106 Prof. W. C. Rontgen on the Change in the Double 
the observer, and negative electricity to the side turned from 
him, then the major axis ran from above on the left, down 
towards the right. 
It is known * that a mechanical compression or dilatation of 
a quartz plate cut at right angles to the axis, in a direction at 
right angles to the axis, produces a change in the system of 
rays which is similar to that just described. The diameters 
of the circles become lengthened in the direction of pressure 
and shortened in the direction at right angles to this; if, on 
the other hand, the plate is dilated, then the major axis of the 
ellipse is at right angles to the direction of expansion. 
The results of the two last experiments would be at once 
explained, if it were allowable to assume that electrical forces 
acting in the direction of an axis of no piezoelectricity 
produce indeed no change of form in the direction of this 
axis, but compression or dilatation, or both at the same time, 
in directions at right angles to the principal axis, and inclined 
at an angle of 45° to the corresponding axis of no piezoelec- 
tricity. How far this assumption is justified could not be 
decided until the piezoelectric experiments which have been 
described had been made; and on that account I have delayed 
the publication of my electro-optical experiments with plates 
cut at right angles to the axis till now. 
The confirmation of the accuracy of this assumption follows 
from the piezoelectric experiments described under (5), and 
from the law of reciprocity of compression and electric charge 
enunciated by Lippmanu, and with it the complete explanation 
of the above experiments. He found, in the place referred to, 
that a pressure exerted upon the quartz at an angle of 45° to 
an axis of no piezoelectricity and at right angles to the prin- 
cipal axis produces piezoelectricity at the ends of that axis, 
which is also greater in quantity than that produced at other 
points. If, then, we communicate to the ends of the axis 
electricity of the same kind as would be produced by pressure 
in the given direction, a dilatation of the quartz in this direc- 
tion must take place ; and, conversely, if electricities are 
communicated of the opposite kinds to those resulting from 
pressure, compression in this direction must take place. There 
are, now, two such directions (which are at right angles to the 
principal axis and inclined at 45° to an axis of no piezoelec- 
tricity) for each of the axes of no piezoelectricity, viz. one on 
each side of the axis. From what was said under (5), it 
further follows that the electricities which are produced when 
a pressure is exerted in one of these two directions are oppo- 
site to the electricities produced by a pressure in the other 
* Pfaff, Pogg. Ann. cvii. p. 133 (1859). 
