ASSOCIATION UNIT OP BESISTANCE IN ABSOLUTE MEASUBE. 
669 
disturbance. The spinnings were then suspended, and the observations already 
obtained were not reduced. 
At the close of the spinnings, Mrs. Sidgwick made a further comparison of our 
platinum-silver coil with the standard units. 
The value arrived at for the B.A. unit ('9865 ohm) differs nearly three parts in a 
thousand from that which we obtained with the original apparatus. This difference 
is not very great, and may possibly be accounted for by errors in the measurement of 
the coil (see p. 114 of former paper). If a coil be imperfectly wound, the mean radius, 
as determined by a tape, is liable to be too great. At any rate, this discrepancy sinks 
into insignificance in comparison with that which exists between either of these 
determinations and that of Professor Kohlratjsch, * according to whom the B.A. unit 
would be as much as 1*0196 ohms. With respect to the method employed by 
Kohlratjsch, I agree with Howland! in thinking it difficult, and unlikely to give the 
highest accuracy; but how in the hands of a skilful experimenter it could lead to a 
result 3 per cent, in error, is difficult to understand. The only suggestion I have 
to make is that possibly sufficient care was not taken in levelling the earth-inductor. 
Although estimates are given of the probable errors due to uncertainties in the various 
data, nothing is said upon this subject. In consequence, however, of the occurrence 
of the horizontal intensity as a square in the final formula, in conjunction with the 
largeness of the angle of dip, the method is especially sensitive to a maladjustment of 
this kind. I calculate that a deviation of the axis of rotation from the vertical 
through 21' in the plane of the meridian, would alter the final result by 3 per cent.J 
According to Howland’s determination, the value of the B.A. unit is '9912 ohm. 
The method consists essentially in comparing the integral current in a secondary 
circuit, due to the reversal of the battery in a primary circuit, with the magnitude of 
the primary current itself. The determination of the secondary current involves the 
use of a ballistic galvanometer, whose damping is small, and whose time of vibration 
can be ascertained with full accuracy; and it is here, I think, that the weakest point 
in the method is to be found. The logarithmic decrement is obtained by observation 
of a long series of vibrations, and it is assumed that the value so arrived at is 
applicable to the correction of the observed throw. I am not aware whether the origin 
of damping in galvanometers has ever been fully investigated, but the effect is usually 
supposed to be represented by a term in the differential equation of motion proportional 
to the momentary velocity. This mode of representation is no doubt applicable to 
that part of the damping which depends upon the induction of currents in the 
galvanometer coil, under the influence of the swinging magnet. If this were all, a 
correction for damping would be accurately effected on the basis of a determination of 
the logarithmic decrement, made with the galvanometer circuit closed in the same 
* POGG. Ann., Erganzungband VI. Phil. Mag., April, 1874. 
t American Journal, April, 1878. 
X See p. 684. 
