378 
LIEUT.-GENERAL SABINE ON TERRESTRIAL MAGNETISM. 
M=+^A'{c— a-|-(c+a) cos 23}, 
N=-£A'^sm23. 
Also 
<P 2 =^M -f+z 2 , 
(phcf>= xhx -\-yty 4- z6z, 
cos 2 3 cos £4-^ sin £ J 4- sin 2 3 j 
=P4-Q cos £+R cos 2£, 
where 
P= + JA' cos 2<l ’ 
Q = 4- -2 A' (c-\-a) sin 2 0, 
R= 4-1 A' — g— (1+cos 20). 
If we suppose 3,, <p,, L,, M,, P 15 Q,, R, to be values of 3, <f>, L, &c. at a base-station, 
then at any other station at which the dip is 0, we have 
L=- 
\ sin 20, 
Qi 
M=M,— Q, cot 23,4- sm 2 g cos 20 
N =4k sin2< - 
L i 
P=P,4-Li cot 3 , — —^r cos 23, 
111 1 sm20, ’ 
Q= 
R= 
Qi 
sin 20/ 
rj AL_( 1+cos2 S). 
It will be observed that P, Q, R are abstract numbers, while L, M, N are angles the 
numerical values of which depend on the assumed unit of angle. The values just given 
may be used without modification if the angular unit be the angle subtended by the 
arc=radius, or 57 0, 3. If the unit of angle be, say V, then in the expression for M we 
must divide Q, by sin 1', and in the expression for P we must multiply L, by sin 1'. 
As a check on the values of N and R, we may observe that we ought to have 
-^=+ri$bs =+ * A ' i(1 -* ) 
= 
in the notation of the Admiralty Manual ; 
And that if we have the value of |A'i|-(l — b ), or determined independently from 
