the Ecu tli s Magnetic Field. 91 



bo that due to placing it in a uniform electric field with 

 polarization F. Now imagine a large charged plate, giving 

 a polarization perpendicular to its surface, of" amount F. 

 Imagine a compass-needle to be placed in this field, and 

 suppose that the two are set in uniform motion, in the 

 direction parallel to the plane of the plate with velocity equal 

 to (oa. "We know that there would be no effect on the compass- 

 needle, so that we can conclude that the magnetic field H', 

 produced by the motion of the induced charge on the compass- 

 needle, is just equal and opposite to the magnetic field 

 AirwaF produced by the motion of the plate. Thus we see 

 that the resultant field acting on a compass-needle on the 

 earth's surface is, at the equator 



H 1 = H-H'= p7r/30)a 2 -47ra>aF. 



Since, neglecting a very small term of the order v 2 /C 2 , 





4 <r 

 6 Of 

 we have 



tj 1°* 2 



i± 1 = — — irpwa 1 . 



The counteracting field due to the motion of the compass- 

 needle thus alters the sign of the charge which we should 

 otherwise have to attribute to the volume elements of the 

 earth in order to account for its magnetic field, the necessary 

 charge being a positive one*. The theory makes the equatorial 

 horizontal field at the surface proportional to wa 2 , for a given 

 volume density, so that the field attainable by the rotation of 

 a sphere in the laboratory would be far too small to detect. 

 Again,, the field corresponding to the rotation of the sun 

 would amount at its equator to 200 C.G.S. units, which is too 

 small to detect by the Zeeman effect. The order of magnitude 



* [Note added May 8th, 1912.] "While the present paper was in process 

 of publication, Prof. Schuster's address to the Physical Society appeared 

 in printed form. In that address, the problem here discussed is treated, 

 and it is further pointed out, that the theory gives the wrong sign for 

 the vertical component. This may leadily be seen on the line of argu- 

 ment here adopted, when we realize that the motion of the magnetic 

 needle cannot affect the observed value of the vertical component, so that 

 the charge necessary to account for this component is a negative one. 

 The difficulty in this respect vanishes in the modified form of the theory 

 discussed next, in which the volume charge is balanced, as far a» its 

 electrostatic effects are concerned, by an equal surface charge. Similar 

 remarks apply to the theory on page 93. 



