Derivative Laws make up the body of the exact sciences, having been assimilated and organised; whilst Empirical Laws are the undigested materials of science.  The theorems of Euclid are good examples of derivative laws in Mathematics; in Astronomy, Kepler’s laws and the laws of the tides; in Physics, the laws of shadows, of perspective, of harmony; in Biology, the law of protective coloration; in Economics, the laws of prices, wages, interest, and rent.

Empirical Laws are such as Bode’s law of the planetary distances; the laws of the expansion of different bodies by heat, and formulae expressing the electrical conductivity of each substance as a function of the temperature.  Strictly speaking, I suppose, all the laws of chemical combination are empirical:  the law of definite proportions is verifiable in all cases that have been examined, except for variations that may be ascribed to errors of experiment.  Much the same is true in Biology; most of the secondary laws are empirical, except so far as structures or functions may be regarded as specialised cases in Physics or Chemistry and deducible from these sciences.  The theory of Natural Selection, however, has been the means of rendering many laws, that were once wholly empirical, at least partially derivative; namely, the laws of the geographical distribution of plants and animals, and of their adaptation in organisation, form and colour, habits and instincts, to their various conditions of life.  The laws that remain empirical in Biology are of all degrees of generality from that of the tendency to variation in size and in every other character shown by every species (though as to the reason of this there are promising hypotheses), down to such curious cases as that the colour of roses and carnations never varies into blue, that scarlet flowers are never sweet-scented, that bullfinches fed on hemp-seed turn black, that the young of white, yellow and dun pigeons are born almost naked (whilst others have plenty of down); and so on.  The derivation of empirical laws is the greater part of the explanation of Nature (Sec.Sec. 5, 6).

A ‘Fact,’ in the common use of the word, is a particular observation:  it is the material of science in its rawest state.  As perceived by a mind, it is, of course, never absolutely particular:  for we cannot perceive anything without classing it, more or less definitely, with things already known to us; nor describe it without using connotative terms which imply a classification of the things denoted.  Still, we may consider an observation as particular, in comparison with a law that includes it with numerous others in one general proposition.  To turn an observation into an experiment, or (where experiment is impracticable) to repeat it with all possible precautions and exactness, and to describe it as to the duration, quantity, quality and order of occurrence of its phenomena, is the first stage of scientific manufacture.  Then comes the formulation of an empirical law; and lastly, if possible, deduction or derivation, either from higher laws previously ascertained, or from an hypothesis.  However, as a word is used in various senses, we often speak of laws as ‘facts’:  we say the law of gravitation is a fact, meaning that it is real, or verifiable by observations or experiments.