1G2 hertz's KESEAKCriES ON ELECTRICAL WAVES. 



makes with the radius drawn to the air space. Then we shall have, 

 approximately, 



F=E cos cp sin ( -^ — "" '^ ) 



and therefore B= — E cos cp sin 6 



B, therefore, is a function simply of the total E. M. f. due both to the 

 electrostatic and electro-dynamic actions. It will vanish when cp = 90° — 

 that is to say, Avhen the total e. m. f. is perpendicular to the plane of the 

 circle, whatever be the position of the air space on the circle. B will 

 also vanish when ^ = 0, — that is to say, when the projection of the E. m, 

 F. on the plane of the circle coincides with the radius through the air 

 sxjace. If the position of the air space on the circle is varied, the angle, 

 B will vary, and therefore also the intensity of the vibration and the 

 sparking- distance. The sparking distance corresponding to the sec- 

 ond term of the expansion for F can therefore be represented approxi- 

 mately by a formula of the form y5 sin 6. 



JSTow the oscillations giving rise to sparks of lengths a and /J sin 6 re- 

 spectively are in the same phase. The resulting oscillations will there 

 fore be in the same phase, and their amplitudes must be added together. 

 The sparking distance being apiH'oximately proportional to the maxi- 

 mum total amplitude, may therefore also be obtained by adding the 

 sparkiug distances due to the two oscillations respectively. The spark- 

 ing distance will therefore be given as a function of the position of the 

 air space on the secondary circuit by the expression «+/i sin 6. Since 

 the direction of the oscillation in the air space does not come into con- 

 sideration we are concerned only with the absolute value of this ex- 

 pression, and not withit sign. The determination of theabsolute values 

 of the quantities a and ft would involve elaborate theoretical investiga- 

 tions, and is moreover unnecessary for the explanation of the experi- 

 mental results. 



Experiments with the secondary circuit in a vertical plane. — When the 

 circle forming the secondary circuit was placed with its plane ver- 

 tical, anywhere in the neighborhood of the primary, the following re- 

 sults were obtained : 



The sparks disappeared for two positions of the air space, separated 

 by 180°, namely, those in which it lay in the horizontal plane through 

 the primary ; but in every other position sparks of greater or less length 

 were observed. 



From this it followed that the value of a must have been constantly 

 zero, and that 6 was zero when the air space was in the horizontal plane 

 through the primary. 



The electro-magnetic lines of force must therefore have been perpen- 

 dicular to this horizontal plane, and therefore consisted of circles with 

 their centers on the primary, while the electro-static lines of force must 

 have been entirely in the horizontal plane, and therefore this system of 

 lines of force consisted of curves lying in planes passing through the 

 primary. Both of these results arc in agreement with theory. 



