149 
The last correction is therefore rather less than the former. 
There is, therefore, a slight positive advantage in working 
with the needle centered at e = — , over Dr. Joule’s method, 
Jj 
even at the special angle a=tan -1 J, and in addition the first 
term of the correction disappears for all angles of deviation 
instead of for one only. 
The accuracy of the formula quoted above turns on the 
circuit being complete (as it never is), on its being accurately 
circular, in the vertical meridian plane, and on the r being 
a definite quantity. If the thickness of the coil be com- 
parable to the magnitudes r and l used, a much more 
complicated formula would replace that given above. 
The instrument in which the needle pivot is at e ~ ^ pos- 
sesses this advantage, that we may arrange a considerable 
number of coils for which this is true, parallel to each other, 
T 
along the smooth surface of a cone whose axis is ^ and whose 
base has the radius r. It is to be observed, however, that 
though the second term in the value for i given by each 
separate parallel coil disappears, the first term 
tan a-j? -£=- becomes tan a -5- -- ^ r 
% r r 2 2tt 8 
and therefore for one same current circulating through 
several coils, for each of which there is a different radius, 
there will not be accurately one same amount of devia- 
tion produced by each. Accordingly, the current through 
two coils has not accurately the effect of a current of 
double intensity, and has only that effect approximately, so 
long as the r of the parallel coils is very nearly the same. 
In fact, no multiplying instruments can approach the 
accuracy of the ordinary circular single meridian coil with 
the needle in the centre, when it is worked at a=tan _1 J, 
(Joule’s arrangement), or of the circular single meridian 
