ON STAXDABDS FOR UfJE IN ELECTRICAL MEASUKEMENTS. 427 



connected, through a commutator K upou the axle, with the ends of the 

 wire R, a delicate reflecting galvanometer g, called in what follows the 

 sero-rjalvanometer, being interposed on one side of the commntator. When 

 the speed of the coll is so adjusted that the zero-galvanometer is not 

 deflected, the electi-omotive force developed in the coil by the magnetism 

 of the earth is equal to the electromotive force exerted by the thermopile 

 between the ends of the conductor r. Conseq^aently, the resistance of this 

 conductor is obtained in absolute measure by dividing the electromotive 

 force of the coil by the strength of the current indicated hy the tangent- 

 galvanometer. 



This result may be expressed in terms of the experimental data, as 

 follows. Let A be the total area included by all the convolutions of the 

 revolving coil — that is, the sum of the areas included by all the turns 

 taken severally, H^ the horizontal magnetic intensity at the place occu- 

 pied by the coil, w the angular velocity of the coil, and 2c( the arc of 

 contact made by the commutator, then E, the electromotive force of the 

 coil, is 



E = H,Aa. ^^^ 



a 



Again, if F is the strength of the magnetic field produced at the centre of 

 the tangent-galvanometer, where the needle is hung, by a current of unit 

 strength flowing through the galvanometer, H^ the horizontal intensity of 

 the earth's magnetic field at the same point, and B the deflection of the 

 galvanometer, the strength C of the current in the galvanometer, and 

 therefore also in the wire v., is 



C=^ tan0. 



Hence, putting (> for the resistance to be measured, that of the wire R, 

 we have 



E ' 



HA T, sm a 

 ^Aw r 



a 



^~ C He tan 6 



2^Ar?i5_« 



or Hf. a 



If the experiment could be made in a region of uniform magnetic force, 



Ho T tan 6 

 if T is the period of one revolution of the coil. 



ssji 



o 



XT 



we should have Hp = Hq, and therefore the ratio -=^ =1, as in Sir 



• He, 

 William Thomson's method. Owinc to the neisfhbourhood of rather large 

 masses of iron, this condition was not fulfilled in the actual experiments. 

 The ratio iu question was accordingly determined by noting the time of 

 vibration of the same magnet when it was suspended alternately in the 

 position of the revolving coil and in that of the galvanometer respectively. 



TT 



It was thus found at the beginning of the experiments that ^- was equal 



He 



to 0-9889. A repetition of the measurement that was afterwards 



attempted was made useless by some large masses of iron being brought 



just outside the Laboratory while it was going on. 



The ring upon which the revolving coil was wound, as well as the 



