. R. Sharpe), Certain types of involutorial space transformations. 20 185-202 Urner, S. E., Certain singularities of point transformations in space of three dimensions. 13 232-264 Van Vleck, E. B., One-parameter projective groups and the Í 13 353-386 classification of collineations.} 13 517 Young, J. W., Two-dimensional chains and the associated collineations. 11 280-293 -(with F. M. Morgan), The geometries associated with a certain system of Cremona groups. 17 233-244 G. Applied Mathematics G 1. General Mechanics Birkhoff, G. D., Dynamical systems with two degrees of freedom. 18 199-300 Gronwall, T. H., On the influence of keyways on the stress distribution in cylindrical shafts. 20 234-244 Kasner, E., The theorem of Thomson and Tait and natural families of trajectories. 11 121-140 Roever, W. H., The southerly deviation of falling bodies. 12 335-353 -The southerly and easterly deviations of falling bodies for an unsymmetrical gravitational field of force. 13 469-490 G 2. Celestial Mechanics Buchanan, D., A new isosceles triangle solution of the three body problem. 16 259-274 MacMillan, W. D., Periodic orbits about an oblate spheroid. 11 55-120 -An existence theorem for periodic solutions. 13 146-158 Moulton, F. R., A class of periodic orbits of superior planets. 13 96-108 1919] INDEX BY SUBJECT MATTER 31 G 3. Elasticity, Hydromechanics, and Sound Vol. Pages Hoskins, L. M., The strain of a gravitating, compressible, elastic sphere. 11 203-248 -The strain of a non-gravitating sphere of variable density 11 494-504 Moulton, E. J., On figures of equilibrium of a rotating com- pressible fluid mass; certain negative results. 17 100-108