TRANSACTIONS OF SECTION A. 613 



and also upon the physical conditions of the medium. For air and all other gases, 

 and generally for all substances classed as ' non-magnetic,' it is a linear function 

 possessing one coefficient or constant only. For such substances the equation may 

 be written 



B = /^H (|3) 



Since the numerical definition of H is at our disposal, we may so define H that n 

 is unity for all the substances above referred to. 



For iron, and generally for all magnetic substances, H is not a linear function 

 of B, and its expression will involve several constants depending upon the medium, 

 and such physical conditions as temperature and strain, and its previous history. 

 The determination of the form of the function for iron in particular has been the 

 subject of a great number of experiments, but no general expression has yet been 

 discovered, and it has usually been found most convenient to record the experi- 

 mental results in the form of a curve referred to rectangular axes, in which the 

 ordinates represent magnetic induction and the abscissae magnetic force. Such 

 curves have been fully investigated for iron of various composition, and under 

 varying physical conditions, among others particularly by G. Wiedemann (' Die 

 Lehre vom Galvanismus,' vol. ii. p. 340, et seq.}, Rowland ('Phil. Mag.' Aug. 1873), 

 Carl Barns and Vincent Strouhal (' Bulletin of the United States Geological 

 Survey,' No. 14, 1885), J. Hopkinson ('Phil. Trans. R.S.' pt. ii. 1885), J. A. 

 Ewing (' Phil. Trans. R.S.' pt. ii. 1885, and pt. ii. 1886, and ' Proc. R.S.' vol. xlii. 

 p. 200, 1887). For convenience we may still express the curve by the equation (/3), 

 H is then the tangent of the angle which the tangent to the cui've makes with the 

 axis of X. 



Secondly, we require to know the relation between the E.M.F. and current. 

 This is well known to be expressed by a linear relation, known as Ohm's law, in- 

 volving one constant coefficient only. 



Having now defined the relation between the flaxes and their corresponding 

 forces, it remains to consider the relation between the fluxes themselves, dependent 

 upon the relative motion of Iheir circuits. This may be expressed in various ways, 

 all of which are the expressions of Faraday's well-known law: e.(/., the line 

 integral of the E.M.F. round the electric circuit is the rate of decrease of the surface 

 integral of magnetic induction through any area bounded by the circuit. 



Excluding for the moment the consideration of magneto machines with perma- 

 nent magnets, and of machines in which iron plays no part whatever, we may more 

 particularly consider that class of dynamos in which the magnetic field is produced 

 by the use of iron excited by a current ; and we then require to know the relation 

 between the current and the induction in the magnetic field produced by the 

 current. Faraday showed that the magnetic field in the neighbourhood of an 

 electric current is the same as that of a magnetic shell bounded by the circuit of 

 the current, and has therefore a similar magnetic potential. This is expressed by 

 saying, that the hue integral of magnetic force round any closed curve is zero, 

 provided the closed curve does not surround the electric current ; and if the current 

 passes through the closed curve, then the line integral is proportional to the number 

 of times it passes through, and is equal to 47rnc, where c is the current and ?i the 

 number of times it passes through the closed curve. 



We have now the materials for a complete investigation of a dynamo of any 

 given configuration and constructed of iron, whose magnetic qualities are known. 

 It is required to determine the E.M.F. and current in the electric circuit, as its 

 configuration relative to the magnetic circuit is changed by the application of ex- 

 ternal forces, and as the magnetic forces in the magnetic circuit are changed either 

 by external electro-magnetic forces, or electro-magnetic forces derived from the 

 current circulating in the electric circuit. The magnetic circuit consists in general 

 of four parts : (i.) The magnet limb, which is surrounded by coils of wire, through 

 which the exciting current is passed, (ii.) The field pieces, or the extended polar 

 extensions of the magnet limb, embracing the armature, (iii.) The air space being 

 the necessary interval between the iron of the pole pieces and the iron of the arma- 

 ture, or in cases where the armature contains no iron, the interval between the 



