3270 Multiple Integrals 



Eeduction, cases. Catalan, E. C. Liege S. Sc. 



Mm. 12 (1885) No. 2, 12-, 17-. 

 , . Maggi, O. A. Mil. I. Lomb. Bd. 19 



(1886) 689-. 

 , . Sonine, N. J. Fschr. Mth. (1889) 



287-. 

 , . Zinin, N. N. Vars. S. Nt. Tr. (1889- 



90) (C. E., Ps. C.) No. 6, 9-. 

 , . Sonin, N. Ja. Bee. Mth. (Moscou) 14 



(1890) 527- ; Vars. S. Nt. Tr. (Mm.) 1 (1891) 



No. 4, 7 pp. 

 , . Black, A. [1897] Camb. Ph. S. T. 16 



(1898) 219-. 



, direct, of class. Silva, J. A. Martins da. 



G. Teix. J. Sc. 3 (1881) 49-. 

 , formula. Sonin, N. Ja. Vars. S. Nt. Tr. 



(1889-90) (C. R., Ps. C.) No. 2, 13-; Fschr. 



Mth. (1889) 287. 



of generalised. La Vallee-Poussin, C. J. de. 

 Liouv. J. Mth. 5 (1899) 191-. 



, quaternion formulae. Carvallo, E. Par. 



S. Mth. Bll. 18 (1890) 80-. 

 , Zinin's treatment of problem. Nekrasov, 



P. A. Bee. Mth. (Moscou) 16 (1893) 823-. 

 Space and surface integrals. Fiske, T. S. 



[1891] A. Mth. 6 (1891-92) 61-, 131. 

 Surface and curvilinear integrals. Gazzaniga, 



T. Mil. I. Lomb. Bd. 33 (1900) 567-. 



integrals, condition of dependence on boun- 

 dary alone, new interpretation. Meray, C. 

 C. B. 128 (1899) 913-. 



, definition. Lebesgue, H. C. B. 131 

 (1900) 867-. 



, evaluation, and application to expansion, 



in series, of potential of ellipsoids. Hobson, 

 E. W. L. Mth. S. P. 24 (1893) 80-. 



in problem of 3 bodies. Wetter, A. As. 



Nr. 74 (1869) 85-. 



, transformation into multiple line in- 

 tegrals. Larmor, J. Mess. Mth. 17 (1888) 

 23-. 



, . McAulay, A. Mess. 



Mth. 18 (1889) 139-. 

 Theorem. Volterra, V. Tor. Ac. Sc. At. 32 



(1896) 597- or 859-. 



of Fourier. Glaisher, J. W. L. [1876] Mess. 

 Mth. 6 (1877) 30-. 



Frullani, extensions. Leudesdorf, C. L. 



Mth. S. P. 9 (1877-78) 118-. 

 Hadamard. Hurwitz, A. C. B. 128 



(1899) 350-. 



Kronecker. Koenigs, G. Liouv. J. Mth. 



2 (1896) 41-, 

 Theorems. Jacobi, C. G. J. Crelle J. 12 



(1834) 1-. 

 , general. Ellis, R. L. Camb. and Dubl. 



Mth. J. 1 (1846) 1-. 



of Green and Cauchy. Chessin, . C. B. 

 128 (1899) 604-. 



Theory. Andrade, J. C. B. 119 (1894) 

 1192-. 



of numbers, application to integral cal- 

 culus. Gegenbauer, L. Wien Ak. Sb. 102 

 (1893) (Ab. 2a) 927-. 



Transformation. Haedenkamp, H. Crelle J. 



22 (1841) 184-. 

 . Boole, G. Camb. Mth. J. 3 (1843) 216- ; 



4 (1845) 20-. 



Calculus of Variations 3280 



Transformation. Svanberg, A. F. Stockh. 



Ofv. 2 (1845) 228-; Ups. N. Acta S. Sc. 13 



(1847) 1-. 



. Chelini, D. G. Arcad. 106 (1846) 127-. 

 . Genocchi, A. Tortolini A. 4 (1853) 401-. 

 . Russell, W. H. L. QJ. Mth. 4 (1861) 



163-, 316-. 

 . Holmgren, H. [1864] Stockh. Ak. Hndl. 



5 (1866) (No. 6) 40 pp. 

 . Tannenberg, W. de. Bordeaux S. Sc. PV. 



(1897-98) 109-. 

 , case. Haedenkamp, H. Crelle J. 20 (1840) 



formula. Cayley, A. Camb. and Dubl. 

 Mth. J. 4 (1849) 50-. 



. Brioschi, F. Bm. B. Ac. Line. Bd. 2 



(1886) (Son. 2) 111-. 



theorem. Minchin, G. M. [1871] QJ. Mth. 

 12 (1873) 172-. 



theorems of Gauss and Stokes. Predella, 

 P. Mil. I. Lomb. Bd. 20 (1887) 215-. 



of variables. Ostrogradsky, M. A. [1836] 

 St Pet. Ac. Sc. Mm. 3 (1838) 401-. 



Triple integrals, case. Le Paige, C. M. M. H. H. 

 Lie"ge S. Sc. Mm. 9 (1882) (No. 3) 4 pp. 



embracing potential of homogeneous 

 ellipsoid as particular case. Mertens, F. 

 Gott. Nr. (1887) 269-. 



, reduction to quadratures. Winckler, A. 



[1853] Crelle J. 50 (1855) 1-. 



, transformation by changing order of 

 integration. Winckler, A. Crelle J. 45 

 (1853) 168-. 



, and determination, case. Unferdinger, 



F. Wien Sb. 61 (1870) (Ab. 2) 105-, 417-. 



-, variation. Abbott, R. B. S. P. 4 (1838) 



42. 



/ dxdy ...dz, whose limits are p 1 = a^ 



... + h l z>0, p 2 >0, ...p n >0, and 



... + z*<l. Schlafti, L. QJ. Mth. 2 (1858) 



269-; 3 (1860) 54-, 97-. 



dx dy ... dz, whose limits are p l = a 1 x + b l y + ... 



+ h i z>0, p z >Q, ...p n >0, and 



+ 2 a <l, expansibility. Schlafii, L.' QJ. 



Mth. 8 (1867) 370-. 



dxdi/dz , 



- , extended over the interior of 



ellipsoid. Bigler, U. Bern Mt. (1887) 52-. 



3280 Calculus of variations. 



Bostut, C. Thomson A. Ph. 9 (1817) 445-. 

 Verhulst, P. F. Gand A. Ac. (1823-24) 30 pp. 

 Walsh, J. Tilloch Ph. Mg. 64 (1824) 330-. 

 Cankrein, H. K. Ph. Mg. 8 (1830) 321-. 

 Cauchy, A. L. Bb. It. 62 (1831) 373-. 

 Poisson, S. D. [1831] Par. Mm. Ac. Sc. 12 



(1833) 223-. 



Miiller, A. Crelle J. 13 (1835) 240-. 

 Jacobi, C. G. J. [1836] Crelle J. 17 (1837) 



68-. 

 (Jacobi.) Liouville, J, Liouv. J. Mth. 3 



(1838) 1-. 

 Bertrand, J. Liouv. J. Mth. 7 (1842) 55-. 



286 



