3280 



Calculus of Variations 



3280 



Maxima and minima of integrals. Markoff, . 



Par. c. Norm. A. 3 (1886) 81-. 

 simple integrals between fixed 



limits. Scheeffer,L. Mth. A. 25 (1885) 522-. 

 with variable limits, criteria. 



Mayer, A. Leip. Mth. Ps. B. 36 (1884) 99-. 

 , solutions, criteria. Culverwell, E. P. 



[1886] Phil. Trans. (A) 178 (1888) 95-. 

 , for finite variations, conditions. 



Culverwell, E. P. [1899] Ir. Ac. P. 5 (1898- 



1900) 377-. 

 Minimum of simple integrals with variable 



limits, criteria. Mayer, A. Leip. Mth. Ps. 



B. 48 (1896) 436-. 

 Multiple integrals. Poisson, S. D. Par. S. 



Phlm. fill. (1816) 82-. 

 . Ostrogradsky, M. A. [1834] St Pet. 



Ac. Sc. Mm. 3 (Sc. Mth. Ps.pte. 1) (1838) 35-. 

 (Ostrogradsky 's formula). Sabinine, . 



Crelle J. 59 (1861) 185-. 



. Sabinine, G. A. Mt. 2 (1899) 203-. 



Osculation function. Zmurko, W. [L.~\ (xn) 



Krk. Ak. (Mt.-Prz.) Pam. 3 (1877) 24-, 94-. 

 Principles. Ampere, A.M. Gergonne A. Mth. 



16 (1825-26) 133-. 



. Crelle, A. L. Berl. Ab. (1833) 1-. 

 , elementary. Du Bois-Reymond, P. Mth. 



A. 15 (1879) 283-, 564-. 



, extension. Challis, J. Ph. Mg. 32 (1866) 



45-. 

 Problems. Pagani, G. M. Crelle J. 15 (1836) 



84-. 

 . Strauch, G. W. Grunert Arch. 3 (1843) 



119-. 



. Scliellbach, C. H. Crelle J. 41 (1851) 293-. 

 . Challis, J. [1866-71] Ph. Mg. 31 (1866) 



218- ; 32 (1866) 278-; 42 (1871) 28-, 302- ; 



43 (1872) 52-. 

 . Todhunter, I. Ph. Mg. 31 (1866) 425-; 



32 (1866) 199- ; 42 (1871) 440-. 

 . Cayley, A. L. Mth. S. P. 3 (1869-71) 



221-. 



. Walton, W. QJ. Mth. 10 (1870) 72-. 

 . Wilkinson, M. M. U. Mess. Mth. 1 (1872) 



175-. 

 . Sonin, N. N. Bs. S. Nt. Mm. (Mth.) 6 



(1885) 1-, 93-; Fschr. Mth. (1885) 359-. 

 . Starkov, A. N. Es. S. Nt. Mm. (Mth.) 6 



(1885) 23-; Fschr. Mth. (1885) 359-; 



Palermo Cir. Mt. Ed. 2 (1888) 116-. 



containing problem of mechanics. Lipschitz , 



B. [1871] Crelle J. 74 (1872) 116-. 



corresponding to straight lines of space. 

 Koenigs, G. C. E. 121 (1895) 1122-. 



, double integrals. Koenigs, G. C. E. 122 



(1896) 126-. 

 , fundamental, generalisation. Whittemore, 



J. K. N. Y. Am. Mth. S. Bll. 6 (1900) 96, 



101-. 

 , one independent variable. Clebsch, A. 



Crelle J. 55 (1858) 335-. 

 , . Mayer, A. C. G. Leip. Mth. 



Ps. B. 30 (1878) 16-. 

 , partial differential equation. KUrschdk, J. 



Mth. A. 44 (1894) 9-. 

 , solution. Challis, J. Ph. Mg. 22 (1861) 



108-. 



Problems, solution. Spitzer, S. Arch. Mth. 



Ps. 42 (1864) 301-. 

 , by theory of quantics. Warren, J. 



[1865] QJ. Mth. 7 (1866) 171-. 

 , solutions, discontinuous. Maxwell, J. C. 



[1873] (vm) Camb. Ph. S. P. 2 (1876) 294-. 

 , , . Erdmann, G. [1875] Crelle J. 



Mth. 82 (1877) 21-. 

 Simple integrals, theory. Lipschitz, R. [1864] 



Crelle J. Mth. 65 (1866) 26-. 

 Surfaces of minimum area. Bonnet, 0. C. E. 



40 (1855) 1107- ; 41 (1855) 1057- ; 42 (1856) 



532-. 

 Theorems. Boole, G. Camb. Mth. J. 2 (1841) 



97-. 

 . Roberts, R. A. Mess. Mth. 15 (1886) 148-. 



corresponding to principle of least action 

 in mechanics. Mayer, A. Mth. A. 2 (1870) 

 143- ; Leip. Mth. Ps. B. 38 (1886) 343-. 



, extension to differential equations. 



Ermakov, V. P. [1889] Fschr. Mth. (1890) 



381. 

 , fundamental, demonstration. Gourieff, S. 



[1797] St Pet. Ac. Sc. N. Acta 13 (1802) 



154-. 

 , , . Lindeloef, L. L. C. E. 50 (1860) 



85-. 

 Theory, new. Picart, A. N. A. Mth. 2 (1883) 



49-. 

 Todhunter's "History of the calculus of 



variations." Mainardi, G. Mil. At. I. Lomb. 



3 (1862) 414-. 



' ' Eesearches, ' ' review. Wilkinson, M. M. U. 

 Mess. Mth. 3 (1874) 184-. 



Trajectory of a point for which a certain 

 integral is minimum. Bresse, . C. E. 74 

 (1872) 1562- . 



Transformations. Walton, W. [1863] QJ. 

 Mth. 8 (1867) 222-. 



of differential equations. Kilrschdk, J. 

 Mth. Termt. 6ts. 17 (1899) 457-; Mth. Nt. 

 B. Ung. 17 (1901) 29-. 



showing maxima and minima. Minding, 

 E. F. A. Crelle J. 55 (1858) 300-. 



Variation of differential coefficient of function 



of n variables. Stanley, A. D. Silliman J. 3 



(1847) 415-. 

 , second, criteria for maximum or minimum 



of simple integrals. Kneser, A. Mth. A. 51 



(1899) 321-. 

 , , sign. Strauch, G. W. Grunert 



Arch. 4 (1844) 39-. 

 , , of multiple integrals. Clebsch, A. 



Crelle J. 56 (1859) 122-. 

 , , . Sabinine, G. Bll. Sc. Mth. 



As. 2 (1878) (Pt. 1) 100-. 

 , , reduction. Clebsch, A. Crelle J. 55 



(1858) 254-. 

 , , . Dixon, A. C. Mess. Mth. 26 



(1897) 65-. 

 , , , Jacobi's. Horner, J. QJ. Mth. 14 



(1877) 218-. 

 , , of simple integrals. Erdmann, G. Z. 



Mth. Ps. 23 (1878) 362-. 

 , , . Escherich, G. von. Wien 



Ak. Sb. 107 (1898) (Ab. 2a) 1191-, 1267-, 



1381- ; 108 (1899) (Ab. 2a) 1269-. 



288 



