:

commutativeness, 35, 160; dis-
junctive relation, 71; unity, 72,
157, 162; identity, 74; contra-
diction, 74, 82; duality, 73, 74,
81, 97, 169; homogeneity, 159;
error, 374; continuity, 615; of
Boyle, 619; natural, 737.
Laws, of thought, 6; empirical
mathematical, 487; of motion,
617 of botanical nomenclature,
727; natural hierarchy of, 742.
Least squares, method of, 386, 393.
Legendre, on geometry, 275; re-
jection of observations, 391;
method of least squares, 377.
Leibnitz, 154, 163; on substitution,
21; propositions, 42; blunder in
probability, 213; on Newton,
515; continuity, 618.
Leslie, differential thermometer,
345; radiating power, 425; on
affectation of accuracy, 482.
Letters, combinations of, 193.
Leverrier, on solar parallax, 562.
Lewis, Sir G. C., on time, 307.
Life is change, 173.
Light, intensity of, 296; unit, 324;
velocity, 535, 560, 561; science of,
538; total reflection, 650; waves
of, 637; classification of, 731.
Lighthouses, Babbage on, 194.
Limited identities, 42; inference of
59.

Lindsay, Prof. T. M., 6, 21.
Linear variation, 474.
Linnæus on synopsis, 712; genera
and species, 725.
Liquid state, 601, 614.
Locke, John, on induction, 121;

origin of number, 157; on proba-
bility, 215; the word power, 221.
Lockyer, J. Norman, classification
of elements, 676.

Logarithms, 148; errors in tables,
242.

Logic, etymology of name, 5.
Logical abacus, 104.

Logical alphabet, 93, 116, 173, 417,
701; table of, 94; connection
with arithmetical triangle, 189;
in probability, 205.
Logical conditions, numerical mean-
ing of, 171.
Logical machine, 107.

Logical relations, number of, 142.
Logical slate, 95.

Logical truths, certainty of, 153.
Lottery, the infinite, 2.
Lovering, Prof., on ether, 606.
Lubbock and Drinkwater-Bethune,
386, 395.

Lucretius, rain of atoms, 223, 741;
indestructibility of matter, 622.

MACHINE, logical, 107.

Macleay, system of classification,

719.

Magnetism of gases, 352.
Mallet, on earthquakes, 314.
Malus, polarised light, 530.
Mammalia, characters of, 681.
Manchester Literary and Philo-
sophical Society, papers quoted,
137, 143, 168.

Mansel, on disjunctive propositions,
69.

369;

Mars, white spots of, 596.
Maskelyne, on personal error, 347;
deviation of plumbline,
density of earth, 566.
Mass, unit of, 317, 325.
Mathematical science, 767; incom-
pleteness of, 754.

Matter, uniform properties of, 603;
variable properties, 606.
Matthiessen, 528.
Maximum points, 371.
Maxwell, Professor Clerk, on the
balance, 304; natural system of
standards, 311, 319; velocity of
electricity, 442 ; on Faraday,
580; his book on Matter and
Motion, 634.

Mayer, proposed repeating circle,
290; on mechanical equivalent of
heat, 568, 572.

Mean, etymology of, 359-360;
geometric, 362; fictitious, 363;
precise, 365; probable, 385;
rejection of, 389; method of,
357, 554.

Mean error, 387.

Meaning, of names, 25; of propo-
sitions, 47.
Measurement, of phenomena, 270;
methods of, 282; instruments,
284; indirect, 296; accuracy of,
303; units and standards of, 305;
explained results of, 554; agree-
ment of modes of, 564.
Mediate statements, 144.
Melodies, possible number of, 191.

Melvill, Thomas, on the spectrum,

429.

Membra dividentia, 68.

Metals, probable character of new,
258; transparency, 548; classi-
fication, 675; density, 706.
Method, indirect, 98; of avoidance
of error, 340; differential, 344;
correction, 346; compensation,
350; reversal, 354; means, 357;
least squares, 377, 386, 393;
variations, 139; graphical, 492;
Baconian, 507.
Meteoric streams, 372.
Meteoric cycle, 537.

Metre, 349; error of, 314.
Metric system, 318, 323.
Michell, speculations, 212;

on

double stars, 247; Pleiades, 248;
torsion balance, 566.
Middle term undistributed, 64.
Mill, John Stuart, disjunctive pro-
positions, 69; induction, 121,
594; music, 191; probability,
200-201, 222; supposed reform
of logic, 227; deductive method,
265, 508; elimination of chance,
385; joint method of agreement
and difference, 425; method of
variations, 484; on collocations,
740; erroneous tendency of his
philosophy, 752.

Miller, Prof. W. H., kilogram, 318.
Mind, powers of, 4; phenomena
of, 672.

Minerals, classification of, 678.
Minor term, illicit process of, 65.
Mistakes, 7.

Modus, tolendo ponens, 77; ponendo
toliens, 78.

Molecular movement, or pedesis,
406.

Molecules, number of, 195.
Momentum, 322, 326.
Monro, C. J., correction by, 172;
on Comte, 753.

Monstrous productions, 657.
Moon, supposed influence on clouds,

410; atmosphere of, 434; mo-
tions, 485; fall towards earth,
555.

Morse alphabet, 193.
Mother of pearl, 419.
Müller, Max, on etymology of intel-
lect, 5.

Multiplication in logic, 161.

Murphy, J. J., on disjunctive
relation, 71.

Murray, introduced use of ice, 343.
Muscular susurrus, 298.

Music, possible combinations of,

191.

NAMES, 25; of persons, ships, &c.,

680.

Nature, 1; laws of, 787; uniform-
ity of, 745.

Nebular theory, 427.
Negation, 44.

Negative arguments, 621.

Negative density, 642.
Negative premises, 63, 103.
Negative propositions, 43.
Negative results of experiment, 434.
Negative terms, 14, 45, 54, 74.
Neil on use of hypothesis, 509.
Neptune, discovery of, 537, 660.
Newton, Sir Isaac, binomial theo-
rem, 231; spectrum, 262, 418,
420, 424, 583; rings of, 288,
470; velocity of sound, 295;
wave-lengths, 297; use of pen-
dulum, 303; on time, 308;
definition of matter, 316; pen-
dulum experiment, 348, 443,
604; centrobaric bodies, 365; on
weight, 422; achromatic lenses,
432; resistance of space, 435;
absorption of light, 445; pla-
netary motions, 249, 457, 463,
466, 467; infinitesimal calculus,
477; as an alchemist, 505; his
knowledge of Bacon's works, 507;
hypotheses non fingo, 515; on vor-
tices, 517; theory of colours,
518; corpuscular theory of light,
520; fits of easy reflection, &c.,
523;
combustible substances,
527; gravity, 555, 650; density of
earth, 566; velocity of sound,
571; third law of motion, 622;
his rules of philosophising, 625;
fluxions, 633; theory of sound,
636; negative density, 642;
rays of light having sides, 662.
Newtonian Method, 581.
Nicholson, discovery of electrolysis,
530.

Ninth Bridgewater Treatise quoted,
743, 757.

Nipher, Professor, on muscular
exertion, 490.

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 in-
verse 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, $66.
Poles, of magnets, 365; of battery,
421.

Political economy, 760.

Porphyry, on the Predicables, 695;
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; in-
verse method, 242; forced vibra
tions, 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 judi-
cial 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 mean-
ing, 47; disjunctive, 66; equi-
valence 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; proposi-
tions, 119.

Quantification of predicate, 41.
Quantitative, reasoning, 48; pro-
positions, 119; questions, 278;
induction, 483.

Quantities, continuous, 274; in-
commensurable, 275.
Quaternions, 160, 634.

Quetelet, 188; experiment on pro-
bability, 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; nu-
merically definite, 168; geome-
trical, 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.

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

Roscoe, Prof., photometrical re-
searches, 273; solubility of salts,
280; constant flame, 441; ab-
sorption 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; ap-
proximate 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; in-
duction 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; terins, 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; un-

dulations, 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; abstrac-
tion, 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 mo-
tions, 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 re-

sisting 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.