Laws of Concomitant Variations may hold good only within certain limits.  That bodies contract as the temperature falls, is not true of water below 39 deg.  F. In Psychology, Weber’s Law is only true within the median range of sensation-intensities, not for very faint, nor for very strong, stimuli.  In such cases the failure of the laws may depend upon something imperfectly understood in the collocation:  as to water, on its molecular constitution; as to sensation, upon the structure of the nervous system.

Sec. 4.  Secondary Laws, again, are either of Succession or of Co-existence.

Those of Succession are either—­(1) of direct causation, as that ’Water quenches fire,’ or (more strictly) that ’Evaporation reduces temperature’; or (2) of the effect of a remote cause, as ’Bad harvests tend to raise the price of bread’; or (3) of the joint effects of the same cause, as that ‘Night follows day’ (from the revolution of the earth), or the course of the seasons (from the inclination of the earth’s axis).

Laws of Co-existence are of several classes. (1) One has the generality of a primary law, though it is proved only by Agreement, namely, ’All gravitating bodies are inert’.  Others, though less general than this, are of very extensive range, as that ’All gases that are not decomposed by rise of temperature have the same rate of expansion’; and, in Botany that ‘All monocotyledonous plants are endogenous’.  These laws of Co-existence are concerned with fundamental properties of bodies.

(2) Next come laws of the Co-existence of those properties which are comprised in the definitions of Natural Kinds.  Mill distinguished between ([alpha]) classes of things that agree among themselves and differ from others only in one or a few attributes (such as ‘red things,’ ‘musical notes’, ‘carnivorous animals’, ’soldiers’), and ([beta]) classes of things that agree among themselves and differ from others in a multitude of characters:  and the latter he calls Natural Kinds.  These comprise the chemical elements and their pure compounds (such as water, alcohol, rock-salt), and the species of plants and animals.  Clearly, each of these is constituted by the co-existence or co-inherence of a multitude of properties, some of which are selected as the basis of their definitions.  Thus, Gold is a metal of high specific gravity, atomic weight 197.2, high melting point, low chemical affinities, great ductility, yellow colour, etc.:  a Horse has ’a vertebral column, mammae, a placental embryo, four legs, a single well-developed toe in each foot provided with a hoof, a bushy tail, and callosities on the inner sides of both the fore and the hind legs’ (Huxley).