5630 Equations of Physics 



Variation of arbitrary constants in mechanics. 

 Poisson, S. D. Par. Mm. Ac. Sc. 1 (1816) 



-- - ---- . Lubbock, J. W. Ph. Mg. 



11 (1837) 492- ; 12 (1838) 254-. 

 Vector conditions of integrability. Tait, P. G. 



[1877] Edinb. B. S. P. 9 (1878) 527-. 



-v^ - a 2 V*<f>=\f/(t, x, y, z), integration. Liou- 



ville, J. Liouv. J. Mth. 4 (1839) 1-. 

 "V" equal to positive unity (Lagrange). 



e. 2) 



Fiona, G. Brux. Ac. Bll. 8 (1841) (pte. 



. Thomson, (Sir) W. 



Liouv. J. Mth. 12 (1847) 493-. 

 V%=0, solution by method of quaternions. 

 Boole, G. Ir. Ac. P. 6 (1853-54) 375-. 



= , integration. Dint, U. A. Mt. 5 (1871- 

 73) 305-. 



= , . Ascoli, G. Mil. I. Lomb. Ed. 19 

 (1886) 285-. 



= , in non-Euclidean space. Bianchi, 

 L. Em. E. Ac. Line. Ed. 9 (1900) (Sem. 2) 



, 333 ~- 

 -pg = a 2 -r-g, integration. Mainardi, G. Tor- 



tolini A. 5 (1854) 161-, 273-, 459-. 



= , applications in acoustics and optics. 

 Klinkerfues, W. Gott. Nr. (1868) 469-. 



= in theory of sound. Amagat, [E. H."] 

 J. de Ps. 9 (1880) 56-. 



- Crelle J> 72 



V 2 v = 0, reduction to ordinary differential equa- 

 tions. Wangerin, F. H. A. Berl. Ak. Mb. 

 (1878) 152-. 



= , V 2 v=-K*v, V z v = c^v, new solutions. 

 Forsyth, A. E. Mess. Mth. 27 (1898) 99-, 

 190. 



= , solutions. Bromwich, T. J. I' A. L. 

 Mth. S. P. 30 (1899) 281-. 



^S + ( + ^2 + -)% = 0. integration. 



Boussinesq, J. C. E. 94 (1882) 514-. 

 V 2 /=0 with n variables. Giuliani, G. G. Mt. 



25 (1887) 109-. 

 V 2 z = 0. Du Bois-Reymond, P. Crelle J. Mth. 



103 (1888)' 204-. 

 V 2 <=0 in orthogonal coordinates. Petrini, H. 



Fschr. Mth. (1890) 982-. 

 V 2 M+fc%=0. B6cher, M. Am. J. Mth. 15 



(1893) 78-. 



= in space of n dimensions. Marcolongo, 



. A. Mt. 24 (1896) 301-. 



, G. Palermo Cir. 



__ R. 



du dv 8 



dx + d~ + dz = Morera, 



Mt. Ed. 7 (1893) 288-. 

 V 2 w=fce tt on closed Eiemann surface. Picard, 



E. Liouv. J. Mth. 9 (1893) 273-. 

 V 2 * + F/(x7/2)<|=0. Petrini, H. Stockh.Ak. 



Hndl. Bh. 19 (Afd. 1) (1894) No. 4, 36 pp. 

 V 2 u=F(u, x, y), integration. Picard, E. C. 



E. 124 (1897) 1488-. 



Integration by Series 5640 



V 4 u = 0, integration. Almansi, E. Tor. Ac. 

 Sc. At. 34 (1898) 68- or 92-. 



= . Goursat, . Par. S. Mth. Bll. 26 



(1898) 236-. 



= , integration. Almansi, E. Em. E. 

 Ac. Line. Ed. 8 (1899) (Sem. 1) 104-, 618. 



= , . Boggio, T. Ven. I. At. (1899- 

 1900) (Pt. 2) 497-. 



V-u = e u and Fuchsian functions. Poincare, H. 

 Liouv. J. Mth. 4 (1898) 137-. 



V 2 0= -j-y for space of n dimensions. Tedone, 



0. A. Mt. 1 (1898) 1-. 



V 2 + +/=0. Zaremba, S. Par. S. Mth. 

 Bll. 26 (1898) 70-. 



= , and harmonic functions. Zaremba, S. 

 Par. EC. Norm. A. 16 (1899) 427-; Prace 

 Mt.-Fiz. 11 (1900) 99-; Fschr. Mth. (1900) 

 375. 



V^^O, integration. Almansi, E. A. Mt. 2 



(1899) 1-. 



V B %, integration. Brajcev, I. R. Eec. Mth. 



(Moscou) 21 (1901) 490- ; Fschr. Mth. (1900) 



376. 

 V' 2 u=k 2 u, problems relating to. Picard, . 



Par. S. Mth. Bll. 28 (1900) 186-. 



5640 Integration of the differen- 

 tial equations of mathematical 

 physics by series. 



Convergence of series in Kepler's problem 



(Carlini). Jacobi, C. G. J. As. Nr. 30 



(1850) 197. 

 serving as integrals of differential 



equations of 1st order. Nazimov, P. S. 



Kazan S. Nt. (Ps.-Mth.) P. 8 (1890) 145- ; 



Fschr. Mth. (1890) 325. 

 Divergent series in differential equations. Horn , 



J. D. Mth. Vr. Jbr. 8 (1900) (Heft 1) 219-. 

 Expansions occurring in theory of conduction 



of heat. Poincare, H. C. E. 118 (1894) 



383-. 

 Formula for calculation of a certain potential. 



Lerch, . Liouv. J. Mth. 5 (1899) 427-. 

 Functions satisfying the equation V 2 w = 0. 



Ascoli, G. Mil. I. Lomb. Ed. 18 (1885) 



474_, 546_, 599-, 617-. 



Gauss's series in experimental physics. Tarn- 

 men, H. G. Carl Epm. 18 (1882) 129-. 

 Heating of a cylinder. Laar, J. J. van. Haarl. 



Ms. Teyl. Arch. 6 (1900) 65-. 

 Integrals of differential equations near essen- 

 tial singularities (viz . ' ' normal ' ' series in 



Poincare's sense). Rajewski, J. Krk. Ak. 



(Mt.-Prz.) Pam. 17 (1890) 166- ; Crc. Ac. 



Sc. Bll. (1890) 62-. 

 , particular, of V*F=F, and their expansion 



in spherical harmonics. Neumann, C. Leip. 



Mth. Ps. B. 38 (1886) 75-. 

 Integration of equations of motion. Sokoloff, 



J. C. E. 55 (1862) 99-. 

 sound with resistance terms. 



Boussinesq, J. C. E. 118 (1894) 162-, 223-, 



271-. 



406 



