492 



INDEX. 



Differential Equation ^2'*'J^~'* = '' discussed, 

 121 ; the complete integral according to ascending 

 series given, 122; the sanie integral also expressed 

 by descending series, ib. ; the relation between the 

 constants in these two integrals determined, 123; 

 the discontinuity of the arbitrary constants deter- 

 mined, 122 



Divisive Method, invention of, attributed to Plato, 

 162 



Donaldson, Dr J. W. On the origin and proper use of 

 the word Argument, 317 ; etymology of Argument, *. ; 

 borne out by the classical usage and technical appli- 

 cation of the word, 319; the proper use of the word 

 in logic to denote the middle term, 321 ; Aristotelian 

 euthymeme may be rendered approximately by argii- 

 ment, 322 ; how argument and topic came to denote 

 the subject of a discourse, 324 ; three meanings of 

 argument in English writers, (1) Proof, (2) process of 

 reasoning, (3) subject of discourse proved by exam- 

 ples, 325 ; the second use ought to be excluded from 

 scientific language, 326 



On Plato's Cosmical system, 305; translation of 



passage in Republic, ib.; examination of points in 

 Greek text of same, 307 ; explanation of meaning of 

 game, 310 



On the Statue of Solon mentioned by jEschines 



and Demosthenes, 231 ; a statue in Museo Borbonico 

 supposed to represent Aristides the Just, ib.; or 

 iElius Aristides, 232 ; or iEschines, 233 ; these theo- 

 ries refuted, ib. ; shewn to be that of Solon, 235 



On the structure of the Athenian Trireme, 84 



Dynamics of material system, with application to motion 



of body of invariable form, 7—20 

 Dynamics and Statics, their relation to each other, 

 11 «. 



Eandi, Vassali, Letter from M. Delamethrie (Journal 

 de Physique, 1799), 25 >; his experiments in support 

 of existence of animal electricity, ib. 



Elastic rod, motion of, fixed at one end, 365; bent 

 within breaking limit may be broken by rebound on 

 being set free, 369 



Eleatic, doctrine, 97 ; dialogue, the Parmenides an, 100, 

 &c.; Stranger, 154 ; school, ib.; logic, confusion at root 

 of, 155; ontology, nothingness of, 156 



Electric Currents, on Quantity and Intensity as Proper- 

 ties of, 52—54 



Electrical science, present state of the theory and 

 requirements of, 27 ; the true method of investiga- 

 tion, ib. 



Electrical and Magnetic problems with reference to 

 spheres, 68—83; i. Theory of Electrical Images, 

 (j8 — 70 ; II. On the effect of a paramagnetic or dia- 

 magnetic sphere in a uniform field of magnetic force, 



70, 71 ; III. Magnetic field of variable intensity, 71, 

 72 ; IV. Two spheres in uniform field, 73 ; v. Two 

 spheres between the poles of a Magnet, 73, 74 ; vi. 

 On the Magneti* Phenomena of a Sphere cut from a 

 substance whose coefficient of resistance is different 

 in different directions, 74 — 76; vii. Permanent mag- 

 netism in a spherical shell, 76; vill. Electromagnetic 

 spherical shell, 77; ix. Effect of the core of the 

 electromagnet, 77, 78; x. Electrotonic functions in 

 spherical electromagnet, 78, 79 ; xi. Spherical elec- 

 tromagnetic Coil-Machine, 79, 80 ; xii. Spherical shell 

 revolving in magnetic field, 81 

 Electricity, current, conduction of, 46 

 Electrodynamics, Weber's physical theory of, stated, 



66, 67 

 Electromagnet, effect of core of, 77, 78 

 Electromagnetism, 55 — 57; Ampfere's laws of, 55 

 Electromagnetic, spherical, coil -machine, theory of, 



79, 80 

 Electromotive forces, 46 



Electrotonic functions, or components of the Electro- 

 tonic intensity, 63 

 Electrotonic intensity round a curve, 65 

 Electrotonic state, meaning of, explained, 51, 52; of 



Faraday, discussion of, 51 — 67 

 Electrotonic state, conditions of conduction of currents 

 within the medium during changes in, 64 ; summary 

 of theory of 65—67 

 Emerson, account of his connexion with the theory 

 of beats and the formula which he obtained, 135 

 and note 

 Enthymeme, instances of use of term, 321 

 Equation, Differential, meaning of solution of, 21 — 26 



djf-a^dx^=0, Buler's solution of, viz. [y—ax + b) 



{y + ax + c) = 0, with opinions of Lacroix and Cauchy 

 thereon, 21; the assertion that the generality of 

 Euler's solution is not restricted by the supposition 

 6 = c examined, 24 

 Equation and Relation, proper meaning of terms, 21 

 Equation of conduction, 39 



Equation, proof of theorem, that every algebraic equa- 

 tion has a root, 283, 327 

 Er the Pauiphylian, 305; same as Zoroaster, 313 

 Errors of observation, theory of, 409 ; deficiency of La- 

 place's investigation, 415; first principlesof, 416; law 

 of, deduced, 418 

 Euclid, Sixth Book, Props, ii — xiii, can be proved in a 

 different manner, 171 ; which is of general application 

 to a number of Theorems involving proportions of 

 straight lines [not areas, &c.), ib. 

 Euler's equations of rotation obtained, 14 

 Euripides, Hercul., explanation of passage in, 93 

 Ex cequali, new treatment, equivalent to EucUd's theo- 

 rem of, 167, 168 



in ordine perturbald, new proof of theorem of, 



by Prof. De Morgan, 172 



