Taylor — Retardation of Alpha Rays by Metals. 369 



Let us suppose that for a given speed of the alpha particle 

 the amount of energy required to produce an ion is the same 

 in all substances. Then for air we would have the relation 



dI A = -/(V)tfE a . 



The corresponding relation in hydrogen is 



dl h = -f(V)dE h . 



Dividing the former by the latter we have 







dh 



dh ~ 



f(V)dE % 



which for 



a given 



speed V in 



each gas reduces to 







d\ 



dl h 



dE a 



~ dE h ' 



From this it is seen that for a given speed of the alpha particle 

 the ratio, of the rates of the consumption of the energy in 

 producing ions in air and hydrogen, is equal to the ratio of the 

 rates at which the ionization is produced in the respective 

 gases. On the basis of our hypothesis let us consider the ratios 

 of the energies consumed in the 4th and 13th centimeters 

 (fig. 2) of the path of the particle in air and hydrogen. This 

 ratio for the fourth centimeter of the path is proportional to 



=— ^ — since the areas are proportional to the ionizations 



area ab 43 a i l 



produced in the gases. The corresponding ratio for the 13th 



i area c, f. 13, 12, e. ml „ 



centimeter is equal to , _. _ _ — . lhe former ratio 



^ area (/, A, 13, 12, g 



is seen from the figure to be greater than the latter. Moreover, 

 it is also seen that the ratio of the energy of the a-particle 

 absorbed by any given centimeter of air to the energy 

 absorbed by the corresponding centimeter of hydrogen, is always 

 greater than the corresponding ratio for the centimeter just 

 beyond the given one. This is in agreement with the results 

 obtained for the air- equivalents of the hydrogen cells ; because 

 the increase in their air-equivalents as the range decreases is 

 due to the fact that the ratio of the energy absorbed by the 

 hydrogen cell to the energy that would be consumed by the 

 air which it displaces, continually increases as the cell is moved 

 away from the source of rays. The thicker the cell the more 

 rapid would be the rate of increase, as could be seen by com- 

 paring the areas which represent the ionization in, say two 

 centimeters of air and hydrogen respectively in figure 3 in 

 two different positions. The increase in the ratio of the ener- 



