350 Mr. A. Schuster on the Diurnal Period 



force remains continuous, but that tangential component 

 which is at right angles to the current suffers a discontinuity 

 depending 011 the intensity of the current. For a spherical 

 current sheet these components will always be of opposite 

 sign on the two sides. If we then find the distribution of 

 magnetic potential on the surface of the earth from the hori- 

 zontal components only, we should get by calculation a vertical 

 component of different sign, according as the cause is inside 

 or outside. A comparison with the observed values will at 

 once decide the question. A more careful analysis is neces- 

 sary if the causes are partly outside and partly inside, and we 

 wish to determine their relative importance. 



I believe that few practical magneticians at the present day 

 read Gauss's memoir, ' On the General Theory of Terrestrial 

 Magnetism'"*; and the loss which cosmical physics has suffered 

 in consequence is, as far as our generation is concerned, quite 

 irretrievable. The memoir is a model of scientific reasoning 

 and full of suggestions, which are as valuable now as they were 

 fifty years ago. The investigations of Gauss are founded on the 

 assumption of a magnetic potential on the surface of the earth ; 

 and he deduces from this assumption the theorem, now well 

 known, that if on every place of the earth we know the compo- 

 nent of magnetic force tending towards the west, we can deter- 

 mine from that component the direction and magnitude of total 

 horizontal force, leaving only a quantity undetermined which 

 may depend on the latitude, but which cannot depend on the 

 longitude, and which therefore is easily found. It appears on 

 investigation that the quantity in question, if it has a diurnal 

 variation at all, must vary on each circle of latitude with the 

 solar time of some particular meridian, and not with local 

 time. There can only be a very small fraction of the observed 

 diurnal variation changing in this fashion. We may then say 

 that, assuming the variation of the westerly component of 

 magnetic force to be known over the surface of the earth, the 

 knowledge of the northerly component will follow. This is of 

 importance, considering the ease with which changes in de- 

 clination are observed compared to change of horizontal force. 

 Nevertheless changes of horizontal force ought to be observed 

 wherever possible, as the two records at any one station will 

 be equivalent to the record of declination only, at two stations. 



Moreover, we cannot assume without proof that the mag- 

 netic changes of diurnal variation are subject to the existence 

 of a potential. If there is any actual discharge through the 

 earth's surface it will not be the case ; and if there is only a 

 variation of electric charge it would be equivalent to an 

 electric current. 



[ * See Taylor's Scientific Memoirs, vol. ii. pp. 184, 313.] 



