432 PROFESSOE W. WATSON ON A DETERMINATION OF THE VALUE OF 
solenoidal condition of this magnetic needle would produce, the Helmholtz arrange¬ 
ment was adopted, in which two equal coils are placed with their planes parallel, 
and at a distance from each other equal to the radius of either. For the comparison 
of the field produced within the coils, when they are traversed by a known current, 
the sine method was chosen, the coils being mounted on a horizontal circle so that 
they could be turned about a vertical axis till the magnetic axis of the needle at 
the centre of the coils was at right angles to the axis of the coils when the 
current was passing. Thus, if F is the field produced at the centre of the coils 
when they are traversed by unit current, and the angle through which the coils have 
to be turned when they are traversed by a current C is 6, the value of the earth’s 
horizontal component, measured in terms of a unit derived from the unit of current, 
is given by H — CF/sin 6. 
In order to measure the current, use was made, in the first jDlace, of a silver 
voltameter. As it is not convenient to make the deflection experiments, involving 
as they do a continual reversal of the current, and hence interruptions of the current 
of uncertain duration, at the same time as a silver deposition is being made, an 
intermediate standard of current was adopted. This was obtained by balancing the 
potential difference between the termina,ls of a standard resistance coil against the 
E.M.F. of a standard cadmium cell. This addition has the further advantage that, 
if we know the value of the resistance, then we can use the results for the E.M.F. 
of the cadmium cell obtained by other observers to obtain the value of the current, 
and thus check the values obtained by the voltameter. 
Degree of Accuracy aimed at in the Measurements .—In designing the apparatus 
and arranging the method to be adopted, a determination of the value of H by 
means of the coil accurate to 1 or 2 parts in 10,000 was aimed at. 
That the current may be known in terms of the electrochemical equivalent of 
silver to the required degree of accuracy, we must be able to measure the weight 
of silver deposited, and the time during wliich the current passes, as well as to 
maintain the current constant, each to about one part in 10,000. Since the weight 
of silver deposited during each experiment was about 1'6 grammes, this involves 
the weighings being correct to within 0T6 milligratnme. The interval during 
which a dej^osition lasted being two hours, the time has to be measured to within 
0’7 secood. Further, owing to the use of the subsidiary standard, namely, the 
resistance cod and standard cell, we have to know the change of the resistance of 
the coil and that of the E.M.F. of the cell to within 1 in 10,000 of the value of the 
resistance of the coil, or the E.M.F. of the cell, as the case may be. 
With reference to the accuracy with which the dimensions of the coils have to be 
known, it is shown in most text-books that if a is the mean radius of either coil and 
'2x is the distance between the mean planes of the coils, h the axial breadth of each 
coil, and d the radial depth, that is, the section of either of the coils is a rectangle of 
length 6 and depth d, N the number of turns in both coils together, F the cod 
