68 Dynamical Principles applied to Physical Phenomena. [Jan. 8, 



of the wire, then Wiedemann's discovery shown that there must be a 

 term in the kinetic energy equal to 



f(a)Xzw. 



where f(a) denotes some function of a 



Thus there will be a force of the type y, i.e., an electromotive force,, 

 along the wire equal to 



- 



so that, if we twist a magnetised iron wire, an electric current will 

 flow along the wire, which will last as long as the wire is being 

 twisted : this is known to be the case. Again, there will be a force 

 of the type z — i.e., a magnetising force along the wire equal to 



so that when a current flows along a twisted wire it magnetises it ; 

 this effect has also been observed. Thns, from the original experi- 

 ment, we have been able, by the use of Lagrange's equation, to deduce 

 two other phenomena. It is shown in the paper that the method 

 indicates a great many relations between various physical phenomena. 

 Some of these have been observed, but there are several which seem 

 not to have been investigated ; as an example of the latter, it is proved 

 that from the effect observed*by Villari and Sir "William Thomson, 

 namely, that when the intensity of magnetisation is below a certain 

 value, an increase in the strain of a magnetised soft iron is accom- 

 panied by an increase in the magnetisation, it follows that when the 

 magnetising force is small, a soft iron bar will contract instead of 

 expanding on magnetisation. 



Lagrange's equations were applied with great success by Maxwell 

 to obtain the equations of the electromagnetic field. 



It is also shown that the effects due to the potential energy of a 

 system A can be produced by the kinetic energy of a system B con- 

 nected with A, if the configuration of B is such chat it can be fixed 

 by gyroscopic coordinates. And thus we may look on the potential 

 energy of any system (A) as being the kinetic energy of a gyro- 

 scopic system (B) connected with A, and so regard all energy as 

 kinetic. If we do this it will simplify some of the dynamical 

 principles very much. We may take the principle of Varying Action 

 as an example : if all the energy is kinetic, its magnitude will remain 

 constant by the Conservation of Energy, and then the principle of 

 Least Action takes the very simple form that, with a given quantity of 

 energy, any material system will, by its unguided motion, pass from 

 one configuration to another in the least possible time, where, in the 



