Whitehead — Magnetic Effect of Electric Disjplacement. 117 



once, suffering retardation of 180° ; owing to the self-induction 

 of the coil the resulting current lags approximately 90°, and 

 so, therefore, does the resulting magnetic field. Consequently, 

 the displacement current and magnetic field are approximately 

 180° apart, that is, in the proper relation to give the electro- 

 magnetic reaction. Actually, since the angle of lag in the 

 coil is 83° 52' instead of 90°, the effect as calculated for coin- 

 cidence must be multiplied by '991:2 = cos 6° 8^ 



The current in the dielectric is thus acted on by a force : 



.994^ = .63 . -J^ . ^M^^ . -9942 . 



10 2K-f-l 10' 10 • 



K 12-8 ^ 



dynes. 



2K-M ' 10' 



when 1-2 amperes flows in each coil, I being the thickness of 



the dielectric, or the length of the displacement current acted 



on by the field, and H the intensity of the magnetic field. 



This force is applied in opposite directions at the two ends of 



the suspended beam, which was 1T*T8^'^ long, giving thus a 



couple of 



K 2-28 , 

 —^ — - . —-- dyne-centimeters. 



2K-f-l 10* ^ 



The angle of twist of a thread of length Z, radius i\ coefficient 

 of rigidity n, acted on by a couple ii is : 



_ 2 lu 1 



The length of the quartz fiber was lOl-e'"" ; its radius was 

 estimated by comparison under a microscope with the spaces 

 of a grating ruled on glass, the grating space of which was 

 known, and did not differ greatly from '0006'^'^. The value of 

 n being taken at 3x10'^ for quartz,^ we have 



^__ K 2X101-6X2-28 _ K 



^-■2K-M-7rX-0006*XlO^X3XlO-~2K-fl-^^''^'^'^"'' 



Taking the value of K for rock salt as 5*8, we have <I> = -1T3, 

 which, since the distance from the mirror to scale was 140^°^, 

 represents a deflection of 2 X 1400 X '173 = 485™'°, or more, since 

 we have taken the tangent as equal to the arc. 



The calculation above assumes that the electric and magnetic 

 fields remain constant through the range of movement of the 

 dielectrics. It was of course foreseen that the electric field 

 would be most intense at the center of the space between the 

 electrodes and so would tend to hold the dielectric within that 

 region ; nevertheless it was thought that a couple of the magni- 



* Threlfall and Boys. 



