102 Miss H. Brooks on the Damping of the 



R is therefore determined in terms of the known resistance. 

 The valne of R determined from a number of observations in 

 which different values of r were used w r as about 2 ohms for 

 a spark of 6 mm. From this of course is to be subtracted 

 the resistance of the leads, which is small in comparison with 

 the total resistance. 



When the resistance of the air-break is known, any un- 

 known resistance r x can be determined in a similar manner ; 

 for if pj and p 2 be the dampings without and with the 

 unknown resistance respectively, then 



logP 2 = R + ri 

 log Pl R 



and r± is therefore determined in terms of R. 



This gives an accurate and practicable method of deter- 

 mining the values of resistances in rapidly alternating fields. 



By inserting a series of increasing electrolytic resistances 

 in the circuit, a curve showing the relation between the 

 damping and the resistance w-as obtained. This experimental 

 curve corresponded very closely with one found by calculating 

 the values of the damping from the formula 



_K+r„ T 



P = e~ 2L -\ 

 different values being substituted for r , and R being deter- 

 mined from one of the points on the experimental curve. 

 The two curves are shown in fig. 5. 



The damping remained unchanged whatever the diameter 

 of the copper wire employed in the circuit, the small increase 

 of resistance with decrease of diameter was not sufficient to 

 have any appreciable effect. When leads of iron wire, 

 however, were substituted, the oscillations were greatly 

 damped down, owing to the circular magnetization of the 

 iron which prevents the current from sinking to any depth, and 

 thus greatly increases the resistance. An iron wire *7 mm. 

 in diameter gives a damping of *72 for a spark of 11 rams., 

 while the damping for a copper wire of same diameter in 

 the same circuit is *85. This increase of the damping for iron 

 wires has been frequently noticed before, but by this method 

 an exact measurement of the increase of resistance of an iron 

 wire for any given rapidly alternating current can be obtained 

 in a manner similar to that used to determine any other 

 unknown resistance in the circuit. The damping was found 

 to increase as the diameter of the iron wire decreased. 



Diameter of wire in mms.... *50 *65 1*2 2 

 Damping -70 -72 '79 -82 



