PYROELECTRICITY AND PIEZOELECTRICITY 159 



Now let us take the condenser round the cycle ABCD, starting 

 from A, one plate being earthed throughout. Along AB the other 

 plate is connected to a source at 07, and F and / are varied as 

 represented by the slope of AB, and charge dm is taken in. AtB 

 the plate is insulated and F and / varied as represented by the slope 

 of BC. At C the plate is connected to a source at x-dx, and we 

 move back along CD till dm is given back to the source. Then the 

 plate is insulated and we return along DA to the initial condition. 



The net electrical energy received is 



xdm (x-dx)dm = dxdm. 



The net work done is represented by the area ABCD, which is 

 easily seen to be 



fd\ 



\tich 



where dl is the increase of/ as we move along AB at constant x. 

 Equating the two expressions for the energy, 



or 



Taking x and F as the independent variables, let us put 



dm = cdx + hdF (2) 



dl = adx + bdF (3) 



Ifrfr = in (2) and (3), 



If dl = 0, we get from (3) 



Substituting from (4) and (5) in (1), 



h= -a 

 so that (2) and (3) become 



dm = cdx adF 

 dl = adx + bdF. 



Applying these formulae to the case of a piezoelectric crystal 

 compressed along an electric axis, let us suppose that the potential 

 is kept constant, and that a force of dF dynes is added Then 



