A.— MATHEMATICAL AND PHYSICAL SCIENCES. 23 



If, however, the charge be distributed uniformly throughout the earth 

 — and this is necessary for uniform intensity of magnetisation- — the value 

 of the horizontal field at the equator is Q<o/5r. It is, however, necessary 

 to explain that a field of this intensity would not be detected by an 

 observer moAang with and on the earth's surface, for in such case there 

 would be no relative motion between such an observer and part of the 

 electrostatic charge. However, a field will be detected. The translatory 

 motion of the charge would also produce a field, and to determine 

 the total effect, i.e. the effect of the earth's rotation on a magnet 

 situated on the surface of the earth, Schuster suggested a method some- 

 what as follows : Imagine the observer to be stationary in space, then 

 the earth, by virtue of the rotation of the charge, will produce a field 

 detectable by him. At the equator such a field will produce a horizontal 

 force, that is, a force parallel to the earth's surface, of the value Qco/5r, where 

 the charge Q is imiformly distributed throughout the volume of the sphere. 

 To produce a stationary effect, that is to make that portion of the earth's 

 surface near the observer have no relative motion with respect to him, 

 let the earth be subjected to a translatory motion equal to the velocity 

 of the part considered, but in the opposite direction. Such velocity is wr. 

 The translatory motion of the charge Q is equivalent to a current 



2r 

 t=Qcor/2r, since the charge Q takes the time — to pass a given point. 



The magnetic force produced by the moving charge will be circular in 

 shape and at right angles to the line of motion, and at the equator the 

 force parallel to the surface will be 



2r^ f * 



hence, the horizontal magnetic force detectable by an observer on the 

 earth's surface at the equator is 



5r r 5/ 15 



In this case the value of H is proportional to cor for a given volume 

 density, and hence a laboratory experiment would fail to detect such an 

 effect. 



If the charge on the earth be negative, the horizontal force at the 

 equator due to rotation is in the direction north to south, and the field 

 at the north pole is vertically upwards. By the translatory motion of the 

 earth a horizontal field at the equator in the direction south to north is 

 produced, and the field at the north pole has no component vertical to 

 the surface of the earth. The resultant field, therefore, is such that there 

 would be an upward vertical component at the north pole, and a south to 

 north horizontal field at the equator. A field of this type does not exist 

 in practice, the field of the earth being such that its direction is south 

 to north at the equator and vertically downwards at the north pole. 

 Moreover, it is not possible to produce by means of a single rotating charge, 

 fields of the correct sign both at the pole and the equator, for if we change 

 the sign of the charge the resultant fields at pole and equator are also 

 changed in sign. 



