Measurement of Electromagnetic Radiation. 47 



direction has again neutralized the charges by the time that it 

 is a maximum ; and in the fourth period, it charges the upper 

 end negatively and has ceased to flow when the negative charge 

 is a maximum. 



Now divide the second period of the time-diagram of cur- 

 rent, T, into n (== j of 3 x 10 10 ) elements, and the upper half of 

 the wire in the quantity-diagram, Q, into the same number of 

 equal parts, which will therefore each be one centimetre long. 

 Now, since the total quantity of electricity represented by the 

 shaded part in Q is equal to the time-integral of the current 

 which is represented by the shaded part in diagram T; and since 

 also each of these is bounded by a quarter-period of a sine 

 curve, and is divided into an equal number of elements, it is 

 clear that each space-element in Q, 1. 2, 3, ... n, must equal the 

 corresponding time-element in T ; or, in words, though the 

 quantity of electricity that has passed the point p in the first 

 element of rime is spread over the upper half of the wire in Q, 

 and so on, yet at the nth. element we may consider that that 

 which passed during the first element of time is stored on 

 the element 1, that which passed during the second element 

 of time is stored on the element 2, and so on. Now, since 

 the current-strength in the first element of time is 1, and 

 since this element of time has been made equal to 1/Qx 10 10 ) 

 second, the quantity of electricity on the end centimetre 

 of wire is l/( J X 10 10 ) electrodynamic unit, or 1 electrostatic 

 unit. This will be repelled by the wire opposite with the 

 same force as that with which the current in the centre 

 element of one wire will be attracted by that in the other 

 wire, both when each is at a maximum and through all the 

 harmonic variations. In the same way, the next element near 

 the end in Q will correspond to the next element near the 

 middle in C, and so on over the whole length of each ; and 

 so, since the electrodynamic attraction over every element 

 in time and space is equal to the electrostatic repulsion in 

 the corresponding element, removed both in time and space by a 

 quarter period, the total force due to one is equal to the total 

 force due to the other. If any other length of wire is taken, and 

 of course its corresponding period, since the number or length 

 of the elements in both T and Q must vary together, the same 

 result will follow; and if any other strength of maximum 

 current is taken, the attractions and repulsions will be changed 

 to an equal extent, and therefore, if two straight wires are 

 placed so close together that the distance between them is 

 very small compared to their length, they will, when their 

 natural electrical oscillations are induced in them, on the 

 whole neither attract nor repel one another. 



