LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
119 
the case, as many observations as possible should be made of the inclination on shore 
and on board, with corresponding - observations of the horizontal force. Such obser- 
vations should be made with great care when the vessel is on or near the magnetic 
equator and before and after any rapid change of magnetic latitude, and whenever the 
vessel returns to a place where the observations have been made before on board the 
same vessel, under the same circumstances as to the distribution of her iron. 
“When the permanent magnetism is symmetrically distributed, Q = 0 and M == 0, 
and the other constants maybe easily, and probably with great accuracy, determined 
from the following equations. The small letter suffixed to the symbol of a function 
indicating the affected value observed with the vessel’s head on the N., W., S., E. 
(affected) points, 
H» + Us (i5.) 
A — 2H V ’ 
Jl 
a tan 6 + = L 
IT - H s 
H„+H, 
+ H e 
2 TIT III 
d tan 6 + 
11 
A'H 
= N = 
H K tan + H s tan Q s 
H„+H s 
(16.) 
(170 
(18.) 
H„tan 8 n — H s tan S s n n , 
C— TT , T T 
"T~ “s 
“ The values of H„, H s , H e , H w , are given by the square of the number of vibrations 
of a horizontal needle made in a given time, and beginning to vibrate in a given arc, 
and require no correction except for temperature. 
“ If n, s, represent the number of vibrations made by such a needle in the same time, 
with the ship’s head successively on the north and south points, and if A represent the 
value of § when = +90, the values of L and A are given by the following simple 
expressions : — 
7 ) 
“ If tan A = — 3 
s 
L = cos 2 A, 
A = 90°— 2 A, 
The equations (18.) and (19.) may be put under the form 
R 
d tan 0 + Tpu = N = 
<p«cos0„ + <p s cos8 s 
<Pn sin 8n — sinfl, 
P«cos 9 n + <p s cos 0s 
( 20 .) 
( 21 .) 
( 22 .) 
(23.) 
and the values of N and c obtained, but probably with less accuracy, from observa- 
tions of the total intensity and inclinations made with a Fox’s instrument. 
“ Note . — The last equation in the former memorandum is erroneous. The value 
of 4 cannot be obtained from two observations of the true azimuth of the ship’s head, 
when ^i + ^2 — 180, independently of a.” 
