1

Academicians of Florence could not detect, because at a low pressure the effect was too small to perceive, and at a high pressure the water oozed through their silver vessel,1 has now become the subject of exact measurement and precise calculation. Independently of Newton, Hooke entertained very remarkable notions concerning the nature of gravitation. In this and other subjects he showed, indeed, a genius for experimental investigation which would have placed him in the first rank in any other age than that of Newton. He correctly conceived that the force of gravity would decrease as we recede from the centre of the earth, and he boldly attempted to prove it by experiment. Having exactly counterpoised two weights in the scales of a balance, or rather one weight against another weight and a long piece of fine cord, he removed his balance to the top of the dome of St. Paul's, and tried whether the balance remained in equilibrium after one weight was allowed to hang down to a depth of 240 feet. No difference could be perceived when the weights were at the same and at different levels, but Hooke rightly held that the failure arose from the insufficient elevation. He says, “Yet I am apt to think some difference might be discovered in greater heights." The radius of the earth. being about 20,922,000 feet, we can now readily calculate from the law of gravity that a height of 240 would not make a greater difference than one part in 40,000 of the weight. Such a difference would doubtless be inappreciable in the balances of that day, though it could readily be detected by balances now frequently constructed. Again, the mutual gravitation of bodies at the earth's surface is so small that Newton appears to have made no attempt to demonstrate its existence experimentally, merely remarking that it was too small to fall under the observation of our senses.3 It has since been successfully detected and measured by Cavendish, Baily, and others.

2

The smallness of the quantities which we can sometimes observe is astonishing. A balance will weigh to one millionth part of the load. Whitworth can measure to the millionth part of an inch. A rise of temperature of

1 Essayes of Natural Experiments, &c. p. 117.

2 Hooke's Posthumous Works, p. 182.

3

* Principia, bk. iii. Prop. vii. Corollary 1.

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.

Our

species. 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. 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