12 Prof. W. A. Norton on Terrestrial Magnetism. 
B to r it can happen that 9 will be increased and 9 diminished, 
and therefore that sin") sin"d’, in formula (4), can remain the 
same. Now Bs=Br cos rBs, or d5’=k cos a’; and Bt=Br cos 
dd cosa ‘ 
rBt, or d}=k cos a. Hence F dea and, by equation (5), 
neglecting the minus sign; putting also w=angle A’BD, 
sin 0 cos 6’ cos @ COs a 
cos d sin 0” cos a’ cos (u—a@)’ 
or, 
sin bcos cos a Leer jennie 
cos dsin 0’ cos ucosa+ sinu sina cos u+ sin wu tana 
sin 9’ cos 9 — sin 6 cos 5 cos u 
* sin 0 cos 0’ sin u 
cot 6 tan 0” 
sin u 
If we put 8=ABA’ uw=180 — 6, and 
cot 9 tan 3 
anf cot 8.3%, j é (G75 
This formula gives the angle DBL. Subtracting this from 90° 
_we obtain »BA, the angle included between the direction of the 
needle and BA(*). he difference between this and ABC w 
be the declination of the needle, which will be east or west, 
according as one or the other of these angles is the greater. 
The first of the equations above gives the following, which 
may be used as a tentative formula in place of equation (6):— 
(7.) 
To make use of formula (6) we must know 4, 0’, and # 
These se Age obtained by solving the two spherical triangles 
B. The latitude and longitude of the place }, 
Whence, tan a 
? 
or, tan a= —cot u. 
tan a= 
tangent of the dip. ihe 
These formule I have compared with a large number of ob- 
(To be continued.) 
