G80 
LORD RAYLEIGH OH THE VALUE OF THE BRITISH 
unnecessary to go into detail in this part of the subject. After a little practice two 
induction throws, starting with opposite directions of the current, and two observations 
of steady deflection, one in each position of the reversing key, could be made in about 
seven minutes. The vibrations of the galvanometer needle were damped by the 
operation of a current in a neighbouring coil, the current being excited by a Leclanche 
cell and controlled by a key within reach of the observer at the telescope. The 
readings were taken by Mrs. Sidgwick, while I reversed the battery current, shifted 
the resistances, and recorded the results. 
In the simple theory of the method the induction throw is supposed to be taken 
when the needle is at rest and when the resistance balance is perfect. Instead of 
waiting to reduce the free swing to insignificance, it was much better to observe its 
actual amount and to allow for it. The first step is, therefore, to read two successive 
elongations, and this should be taken as soon as the needle is fairly quiet. The battery 
current is then reversed, to a signal, as the needle passes the position of equilibrium, 
and a note made whether the free swing is in the same or in the opposite direction to 
the induction throw. We have also to bear in mind that the zero about which the 
vibrations take place is different after reversal from what it was before reversal, in con¬ 
sequence of imperfection in the resistance balance. At the moment after reversal we 
are therefore to regard the needle as displaced from its position of equilibrium, and as 
affected with a velocity due jointly to the induction impulse and to the free swing 
previously existing. If the arc of vibration (i.e., the difference of successive elonga¬ 
tions) be a 0 before reversal, the arc due to induction be a, and if b be the difference of 
zeros, the subsequent vibration is expressed by 
-J(afi:a 0 ) sin nt-\-b cos nt, 
in which t is measured from the moment of reversal, and the damping is for the present 
neglected. The actually observed arc of vibration is therefore 
Zl/{i{a±a<,Y+W} 
or with sufficient approximation 
Cl d~ Cln -J- 
2& 3 
a 
so that 
a —observed arc T a 0 — 
2W 
a. 
In most cases the correction depending upon b was very small; if not insensible. 
The “ observed arc ” was the difference of the readings at the two elongations imme¬ 
diately following the reversal. As a check against mistakes the two next elongations 
also were observed, but were not used further in the reductions. The needle was then 
brought nearly to rest, and two elongations observed in the now reversed position of 
the key, giving with the former ones the data for determining the imperfection of the 
resistance balance. As the needle next passed the position of equilibrium, it was 
