322 Lord Rayleigh, On the mean radius of coils. [Feb. 12, 



traversed by the same current, is given in Maxwell's Treatise, 

 Vol. ii. § 753. 



I have used a slight modification of Maxwell's arrangement 

 which is perhaps an improvement, when the coils to be compared 

 are of copper and therefore liable to change their resistance pretty 

 quickly in sympathy with variations of temperature. The coils 

 are placed as usual approximately in the plane of the meridian so 

 that their centres and axes coincide, and a very short magnet 

 with attached mirror is delicately suspended at the common 

 centre. If the current from a battery be divided between the 

 coils, connected in such a manner that the magnetic effects are 

 opposed, it will be possible by adding resistance to one or other of 

 the branches in multiple arc to annul the magnetic force at the 

 centre, so that the same reading is obtained whichever way the 

 batteiy current may circulate. The ratio of the galvanometer 

 constants is then simply the ratio of the resistances in multiple arc. 



To obtain this ratio in an accurate manner, the two branches 

 already spoken of are combined with two other resistances of 

 german silver, so as to form a Wheatstone's balance. Of these 

 resistances both must be accurately known, and one at least must 

 be adjustable. The electro-magnetic balance is first secured by 

 variation ■ of the resistance associated with one of the given coils 

 which resistance does not require to be known. During this 

 operation the galvanometer of the Wheatstone's bridge is short- 

 circuited. Afterwards the galvanometer is brought into action 

 and the resistance-balance is adjusted. The ratio of the galvano- 

 meter-constants is thus equal to the ratio of the german silver 

 resistances. The two adjustments may be so rapidly alternated as 

 to eliminate any error due to changes of temperature in the 

 copper wires. Indeed, if desired, the final tests of the electro- 

 magnetic and resistance-balances might be made simultaneously. 



If the ratio of galvanometer-constants be the final object of 

 the measurement, there is nothing more to be done ; but if we 

 desire to know the ratio of the mean radii of the coils we must 

 introduce certain small corrections for the finite dimensions of 

 the sections. In the first place, however, it will be desirable to 

 consider a little more closely what should be understood by the 

 mean radius of a coil. 



In Maxwell's treatment of the subject (§ 700) the mean radius 

 of a coil is considered to correspond with the geometrical centre of 

 its rectangular section, that is to say, the windings are assumed to 

 be uniformly distributed over the section. In practice absolute 

 uniformity is not attainable, and it is therefore proper to take into 

 account the effect of a small imperfection in this respect. The 

 density of the windings, i. e. the number of windings per unit area, 



