by means of an obliquely situated Galvanometer Needle. 345 



through the centre of the needle N. If the currents in the 

 coils are of the same frequency and of simple type, the mag- 

 netizing forces along HK may be denoted by A cos nt, 





M 







S 





H 





\ /* 







K 















M 







s 





Bcos(7zf— e), e being the phase-difference. If either force 

 act alone, the deflecting couple is represented by A 2 or by 

 B 2 ; but if the two forces cooperate the corresponding effect is 



C 2 = A 2 + B 2 + 2ABcose, . . . . (1) 

 reducing itself to (A + B) 2 or (A— B) 2 only in the cases where 

 € is zero or two right angles. The method consists in measur- 

 ing upon any common scale all the three quantities A 2 , B 2 , 

 and C 2 , from which e can be deduced by trigonometrical 

 tables, or more simply in many cases by constructing the 

 triangle whose sides are A, B, and C. The determination of 

 the phase-difference between the currents is thus independent 

 of any measurement of their absolute values. 



The best method of estimating the deflecting couples may 

 depend upon the circumstances of the particular case. The 

 most accurate in principle is the restoration of the needle to 

 the zero position by means of a torsion-head. But when the 

 conditions are so arranged that the angular deflexions are 

 moderate, it will usually suffice merely to read them, either 

 objectively by a spot of light thrown upon a scale, or by means 

 of a telescope. In any case where it may be desired to push 

 the deflexions beyond the region where the law of pro- 

 portionality can be relied upon, all risk of error may be 

 avoided by comparison with another instrument of trustworthy 

 calibration, one coil only of the soft iron apparatus being- 

 employed. 



In certain cases the advantages which accompany the 

 restoration of the zero position of the needle may be secured 

 by causing the deflexions themselves to assume a constant 

 value, e. g. by making known changes of resistance in one or 

 both of the circuits, or by motion of the coils altering their 

 efficiencies in a known ratio. 



In the particular experiments for which the apparatus was set 



