not all certain that weight is a compound effect and never under any circumstances or to any extent heteropathic.

The distinction between 'compounded' and 'combined' causes can be applied quite as well when some of the causes tend to counteract the effects of the others as when they all assist each other.

A counteracting cause of the 'combined' sort simply breaks up or nullifies the combination that would otherwise have produced the effect in question. If somebody puts out the chemist's fire and does it soon enough, the combination which he expected will not occur. If a man quarrels with his employer and loses his place, or if the employer fails and cannot pay the man for his work, the quarrel or the failure is not a kind of expenditure that tends according to its amount to counteract the effect of the man's earnings. It puts an end to his earnings altogether. The effect of these counteracting causes is heteropathic'.

A counteracting cause of the compounded' sort simply adds a negative result to the positive one produced by the causes that it is said more or less to counteract; and consequently in calculating the net result we have merely to subtract one set of results from the other. Thus the spending or giving away of money tends according to its amount to counteract the effect of earning it, and if we wish to find the gain or loss during the year we have only to subtract the expenditures from the receipts or vice versa. Here the effects are not heteropathic', but compounded'.

CHAPTER XXIX.

THE METHODS OF RESIDUES AND CONCOMITANT

VARIATIONS.

causes.

WHEN we explain any state of affairs, such as a man's financial balance at the end of the year, as the 'compounded' effect of a number of different causes, Quantitative and when we give figures to show the amount of treatment of the total effect contributed by each, it is evident that we are dealing with the question of causation from the quantitative standpoint. It is no longer a mere question of whether a certain kind of cause was present or not, but it is a question also of its precise amount. If a man's actual balance and the balance shown by his cash account do not agree, there is something which has not been accounted for, and the causal explanation of his financial standing is not complete. This quantitative treatment of a question of cause and effect evidently rests on the assumption that the cause of every event must be capable of producing precisely that amount of effect, no more and no less.

Because we have a right to demand an explanation for the precise amount of every effect as well as for its quality two other methods of causal inquiry can be added to the three already considered: the Method of Residues and the Method of Concomitant Variations. They both depend upon a quantitative application of the Method of Difference.

For the Method of Residues Mill lays down the following canon: "Subtract from any phenomenon such part as is known

Residues.

by previous inductions to be the effect of certain antecedents, and Method of the residue of the phenomenon is the effect of the remaining antecedents. If we know that a man has an annual income of $3200, and if we know that his salary is $2000 and that the annual dividend on his railroad stock is $500, then we can infer that he has some other source or sources of income that produce $700 a year. And if we happen to know that his only other source of income is his share in an iron company, we can infer still further that the iron company pays him a dividend of $700 a year, no more and no less. Similarly, if a man in a position of trust, with a salary of $1000 a year and no private fortune, is spending $5000 a year, his employer will have reason to suspect that the man is stealing or has stolen from him enough to make the difference. To take still another illustration: Suppose we know that the planet Uranus is acted upon by the attraction of the sun and of the planets nearest to it, Jupiter and Saturn, in such a way as to bring it to a certain place at a certain time; and suppose that when the time comes the planet is not there: then we can be sure that if our previous calculation was correct, there is some other force acting on the planet and that this force is just strong enough to drag it from the place where the calculation showed that it ought to be to the place where it actually is. By calculating the strength and direction of such an additional force acting on Uranus the planet Neptune was actually looked for and discovered.

The difference between the Method of Residues and the ordinary Method of Difference does not lie merely in the fact that the Method of Residues considers questions of quantity; for the next variation of the Method of Difference that we are about to consider does that also. It lies rather in the fact that when we use the Method of Difference our knowledge of what happens when the residual cause is not present is gained from direct observation, — -we see what happens when all the causes except the one under investiga

tion are present together. With the Method of Residues we do not directly observe what happens when all the causes except the one in question are present together. We only calculate it from what we know of the way in which they act when they are present separately.

The Method of Residues is attended in practice by three dangers.

The first danger is that in making our subtraction we may overlook the 'combined' or heteropathic effect of some of the causes which we subtract, and thus attribute too much to the remaining causes. For example, three persons, A, B, and C, are in a room from which we hear the sounds of a violent disturbance. We know by previous inductions that A's disposition is quiet and peaceable; we know the same about B; and so we conclude that C is responsible for the disturbance. And yet we may be wrong, for however quiet and peaceable A and B may be in themselves, there may be something about them-some trait of disposition or some old misunderstanding—that makes a conflict almost inevitable when the two are together.

The second danger to which we are exposed in using this Method of Residues is that of overlooking some circumstance that is really present, and of thus attributing an entirely false. value to the presence of something else. It may be that the man whose income we were inquiring about a little while ago has an allowance from his grandfather, of which he says nothing, and that the iron company is a source not of income but of expense; and it may be that the man suspected of peculation is getting an immense royalty, that his employer knows nothing about, from a patent.

The third danger is that even when the data are all correct there may be a blunder somewhere in our calculations. If the bookkeeper has made a serious mistake in his addition or subtraction, all the reasoning by which we prove that a certain transaction 'must' have been responsible for a gain or loss of such an amount is worse than useless.

Of course the way to make sure that we have not been misled by any of these blunders is to try the residual cause by itself and see if it really does produce the precise effect indicated by the calculations. Often it does not, and where this is the case and the calculations are all correct it indicates that there is still another residual cause or group of causes to be looked for. Often, of course, direct experiment is impossible, and then we have to get along as best we can with the abstract calculations.

66

In spite of its difficulties the Method of Residues is one of the most important among our instruments of discovery. Of all the methods of investigating laws of nature, this is the most fertile in unexpected results: often informing us of sequences in which neither the cause nor the effect were sufficiently conspicuous to attract of themselves the attention of observers. The agent C [i.e., the residual cause] may be an obscure circumstance, not likely to have been perceived unless sought for, nor likely to have been sought for until attention had been awakened by the insufficiency of the obvious causes to account for the whole of the effect. And c [the residual effect] may be so disguised by its intermixture with a and b [the effects whose causes are already known] that it would scarcely have presented itself spontaneously as a subject of separate study."'*

The Method of Residues is, like all the rest, a method of exhaustion; for we cannot be sure that a given residual effect is due, or at least partly due, to a certain residual antecedent until we are sure that that residual antecedent is the only one present that could have any influence on the effect.

Method of

Often it is impossible to use any of the methods already discussed, at least without modification, simply because it is impossible to find or to make cases in which Concomitant all of several possible causes are not present. Suppose that we want to know what makes a wheel stop turning after a while, or a pendulum stop swing* Mill: Bk. III, Chap. VIII, Sec. 5.

Variations.