1908] on Recent Researches m Radio-aciivlty. 29 



suppose that A has a much longer period than B. In the hydrauhc 

 analogy A is represented by a high head of water discharging at its 

 base through a circuit of high resistance into the top of another 

 cylinder representing the matter B. The water from the cylinder B 

 escapes at its base through a lower resistance. Suppose that initially 

 only A is present. In this case the water in the cylinder B stands a 

 zero level. On opening the stop-cock connecting with A, water flows 

 into B. The rise of water with time in the cylinder B is traced out 

 in the same way as before by moving the glass plate at a constant 

 rate across the tracing brusli. If the period of A is very long com- 

 pared with that of B the water is supplied to B at a constant rate, 

 and the water in B reaches a constant maximum height when the 

 rate of supply to B equals the rate of escape from the latter. The 

 curve traced out in that case is identical in shape with the " recovery 

 cur^'e " of a radio-active product supplied at a nearly constant rate. 

 The quantity of matter reaches a maximum when the rate of supply 

 equals its own rate of transformation. The relative height of the 

 columns of water in A and B represents at any time the relative 

 amounts of these substances present. 



If the period is comparable with that of B, the height of water in 

 B after reaching a maximum falls again, since as the height of A 

 diminishes, the supply to B decreases. Ultimately, the height of B 

 will decrease in a geometrical progression with the time at a rate 

 corresponding to the longer period of the two. Tliis is an exact 

 illustration of the way the amount of a radio-active substance B 

 varies when initially only the parent substance A is present. By 

 using a number of cylinders in series, each with a suitable resistance, 

 we can in a similar way illustrate in a quantitative manner the 

 variation in amount with time of a number of products arising from 

 successive disintegrations of a primary substance. By suitably 

 adjusting the amount of resistance in the discharge circuits of the 

 various cylinders, the curves could be drawn to scale to imitate 

 approximately the variation in amount of the various products with 

 time when the initial conditions are given. 



During the last few years a very large amount of work has been 

 done in tracing the remarkable succession of transformations that 

 occur in the various radio-active substances. The known products 

 of radium, thorium, actinium, and uranium are shown graphically 

 below, together with the periods of tlie products and the character of 

 the radiations they emit. It will be seen that a large list of these 

 unstable bodies are now known. It is probable, however, that not 

 many more remain to be discovered. The main uncertainty lies in 

 the possibility of overlooking a product of rapid transformation 

 following or succeeding one with a very slow period. In tracing out 

 the succession of changes, the emanations or radio-active gases con- 

 tinuously evolved by radium, thorium, and actinium have marked a 

 very definite and important stage, for these emanations can be easily 



