TKANSACTIONS OF SECTION A. 571 



2. A Suggested Explanation of the Secular Variation of Terrestrial 

 Jfagnetiam. Bij Arthur Schuster, F.R.S. 



It is a matter of great importance to ascertain whether we must consider inter- 

 planetary space to be a conductor of electricity or not. If there is an appreciable 

 conductivity the magnetic system of the earth will, owing to its rotation, induce 

 currents which will react on the earth iu a twofold manner. There will be, in 

 the first place, a mechanical etlect tending to increase the length of the day, and, 

 secondly, a magnetic effect tending to displace the mngnetic axis. It is the object 

 of this communication to give tlie results of some numerical calculations referring 

 to the magnitude and nature of these reactions. 



The problem is of interest apart from any applications to terrestrial magnetism, 

 (liven a magnetic sphere rotating in a conducting medium, what are the mechani- 

 cal and magnetic forces acthig on the sphere ia consequence of electric currents 

 induced in tlie medium? 



The mathematical solution is easily obtained from Lamb's equations for currents 

 induced in spherical conductors; and, without entering into any details of calcula- 

 tion, I here state the principal results for the case when the sphere is uniformly 

 magnetised about an axis not coinciding with the axis of rotation. 



If the medium is either perfectly conducting or perfectly non-conducting, there 

 will be no mechanical etfect tending to stop the rotation of the sphere ; but for all 

 finite conductivities there will be a couple opposing the rotation which is a maxi- 

 mum for a certain specific resistance of the medium. 



If the radius of the sphere is II, the angular velocity co, the specific resistance p 

 producing the maximum retardation is given by the relation 



p — 1'4 R-o), 



where the numerical factor is approximate only. 

 For the earth : R = 6-4 x I0« ; w - 7-27 x 10-= 



p = 4-17 X 10". 



The resistance indicated by this number is such that if 4*17 volts were applied to 

 the two sides of a plate having a thickness of one centimetre there would be a cur- 

 rent of 10^* amperes per square centimetre. I do not know of any facts which 

 would make such a conductivity an impossible one, consistently with the extreme 

 tenuity of matter which we know must exist in space. The next point to consider 

 is the actual value of the maxioaum retarding couple. In C.G.S. units, and for a 

 sphere having the same size and magnetic moment of the earth, it is I'O x 10-*. If 

 this couple was to act continuously it would diminish the earth's rotational velo- 

 city to the extent of one second per day in 14,000 years. Early records of solar 

 eclipses show that the earth as a timekeeper has lost time, but authorities do not 

 agree as to how much. Two causes tending to alter the length of the day have 

 hitherto been considered, tidal friction tending to retard it and the contraction of 

 the earth tending to increase it. To this we must now add a possible retardation 

 due to the conductivity of the medium. 



The maximum magnetic couple calculated above is about six times that given 

 by George Darwin for the eflect of tidal friction, and it would by itself have pro- 

 duced a very marked effect in historical times, and according to Lord Kelvin 

 the effects of the earth's contraction are very small. It is, of course, very impro- 

 bable that the conductivity of space is just that required for the maximum effect. 

 If the conductivity is 100 times less, the couple produced would be equal to the 

 tenth part of the maximum couple, and such a couple would be impossible to 

 separate at present from the other effects, tending to alter the length of the day. 

 There is, therefore, a very large range of electric conductivity, within which that 

 of space may lie without an appreciable effect on the length of the day being pro- 

 duced in historical times. 



Turning our attention next to the magnetic reactions, we find that these will 

 displace the magnetic axis towards the geographical pole and round it from east to 

 west. If the earth behaved like a steel sphere, not subjected to any shocks or 



