metabolon has been suggested as a convenient expression for each of these changing atoms, derived from the successive disintegration of the atoms of the radio-elements. Each metabolon, on an average, exists only for a limited time. In a collection of metabolons of the same kind the number N, which are unchanged at a time t after production, is given by
where N₀ is the original number. Now dN/dt = -λN, or the fraction of the metabolons present, which change in unit time, is equal to λ. The value 1/λ may be taken as the average life of each metabolon.
This may be simply shown as follows:—At any time t after N₀ metabolons have been set aside, the number which change in the time dt is equal to λNdt or
Each metabolon has a life t, so that the average life of the whole number is given by
The various metabolons from the radio-elements are distinguished from ordinary matter by their great instability and consequent rapid rate of change. Since a body which is radio-active must ipso facto be undergoing change, it follows that none of the active products, for example, the emanations and Th X, can consist of any known kind of matter; for there is no evidence to show that inactive matter can be made radio-active, or that two forms of the same element can exist, one radio-active and the other not. For example, half of the matter constituting the radium emanation has undergone change after an interval of four days. After the lapse of about one month the emanation as such has nearly disappeared, having been transformed through several stages into other and more stable types of matter, which are in consequence difficult to detect by their radio-activity.
The striking difference in chemical