result is precisely the same as it would have been if the body on which they are acting had been acted upon by only one force equal to the sum or the difference. In mechanics we speak of the Composition of Forces'; and Mill paraphrases the term and speaks of the Composition of Causes' when the effect of them all can be considered in this way as the algebraic sum of the effects of each of them. The separate

causes and effects which are thus added together he speaks of as Compounded'.

6

To raise a crop

Now for the second kind of joint effects. of onions there must be seeds, air, moisture, warmth, and soil. If any one of these is left out, the result is, not smaller onions or fewer onions, but no onions at all. Moreover if a farmer finds that his onions are getting too much heat from the sun, he cannot even things up by giving them so much less water. In the same way if a cook finds that she has put too much sugar into her cake, she cannot improve matters by leaving out the flour. Cooking is a matter of chemistry, and chemistry is full of examples of this kind of joint effects. Oxygen and hydrogen combine' to form water, whose appearance and action are quite different in almost every respect from those of either of them. In the same way the green poisonous gas chlorine combines' with the very different yellowish metal sodium to form common salt, which again is very different from either of them. Joint effects which differ in this way from the effects of any of the causes separately are called Heteropathic', and since the effect. of uniting the causes is like that of making a chemical combination' the causes are said to be 'Combined'.

To produce heteropathic or combined effects it is necessary that the causes concerned should all be present at the same time or follow each other in some fixed order. If the onion seed is to grow, it must be warmed and moistened after it is put in the soil, not before; if the cake is to taste right, its various ingredients must be mixed before it is cooked, not afterwards. To produce compound effects this is not

necessary. The onions weigh as much whether they are all thrown into the basket at once or one after the other; the ingredients of the cake cost as much whether they are all purchased at the same time or at different times. The parallelogram of forces' in physics is a graphic way of explaining that when a body that can move freely is acted upon by several forces at once it reaches the same point (though it travels along a diagonal) as it would have reached if it had been acted upon by the same forces one after the other.

Because mathematics can be applied freely in calculating the joint effect when causes are 'compounded' but cannot be so applied when they are' combined', we have made a distinct advance in knowledge when we can say beforehand in which way they will be conjoined. For example, it is a great advantage if we can be sure that the weight of a compound, however formed, is always equal to the compounded weight-ie., to the sum of the weights-of its ingredients. According to an old story the Royal Society was once tricked into discussing the question why it was that nothing is added to the weight of a vessel of water when a live fish is put into it; and the discussion of one explanation after another went on for a long time before any one suggested that they try the experiment and see whether what they were trying to explain was really the case. The moral naturally attached to the story is that it is wise to find out whether a fact exists before you try to explain it; but here it is used to illustrate something else. If any one were quite sure that the weight of any body is a compound effect made up of the weight of all its separate parts, he would not think it necessary to try the experiment at all. He could be sure beforehand that an addition of any kind to the contents of the vessel would increase its weight, and he would know that whether the fish put into it were alive or dead could make no possible differIf the Royal Society ever did seriously discuss such a question as this, it must have been when physicists were

ence.

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.

com

WHEN we explain any state of affairs, such as a man's financial balance at the end of the year, as the pounded' 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 Methodof 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