VARIATION OP TERRESTRIAL MAGNETISM. 
517 
whence 
_ (^ + cosh ^ — (6^~^ + 15^“^) sinli ^ 
5.7 Xi(0 cosh ? — shill f 
Here 
^ = (78)^ = (1 + 7) SVv/2 = (1 + 7) say. 
If is moderately large we may put cosh 1/ sinh ^ = 1 approximately. The error 
thus committed is of the order e~^^. Since the value of has six cyjihers after the 
decimal point, this approximation is amply sufficient for ^ > 7, or say for 8 > 100. 
The above fraction is then 
1 - 6^-1 + 15 ^^ - _ (1 - 3 / 3-1 +-h^/ 3 -g) 4. ^(3y3-i _ 
1-r' ~ (l-i/3-i) + ^.i/3-i 
It is by these methods that Tables XX. and XXI. above were calculated. The 
values of p, the specific conductivity, given in the fifth columns, were obtained from 
the formula 
by putting 
p =: 
27rlv = 4T0^ cm,, ‘^Trjp = 86,400/'«r secs., 
where m denotes the number of complete periods in a day, and is therefore = 1 for 
the diurnal and = 2 for the semidiurnal variations. 
As the resistance diminishes, the difference of phase tends to zero, and the ratio 
of normal forces to the value — 1 ; i.e., the total normal force at the surface tends to 
zero, in accordance with the theory of electromagnetic screens. 
The ratio of the total vertical to the total horizontal force in any assigned 
direction is 
— — 
dr 
where denotes a linear element drawn in the proper direction on the Earth’s 
surface. By means of the preceding results this can be put in the form 
_ ~r 1) ^ _ / dll,; 
+ (% + l)y„(7'R) 7 dT^ ' 
The coefficient may be calculated independently, by a proper adaptation of the 
previous methods, or we may deduce its value from the results already obtained, in 
