centuries', and the probability that if existent they would have been seen, increases the probability that they do not exist. We may with somewhat less confidence discredit the existence of any large unrecognised fish, or sea animals, such as the alleged sea-serpent. But as we descend to forms of smaller size negative evidence loses weight from the less probability of our seeing smaller objects. Even the strong induction in favour of the four-fold division of the animal kingdom into Vertebrata, Annulosa, Mollusca, and Coelenterata, may break down by the discovery of intermediate or anomalous forms. As civilisation spreads over the surface of the earth, and unexplored tracts are gradually diminished, negative conclusions will increase in force; but we require to learn much yet concerning the depths of the ocean, almost wholly unexamined as they are, and covering three-fourths of the earth's surface. In geology there are a number of assertions to which considerable probability attaches on account of the large extent of the investigations already made, as, for instance, that true coal is found only in rocks of a particular geological epoch; that gold occurs in secondary and tertiary strata only in exceedingly small quantities", probably derived from the disintegration of earlier rocks. In natural history negative conclusions are exceedingly treacherous and unsatisfactory. The utmost patience will not enable a microscopist or the observer of any living thing to watch the behaviour of the organism under all circumstances continuously for any great length of time. There is always a chance therefore that the critical act or change may take place when the observer's eyes are withdrawn. This certainly happens in some cases; for though t Cuvier's 'Essay on the Theory of the Earth,' translation, p. 61, &c. u Murchison's 'Siluria,' 1st ed. p. 432. the fertilization of orchids by agency of insects is proved as well as any fact in natural history, Mr. Darwin has never been able by the closest watching to detect an insect in the performance of the operation. Mr. Darwin has himself, indeed, adopted one conclusion on purely negative evidence, namely that the Orchis pyramidalis and certain other orchidaceous flowers secrete no nectar. But his caution and unwearying patience in verifying the conclusion give an impressive lesson to the observer. For twenty-three consecutive days, as he tells us, he examined flowers, in all states of the weather, at all hours, in various localities. As the secretion in other flowers sometimes rapidly takes place and might happen at early dawn, that inconvenient hour of observation was specially adopted. Flowers of different ages were subjected to irritating vapours, to water, and every condition likely to bring on the secretion; and only after the invariable failure of this exhaustive inquiry was the barrenness of the nectaries assumed to be proved. In order that a negative argument founded on the nonobservation of an object shall have any considerable force, it must be shown to be probable that the object if existent would have been observed, and it is this probability which defines the value of the negative conclusion. The failure of astronomers to see the planet Vulcan, supposed by some to exist within Mercury's orbit, is no sufficient disproof of its existence. Similarly it would be very difficult, or even impossible, to disprove the existence of a second satellite of small size revolving round the earth. But if any person make a particular assertion, assigning place and time, then observation will either prove or disprove the alleged fact. Thus if it is true that when a French observer professed to have seen a planet on the sun's face, an observer in Brazil was carefully scrutinizing the sun and failed to see x Darwin's Fertilization of Orchids,' p. 48. open to it, we have a conclusive negative proofy. On this account, as it has been well said, false facts in science are more mischievous than false theories. A false theory is every person's criticism, and is ever liable to be judged by its accordance with facts. But a false or grossly erroneous assertion of a fact often stands in the way of science for a long time, because it may be extremely difficult or even impossible to prove the falsity of what has been once recorded. In other sciences the force of a negative argument will often depend upon the number of possible alternatives which may exist. Thus it was long believed that the character or quality of a musical sound, as distinguished from its pitch must depend upon the form of the undulation, because no other cause of it had ever been suggested or was apparently possible. The truth of the conclusion was proved by Helmholtz, who applied a microscope to luminous points attached to the strings of various instruments, and thus actually observed the different modes of undulation2. In mathematics negative inductive arguments have seldom much force, because the possible forms of expression, or the possible combinations of lines and circles in geometry are quite unlimited in number. An enormous number of attempts were made to trisect the angle by the ordinary methods of Euclid's geometry, but their invariable failure did not establish the impossibility of the task. This was shown in a totally different manner, by proving that the problem involves an irreducible cubic equation to which there could be no corresponding plain geometrical solutiona. This is a case of reductio ad absurdum, a form of argument of a totally different y Chambers's 'Astronomy,' 1st ed. p. 31. z Théorie Physiologique de la Musique', Paris, 1868, p. 113. character. Similarly no number of failures to obtain a general solution of equations of the fifth degree would establish the impossibility of the task, but in an indirect mode, equivalent to a reductio ad absurdum, the impossibility is considered to be provedb. b Peacock, Algebra,' vol. ii. p. 359. Serret, Algèbra Supérieure,' 2nd ed. p. 289. CHAPTER XIX. EXPERIMENT. We now come to consider the great facilities which we enjoy for examining the possible combinations of properties and phenomena when objects are within our reach and capable of manipulation. We are said to experiment, when we bring substances together under various conditions of temperature, pressure, electric disturbance, molecular attraction, &c., and then record the changes observed, If we denote by A a certain group of antecedent conditions, and by X a certain series of subsequent phenomena, our object will usually be to ascertain a law of the form A = AX, the meaning of which is that where A is X will happen, and we may sometimes rise to the still simpler and higher law A = X, meaning that where A is, and only where A is, X will happen (see vol. i. pp. 146, 149.) The great object of the art of experiment is to ascertain exactly those circumstances or conditions which are requisite for the happening of any event X. Now the circumstances which might be enumerated as present in the very simplest experiment are very numerous, in fact almost infinite. Rub two sticks together and consider what would be an exhaustive statement of the conditions. There are the form, hardness, organic structure, and all the chemical qualities of the wood; the pressure and velocity of the rubbing; the temperature, pressure, and all the chemical qualities of the surrounding air; the proximity |