92 REPORT—1862. 
axes of the ellipse give the amount of the fore-and-aft transverse inductive 
forces which give rise to the quadrantal deviation. An ellipse so drawn, 
therefore, gives to the eye, at a glance, the whole magnetic character of the 
ship as regards deviation on an even keel. 
If the mean directive force of the needle is not altered, the ellipse be- 
comes a circle, the coordinates of the centre of which are 3% and €, and the 
radius 39, on the scale in which the mean force to north represents unity. 
If we haye no observations of horizontal force, the circle is all we can draw ; 
it gives all the information to be derived from the ellipse, except the diminu- 
tion of the directive force. For the complete representation of the deviation 
and force, it is convenient to have both the circle and the ellipse drawn. 
In the diagrams the direction and force of the earth’s magnetism as the 
ship is on different azimuths are represented by the radius of a circle, of 
which the compass is centre, and which is divided in thé reverse order of 
the compass-card. A line drawn from a point in the circle to the correspond- 
ing point in the ellipse or small circle represents, on the common principle of 
the parallelogram of forces, the direction and amount of the force on the 
needle*. A modification of this diagram is described at p. 96 of the ‘Manual’ 
under the name of ‘ dygogram ” (dynamo-gonio-gram), applied to it from its 
showing the force as well as the angle of deviation of the needle. 
The principle of its construction is the following. If we draw a vertical 
line representing the magnetic meridian, and from a given point in it draw 
lines representing in length and direction the directive force and direction of 
the needle for each azimuth of the ship’s head, the extremities of such lines 
will trace out an epicycloid which is very easily constructed by points when the 
coefficients G, 33, €, 3B, E are determined. The method is applied in plate 2 
to the deviations of the standard compass of the ‘ Warrior,’ and has been 
applied by us to many other ships, and has been found a most efficient aid in 
discussing the observed deviations. 
We now come to what we consider the proper subject of this Report, 
viz., the practical results as to the deviations of the compass which have 
been deduced from actual observation on board ship; and the works to which 
we shall principally confine our attention are the following :— 
« Account of Experiments on Iron-built Ships, instituted for the purpose of 
* A practical application of the diagram to the correction of the compass was suggested 
by its being accidentally held to the light and looked at from behind. When this is done, 
it will be seen that the large circle is divided in the same way as the compass-card. Tf, 
then, the radius of the large circle represent the direction of the disturbed compass-needle, 
the line joining the corresponding points in the large circle and on the ellipse or small 
circle will represent the direction of the magnetic meridian. 
By therefore drawing on an ordinary compass-card a circle of which the coordinates of 
the centre are —33 and +, and the additional coordinates of the north point —3B, and 
dividing the small circle in the reverse order, we get the following rule for the correction of 
the compass :— 
‘Take the given course on the card, and also on the small circle, and suppose a straight 
line drawn through these. Then keep the ship’s head in the direction of the line, disre- 
garding, of course, the lubber-line.” 
+ If X be the force to north in terms of the mean force to north, Y the force to east, 
then X and Y representing rectangular coordinates, 
X=1+% cos 7—€ sin €+ 3B cos 2 7—G sin 2%, 
Y=4+3 sin + € cos 7+3B sin 2 + & cos 2 Z, 
which is the equation to an epicycloid traced out by a point 4/3524 @ from the centre ot 
a circle whose radius is 4/3324 @?, and which rolls on a circle of equal size, and the co- 
ordinates of the centre of which are X=1, Y=@. 
