EARTH'S MACNF.TISM PRODUCED BY THE MOON AND SUN. 301 



As this paper is primarily concerned with the lunar diurnal variation of the earth's 

 magnetism, the numerical values of the coefficients p n * arising from expression (2) 

 owing to the inclination of the magnetic to the geographical axis will not be written 

 down here. This can at once be done, when necessary, from the equations (5), as 

 also the terms in the current potential arising from diurnal and semi-diurnal 

 atmospheric oscillations of degree higher than the type. 



21. The main general result of our investigation is the same in form as that of 

 SCHUSTER'S more special calculations, viz., that the current function R of electric flow 

 induced under the action of the vertical force C cos 6 in a shell of air oscillating with 

 a velocity potential A m T Q m T sin (r. \ + t a), under the influence of a variable resistivity 

 depending on the zenith distance () of the sun, is 



(6) A M T [ 2 p/Q/sin {<r(X + t)-a}+ 2 g.'Q.' sin {<r(\ + *) 



9=0 V= 1 



In order to obtain the magnetic potential of the variation caused by the flow of air, 

 a factor 4ir(/t+l)/(2n+l) must be inserted before each term Q,'. 



We have considered only those terms in the resistivity which depend on cos u> and 

 cos* u>, though the general theory has been given for any numl)er of terms. If then 



cos w+dj cos* u>), 

 we have for the conductivity p, to the same degree of approximation, 



If we put 



Caed *"" d p ' c 



this becomes 



p = p + p l COS o> + p a COS 2 w. 



In SCHUSTER'S calculation, the last term was omitted, so that p, was taken equal to 

 zero, while p, cos $ and p, sin S were written p 9 v and p v respectively. If we make 

 these substitutions in Tables I. and II., it is readily verified that the present results, 

 as far as they go, reduce to those obtained by SCHUSTER. The extra terms depending 



on d 3 -j- give the effect of the term cos a <a in p. 

 d Q 



22. Finally, a word must be said with regard to the legitimacy of our analysis, 

 considering the fact that if p falls to zero, K', the resistivity, must become infinite. 

 Regarding the matter physically, it is evident that an infinite resistivity is not likely 

 to introduce spurious terms into the current potential, and an examination of the 

 equation (l) for R will show that an actual infinity in K would only lead to a 

 /.fro term in R. But such an infinite term should not occur in the analysis, and it 



