Measurement of Electromagnetic Radiation. 53 



violently off the scale, and then a Hertz resonator tuned to 

 the oscillations of the primary was placed in the jar and 

 surrounded by the same acid duster when the sparks in the 

 gap were evident, showing that the proper electromagnetic 

 waves did penetrate into the jar as supposed. 



The turning moment corresponding to a deflexion of J millim. 

 may be found from the following particulars : — 



Period of oscillation of mirror and stem (oscillator re- 

 moved), *947 second. 



Period of oscillation with wire ring hung on, 4'13 second. 



(Wire ring 1*6 centim. diameter outside, made of wire 

 •122 centim. in diameter; mass '4635 gramme.) Hence 



Couple = 1-1 X 10- 5 C.G.S. units, and 



Average value of couple = 3*7 x 10~ 7 C.G.S. units 

 per centim. of wire of resonator, 

 which corresponds to a force of about 3 x 10~ 7 dynes, since 

 the distance from the axis is 1J centim. This is less than a two- 

 hundred-millionth of the weight of a grain, or a three-thousand- 

 millionth of the weight of a gramme. 



Since the wires were only *2 centimetre apart, this shows 

 that, if the currents in the wires, instead of being oscillating, 

 had been simply ordinary steady currents, those currents could 

 not have reached the value of '00017 C.G.S. electromagnetic 

 unit or '0017 ampere. 



Now the moment, if the theory advanced is correct, is due 

 partly to electrostatic repulsion and to electrodynamic attrac- 

 tion which are equal to one another, but owing to the harmonic 

 distribution of both, both in time and in position, and owing 

 to the fact that the weaker part of each of these forces is 

 tending to counteract the stronger part, the total average 

 resultant force is by no means double or even equal to that 

 due to a steady current alone of a strength equal to the actual 

 maximum. 



To find the relation it is necessary to first consider the 

 effect of the harmonic distribution of either, say the current, 

 along the wire. The square of this at any point is a measure 

 of the force at that point, so that the force varies from zero 

 at the ends to its full value in the middle, having passed its 

 half value at the points where the wire crosses the axis of 

 rotation. 



Thus, in fig. 4, the ordinates of the upper curve a b c, which 

 is half a sine curve, represent current strength, those of the 

 lower curve a d b e c, which is a complete sine curve on half 

 the scale, but shifted vertically by the amount of its own 

 maximum ordinate, since 



. o 1 — cos 2a 



