xxxiii
Fig. 6.6 The comparison of the length L[b] with the lengths marked
on the rods a and a* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Fig. 6.7 The concept system about and an example
(just a specialization of Fig. 5.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Fig. 6.8 A traditional classification of concepts (left),
and its implementation in the VIM (right) . . . . . . . . . . . . . . . . . . . . . 170
Fig. 6.9 A simple nomic network laying the groundwork
for the direct measurement of P through multiple
means (where P → Y means that P is the cause of Y) . . . . . . . . . . . . 187
Fig. 6.10 A simple example of a nomic network laying the
groundwork for the indirect measurement of P . . . . . . . . . . . . . . . . . 188
Fig. 7.1 The basic structure of a direct measurement.
(Adapted from Fig. 2.10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
Fig. 7.2 The basic structure of an indirect measurement
(measurement uncertainty is not considered here), including some
unavoidable direct measurements. (Adapted from Fig. 2.11) . . . . . . 201
Fig. 7.3 Calibration as a relation of a public scale and a local scale . . . . . . . . 210
Fig. 7.4 The first stage of direct measurement: transduction
(in the example Θ[a] is the temperature of an object
and X m is a position of the upper surface of alcohol
in the thermometer tube) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
Fig. 7.5 The first two stages of direct measurement: after
transduction, matching (in the example X m is a position
of the upper surface of alcohol in the thermometer
tube and X i
*
is the position of the ith mark etched
on the scale of the thermometer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Fig. 7.6 The first three stages of direct measurement: after transduction
and matching, local scale application (in the example X i
*
is
the position of the ith mark etched on the scale of
the thermometer and x i is a value of position) . . . . . . . . . . . . . . . . . . 213
Fig. 7.7 Pre-measurement, as the composition of transduction,
matching, and local scale application . . . . . . . . . . . . . . . . . . . . . . . . 214
Fig. 7.8 A preliminary stage of direct measurement: public
scale construction (in the example Θ[s j
*
] is the temperature of
the measurement standard s j
*
and θ j is a value of temperature) . . . . . 214
Fig. 7.9 A preliminary stage of direct measurement: calibration . . . . . . . . . . 215
Fig. 7.10 The operational structure of direct measurement,
as a composition of pre-measurement and calibration . . . . . . . . . . . . 216
Fig. 7.11 The operational structure of direct measurement,
highlighting the role of the public scale for the creation
of the calibration map; note that the two transductions
are performed at different times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Fig. 7.12 The operational structure of direct measurement, as based
on the direct comparison of the property under measurement
and the public reference properties . . . . . . . . . . . . . . . . . . . . . . . . . . 218
List of Figures