from a fire which she is lighting will ascend, and that the fire will presently boil water, are previsions which the servant-girl makes equally well with the most learned physicist; they are equally certain, equally exact with his; but they are previsions concerning phenomena in constant and direct relation—­phenomena that follow visibly and immediately after their antecedents—­phenomena of which the causation is neither remote nor obscure—­phenomena which may be predicted by the simplest possible act of reasoning.

If, now, we pass to the previsions constituting what is commonly known as science—­that an eclipse of the moon will happen at a specified time; and when a barometer is taken to the top of a mountain of known height, the mercurial column will descend a stated number of inches; that the poles of a galvanic battery immersed in water will give off, the one an inflammable and the other an inflaming gas, in definite ratio—­we perceive that the relations involved are not of a kind habitually presented to our senses; that they depend, some of them, upon special combinations of causes; and that in some of them the connection between antecedents and consequents is established only by an elaborate series of inferences.  The broad distinction, therefore, between the two orders of knowledge, is not in their nature, but in their remoteness from perception.

If we regard the cases in their most general aspect, we see that the labourer, who, on hearing certain notes in the adjacent hedge, can describe the particular form and colours of the bird making them; and the astronomer, who, having calculated a transit of Venus, can delineate the black spot entering on the sun’s disc, as it will appear through the telescope, at a specified hour; do essentially the same thing.  Each knows that on fulfilling the requisite conditions, he shall have a preconceived impression—­that after a definite series of actions will come a group of sensations of a foreknown kind.  The difference, then, is not in the fundamental character of the mental acts; or in the correctness of the previsions accomplished by them; but in the complexity of the processes required to achieve the previsions.  Much of our commonest knowledge is, as far as it goes, rigorously precise.  Science does not increase this precision; cannot transcend it.  What then does it do?  It reduces other knowledge to the same degree of precision.  That certainty which direct perception gives us respecting coexistences and sequences of the simplest and most accessible kind, science gives us respecting coexistences and sequences, complex in their dependencies or inaccessible to immediate observation.  In brief, regarded from this point of view, science may be called an extension of the perceptions by means of reasoning.