60 
MR. AIRY ON THE OBSERVED DEVIATIONS OF THE COMPASS 
Expanding the last term, this quantity becomes, after all reductions, 
P.sin 2 sin 3A"H-a— ^ sin A"+3a^ . 
It will scarcely be necessary to tabulate the small terms ; an estimate of their general 
effect can very well be formed in the mind. 
The entire process will therefore be the following : — 
1. For the nautical terms N., N.b.E., N.N.E., &c., use the numeral reckoning of 
points 0, 1, 2, &c., as far as 31, which will correspond to N.b.W. And for deviation E 
and deviation W, use the algebraical signs deviation + and deviation — . It will 
always be convenient to place the + deviations and the — deviations in separate 
columns. 
2. Clear the deviations of constant error by adding together all the + deviations, 
adding together all the — deviations, combining them algebraically, taking the mean 
of the sum, and applying this mean with sign changed to every deviation. The 
deviations thus corrected will he the base of all the following operations. 
3. In writing down, in columns, the corrected deviations, repeat those from 0 to 15 
points, in sequence to those from 0 to 31 points ; so that the Table contains forty-eight 
lines, 
4. A conjecture will easily be formed as to the approximate value of the azimuth 
for the “ neutral position and then two or three neighbouring half-points are to be 
adopted for trial. Thus, if the azimuth for neutral position appears to be near 
3 P or 4P, the positions to be tried may be 2P'5, 3P'5, 4P‘5. 
5. The trial of these azimuths will be effected by dividing the series of observed 
deviations, not at these azimuths, but at azimuths distant from them 8 points on each 
side. Thus, to make trial of the assumption 2P’3, the observed deviations are to be 
divided at 26P'5 and 10P‘5. And the criterion will be given by adding algebraically 
all the deviations from 27^ to IQP, both included ; a little accuracy will be gained if 
we also add in a separate sum all the deviations from IIP to 26P, both included, and 
subtract this sum from the former. It will be remarked that the quadrantal devia- 
tion is here eliminated. 
6. If our assumption 2P‘5 for the neutral position were strictly correct, the sum or 
difference of sums found in the manner just stated would =0. As this usually will 
not prove to be true, we must try the next assumption 3 p- 5 in like manner. The 
comparison of the sums or differences of sums will give the correction to be applied 
to 2P’5 with very great accuracy. The azimuth thus determined is strictly an 
‘‘approximate neutral position,” and its supplement to 32 p is the “approximate 
starboard angle.” 
7. The approximate neutral position being thus determined, the observed deviations 
are to be divided into two groups, one division being at the interval in which the 
neutral position falls, the other at the interval distant from it by 16 p. The algebraic 
