1881.] Determination of the Ohm in Absolute Measure. 123 



error in the measurement of h', but also magnifies the effect of an error 

 in the measurement of a. If b r =~Qa, we have nearly 



du da 3 db r 



u a 10 a 



showing that an absolute error in V has about \ of the importance of 

 an equal absolute error in a. 



As will be evident from what has been said already, the treatment of 

 the correction for self-induction is a very important matter. It is 

 probable that L may be best determined from the deflections them- 

 selves with the use of sufficiently varied speeds. If L be arrived at by 

 calculation, or by independent experiments, it is important to keep 

 down the amount of the correction. We have seen, however, that 

 L/GK is almost independent of n, a, and S, so that if we regard tan 

 as given, the magnitude of the correction cannot be controlled so long 

 as a single pair of coils is used. An improvement in this respect would 

 result from the employment of two pairs of coils in perpendicular 

 planes, giving two distinct and independent circuits. In virtue of the 

 conjugate character, the currents in each double coil would be the same 

 as if the other did not exist, and the effects of both would conspire in 

 deflecting the suspended magnet. This doubled deflection would be 

 obtained without increase of the correction for self-induction, such as 

 would arise if the same deflection were arrived at by increasing the 

 speed of rotation with a single pair of coils. A second advantage of 

 this arrangement is to be found in the production of a field of force 

 uniform with respect to time. 



However the correction for self-induction be treated, it is important 

 to obtain trustworthy observations at low speeds. In order to get a 

 zero 'sufficiently independent of air currents, it will be advantageous 

 largely to increase the moment of the suspended magnet. Preliminary 

 experiments have, however, shown that there is some difficulty in get- 

 ting the necessary moment in a very small space, in consequence of 

 the interference with each other of neighbouring magnets, and thus 

 the question presents itself as to the most advantageous arrangement 

 for a compound magnet. 



A sphere of steel, as used by the Committee, has the advantage that 

 if uniformly magnetised it exercises the same action as an infinitely 

 small magnet at its centre. But the weight of such a sphere is con- 

 siderable in proportion to its moment, and it is probable that a combi- 

 nation of detached magnets is preferable. It is possible so to choose 

 the proportions as to imitate pretty closely the action of an infinitely 

 small magnet. Thus, if the magnet consist of a piece of sheet steel 

 bent into a cylinder and uniformly magnetised parallel to the axis, the 

 length of the cylinder should be to the diameter as \/3 to -v/2. In 

 this case the action is the same as of an infinitely small magnet as far 



