DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
197 
Values of //. 
n ; <r = 
T — 1 
T 
T+l 
m-2 
m - 1 
(771 + 7) (771 + r - 1) (m + r - 2 _ 
(771+T) (771 + T-l) , 
771+ T 
2 (2771- 1) (2m +1) 77 
(2771 - 1) (2m +1) J ' 
771 + T 
2 (2m - 1) (2m + 1) Ty 
- T 
2?71 + 1 
m 
(?71 + T)(7?l-T+1) ( 
2 (771 2 - t 2 ) + (2m - 1) 
2r — 1 
2 (2771 - 1) (2771+ 3) '' 
(2771 - 1) (2771 + 3) J/ 
2(2?7i- l)(2m+3) Ty 
m + 1 
— 
(771-T + 1) t 
2m + 1 
—- 
771 + 2 
(771 - T + 2) (771 - T + 3) 
(771 - t + 1) (m - r + 2) 
(m-r+1) 
2 (2771+ 1) (2m+ 3) ; 
(2m+1) (27/1+ 3) 
2 (2m + 1) (2m + 2) ' 
1 
c/S 
The transformation of presents no difficulties. If S be expressed in 
its series according to (30) and the terms re-arranged, the result of the operation is of 
the form Vr/Q/, where r n a is made up of three parts. Independently of y and y', 
we have 
(ft + 2) (?l + cr + 1) 
2 ft + 3 
K 
71 +- 1 
(ft — l) (ft —cr) 
2ft— 1 
K - 
n -1 
(38). 
We have further, multiplied by y', 
ft + cr +1 (ft + 3) (?l + cr + 2) g. 
2ft+ 3 2 ft+5 
ft (ft —CT+ 1) 
2 ft 4-1 
+ 
ft —cr 
2 ft -1 
'(ft+1) (ft + cr) (ft —2) (ft —cr—1) ^ 
271+1 n - 2ft —3 
n—2 
■ (39), 
and finally, multiplied by y, 
(ft + cr + 1) (ft + cr + 2) 
2.2ft + 3 
(ft+ 3) (ft + cr + 3) <r+i_ ft (ft — cr) ,,+j 
2ft+ 5 ,i+2 2ft + 1 * 
(il — cr) (ft —cr — 1) 
~ 2 (271—1) 
' (ft+1) (ft + cr + 1) 
2ft+ 1 
K 
cr + 1 
(ft —2) (ft—cr—2) 
2ft—3 
Kn -2 
cr+1 
1 
2.2ft+3 
1 
+ 
(ft + 3) (ft + cr + l) ^ o—i _ ft (ft —o' + 2) o-i 
2 ft+5 n+2 2ft+1 
' (ft+1) (ft + cr-1) -t (ft-2)(ft-cr) o-i 
2 ft +1 ,l 2 ft -3 B 2 
. . (40). 
2 (2ft—1) 
By means of the values of k already tabulated, the factors r may be calculated. 
