INDEX. 



491 



grounds of every method of aggregation known in 

 mechanics and five theorems following from them, 

 292 ; whence the laws of aggregation of forces either 

 meeting in a point, 293, or parallel, are deduced, 

 294 ; applications to translations, 296 ; and rotations, 

 297; velocity of ditto, 298; statical pressure, 299; 

 dynamical pressure, 302 

 De Morgan, A. On tlio question, what is the solution of 

 a Differential Equation '/ A supplement to the third 

 section of a paper, on some points of the Integral 

 Calculus, printed in Vol. ix. Part li., 21 — 26. The 

 object of the paper is to shew that common theorems 

 about the singularity of tlie constant of integration 

 must be tninsfen-ed from differential equations to 

 differential relations, 22 ; correction which the com- 

 mon theory requires, 25 ; Differential Equation, what 

 is meant by solution of, 21 — 26 



A proof of the E.xistence of a Root in every Alge- 

 braic Equation: with an examination and extension 

 of Cauchy's Theorem on Imaginary Roots and Re- 

 marks on the Proofs of the existence of Roots given 

 by Arg.ind and by Mourey, 261 ; prefix to Sturm's 

 demonstration of Cauchy's theorem on the limits of 

 imaginary roots which establi.slies the existence of 

 roots, 201 — 263; algebraical substitute for a geome- 

 trical step in Sturm's proof, 264, 26.5 ; Cauchy's 

 theorem with an extension thereof, 265, 266 ; Ar- 

 gand's Proof of the existence of Roots, 267 ; Mourey's 

 |iroof, 268, 269; postscript on divergent series and 

 spherical triangles, 269, 270 



• New Proof of Euclid's proposition ex cequaii in 



ordine perturlmto, 166, 172 



On the Syllogism No. III., and on Logic in 



general, 173; modem definition of logic relates to 

 a distinction more familiar to mathematicians than 

 logicians, 175 ; logic both science and art, 181 ; charges 

 of propositions and syllogisms, ib. ; objections to use 

 of mathematical sjinbols in, discussed, 183; the only 

 science which has grown no symbols, 184; hitherto 

 confined to logico-mathematical field but to be ex- 

 tended to the metaphysical field, 184 ; extension 

 and intension claimed for both the mathematical 

 and metaphysical sides of, and symbolised, 184; dis- 

 tinction of extension and comprehension misconceived 

 by recent logicians, 187; ouymalic relations, 190; 

 fourfold mode of thought, denoted and sjaiibolised, 

 ih.; arithmetical whole in logic, 190 — 194; form, 

 quality and quantity of propositions, 194; use oi force 

 to express quantity in metaphysical reading, 197 ; 

 schetical system, 199; spicular notation, 198; mathe- 

 matical and metaphysical views of terminal ambi- 

 guity and precision, 200; first elements of a system 

 of logic, 206 



• — - On the syllogism No. IV., and the logic of Rela- 

 tions, 331 ; influence of the schoolmen on language, 

 332; difficulties in applying laws of thought to un- 



familiar matter, 334; logic not to be confined to the 

 onymatic form, 335; no purely formal proposition 

 except this, ' there is the probability a that X is in 

 the relation Z to Y ; 339 ; necessity of taking ac- 

 count of combinations involving a sign of inherent 

 quantity, 341; table of forms of syllogism, 350; ex- 

 tension to quantified propositions, 352; cases of con- 

 vertible and transitive relations, 353 ; technical exhi- 

 bition of the syllogism not necessary in reasoning, 

 356 ; syllogisms of transposed quantity, *355 



; On Syllogism No. V., and on various points of the 



Onymatic system, 428; criticism of Hamilton's sys- 

 tem, ib. ; explanation of Aristotle's system, 442 ; which 

 is affirmed to be exemplar, 443 ; and misconceived by 

 recent writers, ib ; right of both correlatives in any 

 pair, and of all in any set to equal fulness of treat- 

 ment, 452; application to the distinction of affir- 

 mation, and non-affirmation, ib.; syllogism of inde- 

 cision, 453; eight onymatic forms deduced from 

 purely onymatic meaning, 455 ; alleged demonstration 

 of the necessity and completeness of these forms, ib. ; 

 restrictive propositions, their "affirmation and denial 

 Introduced in every view except the purely onymatic 

 whenever complete treatment of all correlatives is 

 allowed, 4.56 ; completion of exemplar system, 457 ; 

 extended comparison of the onymatic relations, 459 ; 

 system of primary and secondary relations by copula 

 of identification, 463 ; the same when the copula is 

 any one of the simple onymatic relations, 469; the 

 full system at which the Hamiltonian quantification 

 aims, 471 ; logical basis of extension and compre- 

 hension, 475 ; addition on a recent phase of the con- 

 troversy, Dec. 1862, 481 



On the Theory of Errors of Observation, 409 ; 



probability and facility contrasted, ib.; difficulty of 

 passing in argument from the finite to the infinite 

 or infinite to finite, 410; theorem that "all values 

 being positive and the number of letters taking value 

 being infinite, the average of the A" powers of the 

 sura of values is the A'' power of the sum of average 

 values," 412; laws of facility of value discussed, 413; 

 deficiency in Laplace's investigation, 415; first prin- 

 ciples, number of observations finite, 416; average 

 defined, ib. ; law of error deduced from observations, 

 418; mode of deducing probable results, 421; diffi- 

 culties in probability corresponding to indivisibles in 

 geometry, 424 ; process of solving them, ib. ; origin of 

 fluxional notion, 426 



Demosthenes, Statue of Solon mentioned by, 231, 235 



Dialectic, Platonic, 152; Aristotelian, ib.; of School- 

 men, ib. 



Diamagnetic Induction, Theory of, 44 



Diamagnetic or Paramagnetic Sphere, effect of, in a 

 uniform magnetic field, 70, 71 ; case when the field is 

 the teirestrial magnetic field, 71 



Dielectrics, Theory of, 43 



