58 
MR. AIRY ON THE OBSERVED DEVIATIONS OF THE COMPASS 
Use the notation of the paper of 1839, as far as it goes, and use also the following 
notation : — 
In fig. 1, let CA represent the terrestrial horizontal force multiplied by (1 — M), M 
being a constant peculiar to each ship. 
fjtj the modulus, or the proportion of AB to CA. It will be remarked that SP in 
fig. 3 is the representative of AB in fig. 1. 
a the angle QSP, fig. 3, or the starboard angle made by the compound polar- 
magnet-force with the ship’s keel. 
A the true eastern azimuth of the ship’s head. 
A' the eastern azimuth of the ship’s head as referred to the needle disturbed by 
polar-magnet-force only. 
A" the eastern azimuth of the ship’s head as referred to the needle disturbed by 
polar-magnet-force and quadrantal force. 
I Ct 'I 
^ I the corresponding azimuths of the compound polar-magnet-force. A+a is 
A"-j- same as the angle BAD in fig. 1 . 
A' the compass- deviation to the east produced by polar-magnet-force only —A— A' 
= ( A -j- a) — ( A' -}- a) . 
A" the additional deviation produced by the quadrantal force =A'— A"=(A'-l-a) 
-(A"+«). 
And the following double equation is accurate : — 
sin A' 
=sin A'-j-a=- 
sin K+a 
I H- 2j«. cos A-|-«4 -/x^} 
Then, neglecting MP only, the formulae in the paper of 1839 give- 
Whole force to north =I.cosB.(l— M).(l+iM'*cos A-l-c44-P-cos2A) 
Whole force to east =I.cosB.(I— M).((M-.sin A-l-a+P.sin2A). 
Therefore 
tanA'-h A"=y 
]u,.sin A-)-« + P.sin 2 A 
-f-ft.cos A + ct-fP.cos 2A 
But 
tan A' 
j«..sinA-f« 
I -f-j«,.cosA-fa 
Therefore, retaining the complete multiplier of the first power of P, but no higher 
powers of P, 
tan A" = P-s^^^^A-ff^P.sinA— « ^ 
I -f 2/x . cos A a + 
This quantity, however, is not that which we shall have occasion to use, for the 
following reason. The polar-magnet-deviation which we shall take out from the 
Table is taken for an argument which, is referred to the position of the compass- 
needle as disturbed hy all causes ; it is therefore taken out, not for argument 
A'-f-« (which would give us A exactly), but for argument A"-|-a. Let the quantity 
