426 ME. DUGALD M‘KICHAN ON THE DETERMINATION OF THE NUMBER 
The position of the coil with reference to the table was noted by marking on the table 
the position of the front and of the back of the stand. 
The coil was then transferred to the other side of the magnet, and a similar observa- 
tion made. The distance between the two positions of the coil was found to be 42-221 
centims. Accordingly 21 T1 centims. was taken as the distance of the centre of the 
smaller coil from the magnet in each observation. The distance between the centres of 
the large coils, measured directly, was 13T48 centims. ; so that the distance of the centre 
of each from the magnet was 65-74 centims. 
Calling these distances a and b respectively, we have, for zero deflection, the following 
equation : — 
27 r/ir 2 -p, 2rn , r 1 ' 2 2z7tc 2 
(?’ 2 + A 2 )^ (r ,2 + Z> 2 )^ (c 2 -fa 2 )^ 
This is a cubic equation in c 2 , and the solution of it would yield c 1 in terms of the known 
quantities n, n\ r, r', a, b, &c. Two of the roots of this equation are imaginary, the 
coefficient of c 2 , when the equation is reduced to the typical form, x 1 -{-qx-{-r=z 0, being 
positive. 
Without going through the ordinary process of solution to find the third root of this 
equation, which from the complicated form of the coefficients in this case is not conve- 
nient, c can be readily found by the following method of approximation, c is approxi- 
mately known by measurement, and i, the number of turns of wire in the coil, is also 
known. Assuming this value of c in (c 2 -j-a 2 )*, 2 ire 1 is given by the equation. Substi- 
tuting the value of i in this result, a new value of c is obtained. Using this new value 
of c, by means of the equation we obtain a new value for 2 ire 1 , and so on through 
several approximations. 
Thus, starting with c=4’3 centims., we find for ire 2 the successive values 195681, 
195435, 195421, 195420 square centims., with the corresponding values of c 4-25427, 
4-2516, 4-25144, and 4-25143. 
Starting with a value of c on the other side of this limit, c=4’25, we find for ire 1 
195412, 195419, with the corresponding values of c 4-25135, 4*25143. The value of 
ire 2 , 195420, has been adopted in the calculations. 
When the comparison of the coils had been completed, the wire was unwound from 
the coils. The resistance of the wire was measured before unwinding, and also after 
unwinding, to test for short-circuiting. 
Before unwinding (temp. 13° C.) the resistance of the wire of the right coil was 5630 
ohms, after unwinding (temp. 14°T C.) 5654 ohms, the rise of temperature being 
sufficient to account for an increase of resistance of about 20 ohms. 
The resistance of the wire of the left coil before unwinding (temp. 11°*75 C.) was 
5705 ohms, after unwinding (temp. 14°T C.) 5726 ohms. 
From this comparison of resistance it may be inferred that the insulation in the coils 
was very nearly perfect, that the effective length of the wire was that due to all the 
