Intensity of Periodic Fields of Force. 

 The limits of the odd ranges are given by 



9 



25 



2a o-«i-^ <«,—«. « 2 -« 3 



o 25 



and of the even ranges by 



2a -a 2 - 



a x -a z Za^-a-- a -a. 



a n — a A 



<*,-<** 2a o- a s- 



2« n + a, 



a x + «* 



= 0, 



0, 



=o, 



= . 



845 



0.) 



(ii.) 



(iii.) 



(iv.) 



a t +a, 2a + a 4 ' 



The motion within the ranges is of form 



A«*{*(0 -+(*)} + B«-*{*(0 +*(«)}, • • (i) 



where <f>(t) and ^(0 are even and odd functions of t. 



2. For a simple periodic field, x + 2an 2 cos nt . x = 0, the 

 first three ranges of cumulative effect are 0*454 > 2a > 3" 76; 

 3*79>2a>10*64 ; 10*65>2«>20*95. The relative smallness 

 of the ranges of stability is noteworthy. 



