the 8800th part of a degree centigrade. has been detected by Dr. Joule. The spectroscope has revealed the presence of the 10,000,000th part of a gram. It is said that the eye can observe the colour produced in a drop of water by the 50,000,000th part of a gram of fuschine, and about the same quantity of cyanine. By the sense of smell we can probably feel still smaller quantities of odorous matter.1 We must nevertheless remember that quantitative effects of far less amount than these must exist, and we should state our negative results with corresponding caution. We can only disprove the existence of a quantitative phenomenon by showing deductively from the laws of nature, that if present it would amount to a perceptible quantity. As in the case of other negative arguments (p. 414), we must demonstrate that the effect would appear, where it is by experiment found not to appear.

Limits of Experiment.

It will be obvious that there are many operations of nature which we are quite incapable of imitating in our experiments. Our object is to study the conditions under which a certain effect is produced; but one of those conditions may involve a great length of time. There are instances on record of experiments extending over five or ten years, and even over a large part of a lifetime; but such intervals of time are almost nothing to the time during which nature may have been at work. The contents of a mineral vein in Cornwall may have been undergoing gradual change for a hundred million years. All metamorphic rocks have doubtless endured high temperature and enormous pressure for inconceivable periods of time, so that chemical geology is generally beyond the scope of experiment.

Arguments have been brought against Darwin's theory, founded upon the absence of any clear instance of the production of a new species. During an historical interval of perhaps four thousand years, no animal, it is said, has been so much domesticated as to become different in

1 Keill's Introduction to Natural Philosophy, 3rd ed., London, 1733, pp. 48-54.

pecies. It might as well be argued that no geological changes are taking place, because no new mountain has risen in Great Britain within the memory of man. Our actual experience of geological changes is like a point in the infinite progression of time. When we know that rain water falling on limestone will carry away a minute portion of the rock in solution, we do not hesitate to multiply that quantity by millions, and infer that in course of time a mountain may be dissolved away. We have actual experience concerning the rise of land in some parts of the globe and its fall in others to the extent of some feet. Do we hesitate to infer what may thus be done in course of geological ages? As Gabriel Plattes long ago remarked, "The sea never resting, but perpetually winning land in one place and losing in another, doth show what may be done in length of time by a continual operation, not subject unto ceasing or intermission." 1 The action of physical circumstances upon the forms and characters of animals by natural selection is subject to exactly the same remarks. As regards animals living in a state of nature, the change of circumstances which can be ascertained to have occurred is so slight, that we could not expect to observe any change in those animals whatever. Nature has made no experiment at all for us within historical times. Man, however, by taming and domesticating dogs, horses, oxen, pigeons, &c., has made considerable change in their circumstances, and we find considerable change also in their forms and characters. Supposing the state of domestication to continue unchanged, these new forms would continue permanent so far as we know, and in this sense they are permanent. Thus the arguments against Darwin's theory, founded on the non-observation of natural changes within the historical period, are of the weakest character, being purely negative.

1 Discovery of Subterraneal Treasure, 1639, p. 52.

CHAPTER XX.

METHOD OF VARIATIONS.

EXPERIMENTS may be of two kinds, experiments of simple fact, and experiments of quantity. In the first class of experiments we combine certain conditions, and wish to ascertain whether or not a certain effect of any quantity exists. Hooke wished to ascertain whether or not there was any difference in the force of gravity at the top and bottom of St. Paul's Cathedral. The chemist continually performs analyses for the purpose of ascertaining whether or not a given element exists in a particular mineral or mixture; all such experiments and analyses are qualitative rather than quantitative, because though the result may be more or less, the particular amount of the result is not the object of the inquiry.

So soon, however, as a result is known to be discoverable, the scientific man ought to proceed to the quantitative inquiry, how great a result follows from a certain amount of the conditions which are supposed to constitute the cause? The possible numbers of experiments are now infinitely great, for every variation in a quantitative condition will usually produce a variation in the amount of the effect. The method of variation which thus arises is no narrow or special method, but it is the general application of experiment to phenomena capable of continuous variation. As Mr. Fowler has well remarked,1 the observation of variations is really an integration of a supposed infinite number of applications of the so-called method of difference, that is of experiment in its perfect form.

1 Elements of Inductive Logic, 1st edit. p. 175.

In induction we aim at establishing a general law, and if we deal with quantities that law must really be expressed more or less obviously in the form of an equation, or equations. We treat as before of conditions, and of what happens under those conditions. But the conditions will now vary, not in quality, but quantity, and the effect will also vary in quantity, so that the result of quantitative induction is always to arrive at some mathematical expression involving the quantity of each condition, and expressing the quantity of the result. In other words, we wish to know what function the effect is of its conditions. We shall find that it is one thing to obtain the numerical results, and quite another thing to detect the law obeyed by those results, the latter being an operation of an inverse and tentative character.

The Variable and the Variant.

Almost every series of quantitative experiments is directed to obtain the relation between the different values of one quantity which is varied at will, and another quantity which is caused thereby to vary. We may conveniently distinguish these as respectively the variable and the variant. When we are examining the effect of heat in expanding bodies, heat, or one of its dimensions, temperature, is the variable, length the variant. If we compress a body to observe how much it is thereby heated, pressure, or it may be the dimensions of the body, forms the variable, heat the variant. In the thermo-electric pile we make heat the variable and measure electricity as the variant. That one of the two measured quantities which is an antecedent condition of the other will be the variable.

It is always convenient to have the variable entirely under our command. Experiments may indeed be made with accuracy, provided we can exactly measure the variable at the moment when the quantity of the effect is determined. But if we have to trust to the action of some capricious force, there may be great difficulty in making exact measurements, and those results may not be disposed over the whole range of quantity in a convenient manner. It is one prime object of the experi

menter, therefore, to obtain a regular and governable supply of the force which he is investigating. To determine correctly the efficiency of windmills, when the natural winds were constantly varying in force, would be exceedingly difficult. Smeaton, therefore, in his experiments on the subject, created a uniform wind of the required force by moving his models against the air on the extremity of a revolving arm. The velocity of the wind. could thus be rendered greater or less, it could be maintained uniform for any length of time, and its amount could be exactly ascertained. In determining the laws of the chemical action of light it would be out of the question to employ the rays of the sun, which vary in intensity with the clearness of the atmosphere, and with every passing cloud. One great difficulty in photometry and the investigation of the chemical action of light consists in obtaining a uniform and governable source of light rays.2

Fizeau's method of measuring the velocity of light enabled him to appreciate the time occupied by light in travelling through a distance of eight or nine thousand metres. But the revolving mirror of Wheatstone subsequently enabled Foucault and Fizeau to measure the velocity in a space of four metres. In this latter method there was the advantage that various media could be substituted for air, and the temperature, density, and other conditions of the experiment could be accurately governed and measured.

Measurement of the Variable.

There is little use in obtaining exact measurements of an effect unless we can also exactly measure its conditions.

It is absurd to measure the electrical resistance of a piece of metal, its elasticity, tenacity, density, or other physical qualities, if these vary, not only with the minute impurities of the metal, but also with its physical condition. If the same bar changes its properties by being

1 Philosophical Transactions, vol. li. p. 138; abridgment, vol. xi. P. 355.

2 See Bunsen and Roscoe's researches, in Philosophical Transactions (1859), vol. cxlix. p. 880, &c., where they describe a constant flame of carbon monoxide gas.