Chapter XXXI (3)

Ocean, depth of, 297.

Odours, 732.

Oersted, on electro-magnetism, 530, 535.

*Or*, meaning of, 70.

Order, of premises, 114;
of terms, 33.

Orders of combinations, 194.

Original research, 574.

Oscillation, centre of, 364.

Ostensive instances, 608.

Ozone, 663.

π, value of, 234, 529.

Pack of cards, arrangement of, 241.

Paley on design, 762, 763.

Parallax, of stars, 344;
of sun, 560.

Parallel forces, 652.

Paralogism, 62.

Parity of reasoning, 268.

Partial identities, 40, 55, 57, 111;
induction of, 130.

Particular quantity, 56.

Particulars, reasoning from, 227.

Partition, 29.

Pascal, 176;
arithmetical machine, 107;
arithmetical triangle, 182;
binomial formula, 182;
error in probabilities, 213;
barometer, 519.

Passive state of steel, 659.

Pedesis, or molecular movement of microscopic particles, 406, 612.

Peirce, Professor, 23;
on rejection of observations, 391.

Pendulum, 290, 302, 315;
faults of, 311;
vibrations, 453, 454;
cycloidal, 461.

Perfect induction, 146, 149.

Perigon, 306.

Permutations, 173, 178;
distinction from combinations, 177.

Personal error, 347.

Photometry, 288.

Physiology, exceptions in, 666.

Planets, conjunctions of, 181, 187, 657;
discovery of, 412;
motions, 457;
perturbations of, 657;
classification, 683;
system of, 748.

Plants, classification of, 678.

Plateau’s experiments, 427.

Plato on science, 595.

Plattes, Gabriel, 434, 438.

Pliny on tides, 451.

Plumb-line, divergence of, 461.

Plurality, 29, 156.

Poinsot, on probability, 214.

Poisson, on principle of the inverse method, 244;
work on Probability, 395;
Newton’s rings, 470;
simile of ballot box, 524.

Polarisation, 653;
discovery of, 530.

Pole-star, 652;
observations of, 366.

Poles, of magnets, 365;
of battery, 421.

Political economy, 760.

Porphyry, on the Predicables, 698;
tree of, 702.

Port Royal logic, 22.

Positive philosophy, 760, 768.

Pouillet’s pyrheliometer, 337.

Powell, Baden, 623;
on planetary motions, 660.

Power, definition of, 224.

Predicables, 698.

Prediction, 536, 739;
in science of light, 538;
theory of undulations, 540;
other sciences, 542;
by inversion of cause and effect, 545.

Premises, order of, 114.

Prime numbers, 123, 139;
formula for, 230.

*Principia*, Newton’s, 581, 583.

Principle, of probability, 200;
inverse method, 242;
forced vibrations, 451;
approximation, 471;
co-existence of small vibrations, 476;
superposition of small effects, 476.

Probable error, 555.

Probability, etymology of, 197;
theory of, 197;
principles, 200;
calculations, 203;
difficulties of theory, 213;
application of theory, 215;
in induction, 219;
in judicial proceedings, 216;
works on, 394;
results of law, 656.

Problems, to be worked by reader, 126;
inverse problem of two classes, 135;
of three classes, 137.

Proclus, commentaries of, 232.

Proctor, R. A., star-drifts, 248.

Projectiles, theory of, 466.

Proper names, 27.

Properties, generality of, 600;
uniform, 603;
extreme instances, 607;
correlation, 681.

Property, logical, 699;
peculiar, 699.

Proportion, simple, 501.

Propositions, 36;
negative, 43;
conversion of, 46;
twofold meaning, 47;
disjunctive, 66;
equivalence of, 115;
identical, 119;
tautologous, 119.

Protean verses, 175.

Protoplasm, 524, 764.

Prout’s law, 263, 464.

Provisional units, 323.

Proximate statements, 144.

Pyramidal numbers, 185.

Pythagoras, on duality, 95;
on the number seven, 262, 624.

Quadric variation, 474.

Qualitative, reasoning, 48;
propositions, 119.

Quantification of predicate, 41.

Quantitative, reasoning, 48;
propositions, 119;
questions, 278;
induction, 483.

Quantities, continuous, 274;
incommensurable, 275.

Quaternions, 160, 634.

Quetelet, 188;
experiment on probability, 208;
on mean and average, 363;
law of error, 378, 380;
verification of law of error, 385.

Radian, 306.

Radiant matter, 642.

Radiation of heat, 430.

Radiometer, 435.

Rainbow, theory of, 526, 533.

Rainfall, variation of, 430.

Ramean tree, 703, 704.

Ramsden’s balance, 304.

Rankine, on specific heat of air, 557;
reconcentration of energy, 751.

Rational formulæ, 489.

Rayleigh, Lord, on graphical method, 495.

Reasoning, arithmetical, 167;
numerically definite, 168;
geometrical, 458.

Recorde, Robert, 15.

Reduction, of syllogisms, 85;
*ad absurdum*, 415;
of observations, 552, 572.

Reflection, total, 650.

Refraction, atmospheric, 340, 356, 500;
law of, 501;
conical, 540;
double, 585.

Regnault, dilatation of mercury, 342;
measurement of heat, 350;
exact experiment, 397;
on Boyle’s law, 468, 471;
latent heat of steam, 487;
graphical method, 494;
specific heat of air, 557.

Reid, on bifurcate classification, 697.

Reign of law, 741, 759.

Rejection of observations, 390.

Relation, sign of, 17;
logic of, 22;
logical, 35;
axiom of, 164.

Repetition, method of, 287, 288.

Representative hypotheses, 524.

Reproduction, modes of, 730.

Reservation of judgment, 592.

Residual effects, 558;
phenomena, 560, 569.

Resisting medium, 310, 523, 570.

Resonance, 453.

Reusch, on substitution, 21.

Reversal, method of, 354.

Revolution, quantity of, 306.

Robertson, Prof. Croom, 27, 101.

Robison, electric curves, 446.

Rock-salt, 609.

Rœmer, divided circle, 355;
velocity of light, 535.

Roscoe, Prof., photometrical researches, 273;
solubility of salts, 280;
constant flame, 441;
absorption of gases, 499;
vanadium, 528;
atomic weight of vanadium, 392, 649.

Rousseau on geometry, 233.

Rules, of inference, 9, 17;
indirect method of inference, 89;
for calculation of combinations, 180;
of probabilities, 203;
of inverse method, 257;
for elimination of error, 353.

Rumford, Count, experiments on heat, 343, 350, 467.

Ruminants, Cuvier on, 683.

Russell, Scott, on sound, 541.

Sample, use of, 9.

Sandeman, on perigon, 306;
approximate arithmetic, 481.

Saturn, motions of satellites, 293;
rings, 293.

Schehallien, attraction of, 369, 566.

Schottus, on combinations, 179.

Schwabe, on sun-spots, 452.

Science, nature of, 1, 673.

Selenium, 663, 670.

Self-contradiction, 32.

Senior’s definition of wealth, 75.

Senses, fallacious indications of, 276.

Seven, coincidences of number, 262;
fallacies of, 624.

Sextus, fatality of name, 264.

Sieve of Eratosthenes, 82, 123, 139.

Similars, substitution of, 17.

Simple identity, 37, 111;
inference of, 58;
contrapositive, 86;
induction of, 127.

Simple statement, 143.

Simplicity, law of, 33, 58, 72.

Simpson, discovery of property of chloroform, 531.

Simultaneity of knowledge, 34.

Singular names, 27;
terms, 129.

Siren, 10, 298, 421.

Slate, the logical, 95.

Smeaton’s experiments, on water-wheels, 347;
windmills, 401, 441.

Smee, Alfred, logical machines, 107.

Smell, delicacy of, 437.

Smithsonian Institution, 329.

Smyth, Prof. Piazzi, 452.

Socrates, on the sun, 611.

Solids, 602.

Solubility of salts, 279.

*Some*, the adjective, 41, 56.

Sorites, 60.

Sound, observations on, 356;
undulations, 405, 421;
velocity of, 571;
classification of sounds, 732.

Space, relations of, 220.

Species, 698;
infima, 701;
natural, 724.

Specific gravities, 301;
heat of air, 557.

Spence, on boiling point, 546.

Spencer, Herbert, nature of logic, 4, 7;
sign of equality, 15;
rhythmical motion, 448;
abstraction, 705;
philosophy of, 718, 761, 762.

Spectroscope, 437.

Spectrum, 583.

Spiritualism, 671.

Spontaneous generation, 432.

Standards of measurement, 305;
the bar, 312;
terrestrial, 314;
pendulum, 315;
provisional, 318;
natural system, 319.

Stars, discs of, 277;
motions of, 280, 474;
variations of, 281;
approach or recess, 298;
standard stars, 301;
apparent diameter, 390;
variable, 450;
proper motions, 572;
Bruno on, 639;
new, 644;
pole-star, 652;
conflict with wandering stars, 748.

Stas, M., his balance, 304;
on atomic weights, 464.

Statements, kinds of, 144.

Statistical conditions, 168.

Stevinus, on inclined plane, 622.

Stewart, Professor Balfour, on resisting medium, 570;
theory of exchanges, 571.

Stifels, arithmetical triangle, 182.

Stokes, Professor, on resistance, 475;
fluorescence, 664.

Stone, E. J., heat of the stars, 370;
temperature of earth’s surface, 452;
transit of Venus, 562.

Struve on double stars, 247.

Substantial terms, 28.

Substantives, 14.

Substitution of similars, 17, 45, 49, 104, 106;
anticipations of, 21.

Substitutive weighing, 345.

*Sui generis*, 629, 728.

Sulphur, 670.

Summum genus, 93, 701.

Sun, distance, 560;
variations of spots, 452.

Superposition, of small effects, 450;
small motions, 476.

Swan, W., on sodium light, 430.

Syllogism, 140;
moods of, 55, 84, 85, 88, 105, 141;
numerically definite, 168.

Symbols, use of, 13, 31, 32;
of quantity, 33.

Synthesis, 122;
of terms, 30.

Table-turning, 671.

Tacit knowledge, 43.

Tacquet on combinations, 179.

Tait, P. G., 375;
theory of comets, 571.

Talbot on the spectrum, 429.

Tartaglia on projectiles, 466.

Tastes, classification of, 732.

Tautologous propositions, 119.

Teeth, use in classification, 710.

Temperature, variations of, 453.

Tension of aqueous vapour, 500.

Terms, 24;
abstract, 27;
substantial, 28;
collective, 29;
synthesis of, 30;
negative, 45.

Terrot, Bishop, on probability, 212.

Test experiments, 347, 433.

Tetractys, 95.

Thales, predicted eclipse, 537.

Theory, results of, 534;
facts known by, 547;
quantitative, 551;
of exchanges, 571;
freedom of forming, 577;
of evolution, 761.

Thermometer, differential, 345;
reading of, 390;
change of zero, 390.

Thermopile, 300.

Thomas, arithmetical machine, 107.

Thomson, Archbishop, 50, 61.

Thomson, James, prediction by, 542;
on gaseous state, 654.

Thomson, Sir W., lighthouse signals, 194;
size of atoms, 195;
tides, 450;
capillary attraction, 614;
magnetism, 665;
dissipation of energy, 744.

Thomson and Tait, chronometry, 311;
standards of length, 315;
the crowbar, 460;
polarised light, 653.

Thomson, Sir Wyville, 412.

Thunder-cloud, 612.

Tides, 366, 450, 476, 541;
velocity of, 298;
gauge, 368;
atmospheric, 367, 553.

Time, 220;
definition of, 307.

Todhunter, Isaac, *History of the Theory of Probability*, 256, 375, 395;
on insoluble problems, 757.

Tooke, Horne, on cause, 226.

Torricelli, cycloid, 235;
his theorem, 605;
on barometer, 666.

Torsion balance, 272, 287.

Transit of Venus, 294, 348, 562.

Transit-circle, 355.

Tree of Porphyry, 702;
of Ramus, 703.

Triangle, arithmetical, 93, 182.

Triangular numbers, 185.

Trigonometrical survey, 301;
calculations of, 756.

Trisection of angles, 414.

Tuning-fork, 541.

Tycho Brahe, 271;
on star discs, 277;
obliquity of earth’s axis, 289;
circumpolar stars, 366;
Sirius, 390.

Tyndall, Professor, on natural constants, 328;
magnetism of gases, 352;
precaution in experiments, 431;
use of imagination, 509;
on Faraday, 547;
magnetism, 549, 607;
scope for discovery, 753.

Types, of logical conditions, 140, 144;
of statements, 145;
classification by, 722.

Ueberweg’s logic, 6.

Ultimate statements, 144.

Undistributed, attribute, 40;
middle term, 64, 103.

Undulations, of light, 558;
analogy in theory of, 635.

Undulatory theory, 468, 520, 538, 540;
inconceivability of, 510.

Unique objects, 728.

Unit, definition of, 157;
groups, 167;
of measurement, 305;
arcual, 306;
of time, 307;
space, 312;
density, 316;
mass, 317;
subsidiary, 320;
derived, 321;
provisional, 323;
of heat, 325;
magnetical and electrical units, 326, 327.

Unity, law of, 72.

Universe, logical, 43;
infiniteness of, 738;
heat-history of, 744, 749;
possible states of, 749.

Uranus, anomalies of, 660.

Vacuum, Nature’s abhorrence of, 513.

Vapour densities, 548.

Variable, variant, 440, 441, 483.

Variation, linear, elliptic, &c., 474;
method of, 439.

Variations, logical, 140;
periodic, 447;
combined, 450;
integrated, 452;
simple proportional, 501.

Variety, of nature, 173;
of nature and art, 190;
higher orders of, 192.

Velocity, unit of, 321.

Venn, Rev. John, logical problem by, 90;
on Boole, 155;
his work on *Logic of Chance*, 394.

Venus, 449;
transits of, 294.

Verses, Protean, 175.

Vibrations, law of, 295;
principle of forced, 451;
co-existence of small, 476.

Vital force, 523.

Voltaire on fossils, 661.

Vortices, theory of, 513, 517.

Vulcan, supposed planet, 414.

Wallis, 124, 175.

Water, compressibility of, 338;
properties of, 610.

Watt’s parallel motion, 462.

Waves, 599, 635;
nature of, 468;
in canals, 535;
earthquake, 297.

Weak arguments, effect of, 211.

Wells, on dew, 425.

Wenzel, on neutral salts, 295.

Whately, disjunctive propositions, 69;
probable arguments, 210.

Wheatstone, cipher, 124;
galvanometer, 286;
revolving mirror, 299, 308;
kaleidophone, 445;
velocity of electricity, 543.

Whewell, on tides, 371, 542;
method of least squares, 386.

Whitworth, Sir Joseph, 304, 436.

Whitworth, Rev. W. A., on *Choice and Chance*, 395.

Wilbraham, on Boole, 206.

Williamson, Professor A. W., chemical unit, 321;
prediction by, 544.

Wollaston, the goniometer, 287;
light of moon, 302;
spectrum, 429.

Wren, Sir C., on gravity, 581.

X, the substance, 523.

Yard, standard, 397.

Young, Dr. Thomas, tension of aqueous vapour, 500;
use of hypotheses, 508;
ethereal medium, 515.

Zero point, 368.

Zodiacal light, 276.

Zoology, 666.

LONDON: R. CLAY, SONS, AND TAYLOR, PRINTERS,

BY THE SAME AUTHOR.

ELEMENTARY LESSONS IN LOGIC: DEDUCTIVE AND INDUCTIVE. With Copious
Questions and Examples, and a Vocabulary of Logical Terms. Ninth
Edition. Fcap. 8vo. 3*s.* 6*d.*

PRIMER OF LOGIC. With Illustrations and Questions. New Edition. 18mo.
1*s.*

STUDIES IN DEDUCTIVE LOGIC. A Manual for Students. Crown 8vo. 6*s.*

THE SUBSTITUTION OF SIMILARS THE TRUE PRINCIPLE OF REASONING. Derived
from a Modification of Aristotle’s Dictum. Fcap. 8vo. 2*s.* 6*d.*

THE COAL QUESTION: an Inquiry Concerning the Progress of the Nation,
and the probable exhaustion of our Coal Mines. Second Edition,
revised. 8vo. 10*s.* 6*d.*

THE THEORY OF POLITICAL ECONOMY. Second Edition, Revised and
Enlarged, with New Preface. 8vo. 10*s.* 6*d.*

PRIMER OF POLITICAL ECONOMY. New Edition. 18mo. 1*s.*

INVESTIGATIONS IN CURRENCY AND FINANCE. With Diagrams, &c. 8vo.
[*Just ready.*]

THE STATE IN RELATION TO LABOUR (English Citizen Series). Crown 8vo.
3*s.* 6*d.*

MACMILLAN AND CO., LONDON.

ELEMENTARY MANUAL OF THE PRINCIPLES OF CURRENCY.

MONEY AND THE MECHANISM OF EXCHANGE. Fourth Edition. Crown 8vo. 5*s.*
(International Scientific Series.)

HENRY S. KING AND CO.

SPELLING CORRECTIONS

acording → according
aklaline → alkaline
an an → an
aws → laws
beween → between