Orthogonal and Isothermic Surfaces 



8860 



ruled, applicable on surface of revolution. 

 Pellet, A. C. E. 106 (1888) 654. 



, . Bioche, C. C. E. 106 



(1888) 829-. 



skew, applicable on given skew surface. Cay- 

 ley, A. L. Mth. S. P. 23 (1892) 217-. 



susceptible of special infinitesimal deformations. 

 Padova, E. Mil. I. Lomb. Bd. 24 (1891) 

 821-. 



Theory. Weingarten, J. Acta Mth. 22 (1899) 



193-. 

 , continuous group of transformations with 



28 parameters in. Staeckel, P. C. E. 121 



(1895) 396-. 

 , general differential equation in. Craig, T. 



Franklin I. J. 78 (1879) 289-. 



8860 Orthogonal and isothermic 

 surfaces. (See also 5630.) 



Lame, G. (vm) C. E. 17 (1843) 338-. 

 Thomson, (Sir) W. Camb. Mth. J. 3 (1843) 



286-; 4 (1845) 179-. 

 Tail, P. G. [1872] Edinb. E. S. T. 27 (1873) 



105-. 



Pellet, A. C. E. 124 (1897) 552-. 

 Bonnet's problem. Guickard, C. C. E. 125 



(1897) 643-. 

 Condition that family of surfaces should 



belong to orthogonal system. Weingarten, 



J. L. G. J. Crelle J. Mth. 83 (1877) 1-. 

 . Lilienthal, 



E. von. Mth. A. 44 (1894) 449-. 



for isogonal transformation of curvilinear 

 coordinates in 3 dimensions. Maxwell, J. C. 

 [1872] L. Mth. S. P. 4 (1871-73) 117-. 



Confocals of surfaces cut them orthogonally. 



Ltvy, M. C. E. 74 (1872) 176-. 

 Conjugate functions and equipotential curves. 



Brill, J. Camb. Ph. S. P. 6 (1889) 187-. 

 Curves and surfaces normal to one another, 



theory. David, C. A. [1864] (xn) Lille 



S. Mm. 1 (1865) 151-. 

 Cyclidal surfaces, application of physical 



methods to study. Darboux, G. C. E. 83 



(1876) 1037-, 1099-. 



Dirichlet's problem of stationary tempera- 

 tures, and representation of given surface. 



Christoffel, E. B. A. Mt. 1 (1867-68) 89-; 



4 (1870-71) 1-. 



Equations of motions of heat referred to cur- 

 vilinear coordinates. Thomson, (Sir) W. 



Camb. Mth. J. 4 (1845) 33-. 

 Equipotential cylindrical surfaces, class. Pomey, 



J. B. A. Tel. 21 (1894) 460- ; 24 (1898) 



150-. 



surfaces, class. Peirce, B. O. Am. J. Mth. 

 18 (1896) 130-. 



, plane. Burnside, W. Mess. Mth. 27 



(1898) 138-. 



system of curves, singular points. Brill, J. 

 Camb. Ph. S. P. 6 (1889) 313-. 



, (Brill). Burnside, W. 



Camb. Ph. S. P. 7 (1892) 126-. 



8860 



Isothermic coordinate systems. Kotteritzsch, T. 

 Z. Mth. Ps. 19 (1874) 265-. 



curves, plane, property. Burnside, W. Mess. 

 Mth. 20 (1891) 64-. 



ISOTHEEMIC SUEFACES. 



Pellet, A. C. E. 125 (1897) 291-. 

 Darboux, G. C. E. 128 (1899) 1299-, 1538. 

 Guichard, C. C. E. 130 (1900) 159-. 

 Thybaut, A. C. E. 131 (1900) 932-; Par. EC. 



Norm. A. 17 (1900) 541-. 

 application of vectorial geometry. Genty, . 



As. Fr. C. E. (1889) (Pt. 2) 53-. 

 class. Thybaut, A. C. E. 123 (1896) 295-. 

 and deformation of paraboloid. Thybaut, A. 



C. E. 128 (1899) 1274-. 



"doubly eylindric" surfaces. Raffy, L. 

 C. E. 128 (1899) 285-. 



geodesic lines, use of curvilinear coordinates. 

 Salvert, (le vicomte) de. Brux. S. Sc. 

 A. 10 (1886) (Pt. 2) 293-; 11 (1887) (Pt. 2) 



and harmonic equations. Thybaut, A . C. E. 



in heterotropic media. Moutier, J. Par. S. 

 Phlm. Bll. 8 (1884) 184-. 



homogeneous solids in temperature equi- 

 librium. Poisson, S. D. Liouv. J. Mth. 

 2 (1837) 147-. 



paraboloidal. Lame,G. [1843 or 1844] Liouv. 



J. Mth. 19 (1874) 307-. 

 with plane lines of curvature in one or both 



systems. Adam, P. C. E. 116 (1893) 1036- ; 



Par. EC. Norm. A. 10 (1893) 319-. 

 systems, algebraic. Haton de la Goupilliere, 



J. N. C. E. 50 (1860) 307-. 

 , Liouville's, and geodesies. Eicci, G. 



Ven. I. At. (1893-94) 643-. 

 transformation. Guichard, C. C. E. 130 



(1900) 477-. 

 triple systems. Betti, E. A. Mt. 8 (1877) 



138-. 



Isotherms, plane algebraic. Schwarz, C.H.A. 



Crelle J. Mth. 77 (1874) 38-. 

 Laplace's equation, transformations leading to 



new solutions. Forsyth, A. E. L. Mth. S. 



P. 29 (1898) 165-. 

 Non-ruled surfaces applicable on plane. 



Lebesgue, H. C. E. 128 (1899) 1502-. 

 Orthogonal and confocal curves, system. 



Legoux, A. Toul. Fac. Sc. A. 4 (1890) D, 



7 pp. 



curves, two systems. Jamet, V. C. E. 

 106 (1888) 830-. 



Orthogonal surfaces. 



Bouquet, J. Liouv. J. Mth. 11 (1846) 446-. 

 Serret, J. A. Liouv. J. Mth. 12 (1847) 241-. 

 Lebesgue, V. A. N. A. Mth. 10 (1851) 265-. 

 Bonnet, O. C. E. 54 (1862) 554-, 655-. , 

 Darboux, G. C. E. 59 (1864) 240- ; Par. EC. 



Norm. A. 3 (1866) 97-; (rx) Par. S. Phlm. 



Bll. 3 (1866) 16-. 

 Catalan, E. C. Brux. Ac. Bll. 26 (1868) 180-. 



651 



