496 



INDEX. 



364; and applied to determine deflection of a girder 

 suddenly loaded in the middle, 364, 365 ; to deter- 

 mine the motion of an elastic rod fixed at one end 

 and free at the other, 365 — 370 ; Fourier's func- 

 tions do not apply to this case, 365 ; a bent rod with- 

 in the breaking limit at the centre may be broken by 

 the rebound after it is set free, 369 ; to determine 

 the velocity of an arrow discharged from a bow, 

 370 — 372 ; the amount of displacement of the centre 

 of the cord assumed to be four times that of the 

 ends and to be constant during the motion, 370 ; 

 any two bows of same material and of similar figure 

 will impart th6 same maximum velocity to an arrow, 

 provided the arrows and cords are also similar and 

 proportional, 372 ; experiments on the range of the 

 "bolts" and the general power of the steel cross-bow, 

 373 



Root, proof of theorem that every Algebraic equation 

 has a, 283, 327 



Roots of equations, Argand's proof of existence of, 267 ; 

 Mourey's proof, 268, 269 



Rotation of a body about its centre of gravity, solution 

 of problem of, 14 — 17 ; case when no forces act, 17 



Rotations, laws of, 297 



Sailing, great circle, 271; difficulties attending, ib.; 

 windward sailing, 273; composite sailing, 277 



Sauveur, the beats commonly called after Tartini, in 

 reality used by. Smith's accusation against, unfound- 

 ed, 132, 133 



Schetical words needed, 193; system of, 199 



Secretion, Manifestation of Current Force during. See 

 Baxter, H. F., on Organic Polarity, 248 



Secretion, phenomena of, compared with Osmote, 259 



o-eXt'r, 91, 92 



Series divergent, property of, 269 



Shakespeare, his use of the word argument, 324 ; versi- 

 fication of, 387 



Ships, different forms of, Greek, 85 



Simplicius, on Plato's definition of (pavracria, 147 



Smith, Dr Robert. His work on Harmonics, 129 ; beats 

 of, 132 ; his formulae deduced in an independent 

 manner, 139 ; his accusation against Sauveur un- 

 founded, 132, 133 



Socrates, in the Parmenides, 97, &c. ; his exposition of 

 tenets of Ephesian followers of Heraclitus, 158 



Solon, statue of, 231 ; an elegiac poet, 237 



Solution of equation, what requirements as to continuity 

 are conveyed in the term, 23 



Some and all, use of, in Hamilton's system, 433 



Sophista (Plato), on the genuineness of, 146 ; a critique of 

 the doctrines of three other schools, 147 ; arguments 

 in favour of genuineness, ib. ; continuation of These- 

 tetus, 151; connexion with, 152; 'earthborn' of, 

 165 



Spheres, electrical and magnetic, problems with refer- 

 ence to, 68 — S3 



Spherical shell, permanent magnetism in, 76 ; effect of 

 filling up the shell with magnetic or dianiagnetic 

 matter, ib. ; electromagnetic, 77 ; revolution in a 

 uniform magnetic field, 81 



Spherical Triangles, classification of species of, as to 

 character of sides and angles with respect to a right 

 angle, 269, 270 



Spicular notation in logic, 198 



Statics and Dynamics, their relation to each other, 1 1 w. 



Stokes, G. G., M.A., D.C.L. On the discontinuity of 

 Arbitrary Constants which appear in divergent de- 

 velopments, 104 ; principles of the investigation dis- 

 cussed, § 1 — 13 



Sturm's proof of Cauchy's theorem on imaginary roots, 

 algebraical substitute for a geometrical step in, 264, 

 265 ; proposed prefix to, 261 — 263 



'S.ifijj.i.^K, a Platonic word, 147 



'S.vjXTTKoKrj, an Aristotelian not Platonic w6rd, 147 



Supercontrary distinguished from contrary, 201 



Syllogisms, complicated by cluirges, 181 ; defined, 217; 

 strengthened, ib. ; Ojiponent, 218 ; relations of forms 

 of, lb. 



Syllogism, No. III., 173 



Syllogism, No. IV., 331 ; table of forms of, 350 ; exten- 

 sion of, to quantified propositions, 352 ; technical ex- 

 hibition of, not necessary in reasoning, 356 ; of trans- 

 posed quantity, *355 



No. v., 429 ; of indecision, 453 



Symbols, mathematical, use of, in logic, 183 ; logic the 

 only science which has grown none, 184 



System, cosmical of Plato, by Dr Donaldson, 305; source 

 of materials for, 313 



Tangents, theorem concerning pairs of, drawn to three 

 unequal circles proved, 171 



Tartini, account of, 132 w. ; D'Alembert's opinion of his 

 treatise on harmony, ib. ; beats of (so-called), 132; in 

 reality due to Sauveur, 131 ; his grave harmonic, 

 131 ; his beats considered in connexion with Smith's, 

 135—137 



Temperament and tuning, observations on, 141 — 145 



Tendency, defined, 291 ; postulates relating to, 292 



Thalamitse, 88 



Theaitetiu (Plato), 151 ; connexion with Sophista, 152; 

 materialists described in, 158 



Theorems, Analytical, connected with magnetism, 57 

 —62 



Thompson, Prof. On the genuineness of the Sophista 

 of Plato, 146 ; arguments in favour of genuineness, 

 147 ; defence of Politicus against Dr Whewell, 150 ; 

 explanation of connexion between Sophista and Theae- 

 tetus, 152 ; on Bleatic Ontology, 155 ; on the two 

 sects in the Gigantomachy, 157 ; on remarks of Dr 

 Whewell's, 163 ; on the yr}yfv('is of Sophista, 165 



