functional dependence a relationship between variable magnitudes (especially physical magnitudes) and certain properties or processes. In modern physical science there are two types of laws stating such relationships. (1) There are numerical laws stating concomitant variation of certain quantities, where a variation in any one is accompanied by variations in the others. An example is the law for ideal gases: pV % aT, where p is the pressure of the gas, V its volume, T its absolute temperature, and a a constant derived from the mass and the nature of the gas. Such laws say nothing about the temporal order of the variations, and tests of the laws can involve variation of any of the relevant magnitudes. Concomitant variation, not causal sequence, is what is tested for. (2) Other numerical laws state variations of physical magnitudes correlated with times. Galileo’s law of free fall asserts that the change in the unit time of a freely falling body (in a vacuum) in the direction of the earth is equal to gt, where g is a constant and t is the time of the fall, and where the rate of time changes of g is correlative with the temporal interval t. The law is true of any body in a state of free fall and for any duration. Such laws are also called ‘dynamical’ because they refer to temporal processes usually explained by the postulation of forces acting on the objects in question. R.E.B.