1610 Kinetics of Particles 



Brachistochrones, problem, canonical differen- 

 tial equations. Imshenetskil, V. G. (xn) 

 Kharkov Mth. S. Com. (1880) 18-, 53-. 



, , inverse. Haton de la Goupilliere, J. N. 

 Par. Mm. Sav. Etr. 28 (1884) No. 5, 42 pp. 



and problem mentioned by Ewart. Sibson, 

 E. Manch. Ph. S. Mm. 5 (1831) 1-. 



, problem, reduction to canonical equations. 



Andoyer, . C. R. 100 (1885) 1577-. 

 , property. Padelletti, D. G. Mt. [13 (1875)] 



201-. 

 , and propositions in Euler's " Mechanica. " 



Travassos, F. de P. Lisb. Mm. Ac. Sc. 2 



(Cor.) (1799) 3-. 

 , resistance of air and curve being regarded. 



Haton de la Goupilliere, J. N. C. B. 83 



(1876) 884- ; Par. Mm. Sav. Etr. 27 (1883) 



A T o. 4, 26 pp. 

 , 2 theorems on a class. Thue, A. Christi- 



ania F. (1888) No. 9, 15 pp. 

 , trajectories, and funiculars, relations. 



Padelletti, D. Palermo G. Sc. Nt. 14 



(1879) 32-. 

 Brachistochronous and free motion. Townsend, 



E. QJ. Mth. 14 (1877) 85-. 



motion. Pennacchietti, G. Palermo Cir. 

 Mt. Ed. 5 (1891) 59-. 



, special. Formenti, C. Mil. I. Lomb. 



Bd. 26 (1893) 355-. 

 Chords of quickest descent. Roberts, H. A. 



Mth. Gz. 1 (1900) 212-. 

 Circle, times down chords. Pessuti, G. [1806] 



Mod. S. It. Mm. 13 (1807) 181-. 

 Circular arc, time of descent in. Sang, E, 



Edinb. E. S. P. 4 (1862) 419-. 



, vibration in, approximation. 

 Gibbes, L. R. Camb. (M.) Mth. M. 3 (1860) 

 40-. 



path, time of descent of body. Malfatti, 

 G. F. Verona S. It. Mm. 7 (1794) 462-. 



Curve, convex, descent on. Bertrand,J. Liouv. 



J. Mth. 7 (1842) 212-. 

 , , of body along. Fontana, G. Verona 



S. It. Mm. 1 (1782) 174-. 

 , plane, times down arcs and chords. Fouret, 



G. Par. EC. Pol. J. 56 (1886) 171-. 

 , , vertical, velocity acquired by heavy body 



descending. Resti-Ferrari, G. A. Sc. Lomb. 



Ven. 2 (1832) 255-. 

 , skew, characteristics, and accelerations of 



point describing it, relations between. Haag, 



. Par. S. Mth. Bll. 7 (1879) 140-. 



such that time of descent varies as square 

 root of abscissa. Euler, L. [1781] St. Pet. 

 Ac. Sc. Mm. 10 (1826) 7-. 



Descent of particle from given curve, time. 



Collignon, E. As. Fr. C. E. (1899) (Ft. 2) 



40-. 

 Lemniscate, times down arc and chord. Sala- 



dini, G. Bologna Mm. I. It. 1 (1806) (pte. 2) 



43-. 

 , . Fuss, N. [1815] St. Pet. 



Ac. Sc. Mm. 9 (1824) 91-. 

 , . Renal, H. A. [1857] (xn) 



Doubs S. Mm. 3 (1859) 54-. 

 , . Azzarelli, M. A. Mt. 7 



(1865) 284-. 



Constrained Motion 1610 



Lemniscate, times down arc and chord. Resal, 

 H. A. N. A. Mth. 1 (1882) 481-. 



, . Bardelli, E. G. Mil. I. 



Lomb. Ed. 26 (1893) 344-, 379-. 



Minimal trajectories S I *0(v)d* = 0. Schu- 



ringa, P. [1872] Arch^'Neerl. 8 (1873) 1-. 

 Orbits on surface, admitting infinitesimal trans- 

 formations. Staude, O. Leip. Mth. Ps. B. 



44 (1892) 429-; 45 (1893) 511-. 

 Oscillations, small, on any surface. Ball, R. S. 



[1869] QJ. Mth. 10 (1870) 220-. 

 Parabola, vertical, time of descent down. 



Glaisher, J. W. L. QJ. Mth. 19 (1883) 141-. 

 Pendulum, simple, attracted to point at finite 



distance. Hoppe, R. Arch. Mth. Ps. 70 



(1884) 405-. 

 , spherical, curves described by. Gudermann, 



C. Crelle J. 38 (1849) 185-. 

 Straight line and point, line of quickest descent. 



Kosters, . Grunert Arch. 22 (1853) 58-. 

 Surface through curve such that heavy particle 



will describe curve. Catalan, E. C. Liouv. 



J. Mth. 11 (1846) 212-. 

 Surfaces on which point can move according 



to certain law. Saint-Germain, A. de. Liouv. 



J. Mth. 2 (1876) 325-. 

 Tautochrone of cycloid. Resal, H. A. N. A. 



Mth. 1 (1882) 289-. 

 Tautochrones. Biot, J. B. Par. S. Phlm. 



Bll. 3 (1803) 195-. 

 . Puiseux, V. Liouv. J. Mth. 9 (1844) 



409-. 

 . Bertrand, J. Liouv. J. Mth. 12 (1847) 



121- ; 13 (1848) 231-. 

 . Aoust, L. N. A. Mth. 7 (1848) 137-. 

 . Brioschi, F. Tortolini A. 3 (1852) 362-; 



4 (1853) 62-, 106-. 

 . Bertrand, J. Tortolini A. 3 (1852) 547-; 



4 (1853) 65-. 

 . Durrande, H. C. E. 78 (1874) 1550-, 



1697. 

 - . Collignon, E. As. Fr. C. E. (1889) (Pt. 2) 



7-. 

 . Saint-Germain, A. de. Bll. Sc. Mth. 13 



(1889) 257-. 

 . Legoux, A. Toul. Fac. Sc. A. 6 (1892) B, 



16pp. 

 . Koenigs, G. Par. S. Phlm. Bll. 5 (1893) 



195-. 



and brachistochrones for parallel and con- 

 current forces. Townsend, R. QJ. Mth. 12 

 (1873) 247-; 13 (1875) 1-. 



in cases of friction. Hoppe, R. Z. Mth. 

 Ps. 14 (1869) 382-. 



; cycloid only tautochrone in vacua. Guillon , 



E. L. Liouv. J. Mth. 11 (1846) 216. 

 , when force is function of arc. Lespiault, 



G. Bordeaux Mm. S. Sc. 5 (1867) 389-. 

 , problem. Padelletti, D. Palermo G. Sc. 



Nt. (Bll.) 14 (1879) xxiii-. 

 , . Formenti, C. Mil. I. Lomb. Ed. 13 



(1880) 266-. 

 , problems. Euler, L. St. Pet. Ac. Sc. Mm. 



9 (1824) 20-, 35-. 

 , . Fouret, G. C. E. 103 (1886) 1114-, 



1174-. 



123 



