in an Annular Trough. 205 



Hence in the symmetrical class the longest period is 



^V r2 h 12 96 396 ° rl ' 623eCO " d3 - 



The next longest is 



/coth-787.i AOf) , 



2?r V 32. 12. -787 ° r °' 82 SeCOnds ' 



In the ud symmetrical class where n = 1 the longest period is 

 2tt /T 



, seconds or l s, 60. 

 it/ 1 ' V <7/i 



and the next longest is 



K^ Vg~h seconds or °*' 81 - 



There is thus very little difference between the periods for the 

 two cases of n = 0, n = 1 : that is to say, the period is almost 

 exactly the same when there is one nodal diameter as when there 

 is not one. In either case each successive period is very nearly 

 half the next loDgest. 



Between the floating instrument mentioned in the first para- 

 graph and the trough containing the mercury there is everywhere 

 half an inch of free surface. Thus in the actual case, there are 

 two narrow annular free surfaces each ^ inch in width, the one 

 having a mean radius of 19f inches, the other 12£: the depth of 

 fluid is about \ inch. The two longest periods of a free wave on 

 these surfaces are the same for both the inner and the outer 

 surface, viz. S 13 and S 09 : these periods practically do not differ 

 for the two cases of n = or n — 1. 



It may be here stated that the observed period of oscillation of 

 the floating instrument is 9 6 '40. 



It is interesting to compare the periods in the corresponding 

 ones for a circular trough of the same outside diameter and with 

 the same depth of liquid. The values of tc are given by Lamb, 

 Hydrodynamics, Art. 187 ; they are 



*»« 1-2197^: * < 2 >= 2-233^. 

 *«'= 0.586^: * 1 w = 1-697^. 



