286 Dr. Norman Campbell : Experiments on 



And from (31) of Prof. Jones's paper, so long as cw(l + w 2 ) 

 is small compared with unity, 



2\ =([^T 1 4 + 5iT 2 4 )y / (T 1 2 -f-T 2 2 ) 2 . . . . (3) 



*-H& + &)- • (4) 



It is possible to measure accurately the periods of the 

 components of the oscillation only when these periods are 

 very different and r is not nearly equal to 1. This condition 

 will always be fulfilled so long as c is small ; thus so long 

 as c is less than 0*1, r is always greater than 6. Accordingly, 

 in these conditions, we may neglect terms involving 1/r 2 , and 

 write in place of (1) and (2) 



t^TV + TV . . . . (1.1); li'^-tN^ + NV). (2.1) 



c 



We may now determine the constants of the circuits as 

 follows: — 



1. To determine L 1 and T 2 . 



Measure t 2 for different values of C x and plot t 2 against Cj. 

 A straight line should be obtained, of which the intercept on 

 the axis gives T 2 , the inclination I^. 



2. To determine L 2 '. 



Measure t 2 for different values of C 2 ', where C 2 ' is the 

 capacity added to the secondary circuit. Again a straight 

 line should be obtained of which the inclination gives L 2 '. 

 It is assumed that all values of C 2 ' are so great that the 

 current in the secondary is uniform. 



3. To determine c. 



Measure t when Ci is very large. Then 2 . 1 reduces to 

 t ,2 = cT 2 2 ; and since T 2 is already known, c can be determined. 



4. To determine c! and L 21 . 



Measure r' when C 2 is very large. Then r' 2 = c'T 1 2 . d is 

 always known and L x has been determined ; hence T x is 

 known and c' can be deduced. Since c' is a function of 

 Li, L 21 , and L 2 ' only, we can now deduce L 21 . 



To determine the damping coefficients. 



u or fju' can be determined directly by measuring the am- 

 plitudes of successive oscillations. If t or t' is determined 

 at the same time, \ or V is known immediately. 



