alled _an extension of the perceptions by
means of reasoning_.

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