v: 



36 Messrs. E. B. Rosa and A. W. Smith on a Resonance 



loop being the work done by the condenser upon its discharge. 

 Equation°(l), p. 31, shows" the area of this power-curve to 

 consist of two terms, the coefficient of one containing I cos 

 and of the other I sin <£>. JsTow Icos<£ is the component of 

 the total current which is in phase with the E.M.F., and is 

 represented by curve 5. lsin<£ is the condenser current. 

 90° ahead of 'the E.M.F., and is represented by curve 4. 

 The power-curve for 4 is 6 ; its positive and negative loops 

 are equal, and it is the power-curve for a perfect condenser. 

 The power-curve for 5 is 7, and is the total work done, or 

 the energy dissipated. One loop of 6 is energy stored, W, one 



w 

 loop of 7 is energy dissipated, w, and the ratio ^ is the 



relative loss, or 1 — v^ is tne net efficiency. 



The area of one loop of 7 is 



= EJ^ r| _ ^ipp j - = gj, cos f* =Energy pitted. 



The area of one loop of 6 is 



W= EA sin <f> |- cos jptl^t EJl * in * . 2=Energy Stored. 



.'. 6=1— ^ =1 — 7rcot 0, as before. 



If the equivalent resistance of the condenser is taken to be 

 a series resistance then we have E cos <j) for the active E.M.F., 

 E sin cj> for the condenser E.M.F., and the same result follows. 



Example of the Resonance Method. 



The condenser used was one which we had made ourselves, 

 and consisted of paraffined paper and tinfoil. The paper was 

 12x17 centim. and '0038 centim. thick; the tinfoil was 

 •0025 centim. thick, and its effective area was 10 x 15 centim. 

 approximately. The paper and tinfoil were piled up dry and 

 clamped between brass plates. It was then placed in melted 

 paraffin and maintained for some hours at 100° to 150° C. 

 This condenser then had a volume of about 300 cub. centim. 

 and a capacity of about *8 microfarad. 



The resonance-coil consisted of 3000 metres of No. 10 wire 

 (B and S gauge, '259 centim. diameter) wound into a coil of 

 40 centim. internal diameter, 56 centim. external diameter, 

 and 17 centim. axial length. Its resistance was about 10 ohms 

 and its inductance 1*60 henrys. This coil was wound in ten 



