or 



on Stationary Electrical Waves in Wires. 387 



Equating the denominator to zero we find 



cot qa + cot qb=t, 



,2™ ,27Tb 2tt S x m 



This formula, which connects the frequency of the oscillation 

 with the position and capacity of the condenser, might have 

 been deduced from formula (1). For we can imagine the 

 capacity Sj divided into two parts, <x and o 1 ', in such a way 

 that when these parts are attached to the parts a and b of the 

 circuit respectively, the two partial systems oscillate indepen- 

 dently with the same frequency. We have thus from 

 formula (1), 



27ra _ 2-7T a 

 2irb _ 2tt g' 



cot 



On adding we get equation (2) . 



In seeking to test the agreement between the theory and 

 the observations, formula (2) was written 



\ ( . 2rra . 2irb ~\ 7rS. . . 



^< cot — — f- cot-— > =— ^-* = constant. 



A small error in observation of the node position causes an 

 error in the left-hand side very large in proportion, and of 

 amount varying with the position of the condenser in the 

 circuit. In view of this the method adopted was to find the 



S 

 mean value of -J 1 from the observations and, using it, to cal- 

 culate the values of b corresponding to each a. A comparison 

 of the observed and calculated values of b shows a sufficiently 

 good agreement, the discrepancy being greatest when the 

 condenser is too near a bridge. 



One set of observations involving only the circuit AB and 

 formula (2) were taken on a small apparatus at the end near 

 the oscillator. One bridge was kept fixed and the wave- 

 length was the same throughout. Thus only the quantity b 

 was liable to the error in determining the node. The uncer- 

 tainty in this determination amounted to about 5 millim. 

 The wires were about 15 millim. apart, and the condenser 

 consisted of two small copper strips, 1 centim. by 5 centim., 

 hung on the wires. The half wave-length was 37*5 centim. 

 The following table gives the results measured in centimetres : — 



