On further considering the matter, however, it will perhaps be felt that this definition does not express the whole fact—­that inseparable as science may be from common knowledge, and completely as we may fill up the gap between the simplest previsions of the child and the most recondite ones of the natural philosopher, by interposing a series of previsions in which the complexity of reasoning involved is greater and greater, there is yet a difference between the two beyond that which is here described.  And this is true.  But the difference is still not such as enables us to draw the assumed line of demarcation.  It is a difference not between common knowledge and scientific knowledge; but between the successive phases of science itself, or knowledge itself—­whichever we choose to call it.  In its earlier phases science attains only to certainty of foreknowledge; in its later phases it further attains to completeness.  We begin by discovering a relation:  we end by discovering the relation.  Our first achievement is to foretell the kind of phenomenon which will occur under specific conditions:  our last achievement is to foretell not only the kind but the amount.  Or, to reduce the proposition to its most definite form—­undeveloped science is qualitative prevision:  developed science is quantitative prevision.

This will at once be perceived to express the remaining distinction between the lower and the higher stages of positive knowledge.  The prediction that a piece of lead will take more force to lift it than a piece of wood of equal size, exhibits certainty, but not completeness, of foresight.  The kind of effect in which the one body will exceed the other is foreseen; but not the amount by which it will exceed.  There is qualitative prevision only.  On the other hand, the prediction that at a stated time two particular planets will be in conjunction; that by means of a lever having arms in a given ratio, a known force will raise just so many pounds; that to decompose a specified quantity of sulphate of iron by carbonate of soda will require so many grains—­these predictions exhibit foreknowledge, not only of the nature of the effects to be produced, but of the magnitude, either of the effects themselves, of the agencies producing them, or of the distance in time or space at which they will be produced.  There is not only qualitative but quantitative prevision.

And this is the unexpressed difference which leads us to consider certain orders of knowledge as especially scientific when contrasted with knowledge in general.  Are the phenomena measurable? is the test which we unconsciously employ.  Space is measurable:  hence Geometry.  Force and space are measureable:  hence Statics.  Time, force, and space are measureable:  hence Dynamics.  The invention of the barometer enabled men to extend the principles of mechanics to the atmosphere; and Aerostatics existed.  When