The method of agreement is subject to a serious difficulty, called by Mr Mill the Plurality of Causes, consisting in the fact that the same effect may in different instances be owing to different causes. Thus if we inquire accurately into the cause of heat we find that it is produced by friction, by burning or combustion, by electricity, by pressure, &c.; so that it does not follow that if there happened to be one and the same thing present in all the cases we examined this would be the cause. The second method of induction which we will now consider is free from this difficulty, and is known as the Method of Difference. It is stated in Mr Mill's Second Canon as follows:

"If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon."

In other words, we may say that the antecedent which is invariably present when the phenomenon follows, and invariably absent when it is absent, other circumstances remaining the same, is the cause of the phenomenon in those circumstances.

Thus we can clearly prove that friction is one cause of heat, because when two sticks are rubbed together they become heated; when not rubbed they do not become heated. Sir Humphry Davy showed that even two pieces of ice when rubbed together in a vacuum produce heat, as shown by their melting, and thus completely demonstrated that the friction is the source and cause of the heat. We prove that air is the cause of sound being communicated to our ears by striking a bell in the receiver of an air-pump, as Hawksbee first did in 1705, and

then observing that when the receiver is full of air we hear the bell; when it contains little or no air we do not hear the bell. We learn that sodium or any of its compounds produces a spectrum having a bright yellow double line by noticing that there is no such line in the spectrum of light when sodium is not present, but that if the smallest quantity of sodium be thrown into the flame or other source of light, the bright yellow line instantly appears. Oxygen is the cause of respiration and life, because if an animal be put into a jar full of atmospheric air, from which the oxygen has been withdrawn, it soon becomes suffocated.

This is essentially the great method of experiment, and its utility mainly depends upon the precaution of only varying one circumstance at a time, all other circumstances being maintained just as they were. This is expressed in one of the rules for conducting experiments given by Thomson and Tait in their great treatise on Natural Philosophy, Vol. I. p. 307, as follows:-

"In all cases when a particular agent or cause is to be studied, experiments should be arranged in such a way as to lead if possible to results depending on it alone; or, if this cannot be done, they should be arranged so as to increase the effects due to the cause to be studied till these so far exceed the unavoidable concomitants, that the latter may be considered as only disturbing, not essentially modifying the effects of the principal agent."

It would be an imperfect and unsatisfactory experi ment to take air of which the oxygen has been converted into carbonic acid by the burning of carbon, and argue that, because an animal dies in such air, oxygen is the cause of respiration. Instead of merely withdrawing the oxygen we have a new substance, carbonic acid, present, which is quite capable of killing the animal by its own poisonous properties. The animal in fact would be suffo

cated even when a considerable proportion of oxygen remained, so that the presence of the carbonic acid is a disturbing circumstance which confuses and vitiates the experiment.

It is possible to prove the existence, and even to measure the amount of the force of gravity, by delicately suspending a small ball about the size of a marble and then suddenly bringing a very heavy leaden ball weighing a ton or more close to it. The small ball will be attracted and set in motion; but the experiment would not be of the least value unless performed with the utmost precaution. It is obvious that the sudden motion of the large leaden ball would disturb the air, shake the room, cause currents in the air by its coldness or warmth, and even occasion electric attractions or repulsions; and these would probably disturb the small ball far more than the force of gravitation,

Beautiful instances of experiment according to this method are to be found, as Sir John Herschel has pointed out, in the researches by which Dr Wells discovered the cause of dew. If on a clear calm night a sheet or other covering be stretched a foot or two above the earth, so as to screen the ground below from the open sky, dew will be found on the grass around the screen but not beneath it, As the temperature and moistness of the air, and other circumstances, are exactly the same, the open sky must be an indispensable antecedent to dew. The same experiment is indeed tried for us by nature, for if we make observations of dew during two nights which differ in nothing but the absence of clouds in one and their presence in the other, we shall find that the clear open sky is requisite to the formation of dew.

It may often happen that we cannot apply the method of difference perfectly by varying only one circumstance at a time. Thus we cannot, generally speaking, try the

qualities of the same substance in the solid and liquid condition without any other change of circumstances, because it is necessary to alter the temperature of the substance in order to liquefy or solidify it. The temperature might thus be the cause of what we attribute to the liquid or solid condition. Under such circumstances we have to resort to what Mr Mill calls the joint method of agreement and difference, which consists in a double application of the method of agreement, first to a number of instances where an effect is produced, and secondly, to a number of quite different instances where the effect is not produced. It is clearly to be understood, however, that the negative instances differ in several circumstances from the positive ones; for if they differed only in one circumstance we might apply the simple method of difference. Iceland spar, for instance, has a curious power of rendering things seen through it apparently double. This phenomenon, called double refraction, also belongs to many other crystals; and we might at once prove it to be due to crystalline structure could we obtain any transparent substance crystallized and uncrystallized, but subject to no other alteration. We have, however, a pretty satisfactory proof by observing that uniform transparent uncrystallized substances agree in not possessing double refraction, and that crystalline substances, on the other hand, with certain exceptions which are easily explained, agree in possessing the power in question. The principle of the joint method may be stated in the following rule, which is Mr Mill's Third Canon :—

"If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances (always or invariably) differ, is the effect, or the cause,

or an indispensable part of the cause, of the phenomenon."

I have inserted the words in parentheses, as without them the canon seems to me to express exactly the opposite of what Mr Mill intends.

It may facilitate the exact comprehension of these inductive methods if I give the following symbolic representation of them in the manner adopted by Mr Mill. Let A, B, C, D, E, &c., be antecedents which may be variously combined, and let a, b, c, d, e, &c., be effects following from them. If then we can collect the following sets of antecedents and effects

we may apply the method of agreement, and little doubt will remain that A, the sole invariable antecedent, is the cause of a.

The method of difference is sufficiently represented by—

Here while B and C remain perfectly unaltered we find that the presence or absence of A occasions the presence or absence of a, of which it is therefore the cause, in the presence of B and C. But the reader may be cautioned against thinking that this proves A to be the cause of a under all circumstances whatever.

The joint method of agreement and difference is similarly represented by—