605 
Ep) 
surfaces, i.e., 4Q=KAF, where K is the piezoelectric constant of the crys- 
talline material along the electric axis. When a piezoelectric gage is sub- 
jected to hydrostatic pressure, it is convenient to write AQ= KAAP. The 
change in pressure AP acting over area A determines the total force transmit- 
ted to the electrode surface. From the constant KA of a particular gage, the 
change in pressure responsible for a given output of charge is inferred. 
Since values of K are given in the literature, it may be inquired 
why calibration is necessary; why not simply multiply K by A? There are sev- 
eral reasons. The piezo constant is not the same for various specimens of 
tourmaline. It is difficult to know which of the values found in the liter- 
ature is a correct value for the sample used in the gage. 
In the case of the quartz gage there are two sources of possible 
error in computing KA rather than in determining it experimentally. In the 
first place, few quartz crystals are altogether free from "twinning" of 
right-handed and left-handed quartz. Twinning reduces the effective K of the 
crystal, since the two types of quartz show opposite polarities. Secondly, A 
is not known precisely. As pointed out in the Appendix, it is necessary that 
an air gap surround the quartz crystal laterally. The brass cover which 
transmits the external pressure to the crystal is supported partly by the 
erystal and partly by the cylindrical wall of the housing; see Figure 3 on 
page 6. Moreover, a portion of the brass cover lies over the air gap. Thus 
the effective area A subjected to pressure differs from the electrode sur- 
face of the crystal alone. Though it is possible to estimate approximately 
how much of the area over the air gap is supported by the crystal, it is not 
easy to compute this exactly. However, if the gage is calibrated, it is not 
necessary to know A, since the product KA is obtained directly. 
For these reasons it is desirable to determine experimentally the 
constant KAof each gage. Now for any particular method of calibration, re- 
sults of high internal consistency are not incompatible with the occurrence 
of a systematic error. To ensure reliable KAvalues, therefore, it is impor- 
tant to compare the results obtained by a given method of calibration with 
those obtained by another method, and, if possible, by an independent obser- 
ver. At the Taylor Model Basin, in addition to the alternative methods of 
applying a pressure change which have already been described, experiments 
have been made with several different circuits for measuring the charge. One 
or these has proved especially successful, yielding results which not only 
show internal consistency but which agree closely with those obtained for the 
same crystals in other laboratories. Experiments have also been performed by 
two other methods of calibration. One of these used a Compton quadrant elec- 
trometer; the other utilized a "microcoulometer" or high-impedan > current 
