THE AID OF THE ACHROMATIC FRINGES. 71 



This makes Leo = 40 and 37 per telephone and is a fair result. Data of 

 this kind, however, which depend on differences of the squares of 5, are neces- 

 sarily crude, unless some method of smoothing the observations is first 

 resorted to. 



Examples of the results of s varying with capacity at constant resistance 

 are given in figure 77. In both instances the additional R was zero, but the 

 effective resistance of the circuit (telephones, etc.) about 400 ohms. In case 

 of series (6) the fringes were smaller than a scale-part and the sensitiveness 

 about 3 scale-parts per microfarad. In case of series 7 and 8, the fringes 

 were larger and the sensitiveness about 6 scale-parts per microfarad. In these 

 adjustments therefore the detection of o.i microfarad would be very easy. 



Within the range of observation and the values for L, R, and C, the capacity 

 loci are linear, so far as can be made out, although subject to a well-known 

 equation. 



If L be neglected or associated with the constant r of the circuit, the latter 

 may be computed from 



where R in the present experiments is zero. 



Taking the first four observations of figure 77, series 7, cor comes out io 4 X 14. 

 io 4 X8, io 4 Xi2, in the successive pairs of data. We would thus compute r 

 from the mean value of = 25 per second as 700 ohms. The observations are 

 again too crude for this method of treatment. Series 8 comes out similarly 

 if the individual data be taken. The results must first be smoothed as in the 

 figure. Thus is 5 = 36 at 6 microfarads and 19 at 3 microfarads, and if n 25 

 per second, r = 400 effective ohms. The line in series (7 ) similarly treated gives 

 r = 24o ohms. These are reasonable values. 



Finally, it seemed interesting to trace the effect of additional resistance 

 R through a capacity. This is done for a capacity of 6 microfarads in figure 78 

 for resistances up to R= 10,000 ohms. The results below 5,000 ohms are very 

 marked; above 5,000 ohms the curve flattens. In many respects these obser- 

 vations may be regarded as elucidating some of the anomalous results obtained 

 in the capacity experiments in the earlier parts of this paper. Unfortunately 

 it is impracticable to reduce the resistance of the circuit itself below a few 

 hundred ohms, unless the telephones are in parallel (53). 



It is obvious, however, that the measurement of a capacity can be carried 

 out in the secondary by direct comparison with a known capacity, or even in 

 comparison with a given resistance R, if the inductance is relatively negligible. 

 For, if we neglect the L, the C would be given C 2 co 2 = As 2 /AOCR+0) 2 ^ rom ^e 

 data of figure 78. Here A is a differential symbol and r was measured as 280 

 ohms. The values of Ceo came out 780, 970, 1130 for the first 4 pairs of data 



