Up to a certain point the method of science is but the method of ordinary consciousness pursued knowingly and steadily. But ere long the method acquires a distinctive character of its own. It shakes off the pressure of that immediate subservience in which ordinary knowledge stands to man's needs, wishes and interests. Knowledge is pursued--within a wide range--for its own sake, and by a class more or less definitely set apart by humanity for its scientific service,--which is thus performed more systematically and continuously. But the great step which carries ordinary knowledge into its higher region is the discovery, due to reflection and comparison, that there is a double grade of reality-a permanent, essential, uniform, substantial being, which is contrasted with an evanescent, apparent, varying and accidental. To know a thing is in all cases to _relate it_ to something else: to know it in the higher sense_--vere scire_--is to relate it to its essence, its substantial or universal form, its permanent self. Ordinary knowledge, e. g., fixes a thing by referring to its antecedents: scientific knowledge refers it to its 'invariable, 'unconditional' or 'essential' antecedent,--to something which contains it implicitly, and necessarily, and is not merely by accident or juxtaposition associated with it. To discover this permanent, underlying substance or reality comes to be the problem of science--a problem which may be taken in the widest generality, or restricted to some one group of existences. What is asked for, e.g., may be the uniformity and essence in the appearance of the diurnal journey of the sun, or it may be the underlying, invisible, nature which displays itself in all the variety of minerals, and in animal and plant life. The one-and-the-same in a diversity of many; the type-form in individuals: the cause which is the key to understanding an effect that always and unconditionally follows it; the force which finds different expression in actions--are what Science seeks.
In that search two points emerge as regards the method. The first is the importance of quantitative statements or numerical appreciations, and the general law that variations in the qualitative are in some ratio concomitant with variations in the quantitative. Mathematics, in a word, is found to be an invaluable instrument for recording with accuracy the minutest as well as the most immense differences of quality. First, it is seen that qualitative differences within a given range, e.g. various colours or various musical notes, can be accurately expressed by a numerical ratio. But, secondly, it soon appears that even greater divergences of quality, e.g. those of colour and of chemical quality, may possibly be reduced to stages on one quantitative scale. It is not unnatural that such experiences should give rise to a hope--and in sanguine minds, an assurance--that all the phenomena of nature are ultimately phases of some common nature--some elementary being--which runs through an infinite gamut of numerically defined adjustments.