BRIDGMAN. — A SIMPLE PRIMARY GAUGE. 211 



The strain in the cylinder is more difficult to compute because of 

 the uncertainty in the external boundary conditions introduced by the 

 packing. Upon the portion of surface DCB (Figure 3) there is a 

 normal pressure exerted by the packing, equal to 1.32 of the internal 

 hydrostatic pressure. On BAEF there is the normal hydrostatic pres- 

 sure, and from F to G the same distribution of pressure as on the 

 piston, decreasing from the full value at F to zero at G. The maxi- 

 mum radial displacement due to external pressure may be taken as 

 somewhat less than that from a pressure equal to 1.32 P over the 

 entire external surface, because of the supporting action of the part 

 AB, which is subjected to P only, and of the part beyond D, on which 

 there is no pressure. An upper limit to the distortion is probably set 

 by the distortion of an infinite cylinder subjected to 1.32 P on the out- 

 side, and P on the inside. This gives 



_ / _ 0.32a' 4^ + 3* ft'- 1.32a' \ 



* r ~V 2>(a*-6») + 18pc a 2 - ft 2 ) xbxt 



= - 6.9 x 10- 7 X ft X P 



where a is the external radius, T % in. (0.79 cm.), and ft the internal 

 radius, iV in. (0.16 cm.). A value probably nearer the truth is found 

 by assuming for the effective external pressure 1.16 P, i. e., a mean 

 between the maximum and the pressure on AB. This gives 



/ 0.16 a 2 4 ii + 3 k ft 2 - 1.16 a 2 \ . 



\ 2/x(a- — ft") 18 fiK a 1 — b- J 



= - 5.3 X 10- 7 x ft x P 



and this value will be used in this computation. This represents the 

 maximum radial displacement of the cylinder, which occurs at the 

 inner end; at the outer end there is no pressure either external or 

 internal, and the displacement will be assumed to vanish. Through- 

 out the length of the cylinder the displacement at the inner surface 

 will be assumed proportional to the internal pressure at that point, 

 although the approximation is not so good here as for the piston. 



From these displacements of piston and cylinder it is now required 

 to correct for the change in the effective area of the piston. We do 

 this by considering the equilibrium of the escaping liquid. The piston 

 and cylinder each exert on the liquid approximately the same fric- 

 tional force (F). Furthermore, the cylinder exerts on the escaping 

 liquid a pressure P lf which is the negative of the component in the 

 direction of the axis of the pressure of the liquid in the crack on the 

 cylinder. P x corresponds, therefore, to the axial component of pres- 



