We should therefore modify the enunciation and say: If an antecedent _A_ has once produced a consequent _B_, an antecedent _A'_, slightly different from _A_, will produce a consequent _B'_, slightly different from _B_. But how shall we recognize that the antecedents _A_ and _A'_ are 'slightly different'? If some one of the circumstances can be expressed by a number, and this number has in the two cases values very near together, the sense of the phrase 'slightly different' is relatively clear; the principle then signifies that the consequent is a continuous function of the antecedent. And as a practical rule, we reach this conclusion that we have the right to interpolate. This is in fact what scientists do every day, and without interpolation all science would be impossible. Yet observe one thing. The law sought may be represented by a curve. Experiment has taught us certain points of this curve. In virtue of the principle we have just stated, we believe these points may be connected by a continuous graph. We trace this graph with the eye. New experiments will furnish us new points of the curve. If these points are outside of the graph traced in advance, we shall have to modify our curve, but not to abandon our principle. Through any points, however numerous they may be, a continuous curve may always be passed. Doubtless, if this curve is too capricious, we shall be shocked (and we shall even suspect errors of experiment), but the principle will not be directly put at fault. Furthermore, among the circumstances of a phenomenon, there are some that we regard as negligible, and we shall consider _A_ and _A'_ as slightly different if they differ only by these accessory circumstances. For instance, I have ascertained that hydrogen unites with oxygen under the influence of the electric spark, and I am certain that these two gases will unite anew, although the longitude of Jupiter may have changed considerably in the interval. We assume, for instance, that the state of distant bodies can have no sensible influence on terrestrial phenomena, and that seems in fact requisite, but there are cases where the choice of these practically indifferent circumstances admits of more arbitrariness or, if you choose, requires more tact. One more remark: The principle of induction would be inapplicable if there did not exist in nature a great quantity of bodies like one another, or almost alike, and if we could not infer, for instance, from one bit of phosphorus to another bit of phosphorus. If we reflect on these considerations, the problem of determinism and of contingence will appear to us in a new light. Suppose we were able to embrace the series of all phenomena of the universe in the whole sequence of time. We could envisage what might be called the _sequences_; I mean relations between antecedent and consequent. I do not wish to speak of constant relations or laws, I envisage separately (individually, so to speak) the different sequences realized.