1885.] Dynamical Principles to Physical Phenomena, 67 



those which involve the product of the differential coefficients of 

 coordinates of the x and w and of the y and z types. Thus we may- 

 write those terms which depend on the coordinates x f y, z, u, w, in 

 the expression for the kinetic energy of any real dynamical system, 

 in the form 



+${yy}f+ • 



+ \{uu}v? + . 

 + {xw}xw + . 



+ {yz}y&+ • 



when the term {xx}x 2 + . . . indicates a quadratic function of the 

 differential coefficients of the coordinates of the x type. 



Each of these terms is separately considered, and the physical 

 phenomena to which it corresponds are deduced. The method used 

 may be illustrated by considering a term of the form 



when X and fi may be any of the five types of coordinates which we 

 are considering. 



Then, if T be the kinetic energy, we have by Lagrange's equations 

 d dT dT 



dt dX~~ dX =ex ^ eTJ1 * orce °* * n8 tyP e ^' 



If, instead of T, we consider the term {fyijAit, we see by this 

 equation, and the corresponding equation for the coordinate p., 

 that if this term exist there will be a force tending to increase X 

 equal to 



~~ { It ~ } 



and one tending to increase /*, equal to 



and if (Xjll) be a function of any other coordinate v there will be 

 a force tending to increase v equal to 



Thus, to take an example, Wiedemann has discovered that a longi- 

 tudinally magnetised iron wire becomes twisted when an electric 

 current flows through it. If we call y the current through the wire, 

 zw the intensity of magnetisation, and a the twist round the axis 



f2 



