PIEZOELECTRICITY. 491 



The lateral axes of tourmaline produce effects of the same kind, 

 but far feebler than for the principal axes, and the two polarizations 

 are superposed. 



Homohedral crystals present nothing analogous, while all those 

 which possess dissymmetrical hemihedry manifest electrical polariza- 

 tion under the influence of mechanical pressure or tension. 



In all cases the experimental laws are the same as for pyro- 

 electricity : 



i st. The quantities of electricity disengaged at the two ends of 

 an axis, for the same change of form, are equal and of opposite signs. 



2nd. The quantities of electricity disengaged at one end are 

 equal and opposite for two changes of shape which are the con- 

 verse of each other. 



3rd. These quantities of electricity are proportional to the change 

 of pressure or of traction. 



4th. For the same variations of pressure the electricity liberated 

 on the electrode is independent of the dimensions of the crystal if 

 the pressure is parallel to the polarization observed. 



In other words, the electrical density or the intensity I of the 

 piezoelectrical polarization is proportional to the pressure for unit 

 surface that is to say, to the contraction of the crystal for unit 

 length and to the extent of the surface. For a pressure P on a 

 surface S we may then write 



-'I- 



5th. If the pressure is on a surface S' perpendicular to the optical 



axis and to a lateral axis, the polarization may still be represented by 



P 

 k' , and the quantity of electricity liberated on the surface S 



S 

 perpendicular to the axis of polarization is equal to k'P - ; it is 



o 



proportional to the quotient of the length of the crystal parallel to 

 the pressure by the thickness parallel to the electrical axis. 



For reasons arising out of symmetry, it appears that k' should 

 equal -k, which is in agreement with experiment. 



1082. In order to determine in absolute value the quantity of 

 electricity liberated, MM. Curie worked by a method of opposition. 



The needle of an electrometer being electrified, one of the pairs 

 of quadrants is charged from a DanielPs element, the other pair of 



