ST. JOHN. — WAVE LENGTHS OF ELECTRICITY. 243 



In the same way, for 



j Copper (diameter 0.0884 cm.) Z^ _ ^ ^^^ 



(Iron (diameter 0.08847 cm.) L~ ' 



\ Copper (diameter 0.07836 cm.) L' _ 



( Iron (diameter 0.07850 cm.) L 



By the use of Lord Rayleigh's formula for induction under very 

 rapid oscillations, it is easy to calculate the permeability of the iron, 

 since the ratio between the self-induction of the iron and copper are 

 given by the previous calculation. 



Lord Rayleigh's formula is 



Z' = / 



where / is the total length of the circuit ; A^ a constant depending 

 only on the form of the circuit, or / ^ is the self-induction of a similar 

 copper circuit; p., the permeability; i?, the resistance; /> = 2 7rre, 

 where n is the number of complete oscillations per second. 

 The value ol 'p ^ 1 irn = 360,000,000. 

 R for iron wire diameter 0.1186 cm. = .1328 ohms per sec. 

 " " " 0.08847 cm. = .227 " " 



" " " 0.0785 cm. = .301 " " 



For iron diameter 0.1186 cm. 



L! ^ \m\L = l 



{'-^O' 



L + M4L= L + ly^,, 



^ 2pl 



V 2vl' 



- > 



Calculating the value of L for a copper circuit / units long, substi- 

 tuting the value in the above equation, and solving, we find : — 

 For the iron wire diameter 0.1186 cm. ft = 430 

 " « " 0.08847 cm. fx = 389 



'^ « " 0.0785 cm. fx = 336 



These values for the permeability all fall within a reasonable limit, 

 and have for an average /* = 385. These are the values found for 

 different specimens of wire made by the same company, but the speci- 

 mens were wound and unwound and stretched many times during the 

 series of observations. 



