Non-generating Force exerting Cumulative Influence. 169 

 For the limits o£ the range about /x, from (2) and (3) 



1 

 2« 



-©' 



1-4 



©' 



=o, 



and 



-©' 



= 0. 



-© 



2. £. 



and 





(7) 



Again, for the range associated with 2/^/3, 



-(£) 



+ a 



-#;)" 



■«(e) 



whence 



>«-£a- 



=0, 



" 2 ± iV««*)- 



(8) 



These results are in agreement with those obtained previously 

 by another method*. 



5. From the physical point of view interest attaches to 

 the change in the breadth and position of the range about 

 the double frequency when the intensity of the force is 

 increased. For this range the roots approach rapidly 

 towards their limiting values if a. is not too large, and we 

 readily find: — 



a. 



Range of (™ \ . 





Range 



of JL. 

 1-121 



0-25 



0-7607, 1-2560 





0-872, 



0-50 



0-5619, 1-5197 





0-749, 



1-232 



0-75 



0-4423, 1-7873 





0-665, 



1-337 



1-00 



0-4007, 2-0571 





0-633, 



1-434 



1-25 



0-3983, 2-5284 





0-631, 



1-526 



and so on. 



* Loc. cit. 



§3. 







