4. _Limitation of the Second Axiom._--But there may be circumstances in the nature of the case which may further determine the kind of effect which we must take for the measure of the cause. For example, if causes are conceived to be of such a nature as to be capable of addition, the effects taken as their measure must conform to this condition. This is the case with mechanical causes. The weights of two bodies are the causes of the pressure which they exert downwards; and these weights are capable of addition. The weight of the two is the sum of the weight of each. We are therefore not at liberty to say that weights shall be measured by the spaces through which they bend a certain elastic support, except we have first ascertained that the whole weight bends it through a space equal to the sum of the inflections produced by the separate weights. Without this precaution, we might obtain inconsistent results. Two weights, each of the magnitude 3 as measured by their effects, might, if we took the inflections of a spring for the effects, be together equal to 5 or to 7 by the same kind of measurement. For the inflection produced by two weights of 3 might, for aught we can see beforehand, be more or less than twice as great as the inflection produced by one weight of 3. That forces are capable of addition, is a condition which limits, and, as we shall see, in some cases rigorously fixes, the kind of effects which are to be taken as their measures. Causes which are thus capable of addition are to be measured by the repeated addition of equal quantities. Two such causes are _equal_ to each other when they produce exactly the same effect. So far our axiom is applied directly. But these two causes can be _added_ together; and being thus added, they are _double_ of one of them; and the cause composed by addition of _three_ such, is _three_ times as great as the first; and so on for any measure whatever. By this means, and by this {188} means only, we have a complete and consistent measure of those causes which are so conceived as to be subject to this condition of being added and multiplied.