The Collected Mathematical Papers. Volume II: (1854--1873). (Q1491106)

Vgl. die Anzeige des ersten Bandes JFM 35.0020.01, sowie die kritische Besprechung von Bd. I und II in Arch. Math. Phys. (3) 13, 233 (1908). Der zur Besprechung stehende zweite Band bringt in chronologischer Folge 110 Artikel, zumeist also kleine Noten, Eingebungen des Augenblicks, die nach der Gewohnheit Sylvesters rasch zu Papier gebracht und sofort in den Druck gegeben wurden. Die Gegenstände, auf welche sich diese Aufsätze beziehen, gehören allen Gebieten der reinen Mathematik und der analytischen Mechanik an. Als solche Nummern, welche äußerlich den Durchschnitt von sechs Seiten erreichen oder ihn übertreffen, seien die folgenden hervorgehoben. 2. A probationary lecture on geometry (2--9, 1854). 4. On the calculus of forms, otherwise the theory of invariants (11--27, 1854). 10. Note on Bürmann's law for the inversion of the independent variable (44--49, 1854). 16. On the change of systems of independent variables (65--85, 1857). 18. On the partition of numbers (90--99, 1857). 24. On the problem of the virgins, and the general theory of compound partition (113--117, 1858). 26. Outlines of seven lectures on the partitions of numbers (119--175, gehalten 1859, gedruckt 1897). 31. On Poncelet's approximate linear valuation of surd forms (181--199, 1860). 32. Meditation on the idea of Poncelet's theorem (200--207, 1860). 33. Notes to the meditation on Poncelet's theorem, including a valuation of two new definite integrals (208--214, 1860). 34. On the pressure of earth on revetment walls (215--224, 1860). 45. Note on the numbers of Bernoulli and Euler and a new theorem concerning prime numbers (254--263, 1861). 46. Note on the historical origin of the unsymmetrical six-valued function of six letters (264--271, 1861). 47. On a problem in tactic which serves to disclose the existence of a four-valued function of three sets of three each (272--276, 1861). 48. Concluding paper on tactic (277--285, 1861). 49. Remark on the tactic of nine elements (286--289, 1891). 63. Sequel to the theorems relating to ``canonic roots'' (331--337, 1863). 65. On the centre of gravity of a truncated triangular pyramid, and on the principles of barycentric perspective (342--357, 1863). 74. An inquiry into Newton's rule for the discovery of imaginary roots (376--479, 1864). 84, 108. On an elementary proof and generalization of Sir Isaac Newton's hitherto undemonstrated rule for the discovery of imaginary roots (498--513, 1865/6; 704--708, 1871). 87. Astronomical prolusions: commencing with an instantaneous proof of Lambert's and Euler's theorems etc. (519--541, 1866). 89. Note on the periodical changes of orbit, under certain circumstances, etc. (547--558, 1866). 92. Note on the properties of the test operators which occur in the calculus of invariants (567--576, 1866). 93. On the motion of a rigid body acted on by no external forces (577--601, 1866). 96. Thoughts on inverse orthogonal matrices, simultaneous sign-successions etc. (615--628, 1867). 98, 99. On successive involutes to a circle (630--649, 1868). 100. Address to the Mathematical and Physical Section of the British Association (650--661, 1869). 103. Outline trace of the theory of reducible cycloides etc. (663--688, 1869). 106. On two remarkable resultants arising out the theory of rectifiable compound logarithmic waves (694--700, 1869).