164 MESSES. SMITH AND EVANS ON THE EEEECT OE THE LENGTH OE 
The Admiralty Standard compass card, it may be observed, is constructed with 
parallel needles, placed as chords of the circular rim of the card, and so arranged that 
the moment of inertia of the card about every diameter is the same, the object of this 
arrangement being to prevent the “wabbling” motion of a card of which the moments 
of inertia are unequal. It was long ago observed by Mr. Smith, that for this purpose, 
with two uniform needles, it is necessary and sufficient that the ends of the needles 
should be separated by 60° of arc. The object is therefore obtained with tivo uniform 
needles, the extremities of which are 30° measured along the circumference of the card, 
from the extremities of the diameter which is parallel to them, and which needles are 
therefore chords of 60°, or with four uniform needles placed two and two with their 
extremities at equal distances on each side of the chords of 60°. The last is the arrange- 
ment adopted in the Admu’alty Standard compass, the distances of the extremities of 
the needle being 15° on each side of the chords of 60°, so that the extremities of the 
needle are placed at 15° and 45° on each side of the extremities of the parallel diameter. 
The importance of this arrangement with reference to the present question Avill be seen 
hereafter. 
The details of Mr. Evans’s experiments are given in the Table in Appendix II. 
The peculiarities of the several Tables of observations are most conveniently discussed 
by representing the deviations graphically by means of a curve, according to the method 
known as Napiee’s method, and mathematically by means of the formula 
a=A+Bsin ^'+Ccos sin 2^'+E cos 2^' 
+F sin 3^'+G cos 3^'+H sin 4^'+K cos 4^'+&c., 
in which, as before, S represents the deviation, the azimuth of the line corresponding 
in the experiments to the fore-and-aft line in a ship. 
The curves which accompany this paper have been drawn in this way from the actual 
observations made with the magnet and cylinders of soft iron in the same horizontal 
plane with the needle. It has not been thought necessary to lay down the cmTes 
representing the observations with the elevated compass, but their peculiarities mil be 
described. 
From the curves the values of the deviations on each of the thirty-two points, reckoned 
from the disturbed direction of the needle, have been obtained by measurement, and 
the values of the coefficients A, B, C, D, E, F, G, H, K computed by the method of 
least squares by the formulae given in part in the Philosophical Transactions for 1846, 
p. 350, and more conveniently in the “ Supplement to the Practical Eules for ascertain- 
ing the Deviations of the Compass which are caused by the Ship’s Iron,” published by 
order of the Lords Commissioners of the Admiralty (London, Pottee, 1855). 
The following are the values of the coefficients so obtained ; — 
