This paper has heen written to deal with the fundamental theory on which a mercury filled thermometer is based. In analyzing the flat-oval type spiral tube, the writer has first introduced the Wuest's theorem. As the system is filled with uncompressible fluid, the expansion occurred at thermobulb by temperature increase has proved to be equal to the volumetric expansion of the spiral tube. Then he obtained the following equation:
Δθ=ΔV/3abr1{1-r03/(r1+r0)(r12+r02)}
Δθ: Angular displacement of spiral tube
ΔV: Volumetric expansion of mercury
r1: Radial coordinate of fixed end of spiral tube
r0: Radial coordinate of free end of spiral tube
2a: Length of long axis of tube section
2b: Length of short axis of tube section
In addition to this, the writer has found that the equation is affected neither by Young's modulus nor by wall thickness of the tube.
Also discussed is a working principle of force-balanced temperature transmitter. Maximum tube stresses are shown first as the value equivalent to that of ordinarily filled system, secondly as the additional caused by additional tube bulging by pneumatic feed-back and lastly as the subtractive by restriction of tube tip-movement by pneumatic feed-back.
