170 Mr. A. Campbell on the Use of 
the maximum M. The curves also show that the value of q 
for which M vanishes and changes sign becomes greater and 
greater as the mean planes of the coils are set at greater 
distance from one another. The ratio of A/a has been madu 
2 in this example, as that is a suitable proportion for use in a 
practical instrument. Having now the curves connecting M 
with q, the distance between the axes of the two coils, it is 
easy to investigate the variety of angular scales obtainable 
by turning one of the coils round an axis parallel to its own 
axis. 
Let a definite value of b be taken, say 6 = 5, which is 
convenient in practice, and in fig. 14 let the smaller coil be 
movable about an axis perpendicular to the plane of the 
paper at Z, and let the radius ZQ = p. Let the distance ZO' 
of the axis Z from 0' (the point where the axis of the other 
coil cuts the plane of the paper) be h. Let the angular scale 
reading YZQ = c/>. 
Then by choosing various values for p and h we can get a 
wide variety of movement of the centre Q (of the movable 
coil) relatively to 0', and hence a variety of scale calibra- 
tions. Since cos </>=- — ^ , the angle <£ corresponding 
to a reading M can be got from q, /*, and p. The scale can 
be most easily set off by the following geometrical construc- 
tion. Draw a circle with centre Z and radius p, and make 
ZO' equal to h. Then find on the {b = 5) curve in fig. 13 
the q corresponding to a particular value of M. With this 
value of q as radius, a circle with centre 0' will cut the 
circle X at the point of the scale required. By taking suc- 
cessive values of M the direct-reading scale can be set off 
round the circumference of the circle X. 
