deprived of food, and he dies; we have no hesitation in ascribing the disappearance of the phenomenon we call life to the withdrawal of the means by which it is maintained. In these instances, we have certain antecedents, followed by certain consequents, and, observing the simultaneous or successive disappearance of A and a, we have no hesitation in connecting the two as cause and effect.

All crucial instances (instantia 16 crucis, as they are called by Bacon) are applications of the Method of Difference. A crucial instance is some observation or experiment which enables us at once to decide between two or more rival hypotheses. It will be familiar to every one in the form of the chemical test, as where we apply an

16 Inter prærogativas instantiarum ponemus loco decimo quarto instantias crucis; translato vocabulo a crucibus, quæ, erectæ in biviis, indicant et signant viarum separationes. Has etiam instantias decisorias, et judiciales, et in casibus nonnullis instantias oraculi, et mandati, appellare consuevimus. Earum ratio talis est. Cum in inquisitione naturæ alicujus, intellectus ponitur tanquam in æquilibrio, ut incertus sit, utri naturarum e duabus, vel quandoque pluribus, causa naturæ inquisitæ attribui aut assignari debeat, propter complurium naturarum concursum frequentem et ordinarium; instantiæ crucis ostendunt consortium unins ex naturis (quoad naturam inquisitam) fidum et indissolubile, alterius autem varium et separabile; unde terminatur quæstio, et recipitur natura illa prior pro causa, missa altera et repudiata. Itaque hujusmodi instantiæ sunt maximæ lucis, et quasi magnæ auctoritatis; ita ut curriculum interpretationis quandoque in illas desinat, et per illas perficiatur. Interdum autem instantiæ crucis illæ occurrunt et inveniuntur inter jampridem notatas; at ut plurimum novæ sunt, et de industria atque ex composito quæsita et applicatæ, et diligentia sedula et acri tandem erutæ.'-Novum Organum, Lib. II. aph. xxxvi.

acid for the purpose of determining the character of a metal, or a metal for the purpose of detecting latent poison. According to the metaphor, there are two or more ways before us, and the observation or experiment acts as a 'guide-post' (crux) in determining us which to take. The following beautiful example of a Crucial Instance is borrowed from Sir John Herschel 17,

'A curious example is given by M. Fresnel, as decisive, in his mind, of the question between the two great opinions on the nature of light, which, since the time of Newton and Huyghens, have divided philosophers; that is, between what is called 'the emission theory,' according to which light consists of actual particles emitted from luminous bodies, and what is called 'the undulatory theory,' according to which light consists in the vibrations of an elastic medium pervading all space.

'When two very clean glasses are laid one on the other, if they be not perfectly flat, but one or both in an almost imperceptible degree convex or prominent, beautiful and vivid colours will be seen between them; and if these be viewed through a red glass, their appearance will be that of alternate dark and bright stripes. These stripes are formed between the two surfaces in apparent contact, as any one may satisfy himself by using, instead of a flat plate of glass for the upper one, a triangular-shaped piece, called a prism, like a threecornered stick, and looking through the inclined side of it next the eye, by which arrangement the reflection of light from the upper surface is prevented from intermixing with that from the surfaces in contact. Now, the coloured stripes thus produced are explicable on both theories, and are appealed

17 Discourse on the Study of Natural Philosophy, § 218.

to by both as strong confirmatory facts; but there is a difference in one circumstance according as one or the other theory is employed to explain them. In the case of the Huyghenian doctrine, the intervals between the bright stripes ought to appear absolutely black; in the other, half bright, when so viewed through a prism. This curious case of difference was tried as soon as the opposing consequences of the two theories were noted by M. Fresnel, and the result is stated by him to be decisive in favour of that theory which makes light to consist in the vibrations of an elastic medium 18.'

The following is an example of a similar kind. It had been determined, from theoretical considerations, that, on the assumption of the undulatory theory, the velocity of light must be less in the more highly refracting medium, while, according to the emission theory, it ought to be greater. When M. Foucault had invented his apparatus for determining the velocity of light, it became possible to submit the question to direct experiment; and it was established by M. Fizeau that the velocity of light is less in water (the more highly refracting medium) than in air, in the inverse proportion of the refractive indices. The result is, therefore, decisive in

18 Mr. Mill (Logic, Bk. III. ch. xiv. § 6) maintains that it does not follow from this experiment that the phenomena of light are results of the laws of elastic fluids, but at most that they are governed by laws partially identical with these.' But though the experiment may not be decisive as in favour of the Undulatory Theory, it is undoubtedly decisive as against the Emission Theory. It may be necessary to add that the term 'fluids' would now be repudiated by those who hold the Undulatory Theory.

favour of the undulatory, or at least, against the emission theory 19

There is no science, perhaps, in which the Method of Difference is so extensively used as the science of Chemistry, and that because chemistry is emphatically a science of experiment. Almost any chemical experiment will serve as an instance of the Method of Difference. Mix, for example, chloride of mercury with iodide of potassium, and the result will be a colourless liquid at the top of the vessel with a brilliant red precipitate at the bottom. There can be no hesitation in ascribing this result to the mixture of the two liquids; and two similar experiments will enable us to determine that the chlorine has been set free from the mercury and united with the potassium, which itself has been set free from the iodine with which it was previously united, while the iodine has united with the mercury, the former producing chloride of potassium (dissolved in the colourless liquid), the latter iodide of mercury (the red precipitate).

The science of Heat (or, as Dr. Whewell proposes to call it, Thermotics) also furnishes excellent examples of the Method of Difference. The following instances are adapted from Professor Tyndall's Heat a Mode of Motion 20:

'Here is a brass tube, four inches long, and of threequarters of an inch interior diameter. It is stopped at the

19 See Lloyd's Wave Theory of Light, Art. 37; Ganot's Physics, English translation, third edition, Art. 436.

20 Third Edition, ch. i. §§ 14-16.

bottom, and screwed on to a whirling table, by means of which the upright tube can be caused to rotate very rapidly. These two pieces of oak are united by a hinge, in which are two semicircular grooves, intended to embrace the brass tube. Thus the pieces of wood form a kind of tongs, the gentle squeezing of which produces friction when the tube rotates. I partially fill the tube with cold water, stop it with a cork to prevent the splashing out of the liquid, and now put the machine in motion. As the action continues, the temperature of the water rises, and now the tube is too hot to be held in the fingers. Continuing the action a little longer, the cork is driven out with explosive violence, the steam which follows it producing by its precipitation a small cloud in the atmosphere.'

In this experiment it will be noticed that only one new antecedent is introduced, namely the motion of the machine; hence the increased temperature of the water and the various effects which follow upon it are due to the motion as a cause. The experiment, then, shows that heat is generated by the action of mechanical force.

The converse of this proposition, namely that heat is consumed in mechanical work, or, as it is often stated, transmuted into mechanical energy, is proved by the two next experiments.

'This strong vessel is filled at the present moment with compressed air. It has lain here for some hours, so that the temperature of the air within the vessel is now the same as that of the air of the room without it. At the present moment this inner air is pressing against the sides of the vessel, and if this cock be opened a portion of the air will rush violently out. The word "rush," however, but vaguely expresses the true state of things; the air which issues is driven