December 17, 1915] 



SCIENCE 



855 



so far as our knowledge extends, an un- 

 alterable and unvarying factor. It may be 

 defined in terms of the fraction of the whole 

 amount of the element present which under- 

 goes transformation in any convenient unit 

 of time, a year for example. This factor 

 is called the constant of disintegration of 

 the radio-element. Its character is such 

 that if P represents the number of atoms 

 of a radio-element initially present, e is the 

 base of the natural system of logarithms, 

 t is the time expressed in the chosen units, 

 and A is the disintegration constant; then 

 the number of atoms, Pt, of the element 

 which will remain unchanged after the ex- 

 piration of an interval t units from the 

 start will be expressed by 



Now, in any radioactive system compris- 

 ing a parent substance like uranium and a 

 series of disintegration products, including 

 radium, for example, when a state of radio- 

 active equilibrium has been established the 

 conditions will be such that the number of 

 atoms of each of the radio-elements in the 

 series which undergo change in a given in- 

 terval will be the same and equal. Thus if 

 U be the number of atoms of uranium and 

 A.1 be its constant of change, and if Ra be 

 the number of atoms of radium with a con- 

 stant of change A,, then \JI = X.,Ba, and 

 this will also equal the product of the num- 

 her of atoms of any other radio-element in 

 the series multiplied by its disintegration 

 constant. It should be evident from these 

 considerations that the quantity (number 

 of atoms) of radium formed in any given 

 interval will be equal to the quantity (num- 

 ber of atoms) of radium which is trans- 

 formed in the same interval, an essential 

 requirement to the postulated condition of 

 equilibrium. If, then, we can determine by 

 experiment the quantity of radium which 

 is formed in such a system, we obtain 



through this a direct measure of the quan- 

 tity of radium which has changed to other 

 elements during the observed period, and 

 if we know the amount of radium present in 

 the system we can determine the ratio of the 

 two amounts which will be the disintegra- 

 tion constant of the radium. If radium 

 were formed directly from uranium it 

 would be easily possible to separate the 

 uranium from a quantity of mineral con- 

 taining a known amount of radium, purify 

 it from all but traces of radium, allow it 

 to remain until measurable amounts of 

 radium had been produced within it, and 

 then compare the radium formed from the 

 uranium with the radium present initially 

 in the mineral. This was attempted, but it 

 was found that the rate of production of 

 radium was too slow to be determined with 

 any accuracy and was far less than was to 

 be expected from theoretical considerations. 

 This obstacle was overcome when in 1907 

 the writer was able to separate from ura- 

 nium minerals a previously unidentified 

 radio-element which was intermediate be- 

 tween uranium and radium in the series of 

 atomic transformations, and which by its 

 own disintegration produced radium in 

 readily measurable quantities. To this ele- 

 ment the name "ionium" was given. It 

 thus became possible to separate the ionium 

 from a mineral containing a known amount 

 of radium, and to determine the rate of 

 growth of radium in this ionium. This is 

 a measure of the rate of production of 

 radium in the mineral and therefore a meas- 

 ure of the rate of disintegration of the 

 radium. 



The two diagrams (Figs. 1 and 2) will 

 perhaps be useful in making the general 

 conditions and method of procedure more 

 easily understood to those without a tech- 

 nical knowledge of the subject. In the 

 first (Fig. 1) the amount of uranium 

 changing per year relative to the total 



