400 3Ir. Frederick Sodcly [March 15, 



separable portion of the radioactivity was found to occur not only with 

 thorium, but also with radium and with uranium. If a chemist 

 observed that after a substance had been separated from impurities 

 these impurities made their appearance again with the lapse of time, 

 he would scarcely credit his observations. If such observations were 

 confirmed and shown to be the invariable consequence, impurities 

 after chemical separation being regenerated with lapse of time, the 

 view that the elements were the ultimate unchanging constituents of 

 matter would be undermined. The theory of atomic disintegration 

 was founded on facts of this simple chemical nature, and not, as has 

 sometimes been asserted, on any mathematical or physical theories as 

 to the nature of the atoms of matter. The question immediately 

 arose whether over long periods of time the intensely radioactive con- 

 stituents separated from uranium minerals were being regenerated by 

 the disintegration of one or more of the other elements in these 

 minerals : and this question, as regards radium, forms the subject of 

 the lecture. 



The law of radioactive change is the simplest possible expression 

 of what has been termed by chemists Mass Action, and has been 

 familiar to them as " the law of mono-molecular reaction " since the 

 classical researches of Wilhelmy in 1850, and of Harcourt and Esson 

 in 1865. The "velocity" of the change, that is the quantity changing 

 in the unit of time, is always some definite fraction, signified by the 

 symbol A, and known as the radioactive constant, of the amount re- 

 maining unchanged. The period of average life of the changing 

 atom is the reciprocal of this radioactive constant, that is 1/A. The 

 peculiarities of radioactive changes depend upon the fact that 

 frequently several successive changes occur in series, a substance A 

 changing at a definite speed accordirtg to the law stated and forming 

 a product B, which changes according to the same law but at its own 

 peculiar rate, forming the product C, and so on. All through, the 

 number of atoms, of any one member of the series, changing in a 

 given time is the number of atoms of the next product formed, the 

 general differential equation being 



<;,-«= A, p- A, Q 



where P and Q are the quantities of any two successive members in 

 the series and Ap and Aq, their radioactive constants. 



The machine exhibited (Fig. 1), of which a full description will 

 be published separately, is designed to illustrate radioactive change, 

 even in some of its more complicated cases, and to draw the graphs 

 connecting the quantity of the radioactive substance with the lapse 

 of time, when the substance in question is the first, second, third, or, 

 in certain cases, the fourth product of the successive changes. It con- 

 sists of three separate units, one of which is sketched in Fig. '1. The 

 height of the nnt on its screw represents the quantity of the radio- 



