LIEUT.-COLONEL SABINE ON TERRESTRIAL MAGNETISM. 
149 
values calculated in the manner described above. A table of the affected dip, and of 
the dip corrections on each course, may then be calculated from (14.), or more easily 
from (12.) and (13.) ; observing that (12.) must not be used when the ship’s course 
is nearly north or south, and that (13.) must not be used when the ship’s course is 
nearly east or west, and that the values of £ should be tabular, not observed. 
“ The constants may also be determined from observations of the total intensity, 
by means of the first four equations, and tables for the correction of the observed 
intensities may be constructed by means of these equations. For this purpose, equa- 
tion (3.) should be used when the dip is large, and the others when the dip is small. 
“ The values of a and b may be determined very readily, and probably with great 
accuracy, from observations of the horizontal intensity with the ship’s head on the four 
principal compass courses. For if H w , H w , H s , H e represent the values so observed, then 
a tan 6 = 
b = 
H„ — H s 
H» + H,’ 
+ H e 
2 \/H w H s 
(15.) 
(16.) 
“ If observations are made at equal intervals of time with the ship’s head success- 
ively on the N., W., S., E., and N. points, the values of a and b thus determined will 
be independent of any regular increase or diminution of the intensity. If n, w, s, e re- 
present the number of vibrations in equal times, on the four principal courses, of the 
same horizontal needle, beginning to vibrate in the same arc, and corrected for tem- 
perature alone, 
7$ — S' ^ 
atan ^ == ^+V 2 ’ C 1 ?-) 
w 2 + e 2 
2 ns 
(18.) 
“ The true declination may be found independently of the dip and of the constant 
a, by means of observations of the true azimuth of the ship’s head on two courses. 
Let \]y represent the declination, which is considered positive when the north end of 
the needle is to the west of the true north, u the true azimuth of the ship’s head, 
which is positive when the ship’s head is to the west of the true north ; so that 
£ = a — 4'- And let & and -2, & represent the observed values of u and on the 
two courses, 
tan (4, - + gj> 
2 sin f'j sin $' 2 — b sin (g l 1 — $' 2 ) cot M>1 - 
“ If the observations are made with the ship’s head on exactly opposite courses, 
aj 1 — m 2 = 1 80° ; and we have 
tan (&>! — 4) — 
2 sin £'j sin £' 2 
b sin + sy ; 
x 2 
