SYL] 



902 



[SYL 



Sylvester, James Joseph. 33. On extensions 

 of the dialytic method of elimination. Phil. 

 Mag. II., 1851, pp. 221-230. 



34. On a remarkable discovery in the 



theory of canonical forms and of hyperdetermm- 

 ants. Phil. Mag. II., 1851, pp. 391-410. 



35. On the principles of the calculus of 

 forms. Camb. and Dubl. Math. Journ. VII., 

 1852, pp. 52-97, 179-217 ; VIII., 1853, pp. 

 256-296. 



36. Sur uneproprietenouvelle del'equation 



qui sert a determiner les inegalites seculaires des 

 planetes. Nouv. Ann. Math. XI., 1852, pp. 

 434-440. 



37. On a remarkable theorem in the theory 



of equal roots and multiple points. Phil. Mag. 



III., 1852, pp. 375-378. 

 38. On a new theory 



of multiplicity. 



Phil. Mag. III., 1852, pp. 460-467. 



39. Theorems of polygons and polyhedrons. 



Phil. Mag. IV., 1852, pp. 335-345. 



4O. On a simple geometrical problem 



illustrating a conjectured principle in the theory 

 of geometrical method. Phil. Mag. IV., 1852, 

 pp. 366-369. 



41. On the expressions for the quotients 



which appear in the application of STI/UM'S 

 method to the discovery of the real roots of an 

 equation. Brit. Assoc. Rep. 1853 (pt. 2), pp. 1-3. 



42. On a theorem concerning the com- 

 bination of determinants. Camb. and Dubl. 

 Math. Journ. VIII., 1853, pp. 60-62. 



43. Note on the calculus of forms. Camb. 



and Dubl. Math. Jouru. VIII., 1853, pp. 62-64. 



44. On the relation between the volume of 



a tetrahedron and the product of the sixteen 

 algebraical values of its superficies. Camb. and 

 Dubl. Math. Journ. VIII., 1853, pp. 171-178. 



45. Theoreme sur les limites des racines 



reelles des equations algebriques. Nouv. Ann. 

 Math. XII., 1853, pp. 286-287. 



46. Nouvelle methode pour trouver une 



limite superieure et une limite inferieure des 

 racines reelles d'une equation algebrique quel- 

 conque. Nouv. Ann. Math. XII., 1853, pp. 

 329-336. 



47. On polynomial functions which admit 



of reduction in the number of variables. Phil. 

 Mag. V., 1853, pp. 119-126. 



48. On Mr. CAYLEY'S impromptu demon- 

 stration of the rule for determining at sight 

 the degree of any symmetrical function of the 

 roots of an equation expressed in terms of the 

 coefficients. Phil. Mag. V., 1853, pp. 199-202. 



49. A proof that all the invariants to a 



cubic ternary form are rational functions of 

 ARONUOLD'S invariants and of a cognate theorem 

 for biquadratic binary forms. Phil. Mag. V., 

 1853, pp. 299-303, 367-372. 



Sylvester, James Joseph. 50. On a remark- 

 able modification of STURM'S theorem. Phil. 

 Mag. V., 1853, pp. 446-456. 



51. On a remarkable modification of 

 STURM'S theorem, and on a new rule for finding 

 superior and inferior limits to the roots of an 

 equation. Phil. Mag. VI., 1853, pp. 14-20. 



52. On the new rule for finding superior 

 and inferior limits to the real roots of any 

 algebraical equation. Phil. Mag. VI., 1853, 

 pp. 138-140. 



53. On the new rule of limits. Phil. Mag. 



VI., 1853, pp. 210-213. 



54. The algebraical theory of the secular- 

 inequality determinantive equation generalized. 

 Phil. Mag. VI., 1853, pp. 214-216. 



55. On the explicit values of STURM'S 

 quotients. Phil. Mag. VI., 1853, pp. 293-296. 



56. On a fundamental rule in the algorithm 



of continued fractions. Phil. Mag. VI., 1853, 

 pp. 297-299. 



57. On a generalization of the Lagrangian 



theorem of interpolation. Phil. Mag. VI., 1853, 

 pp. 374-376. 



58. On a theory of the syzygetic relations 

 of two rational integral functions, comprising an 

 application to the theory of STURM'S Functions, 

 and that of the greatest algebraical common 

 measure. Phil. Trans. 1853, pp. 407-576. 



59. Note on Sir John WILSON'S theorem. 



Camb. and Dubl. Math. Jouru. IX., 1854, pp. 

 84-85. 



60. On the calculus of forms, otherwise 



the theory of invariants. Camb. and Dubl. 

 Math. Jouru. IX., 1854, pp. 85-103. 



61. Relation entre le volume d'un tetraedre 



et la norme de sa surface. Nouv. Ann. Math. 

 XIII., 1854, pp. 203-209. 



62. On a point of notation. Phil. Mag. 



VII., 1854, pp. 50-51. 



63. On the enumeration of the contacts of 



lines and surfaces of the second order. Phil. 

 Mag. VII., 1854, pp. 331-334. 



64. On a formula by aid of which and of 



a table of single entry the continued product of 

 any set of numbers may be f fleeted without the 

 use of Logarithms. Phil. Mag. VII., 1854, pp. 

 430-436. 



65. On some new theorems in arithmetic. 



Phil. Mag. VIII., 1854, pp. 187-190. 



66. Note on BURMAN'S law for the inver- 

 sion of the independent variable. Phil. Mag. 

 VIII., 1854, p. 535. 



67. On differential transformation and the 



reversion of serieses. Roy. Soc. Proc. VII., 

 1854-55, pp. 219-224 ; Phil. Mag. IX., 1855, 

 pp. 391-394. 



68. On projectiles. Phil. Mag. XI., 1856, 

 pp. 450-453. 



