association unit of resistance in absolute measure. 
677 
whence 
S( 1 + tan/x sec <^>) + v / {i(l+ tan/x sec </>) 3 —U(tan (/>— tan <£ 0 ) 3 }] 
where 
2L | 
[ 2L 
tan </> 
(UK)] 
[(GK) 
tan </> — tan </> 0 J 
L by direct experiment * 
Although the calculated value of L was the result of two independent computations, 
I considered that it would be satisfactory still further to verify it by an experiment 
with Wheatstone’s balance. The statement of this method and the final formula, 
as given on p. 116 of the former paper, being approximate only, it will be convenient 
here to repeat them with the necessary corrections. 
The four resistances in the balance are two equal resistances (10 units each), that of 
the copper coil P, and a fourth resistance Q (nearly equal to P) taken from resistance 
boxes, of which P is the only one associated with sensible self-induction. When 
P and Q are equal, there is no permanent current through the galvanometer; but if 
the galvanometer circuit be first closed and then the battery current be made, broken, 
or reversed, the needle receives an impulse, whose magnitude depends upon L. 
If x denote the change of current in the branch P, the action of self-induction is 
the same as that of an electromotive impulse in that branch of magnitude Lx, and 
the effect upon the galvanometer is that due to this electromotive impulse acting 
independently of the electromotive force in the battery branch. 
In order now to get a second quantity with which to compare the induction throw, 
the resistance balance is upset in a known manner. If while Q remains unaltered, 
P be increased to P-f-SP, there is a steady current through the galvanometer, which 
we may regard as due to an electromotive force SP.A in the branch Pfi-SP, x being 
the current through the branch. If 6 be the deflection of the needle under the action 
of the steady current, a the angular throw, and T the time of swing from rest to rest, 
we have by the theory of the ballistic galvanometer as the ratio of the instantaneous 
to the steady electromotive force 
T 2 sin \ol 
7 r tan 6 ’ 
subject to a correction for damping; so that this expression represents the ratio of 
Lx : SP .x. If the induction throw be due to the make or break of the battery circuit, 
x represents simply the current in the branch P. In the case where the battery 
* In consequence of the necessity which ultimately appeared of introducing an arbitrary correction 
proportional to the square of the speed of rotation, the result of the present section does not influence 
the final number expressing the B.A. unit in absolute measure. The method, however, is of some 
interest, and (it is believed) has not been carried out before with the precautions necessary to secure a 
satisfactory result. 
