352 Mr. A. Schuster on the Diurnal Period 



taken on the earth's surface. In our latitudes we should 

 almost certainly find that it does vanish ; but the observations 

 of Sabine near the magnetic pole tend to show an appreciable 

 effect. 



It is, then, to circumpolar and equatorial observations that 

 we must look for an answer ; and as the point is of importance, 

 steps ought to be taken to settle it. Accurate and uniform ob- 

 servations over a limited area will be more valuable than less 

 uniform observations over a more extended area. Two or 

 three declination-magnetographs distributed over the northern 

 frontier of India, together with one additional vertical-force 

 instrument in Central India, would, I believe, w*hen taken 

 together with the Madras and Bombay observations, give 

 definite results in the course of one year, and the instruments 

 might then become available for other w r ork. 



The following calculation, however, seems to justify us in 

 neglecting^ until we have more definite information, the ver- 

 tical discharges through the earth. 



In the first place it is necessary to draw attention to the 

 fact that, as concerns the subject of discussion, everything 

 tHat holds for any set of observations taken over the earth's 

 surface at any particular time, must also be true of the average 

 values taken over a certain period of time ; and hence we may 

 deal with the averages which give us the daily variations 

 exactly in the same manner as we should deal with the whole 

 components of force at any particular time. All we assume 

 is, that no part of the mean magnetic force is due to vertical 

 currents crossing the earth's surface. 



Suppose the periodic forces on which the diurnal variation 

 depends to be expressed all over the earth in terms of longi- 

 tude, latitude, and the time of a given meridian. Observation 

 tells us, that all over a given circle of latitude we may take 

 the variation to be very nearly the same for a given local 

 time ; that is to say, we may write 



dX_dX dY = dY. 

 dt ~~ dX ' dt ~~ dX ' 



.where X and Y are the components of force towards the geo- 

 graphical north and w T est respectively, and X the longitude 

 measured towards the east. If u is the co-latitude, we have, 

 assuming the existence of a potential, 



d v . __ dX. _ dX. _ 

 du ~~ d\~ dt ' 



Y, considered as a function of the time, is nearly of the same 

 type at places differing widely in latitude ; and we may there- 



