58 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
theoretical equinoctial amplitudes of the magnetic variations are obtained.* The 
ratios of these to the observed values of Table J are also given. 
Table Q. 
Qd- 
Qd. 
Qd. 
Qo 4 . 
Theoretical relative amplitudes . . 
25 • 3k 
6'5 k 
0 • 6 ok 
0•0217 
Calculated 
1-0 
1-0 
1*3 
0-8 
Observed 
The relative amplitudes of all four components now show very fair agreement. 
Clearly (72) is a great improvement on (7l) as a representation of the law of 
variation of the electrical conductivity. Probably the true law is more complicated 
than (72), but we shall not trouble to seek for a closer approximation. The 
point gained is that, by taking a law which gives a general representation of the 
variation known to be probable on other physical grounds, we have been able to 
explain the presence and order of magnitude of magnetic variations of periods other 
than that of the primary atmospheric semi-diurnal oscillation. 
The calculated amplitudes of the variations arising from yxr 1 , and so on, 
comparable with those in Table Q, are found to be 
Q,2 _1 . Qs~ 2 . Q,4- 3 . Qo- 4 . 
(74) -4'4 0’8 0 0 
In the case of the lunar diurnal magnetic variations, however, these change their 
phases with great rapidity, and are not included in the “ observed ” amplitudes given 
in Table J. 
We may proceed further to examine the seasonal changes in the relative 
amplitudes of the various components. The numbers in Table Q relate to the 
equinoctial variations, and are obtained by taking S to be zero in Table O. During 
the solstitial quarters, however, S is approximately 20 degrees. If this value is 
substituted, the following numbers, corresponding to those in Table Q, are 
obtained :— 
Qd. Qs 2 - Qd. Qd 4 . 
(75) 24‘0 6‘5 0'61 Q’018 
* The numbers given are 60 {(m+ l)/(2 m+ 1)} p m n (R/r) m , the factor 60 being inserted for convenience. 
The factor (R/r) m allows for the fact that the magnetic variations are produced at some considerable height 
above the surface regions where observations are made; R/r is taken as O'98 (rf. §§ 21, 22). 
Formulae resembling those of Table O were given in my first memoir, but only carried as far as afi 2 and 
cio; in this paper some small corrections are made, and a further approximation is made by including the 
terms a i 3 , aia 2 , «d, a{ 2 a- 2 , and a 2 ' 2 . With the above values of r.i\ and « 2 the results seem to show satisfactory 
numerical convergence. 
