40 
MESSRS. G. F. C. SEARLE AND T. G. BEDFORD 
larly J Hc/B for the semi-cycle — Cq to -f- Cq is given hy (area Vc'ad) — (area a'h'd'). 
The value of J Hr/B for the whole cycle is thus the area of the B—H curve ahca'h'c'a. 
If 0, and 9c. he the two throws of the dynamometer for the two semi-cycles, we 
have hy (8) 
and hence, since W is the sum of the two quantities on the left sides of these 
equations, 
■VP'P 
= + .0). 
Thus to hud W Ave have simply to add together the two throws for the two 
semi-cycles, and then multiply the result l)y the factor NC'P/A??^. 
The expression (9) is the fundamental formula of the method emjoloyed by us for 
the measurement of hysteresis. From it we see that all that is needed in addition to 
the electro-dynamometer for the measurement of W is an ampere-meter by which 
to determine C', and an earth-inductor or some other means of producing a known 
change of induction (P) through the secondary circuit. 
Complete Theory of the Method. 
^7. In the elementary tiieory of ^ 4, the resistance, S, of the secondary circuit 
is supposed to l)e so large, and the induced current in consequence so feeble, that 
tlje magnetic force due to tlie induced current is negligilde in comparison with that 
due to the primary current. It is thus necessary to proceed to a closer examination 
of the theory in oixler to find the correcting term which appears when S is only 
finite. In this examination we take account also of the energy dissipated hy the 
eddy currents, whicli cii'culate in tlie siiecimen in consecpience of the variations of 
the applied magnetic force. We use tlie notation already employed in the elementary 
tlieory. 
^ 8. In the primary circuit let tlie magnetising coil and the dynamometer coil he 
placed next to each otlier m the circuit, and let E he the voltage at any instant 
between the ends of the conductor so formed. Now the induction through either 
circuit depends not only upon the magnetic induction, B, in the iron, lint also upon 
the magnetic force in the space betiveen the coils and the iron, as well as upon the 
magnetic force near the coils of tlie dynamometer. In each case the magnetic force 
depends only upon C and c, and not at all upon B, since the iron is formed into a 
ring. Thus if It he the resistance of the }irlmary circuit hetAveen the two points 
hetAveen Avhich the voltage is E, the equations for the primary and secondary currents 
may he Avritten 
1? = !!<:+ (N/AB + T/f + Me) 
0 = Sc + (liA B + MC + Lo) . 
■ ( 10 ), 
■ ( 11 ). 
