574 DR EDWIN H. BARTON ON THE TEMPERATURE VARIATION 



H' the impressed magnetic field = <y(4:irpC), (1) 



7 being a factor less than unity to correct for the effect of the ends of P and P'. 

 H the actual field within the composition * = H' — JSU = H' - iVicH, so that 



H =i¥m- < 2 > 



where k is the magnetic susceptibility of the substance, and N a constant 

 depending upon the dimensions of the magnetic body introduced into the 

 field. 

 r the entire constant of the galvanometer, i.e. : — 





H being the magnetic field at galvanometer when no current flows through 

 it ; G the field produced at galvanometer needle by absolute unit current 

 passing through galvanometer ; T the complete period of an oscillation of 

 galvanometer needle ; X its logarithmic decrement. 

 R the total resistance of the secondary circuit. 



Now, first, put the long cylinder of composition in P. Then the total magnetic flux 

 through S and S' is given by 



Hs(&+47tkv4) - H'(a's') or 



r ^ F/c [s(a+4 7 r^)-aV(l + iV K )] (3) 



S' being arranged so as to oppose S. 



Hence the quantity of electricity passing through the galvanometer on reversal of 



2 

 primary current is -^ times the expression (3). Thus, if the resulting kick is a counted 



positive if in the direction due to S, we have 



I ^[s(a + 47r^)-aV(l + iV/c)] = rsin| .... (4) 



2 

 B 



Similarly when, second, the long cylinder of composition is put in P', and the kick 

 /3 obtained counted positive if in the direction due to S, we have 



|. r ^ c [^(l + ^)-s'(«' + 47r^)] = rsin| .... (5) 



Hence, neglecting the differences between tangents, arcs, and sines of small angles, 

 we obtain from (4) and (5) 



{s(a + 4:ttkA) - aV(l + N K )}/3={as(l + Nk) - s'(a + 4ttk-4)} a 



or 



(a — j8)(as — a's') 



4TrA( a s + /3s) - N( a as + /3a s') 

 * Magnetic Induction in Iron and other Mstals, by J. A. Ewing, F.R.S., pp. 24, 25. 



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