138 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2‘

or in words: For an ideal gas kept at constant temperature in
a closed container with alterable volume, pressure P times
volume V is constant. In the accuracy of ordinary scale readings,
 BOYLE’s law holds as a deterministic relation. Typical
inferences from BoYLE’s law are that if the volume of the container
 is known, say V, the gas pressure is given by

PLY,

“IG

- Stochastic variables subject to observational error. a)-b) Same
variables as in Fig. 4 a-b.

and if the pressure is known, say P,, the volume is

(44)

V=c/P,

If an experiment is performed to demonstrate BoyLE’s law
there will be small deviations owing to observational errors in
P and V, as shown in Fig. 3b. Taking the constant c to be
unknown it can be estimated from the data, for example by
the method of least squares as applied to the logarithmic
relation

45,

log P+log V =log c

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