Siemens Mercury Unit of Electrical Resistance. 305 



so that the resistance finally becomes 



^-qqS'T' t ( \ X \ AB /A\; 



2 A -U# 







IV. Investigation of the possible Errors, 

 Since X is always small and can be determined very accu- 

 rately, and the last factor does not differ greatly from unity, if 

 we bear in mind moreover that A, 2 is always small in comparison 

 with 7r 2 , in investigating the possible errors we may take the 

 approximate expression 



__ 32 S 2 T%\ AB 

 W ~~7T 2 K (A 2 + B 2 ) 2 * 

 1. The principal share of the uncertainty must be ascribed to 

 the horizontal component of the earth's magnetic force T, the per- 

 centage error of which affects the resistance in a twofold degree. 

 The difficulty of accurately determining this element (a difficulty 

 which is no doubt in general underrated) makes it essential that 

 the observations should be carried out in a very completely 

 equipped magnetic observatory. It is evident also that the 

 variations of the earth's magnetism must be taken into account; 

 for the horizontal intensity varies with us to the extent of about 

 \ per cent. ; so that, without observing the variation- apparatus, 

 an error of 1 per cent, might arise in the calculation of the re- 

 sistance. 



The observatory of Gottingen without doubt answers to the 

 requirements of the case more completely than any other place, 

 inasmuch as the arrangements that have been carried out there 

 by Weber for determining the horizontal intensity far surpass, 

 in delicacy and convenience, those in use elsewhere. The great- 

 est sources of error in the absolute measurement unquestionably 

 lie in the determination of the moment of inertia and the measure- 

 ment of distances ; in long series of observations of variations 

 the change in the magnetism of rhe bifilar needle also introduces 

 difficulties that are not inconsiderable. Essential improvements 

 have been effected affecting precisely these points. The dis- 

 tances to be measured are solely those between the suspending 

 fibres of magnets, and therefore can be determined with the 

 utmost accuracy. The weights for determining the moment of 

 inertia are more firmly connected with the magnetometer ; they 



* In practice, sj^j^ ca n always be taken as =7r; and so long as X 



is not great, we have as a close approximation (in the present case, for 

 instance, within 0*05 per cent. ) 



Phil Mag. S. 4. Vol. 47. No. 312. April 1874. X 



