242 PROCEEDINGS OF THE AMERICAN ACADEMY. 



but the copper being the smaller one in the second case. In other 

 respects the circuits compared were as nearly identical as possible. 

 The capacity per unit length being the same for wires of the same 

 diameter, the shortening of the wave length when iron displaced cop- 

 per of the same diameter must be caused by an increase in self-induc- 

 tion due to the magnetic properties of the iron. If this is true, it 

 means that the magnetization of iron can be produced and reversed 

 115 million times per second. This reduces the " time-lag" of mag- 

 netization to a very small (quantity, if magnetizing forces of such 

 duration are capable of bringing the magnetic properties of the iron 

 into play. 



In the case of extremely rapid oscillations, Prof. J. J. Thompson has 

 shown (Recent Researches in Electricity and Magnetism, § 295) that 



2 v" 



approximately y^ — 77-7^? where — -g is the square of the frequency, 



and L' is the self-induction for any rapid oscillations, and G the 

 capacity of the system. It is easy from this to calculate an approxi- 

 mate value for the ratio between the self-induction per unit length of 

 the iron and the copper. 



Let L = the self-induction of the copper per unit length. 

 Let L' = the self-induction of the iron per unit length. 

 Let C = the capacity of either per unit length. 



Usins: as a basis of calculation the data from the third maximum 

 G of the curves of Figure 4 of the Plate, the total length of the copper 

 circuit (diameter 0.1201 cm.) is: — 



The sides, 562.5 x 2 = 1125 cm. 



The closed end, = 30 cm. 



The equivalent of the end capacities. 02x2= 124 cm. 



1279 cm. 



For the iron (diameter 0.1186 cm.) the length is : — 



The sides, 553 X 2 = 1106 cm. 



The closed end, = 30 cm. 



The equivalent of the end capacities, 61 X 2 = 122 cm. 



1 258 cm. 



Since the two circuits have the same frequency, the products of the 

 self-induction by the capacity are equal. 



12532 Z' Q^ 1279' LO. 

 ^ = 1.034. 



