EARTH'S MAGNETISM PRODUCED BY THE MOON AND SUN. 



303 



lunar term in the magnetic variation, Qa*, has a coefficient p' which does not (to the 

 order of accuracy of our calculations) show any dependence on solar declination. Thus 

 any seasonal change in this term of the magnetic potential cannot be referred to the 

 effect of the varying declination of the sun. This is not quite the case with regard 

 to the main diurnal term in the solar diurnal magnetic variation. 



24. We will now consider what are likely values of p,/p and p.Jp a to substitute in 

 our formuLe, in order to get a comparison with the observed data. The conductivity 

 should rise to a maximum during the daytime and fall to a minimum about midnight. 

 It cannot actually be less than zero, though it is not so clear that it is better to have 

 the least value of p zero than to have it slightly less, in order to make the mean 

 nightly conductivity small in amount. However, we will keep to this condition, and 

 make p mln . = ; it is found that the following is a very satisfactory expression for the 



representation of a function of 6 which is large for values of 6 up to -, and much 



2i 



smaller, while never negative, from 6 = to -IT : 



The following table and figure gives the value of 4p/p for every 10. It is seen 

 that the mean of the nine day values is '24' 1 times that of the nine night values. 

 The function has a physically false maximum at midnight, but this is of very small 

 amount, and some such feature cannot be avoided with so simple an expression 

 for p : 



* I might remark here that in working out Part II. of this paper I had not contemplated the possibility 

 of the coefficients of p/p being greater than unity, as seems to be necessary if the atmospheric conductivity 

 is small and nearly constant at night. The size of these coefficients makes it necessary to carry the 

 calculations some steps further than I have already done, before a sufficient degree of approximation is 

 arrived at. The present work suffices, however, to establish the point with which I am most immediately 

 concerned, viz., that the size of the fourth harmonic in the lunar variation is inexplicable with the form 

 a + fccosw for p, while the addition of a term ccos 3 ui introduces a fourth harmonic in the theoretical 

 result, which agrees, as to order of magnitude, with the observed quantity. Better olwerved data are now 

 lifing obtained, and concurrently I shall proceed to carry the theoretical calculations further, in order to 

 test the exact numerical agreement between theory and observation. June 11, 1913. 



