the Excited Activity of Radium to the Cathode. 535 

 Equation (3) may now be written 



7T n 



cos^[y (/*sec^>)— ^7 2 (^sec0)— Jy 4 (/*sec (/>)-...]# (7) 

 TJo 



We also have 



1 



7u 



(,)=±(l-«-), 



, N i i i - i , 



Also y n (z) decreases continuously as either z or n increases. 



1£ f6=— , we have, if z=fisec<j>, 

 o 



-e~ z < - «^m < -012, 



2 7a(*)< g 72<»< '015, 



and with an error of order 3 per cent, we may write 



4 f- 77 1 

 s = — I 2 cos 2 6 dd> = - (9) 



/*7Tj /A 



This simplified result should therefore hold if the defect 

 from the maximum deposit of activity on the cathode is less 

 than 30 per cent. Hence, with this restriction, the deposit of 

 activity y should be given by the formula 



«=N (l-,)=N (l-i^. . . . (10) 



But the mean free path varies inversely as the pressure, and 

 hence, if L be the mean free path for a pressure of 1 cm. 

 of mercury, and x cm. denote any other pressure, we obtain 



This equation affords a means of determining the values of 



N and ^ which best suit each of the Tables I., II., III. 



obtained by Mr. Makower. Owing to the restriction that the 

 value of y must be greater than'7N , it is found that this is an 



