Chapter XXXI (2)

We may rely upon it that immense, and to us inconceivable, advances will be made by the human intellect, in the absence of any catastrophe to the species or the globe. Within historical periods we can trace the rise of mathematical science from its simplest germs. We can prove our descent from ancestors who counted only on their fingers. How infinitely is a Newton or a Laplace above those simple savages. Pythagoras is said to have sacrificed a hecatomb when he discovered the forty-seventh proposition of Euclid, and the occasion was worthy of the sacrifice. Archimedes was beside himself when he first perceived his beautiful mode of determining specific gravities. Yet these great discoveries are the commonplaces of our school books. Step by step we can trace upwards the acquirement of new mental powers. What could be more wonderful than Napier’s discovery of logarithms, a new mode of calculation which has multiplied perhaps a hundredfold the working powers of every computer, and has rendered easy calculations which were before impracticable? Since the time of Newton and Leibnitz worlds of problems have been solved which before were hardly conceived as matters of inquiry. In our own day extended methods of mathematical reasoning, such as the system of quaternions, have been brought into existence. What intelligent man will doubt that the recondite speculations of a Cayley, a Sylvester, or a Clifford may lead to some new development of new mathematical power, at the simplicity of which a future age will wonder, and yet wonder more that to us they were so dark and difficult. May we not repeat the words of Seneca: “Veniet tempus, quo ista quæ nunc latent, in lucem dies extrahat, et longioris ævi diligentia: ad inquisitionem tantorum ætas una non sufficit. Veniet tempus, quo posteri nostri tam aperta nos nescisse mirentur.”

*The Reign of Law in Mental and Social Phenomena.*

After we pass from the so-called physical sciences to those which attempt to investigate mental and social phenomena, the same general conclusions will hold true. No one will be found to deny that there are certain uniformities of thinking and acting which can be detected in reasoning beings, and so far as we detect such laws we successfully apply scientific method. But those who attempt to establish social or moral sciences soon become aware that they are dealing with subjects of enormous perplexity. Take as an instance the science of political economy. If a science at all, it must be a mathematical science, because it deals with quantities of commodities. But as soon as we attempt to draw out the equations expressing the laws of demand and supply, we discover that they have a complexity entirely surpassing our powers of mathematical treatment. We may lay down the general form of the equations, expressing the demand and supply for two or three commodities among two or three trading bodies, but all the functions involved are so complicated in character that there is not much fear of scientific method making rapid progress in this direction. If such be the prospects of a comparatively formal science, like political economy, what shall we say of moral science? Any complete theory of morals must deal with quantities of pleasure and pain, as Bentham pointed out, and must sum up the general tendency of each kind of action upon the good of the community. If we are to apply scientific method to morals, we must have a calculus of moral effects, a kind of physical astronomy investigating the mutual perturbations of individuals. But as astronomers have not yet fully solved the problem of three gravitating bodies, when shall we have a solution of the problem of three moral bodies?

The sciences of political economy and morality are comparatively abstract and general, treating mankind from simple points of view, and attempting to detect general principles of action. They are to social phenomena what the abstract sciences of chemistry, heat, and electricity are to the concrete science of meteorology. Before we can investigate the actions of any aggregate of men, we must have fairly mastered all the more abstract sciences applying to them, somewhat in the way that we have acquired a fair comprehension of the simpler truths of chemistry and physics. But all our physical sciences do not enable us to predict the weather two days hence with any great probability, and the general problem of meteorology is almost unattempted as yet. What shall we say then of the general problem of social science, which shall enable us to predict the course of events in a nation?

Several writers have proposed to lay the foundations of the science of history. Buckle undertook to write the *History of Civilisation in England*, and to show how the character of a nation could be explained by the nature of the climate and the fertility of the soil. He omitted to explain the contrast between the ancient Greek nation and the present one; there must have been an extraordinary revolution in the climate or the soil. Auguste Comte detected the simple laws of the course of development through which nations pass. There are always three phases of intellectual condition,--the theological, the metaphysical, and the positive; applying this general law of progress to concrete cases, Comte was enabled to predict that in the hierarchy of European nations, Spain would necessarily hold the highest place. Such are the parodies of science offered to us by the *positive* philosophers.

A science of history in the true sense of the term is an absurd notion. A nation is not a mere sum of individuals whom we can treat by the method of averages; it is an organic whole, held together by ties of infinite complexity. Each individual acts and re-acts upon his smaller or greater circle of friends, and those who acquire a public position exert an influence on much larger sections of the nation. There will always be a few great leaders of exceptional genius or opportunities, the unaccountable phases of whose opinions and inclinations sway the whole body. From time to time arise critical situations, battles, delicate negotiations, internal disturbances, in which the slightest incidents may change the course of history. A rainy day may hinder a forced march, and change the course of a campaign; a few injudicious words in a despatch may irritate the national pride; the accidental discharge of a gun may precipitate a collision the effects of which will last for centuries. It is said that the history of Europe depended at one moment upon the question whether the look-out man upon Nelson’s vessel would or would not descry a ship of Napoleon’s expedition to Egypt which was passing not far off. In human affairs, then, the smallest causes may produce the greatest effects, and the real application of scientific method is out of the question.

*The Theory of Evolution.*

Profound philosophers have lately generalised concerning the production of living forms and the mental and moral phenomena regarded as their highest development. Herbert Spencer’s theory of evolution purports to explain the origin of all specific differences, so that not even the rise of a Homer or a Beethoven would escape from his broad theories. The homogeneous is unstable and must differentiate itself, says Spencer, and hence comes the variety of human institutions and characters. In order that a living form shall continue to exist and propagate its kind, says Darwin, it must be suitable to its circumstances, and the most suitable forms will prevail over and extirpate those which are less suitable. From these fruitful ideas are developed theories of evolution and natural selection which go far towards accounting for the existence of immense numbers of living creatures--plants, and animals. Apparent adaptations of organs to useful purposes, which Paley regarded as distinct products of creative intelligence, are now seen to follow as natural effects of a constantly acting tendency. Even man, according to these theories, is no distinct creation, but rather an extreme case of brain development. His nearest cousins are the apes, and his pedigree extends backwards until it joins that of the lowliest zoophytes.

The theories of Darwin and Spencer are doubtless not demonstrated; they are to some extent hypothetical, just as all the theories of physical science are to some extent hypothetical, and open to doubt. Judging from the immense numbers of diverse facts which they harmonise and explain, I venture to look upon the theories of evolution and natural selection in their main features as two of the most probable hypotheses ever proposed. I question whether any scientific works which have appeared since the *Principia* of Newton are comparable in importance with those of Darwin and Spencer, revolutionising as they do all our views of the origin of bodily, mental, moral, and social phenomena.

Granting all this, I cannot for a moment admit that the theory of evolution will destroy theology. That theory embraces several laws or uniformities which are observed to be true in the production of living forms; but these laws do not determine the size and figure of living creatures, any more than the law of gravitation determines the magnitudes and distances of the planets. Suppose that Darwin is correct in saying that man is descended from the Ascidians: yet the precise form of the human body must have been influenced by an infinite train of circumstances affecting the reproduction, growth, and health of the whole chain of intermediate beings. No doubt, the circumstances being what they were, man could not be otherwise than he is, and if in any other part of the universe an exactly similar earth, furnished with exactly similar germs of life, existed, a race must have grown up there exactly similar to the human race.

By a different distribution of atoms in the primeval world a different series of living forms on this earth would have been produced. From the same causes acting according to the same laws, the same results will follow; but from different causes acting according to the same laws, different results will follow. So far as we can see, then, infinitely diverse living creatures might have been created consistently with the theory of evolution, and the precise reason why we have a backbone, two hands with opposable thumbs, an erect stature, a complex brain, about 223 bones, and many other peculiarities, is only to be found in the original act of creation. I do not, any less than Paley, believe that the eye of man manifests design. I believe that the eye was gradually developed, and we can in fact trace its gradual development from the first germ of a nerve affected by light-rays in some simple zoophyte. In proportion as the eye became a more accurate instrument of vision, it enabled its possessor the better to escape destruction, but the ultimate result must have been contained in the aggregate of the causes, and these causes, as far as we can see, were subject to the arbitrary choice of the Creator.

Although Agassiz was clearly wrong in holding that every species of living creature appeared on earth by the immediate intervention of the Creator, which would amount to saying that no laws of connection between forms are discoverable, yet he seems to be right in asserting that living forms are distinct from those produced by purely physical causes. “The products of what are commonly called physical agents,” he says,[620] “are everywhere the same (*i.e.* upon the whole surface of the earth), and have always been the same (*i.e.* during all geological periods); while organised beings are everywhere different and have differed in all ages. Between two such series of phenomena there can be no causal or genetic connection.” Living forms as we now regard them are essentially variable, but from constant mechanical causes constant effects would ensue. If vegetable cells are formed on geometrical principles being first spherical, and then by mutual compression dodecahedral, then all cells should have similar forms. In the Foraminifera and some other lowly organisms, we seem to observe the production of complex forms on geometrical principles. But from similar causes acting according to similar laws only similar results could be produced. If the original life germ of each creature is a simple particle of protoplasm, unendowed with any distinctive forces, then the whole of the complex phenomena of animal and vegetable life are effects without causes. Protoplasm may be chemically the same substance, and the germ-cell of a man and of a fish may be apparently the same, so far as the microscope can decide; but if certain cells produce men, and others as uniformly produce a species of fish, there must be a hidden constitution determining the extremely different results. If this were not so, the generation of every living creature from the uniform germ would have to be regarded as a distinct act of creation.

[620] Agassiz, *Essay on Classification*, p. 75.

Theologians have dreaded the establishment of the theories of Darwin and Huxley and Spencer, as if they thought that those theories could explain everything upon the purest mechanical and material principles, and exclude all notions of design. They do not see that those theories have opened up more questions than they have closed. The doctrine of evolution gives a complete explanation of no single living form. While showing the general principles which prevail in the variation of living creatures, it only points out the infinite complexity of the causes and circumstances which have led to the present state of things. Any one of Mr. Darwin’s books, admirable though they all are, consists but in the setting forth of a multitude of indeterminate problems. He proves in the most beautiful manner that each flower of an orchid is adapted to some insect which frequents and fertilises it, and these adaptations are but a few cases of those immensely numerous ones which have occurred in the lives of plants and animals. But why orchids should have been formed so differently from other plants, why anything, indeed, should be as it is, rather than in some of the other infinitely numerous possible modes of existence, he can never show. The origin of everything that exists is wrapped up in the past history of the universe. At some one or more points in past time there must have been arbitrary determinations which led to the production of things as they are.

*Possibility of Divine Interference.*

I will now draw the reader’s attention to pages 149 to 152. I there pointed out that all inductive inference involves the assumption that our knowledge of what exists is complete, and that the conditions of things remain unaltered between the time of our experience and the time to which our inferences refer. Recurring to the illustration of a ballot-box, employed in the chapter on the inverse method of probabilities, we assume when predicting the probable nature of the next drawing, firstly, that our previous drawings have been sufficiently numerous to give us knowledge of the contents of the box; and, secondly, that no interference with the ballot-box takes place between the previous and the next drawings. The results yielded by the theory of probability are quite plain. No finite number of casual drawings can give us sure knowledge of the contents of the box, so that, even in the absence of all disturbance, our inferences are merely the best which can be made, and do not approach to infallibility. If, however, interference be possible, even the theory of probability ceases to be applicable, for, the amount and nature of that interference being arbitrary and unknown, there ceases to be any connection between premises and conclusion. Many years of reflection have not enabled me to see the way of avoiding this hiatus in scientific certainty. The conclusions of scientific inference appear to be always of a hypothetical and provisional nature. Given certain experience, the theory of probability yields us the true interpretation of that experience and is the surest guide open to us. But the best calculated results which it can give are never absolute probabilities; they are purely relative to the extent of our information. It seems to be impossible for us to judge how far our experience gives us adequate information of the universe as a whole, and of all the forces and phenomena which can have place therein.

I feel that I cannot in the space remaining at my command in the present volume, sufficiently follow out the lines of thought suggested, or define with precision my own conclusions. This chapter contains merely *Reflections* upon subjects of so weighty a character that I should myself wish for many years--nay for more than a lifetime of further reflection. My purpose, as I have repeatedly said, is the purely negative one of showing that atheism and materialism are no necessary results of scientific method. From the preceding reviews of the value of our scientific knowledge, I draw one distinct conclusion, that we cannot disprove the possibility of Divine interference in the course of nature. Such interference might arise, so far as our knowledge extends, in two ways. It might consist in the disclosure of the existence of some agent or spring of energy previously unknown, but which effects a given purpose at a given moment. Like the pre-arranged change of law in Babbage’s imaginary calculating machine, there may exist pre-arranged surprises in the order of nature, as it presents itself to us. Secondly, the same Power, which created material nature, might, so far as I can see, create additions to it, or annihilate portions which do exist. Such events are in a certain sense inconceivable to us; yet they are no more inconceivable than the existence of the world as it is. The indestructibility of matter, and the conservation of energy, are very probable scientific hypotheses, which accord satisfactorily with experiments of scientific men during a few years past, but it would be gross misconception of scientific inference to suppose that they are certain in the sense that a proposition in geometry is certain. Philosophers no doubt hold that *de nihilo nihil fit*, that is to say, their senses give them no means of imagining to the mind how creation can take place. But we are on the horns of a trilemma; we must either deny that anything exists, or we must allow that it was created out of nothing at some moment of past time, or that it existed from eternity. The first alternative is absurd; the other two seem to me equally conceivable.

*Conclusion.*

It may seem that there is one point where our speculations must end, namely where contradiction begins. The laws of Identity and Difference and Duality were the foundations from which we started, and they are, so far as I can see, the foundations which we can never quit without tottering. Scientific Method must begin and end with the laws of thought, but it does not follow that it will save us from encountering inexplicable, and at least apparently contradictory results. The nature of continuous quantity leads us into extreme difficulties. Any finite space is composed of an infinite number of infinitely small spaces, each of which, again, is composed of an infinite number of spaces of a second order of smallness; these spaces of the second order are composed, again, of infinitely small spaces of the third order. Even these spaces of the third order are not absolute geometrical points answering to Euclid’s definition of a point, as position without magnitude. Go on as far as we will, in the subdivision of continuous quantity, yet we never get down to the absolute point. Thus scientific method leads us to the inevitable conception of an infinite series of successive orders of infinitely small quantities. If so, there is nothing impossible in the existence of a myriad universes within the compass of a needle’s point, each with its stellar systems, and its suns and planets, in number and variety unlimited. Science does nothing to reduce the number of strange things that we may believe. When fairly pursued it makes absurd drafts upon our powers of comprehension and belief.

Some of the most precise and beautiful theorems in mathematical science seem to me to involve apparent contradiction. Can we imagine that a point moving along a perfectly straight line towards the west would ever get round to the east and come back again, having performed, as it were, a circuit through infinite space, yet without ever diverging from a perfectly straight direction? Yet this is what happens to the intersecting point of two straight lines in the same plane, when one line revolves. The same paradox is exhibited in the hyperbola regarded as an infinite ellipse, one extremity of which has passed to an infinite distance and come back in the opposite direction. A varying quantity may change its sign by passing either through zero or through infinity. In the latter case there must be one intermediate value of the variable for which the variant is indifferently negative infinity and positive infinity. Professor Clifford tells me that he has found a mathematical function which approaches infinity as the variable approaches a certain limit; yet at the limit the function is finite! Mathematicians may shirk difficulties, but they cannot make such results of mathematical principles appear otherwise than contradictory to our common notions of space.

The hypothesis that there is a Creator at once all-powerful and all-benevolent is pressed, as it must seem to every candid investigator, with difficulties verging closely upon logical contradiction. The existence of the smallest amount of pain and evil would seem to show that He is either not perfectly benevolent, or not all-powerful. No one can have lived long without experiencing sorrowful events of which the significance is inexplicable. But if we cannot succeed in avoiding contradiction in our notions of elementary geometry, can we expect that the ultimate purposes of existence shall present themselves to us with perfect clearness? I can see nothing to forbid the notion that in a higher state of intelligence much that is now obscure may become clear. We perpetually find ourselves in the position of finite minds attempting infinite problems, and can we be sure that where we see contradiction, an infinite intelligence might not discover perfect logical harmony?

From science, modestly pursued, with a due consciousness of the extreme finitude of our intellectual powers, there can arise only nobler and wider notions of the purpose of Creation. Our philosophy will be an affirmative one, not the false and negative dogmas of Auguste Comte, which have usurped the name, and misrepresented the tendencies of a true *positive philosophy*. True science will not deny the existence of things because they cannot be weighed and measured. It will rather lead us to believe that the wonders and subtleties of possible existence surpass all that our mental powers allow us clearly to perceive. The study of logical and mathematical forms has convinced me that even space itself is no requisite condition of conceivable existence. Everything, we are told by materialists, must be here or there, nearer or further, before or after. I deny this, and point to logical relations as my proof.

There formerly seemed to me to be something mysterious in the denominators of the binomial expansion (p. 190), which are reproduced in the natural constant ε, or

1 + 1/1 + 1/(1 . 2) + 1/(1 . 2 . 3) + ...

and in many results of mathematical analysis. I now perceive, as already explained (pp. 33, 160, 383), that they arise out of the fact that the relations of space do not apply to the logical conditions governing the numbers of combinations as contrasted to those of permutations. So far am I from accepting Kant’s doctrine that space is a necessary form of thought, that I regard it as an accident, and an impediment to pure logical reasoning. Material existences must exist in space, no doubt, but intellectual existences may be neither in space nor out of space; they may have no relation to space at all, just as space itself has no relation to time. For all that I can see, then, there may be intellectual existences to which both time and space are nullities.

Now among the most unquestionable rules of scientific method is that first law that *whatever phenomenon is, is*. We must ignore no existence whatever; we may variously interpret or explain its meaning and origin, but, if a phenomenon does exist, it demands some kind of explanation. If then there is to be competition for scientific recognition, the world without us must yield to the undoubted existence of the spirit within. Our own hopes and wishes and determinations are the most undoubted phenomena within the sphere of consciousness. If men do act, feel, and live as if they were not merely the brief products of a casual conjunction of atoms, but the instruments of a far-reaching purpose, are we to record all other phenomena and pass over these? We investigate the instincts of the ant and the bee and the beaver, and discover that they are led by an inscrutable agency to work towards a distant purpose. Let us be faithful to our scientific method, and investigate also those instincts of the human mind by which man is led to work as if the approval of a Higher Being were the aim of life.

INDEX.

Abacus, logical, 104;
arithmetical, 107;
Panchrestus, 182.

Aberration of light, 561;
systematic, 547.

Abscissio infiniti, 79, 713.

Abstract terms, 27;
number, 159.

Abstraction, 704;
logical, 25;
numerical, 158;
of indifferent circumstances, 97.

Accademia del Cimento, 427, 432, 436, 527.

Accident, logical, 700.

Accidental discovery, 529.

Achromatic lenses, 432.

Actinometer, 337.

Adamantine medium, 605, 751.

Adjectives, 14, 30, 31, 35;
indeterminate, 41.

Adrain, of New Brunswick, 375.

Affirmation, 44.

Agassiz, on genera, 726;
on creation of species, 763.

Agreement, 44.

Airy, Sir George Biddell, on perpetual motion, 223;
new property of sphere, 232;
pendulum experiments, 291, 304, 348, 567;
standard clock, 353;
book on *Errors of Observation*, 395;
tides, 488;
extra-polation, 495;
Thales’ eclipse, 537;
interference of light, 539;
density of earth, 291.

Alchemists, 505;
how misled, 428.

Algebra, 123, 155, 164;
Diophantine, 631.

Algebraic, equations, 123;
geometry, 633.

Allotropic state, 663, 670.

Alloys, possible number, 191;
properties, 528.

Alphabet, the Logical, 93, 104, 125;
Morse, 193.

Alphabet, permutations of letters of the, 174, 179.

Alphabetic indexes, 714.

Alternative relations, 67;
exclusive and unexclusive, 205.

Ampère, electricity, 547;
classification, 679.

Anagrams, 128.

Analogy, 627;
of logical and numerical terms, 160;
and generalisation, 596;
in mathematical sciences, 631;
in theory of undulations, 635;
in astronomy, 638;
failure of, 641.

Analysis, logical, 122.

Andrews, Prof. Thomas, experiments on gaseous state, 71, 613, 665, 753.

Angström, on spectrum, 424.

Angular magnitude, 305, 306, 326.

Antecedent defined, 225.

Anticipation of Nature, 509.

Anticipations, of Principle of Substitution, 21;
of electric telegraph, 671.

Apparent, equality, 275;
sequence of events, 409.

Approximation, theory of, 456;
to exact laws, 462;
mathematical principles of, 471;
arithmetic of, 481.

Aqueous vapour, 500.

Aquinas, on disjunctive propositions, 69.

Arago, photometer, 288;
rotating disc, 535;
his philosophic character, 592.

Archimedes, *De Arenæ Numero*, 195;
centre of gravity, 363.

Arcual unit, 306, 330.

Argyll, Duke of, 741.

Aristarchus on sun’s and moon’s distances, 294.

Aristotelian doctrines, 666.

Aristotle, dictum, 21;
singular terms, 39;
overlooked simple identities, 40;
order of premises, 114;
logical error, 117;
definition of time, 307;
on science, 595;
on white swans, 666.

Arithmetic, reasoning in, 167;
of approximate quantities, 481.

Arithmetical triangle, 93, 143, 182, 202, 378, 383;
diagram of, 184;
connection with Logical Alphabet, 189;
in probability, 208.

Asteroids, discovery of, 412, 748.

Astronomy, physical, 459.

Atmospheric tides, 553.

Atomic theory, 662.

Atomic weights, 563.

Atoms, size of, 195;
impossibility of observing, 406.

Augustin on time, 307.

Average, 359, 360;
divergence from, 188;
etymology of, 363.

Axes of crystals, 686.

Axioms of algebra, 164.

Babbage, Charles, calculating machine, 107, 231, 743;
lighthouse signals, 194;
natural constants, 329;
Mosaic history, 412;
universal and general truths, 646;
change of law, 230;
persistence of effects, 757.

Bacon, Francis Lord, *Novum Organum*, 107;
on induction, 121;
biliteral cipher, 193;
First Aphorism, 219;
on causes, 221;
Copernican system, 249, 638;
deficient powers of senses, 278;
observation, 402;
Natural History, 403;
use of hypothesis, 506;
his method, 507;
*experimentum crucis*, 519;
error of his method, 576;
ostensive, clandestine instances, &c., 608, 610;
*latens precessus*, 619.

Bacon, Roger, on the rainbow, 526, 598.

Baily, Francis, 272;
density of earth, 342, 566;
experiments with torsion balance, 370, 397, 432, 567–8;
motions of stars, 572.

Bain, Alexander, on powers of mind, 4;
Mill’s reform of logic, 227.

Baker’s poem, *The Universe*, 621.

Balance, use of the chemical, 292, 351, 354, 369;
delicacy of, 304;
vibrations of, 369.

Ballot, Buys, experiment on sound, 541.

Ballot-box, simile of, 150, 251–6, 765.

Barbara, 55, 57, 88, 105, 141.

Baroko, 85.

Barometer, 659;
Gay Lussac’s standard, 346;
variations, 337, 346, 349.

Bartholinus on double refraction, 585.

Base-line, measurement of, 304.

Bauhusius, verses of, 175.

Baxendell, Joseph, 552.

Beneke, on substitution, 21.

Bennet, momentum of light, 435.

Bentham, George, 15;
bifurcate classification, 695;
infima species, 702;
works on classification, 703;
analytical key to flora, 712.

Bentham, Jeremy, on analogy, 629;
bifurcate classification, 703.

Benzenberg’s experiment, 388.

Bernoulli, Daniel, planetary orbits, 250;
resisting media and projectiles, 467;
vibrations, 476.

Bernoulli, James, 154;
numbers of, 124;
Protean verses, 175;
*De Arte Conjectandi* quoted, 176, 183;
on figurate numbers, 183;
theorem of, 209;
false solution in probability, 213;
solution of inverse problem, 261.

Bessel, F. W., 375;
law of error, 384;
formula for periodic variations, 488;
use of hypothesis, 506;
solar parallax, 560–2;
ellipticity of earth, 565;
pendulum experiments, 604.

Bias, 393, 402.

Biela’s comet, 746.

Bifurcate classification, 694.

Binomial theorem, 190;
discovery of, 231.

Biot, on tension of vapour, 500.

Blind experiments, 433.

Bode’s law, 147, 257, 660.

Boethius, quoted, 33;
on kinds of mean, 360.

Boiling point, 442, 659.

Bonnet’s theory of reproduction, 621.

Boole, George, on sign of equality, 15;
his calculus of logic, 23, 113, 634;
on logical terms, 33;
law of commutativeness, 35;
use of *some*, 41–2;
disjunctive propositions, 70;
Venn on his method, 90;
*Laws of Thought*, 155;
statistical conditions, 168;
propositions numerically definite, 172;
on probability, 199;
general method in probabilities, 206;
Laplace’s solution of inverse problem, 256;
law of error, 377.

Borda, his repeating circle, 290.

Boscovich’s hypothesis, 512.

Botany, 666, 678, 681;
modes of classification, 678;
systematic, 722;
nomenclature of, 727.

Bowen, Prof. Francis, on inference, 118;
classification, 674.

Boyle’s, Robert, law of gaseous pressure, 468, 470, 619;
on hypothesis, 510;
barometer, 659.

Bradley, his observations, 384;
accuracy of, 271;
aberration of light, 535.

Bravais, on law of error, 375.

Brewer, W. H., 142.

Brewster, Sir David, iridescent colours, 419;
spectrum, 429;
Newton’s theory of colours, 518;
refractive indices, 10, 527;
optic axes, 446.

British Museum, catalogue of, 717.

Brodie, Sir B. C., on errors of experiment, 388, 464;
ozone, 663.

Brown, Thomas, on cause, 224.

Buckle, Thomas, on constancy of average, 656;
science of history, 760.

Buffon, on probability, 215;
definition of genius, 576.

Bunsen, Robert, spectrum, 244;
photometrical researches, 273, 324, 441;
calorimeter, 343.

Butler, Bishop, on probability, 197.

Calorescence, 664.

Camestres, 84.

Canton, on compressibility of water, 338.

Carbon, 640, 728;
conductibility of, 442.

Cardan, on inclined plane, 501.

Cards, combinations of, 190.

Carlini, pendulum experiments, 567.

Carnot’s law, 606.

Carpenter, Dr. W. B., 412.

Catalogues, art of making, 714.

Cauchy, undulatory theory, 468.

Cause, 220;
definition of, 224.

Cavendish’s experiment, 272, 566.

Cayley, Professor, 145;
on mathematical tables, 331;
numbers of chemical compounds, 544.

Celarent, 55.

Centre of gravity, 363, 524;
of oscillation, gyration, &c., 364.

Centrobaric bodies, 364.

Certainty, 235, 266.

Cesare, 85.

Chalmers, on collocations, 740.

Chance, 198.

Character, human, 733.

Characteristics, 708.

Chauvenet, Professor W., on treatment of observations, 391.

Chemical affinity, 614;
analysis, 713.

Chladni, 446.

Chloroform, discovery of, 531.

Chronoscope, 616.

Cipher, 32;
Bacon’s, 193.

Circle, circumference of, 389.

Circumstances, indifferent, 419.

Circumstantial evidence, 264.

Clairaut, 650, 651;
on gravity, 463.

Classes, 25;
problem of common part of three, 170.

Classification, 673;
involving induction, 675;
multiplicity of modes, 677;
natural and artificial systems, 679;
in crystallography, 685;
symbolic statement of, 692;
bifurcate, 694;
an inverse and tentative operation, 689;
diagnostic, 710;
by indexes, 714;
of books, 715;
in biological sciences, 718;
genealogical, 719;
by types, 722;
limits of, 730.

Clifford, Professor, on types of compound statements, 143, 529;
first and last catastrophe, 744;
mathematical function, 768.

Clocks, astronomical, 340, 353.

Clouds, 447;
cirrous, 411.

Coincidences, 128;
fortuitous, 261;
measurement by, 292;
method of, 291.

Collective terms, 29, 39.

Collocations of matter, 740.

Colours, iridescent, 419;
natural, 518;
perception of, 437;
of spectrum, 584.

Combinations, 135, 142;
doctrine of, 173;
of letters of alphabet, 174;
calculations of, 180;
higher orders of, 194.

Combinatorial analysis, 176.

Comets, 449;
number of, 408;
hyperbolic, 407;
classification of, 684;
conflict with, 746–7;
Halley’s comet, 537;
Lexell’s comet, 651.

Commutativeness, law of, 35, 72, 177.

Comparative use of instruments, 299.

Compass, variations of, 281.

Complementary statements, 144.

Compossible alternatives, 69.

Compound statements, 144;
events, 204.

Compounds, chemical, 192.

Comte, Auguste, on probability, 200, 214;
on prevision, 536;
his positive philosophy, 752, 760, 768.

Concrete number, 159.

Conditions, of logical symbols, 32;
removal of usual, 426;
interference of unsuspected, 428;
maintenance of similar, 443;
approximation to natural, 465.

Condorcet, 2;
his problem, 253.

Confusion of elements, 237.

Conical refraction, 653.

Conjunction of planets, 293, 657.

Consequent, definition of, 225.

Conservation of energy, 738.

Constant numbers of nature, 328;
mathematical, 330;
physical, 331;
astronomical, 332;
terrestrial, 333;
organic, 333;
social, 334.

Continuity, law of, 615, 729;
sense of, 493;
detection of, 610;
failure of, 619.

Continuous quantity, 274, 485.

Contradiction, law of, 31, 74.

Contrapositive, proposition, 84, 136;
conversion, 83.

Conversion of propositions, 46, 118.

Copernican theory, 522, 625, 638, 647.

Copula, 16.

Cornu, velocity of light, 561.

Corpuscular theory, 520, 538, 667.

Correction, method of, 346.

Correlation, 678, 681.

Cotes, Roger, use of mean, 359;
method of least squares, 377.

Coulomb, 272.

Couple, mechanical, 653.

Creation, problem of, 740.

Crookes’ radiometer, 435.

Cross divisions, 144.

Crystallography, 648, 654, 658, 678, 754;
systems of, 133;
classification in, 685.

Crystals, 602;
Dana’s classification of, 711;
pseudomorphic, 658.

Curves, use of, 392, 491, 496;
of various degrees, 473.

Cuvier, on experiment, 423;
on inferences, 682.

Cyanite, 609.

Cycloid, 633.

Cycloidal pendulum, 461.

Cypher, 124.

D’Alembert, blunders in probability, 213, 214;
on gravity, 463.

Dalton, laws of, 464, 471;
atomic theory, 662.

Darapti, 59.

Darii, 56.

Darwin, Charles, his works, 131;
negative results of observation, 413;
arguments against his theory, 437;
cultivated plants, 531;
his influence, 575;
classification, 718;
constancy of character in classification, 720–1;
on definition, 726;
restoration of limbs, 730;
tendency of his theory, 762, 764.

Davy, Sir H., on new instruments, 270;
nature of heat, 343, 417;
detection of salt in electrolysis, 428.

Day, sidereal, 310;
length of, 289.

Decandolle, on classification, 696.

Decyphering, 124.

Deduction, 11, 49.

Deductive reasoning, 534;
miscellaneous forms of, 60;
probable, 209.

Definition, 39, 62, 711, 723;
purpose of, 54;
of cause and power, 224.

De Morgan, Augustus, negative terms, 14;
Aristotle’s logic, 18;
relatives, 23;
logical universe, 43;
complex propositions, 75;
contraposition, 83;
formal logic quoted, 101;
error of his system, 117;
anagram of his name, 128;
numerically definite reasoning, 168–172;
probability, 198;
belief, 199;
experiments in probability, 207;
probable deductive arguments, 209–210;
trisection of angle, 233;
probability of inference, 259;
arcual unit, 306;
mathematical tables, 331;
personal error, 348;
average, 363;
his works on probability, 394–395;
apparent sequence, 409;
sub-equality, 480;
rule of approximation, 481;
negative areas, 529;
generalisation, 600;
double algebra, 634;
bibliography, 716;
catalogues, 716;
extensions of algebra, 758.

Density, unit of, 316;
of earth, 387;
negative, 642.

Descartes, vortices, 517;
geometry, 632.

Description, 62.

Design, 762–763.

Determinants, inference by, 50.

Development, logical, 89, 97.

Diagnosis, 708.

Dichotomy, 703.

Difference, 44;
law of, 5;
sign of, 17;
representation of, 45;
inference with, 52, 166;
form of, 158.

Differences of numbers, 185.

Differential calculus, 477.

Differential thermometer, 345.

Diffraction of light, 420.

Dimensions, theory of, 325.

Dip-needle, observation of, 355.

Direct deduction, 49.

Direction of motion, 47.

Discontinuity, 620.

Discordance, of theory and experiment, 558;
of theories, 587.

Discoveries, accidental, 529;
predicted, 536;
scope for, 752.

Discrimination, 24;
power of, 4.

Disjunctive, terms, 66;
conjunction, 67;
propositions, 66;
syllogism, 77;
argument, 106.

Dissipation of energy, 310.

Distance of statements, 144.

Divergence from average, 188.

Diversity, 156.

Divine interference, 765.

Dollond, achromatic lenses, 608.

Donkin, Professor, 375;
on probability, 199, 216;
principle of inverse method, 244.

Double refraction, 426.

Dove’s law of winds, 534.

Draper’s law, 606.

Drobitsch, 15.

Duality, 73, 81;
law of, 5, 45, 92, 97.

Dulong and Petit, 341, 471.

Duration, 308.

ε, 330, 769.

Earth, density of, 387;
ellipticity, 565.

Eclipses, 656;
Egyptian records of, 246;
of Jupiter’s satellites, 294, 372;
solar, 486.

Electric, sense, 405;
acid, 428;
fluid, 523.

Electric telegraph, anticipations of, 671.

Electricity, theories of, 522;
duality of, 590.

Electrolysis, 428, 530.

Electro-magnet, use of, 423.

Elements, confusion of, 237;
definition, 427;
classification, 676, 677, 690.

Elimination, 58.

Ellicott, observation on clocks, 455.

Ellipsis, 41;
of terms, 57.

Elliptic variation, 474.

Ellipticity of earth, 565.

Ellis, A. J., contributions to formal logic, 172.

Ellie, Leslie, 23, 375.

Ellis, W., on moon’s influence, 410.

Emanation, law of, 463.

Emotions, 732.

Empirical, knowledge, 505, 525–526;
measurement, 552.

Encke, on mean, 386, 389;
his comet, 570, 605;
on resisting medium, 523;
solar parallax, 562.

Energy, unit of, 322;
conservation of, 465;
reconcentration of, 751.

English language, words in, 175.

Eözoon canadense, 412, 668.

Equality, sign of, 14;
axiom, 163;
four meanings of, 479.

Equations, 46, 53, 160;
solution of, 123.

Equilibrium, unstable, 276, 654.

Equisetaceæ, 721.

Equivalence of propositions, 115, 120, 132;
remarkable case of, 529, 657.

Eratosthenes, sieve of, 82, 123, 139;
measurement of degree, 293.

Error, function, 330, 376, 381;
elimination of, 339, 353;
personal, 347;
law of, 374;
origin of law, 383;
verification of law, 383;
probable, 386;
mean, 387;
constant, 396;
variation of small errors, 479.

Ether, luminiferous, 512, 514, 605.

Euclid, axioms, 51, 163;
indirect proof, 84;
10th book, 117th proposition, 275;
on analogy, 631.

Euler, on certainty of inference, 238;
corpuscular theory, 435;
gravity, 463;
on ether, 514.

Everett, Professor, unit of angle, 306;
metric system, 328.

Evolution, theory of, 761.

Exact science, 456.

Exceptions, 132, 644, 728;
classification of, 645;
imaginary, 647;
apparent, 649;
singular, 652;
divergent, 655;
accidental, 658;
novel, 661;
limiting, 663;
real, 666;
unclassed, 668.

Excluded middle, law of, 6.

Exclusive alternatives, 68.

Exhaustive investigation, 418.

Expansion, of bodies, 478;
of liquids, 488.

Experiment, 400, 416;
in probability, 208;
test or blind, 433;
negative results of, 434;
limits of, 437;
collective, 445;
simplification of, 422;
failure in simplification, 424.

Experimentalist, character of, 574, 592.

Experimentum crucis, 518, 667.

Explanation, 532.

Extent of meaning, 26;
of terms, 48.

Extrapolation, 495.

Factorials, 179.

Facts, importance of false, 414;
conformity with, 516.

Fallacies, 62;
analysed by indirect method, 102;
of observation, 408.

Faraday, Michael, measurement of gold-leaf, 296;
on gravity, 342, 589;
magnetism of gases, 352;
vibrating plate, 419;
electric poles, 421;
circularly polarised light, 424, 588, 630;
freezing mixtures, 427;
magnetic experiments, 431, 434;
lines of magnetic force, 446, 580;
errors of experiment, 465;
electrolysis, 502;
velocity of light, 520;
prediction, 543;
relations of physical forces, 547;
character of, 578, 587;
ray vibrations, 579;
mathematical power, 580;
philosophic reservation of opinion, 592;
use of heavy glass, 609;
electricity, 612;
radiant matter, 642;
hydrogen, 691.

Fatality, belief in, 264.

Ferio, 56.

Figurate numbers, 183, 186.

Figure of earth, 459, 565.

Fizeau, use of Newton’s rings, 297, 582;
fixity of properties, 313;
velocity of light, 441, 561.

Flamsteed, use of wells, 294;
standard stars, 301;
parallax of pole-star, 338;
selection of observations, 358;
astronomical instruments, 391;
solar eclipses, 486.

Fluorescence, 664.

Fontenelle on the senses, 405.

Forbes, J. D., 248.

Force, unit of, 322, 326;
emanating, 464;
representation of, 633.

Formulæ, empirical, 487;
rational, 489.

Fortia, *Traité des Progressions*, 183.

Fortuitous coincidences, 261.

Fossils, 661.

Foster, G. C., on classification, 691.

Foucault, rotating mirror, 299;
pendulum, 342, 431, 522;
on velocity of light, 441, 521, 561.

Fourier, Joseph, theory of dimensions, 325;
theory of heat, 469, 744.

Fowler, Thomas, on method of difference, 439;
reasoning from case to case, 227.

Frankland, Professor Edward, on spectrum of gases, 606.

Franklin’s experiments on heat, 424.

Fraunhofer, dark lines of spectrum, 429.

Freezing-point, 546.

Freezing mixtures, 546.

Fresnel, inflexion of light, 420;
corpuscular theory, 521;
on use of hypothesis, 538;
double refraction, 539.

Friction, 417;
determination of, 347.

Function, definitions of, 489.

Functions, discovery of, 496.

Galileo, 626;
on cycloid, 232, 235;
differential method of observation, 344;
projectiles, 447, 466;
use of telescope, 522;
gravity, 604;
principle of continuity, 617.

Gallon, definition of, 318.

Galton, Francis, divergence from mean, 188;
works by, 188, 655;
on hereditary genius, 385, 655.

Galvanometer, 351.

Ganières, de, 182.

Gases, 613;
properties of, 601, 602;
perfect, 470;
liquefiable, 665.

Gauss, pendulum experiments, 316;
law of error, 375–6;
detection of error, 396;
on gravity, 463.

Gay Lussac, on boiling point, 659;
law of, 669.

Genealogical classification, 680, 719.

General, terms, 29;
truths, 647;
notions, 673.

Generalisation, 2, 594, 704;
mathematical, 168;
two meanings of, 597;
value of, 599;
hasty, 623.

Genius, nature of, 575.

Genus, 433, 698;
generalissimum, 701;
natural, 724.

Geology, 667;
records in, 408;
slowness of changes, 438;
exceptions in, 660.

Geometric mean, 361.

Geometric reasoning, 458;
certainty of, 267.

Giffard’s injector, 536.

Gilbert, on rotation of earth, 249;
magnetism of silver, 431;
experimentation, 443.

Gladstone, J. H., 445.

Glaisher, J. W. L., on mathematical tables, 331;
law of error, 375, 395.

Gold, discovery of, 413.

Gold-assay process, 434.

Gold-leaf, thickness of, 296.

Graham, Professor Thomas, on chemical affinity, 614;
continuity, 616;
nature of hydrogen, 691.

Grammar, 39;
rules of, 31.

Grammatical, change, 119;
equivalence, 120.

Gramme, 317.

Graphical method, 492.

Gravesande, on inflection of light, 420.

Gravity, 422, 512, 514, 604, 740;
determination of, 302;
elimination of, 427;
law of, 458, 462, 474;
inconceivability of, 510;
Newton’s theory, 555;
variation of, 565;
discovery of law, 581;
Faraday on, 589;
discontinuity in, 620;
Aristotle on, 649;
Hooke’s experiment, 436.

Grimaldi on the spectrum, 584.

Grove, Mr. Justice, on ether, 514;
electricity, 615.

Guericke, Otto von, 432.

Habit, formation of, 618.

Halley, trade-winds, 534.

Halley’s comet, 537, 570.

Hamilton, Sir William, disjunctive propositions, 69;
inference, 118;
free-will, 223.

Hamilton, Sir W. Rowan, on conical refraction, 540;
quaternions, 634.

Harley, Rev. Robert, on Boole’s logic, 23, 155.

Harris, standards of length, 312.

Hartley, on logic, 7.

Hatchett, on alloys, 191.

Haughton, Professor, on tides, 450;
muscular exertion, 490.

Haüy, on crystallography, 529.

Hayward, R. B., 142.

Heat, unit of, 324;
measurement of, 349;
experiments on, 444;
mechanical equivalent of, 568.

Heavy glass, 588, 609.

Helmholtz, on microscopy, 406;
undulations, 414;
sound, 476.

Hemihedral crystals, 649.

Herschel, Sir John, on rotation of plane of polarisation of light, 129, 630;
quartz crystals, 246;
numerical precision, 273;
photometry, 273;
light of stars, 302;
actinometer, 337;
mean and average, 363;
eclipses of Jupiter’s satellites, 372;
law of error, 377;
error in observations, 392;
on observation, 400;
moon’s influence on clouds, 410;
comets, 411;
spectrum analysis, 429;
collective instances, 447;
principle of forced vibrations, 451, 663;
meteorological variations, 489;
double stars, 499, 685;
direct action, 502;
use of theory, 508;
ether, 515;
*experimentum crucis*, 519;
interference of light, 539;
interference of sound, 540;
density of earth, 567;
residual phenomena, 569;
helicoidal dissymmetry, 630;
fluorescence, 664.

Hindenburg, on combinatorial analysis, 176.

Hipparchus, used method of repetition, 289;
longitudes of stars, 294.

Hippocrates, area of lunule, 480.

History, science of, 760.

Hobbes, Thomas, definition of cause, 224;
definition of time, 307;
on hypothesis, 510.

Hofmann, unit called crith, 321;
on prediction, 544;
on anomalies, 670.

Homogeneity, law of, 159, 327.

Hooke, on gravitation, 436, 581;
philosophical method, 507;
on strange things, 671.

Hopkinson, John, 194;
method of interpolation, 497.

Horrocks, use of mean, 358;
use of hypothesis, 507.

Hume on perception, 34.

Hutton, density of earth, 566.

Huxley, Professor Thomas, 764;
on hypothesis, 509;
classification, 676;
mammalia, 682;
palæontology, 682.

Huyghens, theory of pendulum, 302;
pendulum standard, 315;
cycloidal pendulum, 341;
differential method, 344;
distant stars, 405;
use of hypothesis, 508;
philosophical method of, 585;
on analogy, 639.

Hybrids, 727.

Hydrogen, expansion of, 471;
refractive power, 527;
metallic nature of, 691.

Hygrometry, 563.

Hypotheses, use of, 265, 504;
substitution of simple hypotheses, 458;
working hypotheses, 509;
requisites of, 510;
descriptive, 522, 686;
representative, 524;
probability of, 559.

Identical propositions, 119.

Identities, simple, 37;
partial, 40;
limited, 42;
simple and partial, 111;
inference from, 51, 55.

Identity, law of, 5, 6, 74;
expression of, 14;
propagating power, 20;
reciprocal, 46.

Illicit process, of major term, 65, 103;
of minor term, 65.

Immediate inference, 50, 61.

Imperfect induction, 146, 149.

Inclusion, relation of, 40.

Incommensurable quantities, 275.

Incompossible events, 205.

Independence of small effects, 475.

Independent events, 204.

Indestructibility of matter, 465.

Indexes, classification by, 714;
formation of, 717.

India-rubber, properties of, 545.

Indirect method of deduction, 49, 81;
illustrations of, 98;
fallacies analysed by, 102;
the test of equivalence, 115.

Induction, 11, 121;
symbolic statement of, 131;
perfect, 146;
imperfect, 149;
philosophy of, 218;
grounds of, 228;
illustrations of, 229;
quantitative, 483;
problem of two classes, 134;
problem of three classes, 137.

Inductive truths, classes of, 219.

Inequalities, reasoning by, 47, 163, 165–166.

Inference, 9;
general formula of, 17;
immediate, 50;
with two simple identities, 51;
from simple and partial identity, 53;
with partial identities, 55;
by sum of predicates, 61;
by disjunctive propositions, 76;
indirect method of, 81;
nature of, 118;
principle of mathematical, 162;
certainty of, 236.

Infima species, 701, 702.

Infiniteness of universe, 738.

Inflection of light, 420.

Instantiæ, citantes, evocantes, radii, curriculi, 270;
monodicæ, irregulares, heteroclitæ, 608;
clandestinæ, 610.

Instruments of measurement, 284.

Insufficient enumeration, 176.

Integration, 123.

Intellect, etymology of, 5.

Intension of logical terms, 26, 48;
of propositions, 47.

Interchangeable system, 20.

Interpolation, 495;
in meteorology, 497.

Inverse, process, 12;
operation, 122, 689;
problem of two classes, 134;
problem of three classes, 137;
problem of probability, 240, 251;
rules of inverse method, 257;
simple illustrations, 253;
general solution, 255.

Iodine, the substance X, 523.

Iron, properties of, 528, 670.

*Is*, ambiguity of verb, 16, 41.

Isomorphism, 662.

Ivory, 375.

James, Sir H., on density of earth, 567.

Jenkin, Professor Fleming, 328.

Jevons, W. S., on use of mean, 361;
on pedesis or molecular movement of microscopic particles, 406, 549;
cirrous clouds, 411;
spectrum analysis, 429;
elevated rain-gauges, 430;
experiments on clouds, 447;
on muscular exertion, 490;
resisting medium, 570;
anticipations of the electric telegraph, 671.

Jones, Dr. Bence, Life of Faraday, 578.

Jordanus, on the mean, 360.

Joule, 545;
on thermopile, 299, 300;
mechanical equivalent of heat, 325, 347, 568;
temperature of air, 343;
rarefaction, 444;
on Thomson’s prediction, 543;
molecular theory of gases, 548;
friction, 549;
thermal phenomena of fluids, 557.

Jupiter, satellites of, 372, 458, 638, 656;
long inequality of, 455;
figure of, 556.

Kames, Lord, on bifurcate classification, 697.

Kant, disjunctive propositions, 69;
analogy, 597;
doctrine of space, 769.

Kater’s pendulum, 316.

Keill, law of emanating forces, 464;
axiom of simplicity, 625.

Kepler, on star-discs, 390;
comets, 408;
laws of, 456;
refraction, 501;
character of, 578.

Kinds of things, 718.

King Charles and the Royal Society, 647.

Kirchhoff, on lines of spectrum, 245.

Kohlrausch, rules of approximate calculation, 479.

Lagrange, formula for interpolation, 497;
accidental discovery, 531;
union of algebra and geometry, 633.

Lambert, 15.

Lamont, 452.

Language, 8, 628, 643.

Laplace, on probability, 200, 216;
principles of inverse method, 242;
solution of inverse problem, 256;
planetary motions, 249, 250;
conjunctions of planets, 293;
observation of tides, 372;
atmospheric tides, 367;
law of errors, 378;
dark stars, 404;
hyperbolic comets, 407;
his works on probability, 395;
velocity of gravity, 435;
stability of planetary system, 448, 746;
form of Jupiter, 556;
corpuscular theory, 521;
ellipticity of earth, 565;
velocity of sound, 571;
analogy, 597;
law of gravity, 615;
inhabitants of planets, 640;
laws of motion, 706;
power of science, 739.

Lavoisier, mistaken inference of, 238;
pyrometer, 287;
on experiments, 423;
prediction of, 544;
theory, 611;
on acids, 667

Law, 3;
of simplicity, 33, 72, 161;
commutativeness, 35, 160;
disjunctive relation, 71;
unity, 72, 157, 162;
identity, 74;
contradiction, 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;
rejection 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 probability, 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 meaning 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 Philosophical Society, papers quoted, 137, 143, 168.

Mansel, on disjunctive propositions, 69.

Mars, white spots of, 596.

Maskelyne, on personal error, 347;
deviation of plumbline, 369;
density of earth, 566.

Mass, unit of, 317, 325.

Mathematical science, 767;
incompleteness 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 propositions, 47.

Measurement, of phenomena, 270;
methods of, 282;
instruments, 284;
indirect, 296;
accuracy of, 303;
units and standards of, 305;
explained results of, 554;
agreement 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;
classification, 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, 439;
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 propositions, 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 tollens*, 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;
motions, 485;
fall towards earth, 555.

Morse alphabet, 193.

Mother of pearl, 419.

Müller, Max, on etymology of intellect, 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, 737;
uniformity 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 theorem, 231;
spectrum, 262, 418, 420, 424, 583;
rings of, 288, 470;
velocity of sound, 295;
wave-lengths, 297;
use of pendulum, 303;
on time, 308;
definition of matter, 316;
pendulum experiment, 348, 443, 604;
centrobaric bodies, 365;
on weight, 422;
achromatic lenses, 432;
resistance of space, 435;
absorption of light, 445;
planetary 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 vortices, 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.

Noble, Captain, chronoscope, 308, 616.

Nomenclature, laws of botanical, 727.

Non-observation, arguments from, 411.

Norwood’s measurement of a degree, 272.

Nothing, 32.

Number, nature of, 153, 156;
concrete and abstract, 159, 305.

Numbers, prime, 123;
of Bernoulli, 124;
figurate, 183;
triangular, &c., 185.

Numerical abstraction, 158.

Observation, 399;
mental conditions, 402;
instrumental and sensual conditions, 404;
external conditions, 407.

Obverse statements, 144.