Sentence Examples


  • Among his principal publications are An Examination of Ferrier's "Knowing and Being," and the Scottish Philosophy - (a work which gave him the reputation of being an independent Hamiltonian in philosophy); Memoir of John Brown, D.D.
  • If the system is supposed to obey the conservation of energy and to move solely under its own internal forces, the changes in the co-ordinates and momenta can be found from the Hamiltonian equations aE aE qr = 49 - 1 57., gr where q r denotes dg r ldt, &c., and E is the total energy expressed as a function of pi, qi,.
  • The scope of his researches was described by Arthur Cayley, his friend and fellow worker, in the following words: "They relate chiefly to finite analysis, and cover by their subjects a large part of it - algebra, determinants, elimination, the theory of equations, partitions, tactic, the theory of forms, matrices, reciprocants, the Hamiltonian numbers, &c.; analytical and pure geometry occupy a less prominent position; and mechanics, optics and astronomy are not absent."
  • To this reaction Hamilton explicitly appealed in the convention of 1787; and of this reaction various features of the constitution, and Hamiltonian federalism generally, were direct fruits.
  • It is, however, unquestionably true, that as a startling protest against measures" to silence,"in Jefferson's words," by force and not by reason the complaints or criticisms, just or unjust, of our citizens against the conduct of our agents,"they served, in this respect, a useful purpose; and as a counterblast against Hamiltonian principles of centralization they were probably, at that moment, very salutary; while even as pieces of constitutional interpretation it is to be remembered that they did not contemplate nullification by any single state, and, moreover, are not to be judged by constitutional principles established later by courts and war.

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