Oscillations in Coupled Circuits. 35 



a result which is deduced from the more general formula (4zj 

 below, by neglecting the square and higher powers of the 

 small fraction LsCg/LiCj. Now C a was known approximately, 

 and this approximate value being used in the small term in 

 the brackets, the inductances being also known, and n deter- 

 mined from the photographic plates, a more accurate value 

 of Ox was calculated from the above formula. The capacities 

 of the paraffin-paper condensers were thus determined under 

 conditions not differing greatly from those existing when the 

 double-period oscillation curves were photographed. With 

 either of the paraffin-paper condensers in the primary circuit, 

 the frequency of the oscillations when the secondary capacity 

 was very small was, in fact, intermediate between the two 

 frequencies when one of the leyden-jars was connected to 

 the secondary coil. 



The values of the capacities are given in the accompanying 

 tables. 



(3) The Double-period Curves. 



Four cases of coupled oscillating circuits were worked out, 

 particulars of which are given in the following table. 



Table I. 



L, = '004619 X 10 9 cm. L 2 = 70-15 X 10 9 cm. 



M = -2192 x 10 9 cm. KyL.U^'US'd. 



R x = 1-0378 ohm. R 2 = 14022 ohms. 





microfarads. 



C 2 , 

 micro farads. 



L^XlO 8 . 



I 

 L 2 C 2 x 10 s . 



^X106. 



I 



955 



001063 



4-411 



7-455 



6-203 



IT 



9-55 



•000875 



4-411 



6-138 



o - o4o 



Ill 



11-87 



•001063 



.3-482 



7-455 



6 805 



IV 



1187 



■O0OS75 



5-482 



6-138 



6147 



The frequencies n x and n 2 of the two oscillations were cal- 

 culated from Oberbeck's approximate formula 



, ._ 1 r 1 1 / (-/ 1 1 X 2 . 4M 2 -\l 



^ n "~ l-M^La LJLi C L 2 C 2 ± V l\LA L 2 cJ I^L/dCJ, J J* 



... v 4 ) 



Hence the values of T and T', i. e. l/Simi and l/27ra 2 , were 

 obtained, and /3 was calculated from (2). 



D'2 



